tcs placement papers

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tcs placement papers..

Answer / sandeep kaur

TCS PAPER PATTERN
Pattern 1: Q) (1/2) of a number is 3 more than the (1/6) of the same
number? a) 6 b)7 c)8 d)9
Sol: Let the number be x, ((1/2)*x)=3+(1/6)*x, Then solve x
Q) (1/3) of a number is 3 more than the (1/6) of the same number? a) 6 b)16
c)18 d)21
Q) (1/3) of a number is 6 more than the (1/6) of the same number? a) 6 b)18
c)36 d)24
Q) (2/3) of a number is 4 more than the (1/6) of the same number? a) 6 b)8
c)36 d)24
Q) (1/3) of a number is 5 more than the (1/6) of the same number? a) 6 b)36
c)30 d)72
Pattern 2: Q)There are two water tanks A and B, A is much smaller than B.
While water fills at the rate of 1 liter every hour in A, it gets filled up
like, 10, 20, 40,80, 160…..in tank B. (At the end of first hour, B has 10
liters, second hour it has 20 liters and so on). If tank B is 1/32 filled
of the 21 hours, what is total duration of hours required to fill it
completely? a) 26 B)25 c)5 d)27
Sol: Given that B fills up at the rate 10,20,40 etc... This is a geometric
progression where a = 10 r = 2 so after 21 hrs lts in B = a*r21 = 10 * 221
This is equal to 1/32 volume of B SO TOTAL VOLUME OF B = 32 * 10 * 221
which is =10 * 226 So hrs required to fill up B is 26
Or
for every hour water in tank in B is doubled, Let the duration to fill the
tank B is x hours. x/32 part of water in tank of B is filled in 21 hours,
Next hour it is doubled so, 2*(x/32) part i.e (x/16) part is filled in 22
hours, Similarly (x/8)th part in 23 hours,(x/4)th part is filled in 24
hours, (x/2)th part is filled in 25 hours, (x)th part is filled in 26 hours
So answer is 26 hours.
Q)There are two pipes A and B. If A filled 10 liters in an hour, B can fill
20 liters in same time. Likewise B can fill 10, 20, 40, 80, 160…... If B
filled in 1/16 of a tank in 3 hours, how much time will it take to fill the
tank completely? a) 9 B)8 c)7 d)6
Q)There are two water tanks A and B, A is much smaller than B. While water
fills at the rate of 1 liter every hour in A, it gets filled up like, 10,
20, 40,80, 160…..in tank B. 1/8 th of the tank B is filled in 22 hours.
What is the time to fill the tank fully? a) 26 B)25 c)5 d)27
Q)A tank is filled with water. In first hour 10 liters, second hours 20
liters, and third hour 40 liters and so on…If time taken to fill ¼ of the
tank if 5 hours. What is the time taken to fill up the tank? a) 5 B)8 c)7
d)12.5
Q)If a tank A can be filled within 10 hours and tank B can be filled ¼ in
19 hours then, what is the time taken to fill up the tank completely? a) 21
B)38 c)57 d)76
Pattern 3: Q)6 persons standing in queue with different age group, after
two years their average age will be 43 and seventh person joined with them.
Hence the current average age has become 45. Find the age of seventh
person? a) 43 b)69 c)52 d)31
Sol: a+b+c+d+e+f+ Z = 45*7 =315 a+b+c+d+e+f+ 12 = 43*6 = 258 therefore :
a+b+c+d+e+f = 246 so age of seventh person "Z" is = 315 - 246 = 69
Q)In a market 4 men are standing. The average age of the four before 4years
is 45, after some days one man is added and his age is 49. What is the
average age of all? a) 43 b)45 c)47 d)49
Sol: Avg 4 yrs ago = 45 so avg now = 49 a person of age 49 is added so avg
remains 49
Q)In a shopping mall with a staff of 5 members the average age is 45 years.
After 5 years a person joined them and the average age is again 45 years.
What‟s the age of 6th person? a) 25 b)20 c)45 d)30
Sol: After 5 years average age becums 50 Total age = 250 new member joins
suppose age x so (250 + x) / 6 = 45 x = 20
Q)In a market 4 men are standing .The average age of the four before 2
years is 55, after some days one man is added and his age is 45. What is
the average age of all? a) 55 b)54.5 c)54.6 d)54.7
Sol: After 2 years average age becomes 57
Total age=228
New member joins, his age is 45
So, (228 + 45)/6 = 54.6 ans
Pattern 4: Q)In the reading room of a library, there are 23 reading spots.
Each reading spot consists of a round table with 9 chairs placed around it.
There are some readers such that in each occupied reading spot there are
different numbers of readers. If in all there are 36 readers, how many
reading spots do not have even a single reader? a)8 b)none c)16 d)15 Sol:
There are some readers such that in each
occupied reading spot there are different numbers of
readers.
1+2+3+4+5+6+7+8= 36 readers
so ,8 spots have different readers.
remainings are 23-8= 15.
15 spots are empty.
Or
he just said that in each different spot there are different
number of readers. So there will be many possibilities...
It is same as number of ways in which you can make a sum of
9 using only digits from 1 to 9 each at most once...
Consider
1+2+3+6+7+8+9 = 36
In this case answer is: 23-7 = 16
but different answers are possible depending on case u choose
Q)In the reading room of a library, there are 10 tables, 4 chairs per
table. In each table there are different numbers of people seated. How many
tables will be left out without at least 1 person? a) 8 b)6 c)2 d)7 Q)In
the reading room of a library, there are 10 tables, 4 chairs per table. In
each table there are different numbers of people seated. How many ways they
will sit in the library so that no chair would be blank? a) 8 b)6 c)2 d)7
Sol: 10 tables, each with 4 chairs
Each table has a different number of persons sitting....This is not
possible as there are only 4 chairs.. The different combinations can be 0,
1, 2, 3 and 4...the sixth table would have one of the above
combinations..Thus the rule is violated.. Plus, if different numbers of
people occupy a table, there would be blank spaces...so how can we
calculate the possibilities of the library being fulling occupied.. This is
an ambiguous question! Pattern 5: Q)A man jogs at 6 mph over a certain
journey and walks over the same route at 4 mph. What is his average speed
for the journey? a) 2.4 mph b) 4.8 mph c) 4 mph d) 5 mph
Sol: Average speed=2*x*y/(x+y)=2*6*4/(6+4)=4.8 kmph
Q)A man travels from A to B at 4 mph over a certain journey and returns
over the same route to A, at 5 mph. What is his average speed for the
journey? a) 4.44 mph b) 4.8 mph c) 4.887 mph d)5 mph
Q)A person is rock climbing at an altitude of 800 m. He go up by 7 mph. and
come down by 9 mph. what was his average speed? a) 7.875 mph b) 7.125 mph
c) 7mph d) 7.5 mph
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down
at an altitude of 200m? a) 28.8 mph b) 27.8 mph c) 27.5mph d) 30 mph
Q)Person travels to a hill, if he goes from A to B with speed of 4kmph and
returns back to B with speed of 5kmph. What is his average speed of
journey? a) 4.5kmph b) 4.44kmph c) 9kmph d) 4.245kmph
Q)A man travels from A to B at 70 mph over a certain journey and returns
over the same route to A, at 80 mph. What is his average speed for the
journey? a) 74.66 b)75 c)74.33 d)74.99
Q)Find average speed if a man travels at speed of 24kmph up and 36kmph down
at an altitude of 200m. a) 28.8 b)28 c)27 d)28.6 Pattern 6 Q)Susan made a
block with small cubes of 8 cubic cm volume to make a block ,3 small cubes
long, 9 small cubes wide and 5 small cubes deep. She realizes that she has
used more small cubes than she really needed. She realized that she could
have glued a fewer number of cubes together to lock like a block with same
dimensions, if it were made hollow. What is the minimum number of cubes
that she needs to make the block? a) 114 b) 135 c) 21 d) 71 Sol: dimensions
of small cube = 2*2*2 Length of cube = 3 small cubes long = 6 cm Breadth =
9 small cubes wide = 18 cm Height = 5 small cubes deep = 10 cm Volume =
6*18*10 = 1080cm^3 Volume of hollow cube = (6-4)(18-4)(10-4) = 168 cm^3
total number of blocks needed = 1080-168 /8 = 912/8 = 114 Q)A boy wants to
make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later
he realized he can make same cuboids by making it hollow. Then it takes
some cubes less. What is the number of the cubes to be removed? a) 2000 b)
5000 c) 3000 d) 7000 Sol: Total volume of cube = 5 * 6 * 7 = 210 m cube
volume of smaller cube 0.03 Total cubes reqd = 7000 for hollow cube no. of
small cubes reqd = 5/0.03 *4 + 6/.03 * 4 + 7/0.03 *4 which is approx 2000
so 5000 cubes have to be removed
Note:4 sides of 5,6 and 7 in the cube...so multiplied by 4 Q)Smita was
making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number
of cubes needed to make a hollow cube looking of the same shape?
a) 98 b) 104 c) 100 d) 61 Sol: Jst count the no. of cubes for each face
take the 1st one 25 small cubes reqd now for 2 faces adjacent to it 20 are
reqd 2 faces adjacent to all these 12 are reqd and for the last one 9 are
reqd so 98 Q)Leena cut small cubes of 10 cm dimension each. She joined it
to make a cuboid of length 100 cm, width 50 cm and depth 50 cm. How many
more cubes does she need to make a perfect cube? a)500 b)250 c)750 d)650
Sol: Volume left for perfect cube = 100*100*100 - 100*50*50 No. of cubes
reqd = (100*100*100 - 100*50*50)/10*10*10 = 750 Q)Leena cut small cubes of
3 cubic cm each. She joined it to make a cuboid of length 10 cm, width 3 cm
and depth 3 cm. How many more cubes does she need to make a perfect cube?
a) 910 b) 250 c) 750 d) 650 Q)A lady builds 9cm length, 10cm width,3cm
height box using 1 cubic cm cubes. What is the minimum number of cubes
required to build the box? a) 730 b) 270 c) 720 d) 310 Sol: no. of cubes
required = 9*10*3 /1 = 270 Pattern 8: Q) (40*40*40 –
31*31*31)/(40*40+40*31+31*31)=? a)8 b)9 c)71 d)51
Q) (98*98*98 – 73*73*73)/( 98*98*98 – 73*73*73)=? a).171 b).4 c).420 d).415
Q) (209*144)^2 + (209*209)+(209*144)+(144*144) = ? a)905863729 b)905368729
c)905729368 d)65 Pattern 9: Q) ((4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2
a)8 b)none c)16 d)15
Q)x/2y = 2a,then 2x/x-2ay=? a)4 b)8 c)16 d)2
Q)3X/5Y = 5Y/3X…..Find the value of X/Y a)3/5 b)5/3 c)2/5 d)5/2
Q)What is the value of (3X+8Y)/(X-2Y), if X/2Y=2 a)8 b)none c)10 d)13
Q) (4x+3y)+(5x+9y))/(5x+5y) = ? as (x/2y) = 2 a)48/5 b)46/5 c)47/5 d)49/5
Q) ((4x+2y)/(4x-2y)= ? as (x/2y) = 2 a)8/7 b)9/7 c)11/7 d)6/7 Pattern 10:
Q)A girl has to make pizza with different toppings. There are 8 different
toppings. In how many ways can she make pizzas with 2 different toppings?
a)16 b)56 c)112 d)28
Sol: The number of ways of choosing r distinct objects from n distinct
objects is given by the formula C(n, r) = n!/r!*(n-r)! where n! =
n(n-1)(n-2).......3*2*1 If order was important, the number of arrangements
is P(n,r) n!/(n-r)! Now suppose you wanted to display one topping in the
middle and the other around the edge, you would be considering arrangements
and the answer would be P(8, 2) = 8!/6! = 8*7
= 56 However, suppose that you wish to sprinkle toppings randomly over the
pizza base. Since it does not matter what the arrangements are, the number
of ways is C(8, 2) = 8! / 2!*6! = 8*7 / 2*1 = 56/2 = 28 This is correct.
Q)A pizza shop made pizzas with many flavors. There are 10 different
flavors, in that 7 flavors are taken to make pizza. In how many ways they
can arrange? a)240 b)120 c)65 d)210
Sol: 10c7=10c3=120
Q)A pizza shop made pizzas with many flavors. There are 9 different
flavors, in that 2 flavors are taken to make pizza. In how many ways they
can arrange? a)16 b)26 c)36 d)46 Sol: 9c7=9c2=36 Pattern 11: Q)3, 22, 7,
45, 15,? , 31 a)91 b)151 c)90 d)5
Sol: we can divide this into two series Series 1: 3, 7, 15, 31 Here, every
next number = 2*n + 1, where n is the preceding number Series 2: 22, 45, x
This is the same as Series 1 So, x = 45*2+1 = 91
Q)2. 8 6 17 14 35 31 75 _ 143? Sol: From the given question it is clear
that the difference between the consecutive two digits is 2,3,4,.... 8-6=2
17-14=3 35-31=4 75-x=5; from the above equation we get that x value is 70
final solution is 70 the series become 8 6 17 14 35 31 75 70 143
137.......... Q)Inspired by Fibonacci series Sangeet decided to create his
own series which is 1, 2, 3, 7, 7, 22, 15, 67, 31, _, 63? a)202 b)31 c)76 d)49
Sol: Ans=202 bcos in the given series there are two other series..in the
form of 1 ,2 ,3 ,7 ,7 ,22 ,15 ,67 ,31 ,_ ,63; choose the alternate
digits:1,3,7,15,31,63 these are follow the pattern like n*2+1 1
3=n*2+1(wher n=1) 7=n*2+1(wher n is the previous number) 15=7*2+1(where
n=7) 31=15*2+1(wher n=15) 63=31*2+1(where n=31) but we dont need this
series.just for understanding i gave the above matter anothe series in the
given series in:2 ,7 ,22 ,67 ,_ we hav to find the number in the blank this
series is in the form of n*3+1 so the series consists of the following
numbers 2 7=2*3+1(where n=2) 22=7*3+1(wher n=7)
67=22*3+1(wher n=22) for the next number we need to multiply the previous
number with 3 and add a 1 to the result finally next digit=67*3+1=202 the
final series 1,2,3,7,7,22,15,67,31,202,63
Q)3, 12, 7, 26, 15, ? a)54 b)27 c)108 d)31
Sol: Series 1: 3, 7, 15 …
Series 2:12, (12*2+2)26, (26*2+2)54 ans
Q)1! + 2! + ……. + 50!=? a)3.1035*10^64 b)2.1021*10^65 c)3.1035*10^63
d)3.1035*10^62
Sol: The answer is 3.10351E+64 There is no formula as such We can find this
by solving it in Microsoft Excel!
Q)1, 2, 3, 6, 7, 14, _, 32?
Sol: its obviously 16. divide in two two pairs such that it is 1-2 3-6 7-14
_-32 see the pattern is going n- n*2 therfore _-16*2 gives 16_16*2 hence
answer is 16.
Q)5, 9, 12, 18, 26, 36, 47, 72, _? a)75 b)135 c)100 d)55
Sol: Series1: 9,18,36,72….2*n
Series2: 5,12,26,47,75….difference is 7 multiples, so ans :75
Q)3, 15, x, 51, 53,159,161 a)17 b)34 c)54 d)112
Sol: Difference between the two consecutive numbers is 2; exclude 3 here
consider 17 here then 17-15=2 and next number will be 17*3=51 same process
continued. 53-51=2 and next number is 53*3=159 Ans is 17
Pattern 12: Q)Simple question but big one on average age.sth like a, b, c
weighted separately 1st a, b, c ,then a& b, then b &c ,then c & a at last
abc, the last weight was 167,then what will be the average weight of the 7
reading? a)95 b)95.428 c)95.45 d)94
Sol: a+b+c =167 given first a is weighd then b then c then a+b , b+ c , c+
a and lastly a+b+c so total = a + b + c+ (a+ b) + (b+c) + (c+a) + (a+b+c) =
4(a+b+c) so avg of 7 weighs = 4/7 * 167 = 95.428 Pattern 13: Q)A toy train
produces 10 different sounds when it moves around a circular toy track of
radius 5 m at 10 m per min. However, the toy train is defective and it now
produces only 2 different tunes at random. What are the odds that the train
produces for consecutive music tones of the same type? a) 1 in 16 B)1 in 4
c)1 in 8 d)1 in 32
Sol: it can produce sound A , prob = 1/2 * 1/2 * 1/2 * 1/2 = 1/8 or sound B
, prob = 1/8 so prob of consecutive sound = 1/8 + 1/8 = 1/4
or
Total number of cases 2 can be chosen out of 10 = 10c2 = 45 ways. first
note in 10 ways , second note in 1 way only. so prob = 10/45 = 2 out of 9
or
First Time choose sound =1/2 second third fourth fifth =1/2 total=(1/2)^5=1/32
Q)A car manufacturer produces only red and blue models which come out of
the final testing area at random. What are the odds that five consecutive
cars of same color will come through the test area at any one time? a)1 in
16 b)1 in 125 c)1 in 32 d)1 in 25
Sol: Probability that a car is red or blue = 1/2 So, probability that each
of the five cars are of a color = Probability that a car is blue +
Probability that a car is red = (1/2)5 + (1/2)5 = 2*(1/2)5 =1/16 Pattern
15: Q)A triangle is made from a rope. The sides of the triangle are 25 cm,
11 cm and 31 cm. What will be the area of the square made from the same
rope? a)280.5625 b)240.5625 c)280.125 d)240
Sol: Length of the rope = 67 Length of side of square = 67/4 Area of square
= (67/4)2 Q)A triangle is made from a rope. The sides of the triangle are
21 cm, 24 cm and 28 cm. What will be the area of the square made from the
same rope? a)280.5625 b)333.0625 c)333.0125 d)400 Sol: Length of the rope =
73 Length of side of square = 73/4 Area of square = (73/4)2 Pattern 16:
Q)What is the distance between the z-intercept from the x-intercept in the
equation ax+by+cz+d=0
Sol: ax + by + cz + d = 0 At the z-intercept, 'x' and 'y' are both zero. cz
+ d = 0 --> z = -d/c --> The z-intercept is the point (0, 0, -d/c). At the
x-intercept, 'y' and 'z' are zero. ax + d = 0 --> x = -d/a --> The
x-intercept is the point (-d/a, 0, 0). The distance between the points (0,
0, -d/c) and (-d/a, 0, 0) is sqrt[ (-d/a)2 + (-d/c)2 ] = sqrt (d2/a2 +
d2/c2) = d sqrt(1/a2 + 1/c2)
Pattern 17: Q)A scientist was researching on animal behavior in his lab. He
was very interested in analyzing the behavior of bear. For some reason he
travelled 1mile in north direction & reached at North Pole. There he saw a
bear. He then followed the bear around 1 hr with a speed of 2km/hr in east
direction. After that he travelled in south direction & reached at his lab
in2 hrs. Then what is the color of the bear? a)white b)black c)gray d)brown
Sol: Since it is the north pole, the colour of the bear is white! As brown
and black bears are not found on the poles!
Pattern-18: Q)Out of 7 children the youngest is boy then find the
probability that all the remaining children are boys a)1/64 b)1/32 c)1/128
d)1/256
Sol: the first result doesn't affect subsequent ones. for each birth,
P[boy] will be 1/2 using the multiplicative principle,. P[next 5 are boys]
= 1/2 *1/2 *1/2 *1/2 *1/2 = 1/32 <------- Pattern 19: Q)Usha bought a linen
cloth and rope to build a tent. If the rope is 153 m long and it is to be
cut into pieces of 1m length, then how many cuts are to be made to cut the
ropes into 153 pieces? a)153 b)152 c)154 d)155
Sol: Number of cuts = n - 1 so it will be 152 cuts
Q)A person has to make 146 pieces of a long bar. He takes 4 seconds to cut
a piece. What is the total time taken by him in seconds to make 146 pieces?
a)584 b)580 c)730 d)725
Sol: Number of cuts=146-1
145*4=580
Q)A person has to make 141 pieces of a long bar. He takes 2 seconds to cut
a piece. What is the total time taken by him in seconds to make 141 pieces?
a)560 b)280 c)112 d)324
Sol: Number of cuts=141-1
140*2=280
Pattern 20: Q)Spores of a fungus, called late blight, grow and spread
infection rapidly. These pathogens were responsible for the Irish potato
famine of the mid-19th century. These seem to have attacked the tomato
crops in England this year. The tomato crops have reduced and the price of
the crop has risen up. The price has already gone up to $45 a box from $27
a box a month ago. How much more would a vegetable vendor need to pay to
buy 27 boxes this month over what he would have paid last month? a) $27 b)$
18 c)$45 d)$ 486 Sol: Change in price = 45 - 27 = 18 So for 27 boxes = 27 *
18 = 486 Pattern 21: Q)A Person buys a horse for 15 ponds, after one year
he sells it for 20 pounds. After one year, again he buys the same horse at
30 pounds and sells it for 40 pounds. What is the profit for that person?
Sol: 20 - 15 = 5 40 - 30 = 10 total Profit=15
Pattern 22: Q)John buys a cycle for 31 dollars and given a cheque of amount
35 dollars. Shop Keeper exchanged the cheque with his neighbor and gave
change to John. After 2 days, it is known that cheque is bounced. Shop
keeper paid the amount to his neighbor. The cost price of cycle is 19
dollars. What is the profit/loss for shop keeper? a)loss 23 b)gain 23
c)gain 54 d)Loss 54 Sol: Shopkeeper paid 4 $ to john while giving change He
also paid neighbor 35 $ Total payment 39 $ Cost 19 $ Loss 20 $ Pattern 23:
Q)A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25
yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She
takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of
each color? a)50 b)8 c)60 d)42
Sol: since it is dark....
take worst case
satisfy largest number first.....
since she wants it in pair
32 red
24 yellow
1+1 yellow+blue
2 blue
=60
Q)A lady has fine gloves and hats in her closet- 14 blue, 20 red, and 18
yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She
takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of
each color?
Sol: Since its dark….
Take worst case..
Satisfy largest number first….
20 red
18 yellow
2 blue
=40 Q)A lady has fine gloves and hats in her closet- 13 blue, 27 red, and
40 yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She
takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of
each color? Sol: Since its dark…
Take worst case…
Satisfy largest number first…
40 yellow
26 red
1 +1 red + blue
2 blue
=70 Q)A lady has fine gloves and hats in her closet- 25blue, 7 red, and 9
yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She
takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of
each color? Q)A lady has fine gloves and hats in her closet- 26 blue, 30
red, and 56 yellow. The lights are out and it is totally dark. In spite of
the darkness, she can make out the difference between a hat and a glove.
She takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of
each color? Pattern 24: Q)Sangakara and Ponting selects batting by using a
dice, but dice is biased. So to resolve, Ponting takes out a coin. What is
the probability that coin shows correct option? a)1/2 b)1/6 c)1/12 d)6/10
Sol: 1/2
Q)There is a die with 10 faces. It is not known that fair or not. 2
captains want to toss die for batting selection. What is the possible
solution among the following? a) If no. is odd it is head, if no. is even
it is tail b) If no. is odd it is tail, if no. is even it is head c) Toss a
die until all the 10 digits appear on top face. And if first no. in the
sequence is odd then consider it as tail. If it is even consider it as
head. Sol: ans is c) in question itself it will clearly mentioned whether
that is it was a not known fair or not. so first we have to check whether
it is fair or not. so we toss a die until all the 10 faces appear on top,
then only we can decide which one is odd and which one is even Pattern 25:
Q)In a family there are some boys and girls. All boys told that they are
having equal no of brothers and sisters and girls told that they are having
twice the no. of brothers than sisters. How many boys and girls present in
a family? a)4 boys and 3 girls b)3 boys and 4 girls c)2 boys and 5 girls
d)5 boys and 2 girls Sol: for each boy in option 1 there are 3 brothers and
3 sisters for each girl in option 1 there are 2 sisters and 4 brothers so
answer is option 1 Pattern 26; Q)10men and 10 women are there, they dance
with each other, is there possibility that 2 men are dancing with same
women and vice versa? a)22 b)20 c)10 d)none
Sol: Since 10 is an even number, and people dance in couples, there
wouldn't be a lone dancer. So never!
Q)There are 100 men and 100 women on the dance floor. They want to dance
with each other. Then which of the following statements is always true: a)
There are 2 men who danced with equal no. of women‟s b) There are 2 women
who danced with equal no. of men a) both a and b b)only a c)only b d)none
Sol: none Pattern 27: Q)Middle- earth is a fictional land inhabited by
hobbits, elves, dwarves and men. The hobbits and elves are peaceful
creatures that prefer slow, silent lives and appreciate nature and art. The
dwarves and the men engage in physical games. The game is as follows. A
tournament is one where out of the two teams that play a match, the one
that loses get eliminated. The matches are played in different rounds,
where in every round; half of the teams get eliminated from the tournament.
If there are 8 rounds played in knock out tournament, how many matches were
played? a)257 b)256 c)72 d)255 Sol: The number of teams for 8 rounds is:
256->128->64->32->16->8->4->2->1 Thus initially der wer 256 teams. But wat
is askd is the numbr of matches that were played to reach the winner. The
number of matches for 8 rounds is: 128->64->32->16->16->8->4->2->1
128+64+32+16+8+4+2+1=255 Q)A game is played between 2 players and one
player is declared as winner. All the winners from first round are played
in second round. All the winners from second round are played in third
round and so on. If 8 rounds are played to declare only one player as
winner, how many players are played in first round? a)256 b)512 c)64 d)128
Sol: 256 Pattern 28: Q)Metal strip of width „x‟ cm. 2 metal strips are
placed one over the other, then the combine length of 2 strips is „y‟. If
„z‟ strips are placed in that manner. What is the final width of that
arrangement? Sol: only the height of the metal strip changes,the length as
well the width of the metal strip remains same....so the answer can be
concluded as 'x' Q)A, B, C, D, E are there among A, B, C are boys and D, E
are girls D is to the left of A and no girl sits at the middle and at the
extemes. Then what is the order of their sittings. Sol: There are two
possibilities Case 1: _ D A E _ Case 2: _E _ D A The blanks can be filled
by the two boys that are left Given proper options, we can choose the
appropriate one Pattern 29: Q)There is 7 friends (A1, A2, A3....A7).If A1
have to have shake with all without repeat(distinct=>Permutaion). How many
handshakes possible? a)6 b)21 c)28 d)7 Sol: A1 can shake hands with 6
people, A2-A7 A2 can shake hands with 5 people, A3-A7 and so on If there
are n people, there are (n-1)! ways for them to shake hands. In this case,
6!=720 ways.
Q)49 members attended the party. In that 22 are males, 17 are females. The
shake hands between males, females, male and female. Total 12 people given
shake hands. How many such kinds of such shake hands are possible? a)122
b)66 c)48 d)128 Sol: 12C2 = 66 Pattern 30: Q)B is taller than j and 3
pillars. P is shorter than B and 2 pillars is j shorter/taller than P?
a)yes b)no c)may be d)can‟t find Sol: According to the first condition, B >
j + 3 pillars According to the second condition, B + 2 pillars > P
Rewriting the first equation, B + 2 pillars > j + 5 pillars Comparing it
with the second equation,
we can't say any thing about P and j! Q)There are 1000 pillars for a
temple. 3 friends Linda, Chelsey, Juli visited that temple. (Some unrelated
stuff) Linda is taller than Chelsea and taller than 2 of 1000 pillars.
Julia is shorter than Linda. Find the correct sentence? a) Linda is shorter
among them b) Chelsea is taller than Julia c) Chelsea is shorter than Julia
d) Cannot determine who is taller among Chelsea and Julia Sol: J<C< L or C<J<L
Therefore ans is d Pattern-31 Q)Entry ticket to an exhibition ranges from
1p to 31p. You need to provide exact change at the counter. You have 31p
coin. In how many parts will u divide 31p so that u will provide the exact
change required and carry as less coins as possible? a)4 b)5 c)6 d)7 Sol:
2n => n=0,1,2,3,4 < 25(32) Since given 31p, 2n results in 1,2,4,8,16
Through any combination of 1,2,4,8,16 we can acquire any denomination
needed at counter..... So, total 5 combinations Pattern 32 Q)Peter and Paul
are two friends. The sum of their ages is 35 years. Peter is twice as old
as Paul was when Peter was as old as Paul is now. What is the present age
of Peter? a)8 b)20 c)16 d)15 Sol: go fr options .. take 20 as peter's
present age den pauls age wud be 15(20+15)=35.. also when peter was 15,i.e
at the age of paul.(20-15)=5.then pauls age wud be (15-5)=10 and it was
double that of peters present age .'.optin 2
OR
let pauls age be 'a' and peters be 'e' e+a=35 (given) e=35-a ------eq1 when
peter was as old as paul that is when peter's age was 'a' i.e e-(e-a) [for
example if e was 9 and a was 5, e-a is 4,9-4=5 so e-(e-a)] pauls age was
a-(e-a) =2a-e now peters age is e=2(2a-e) e=4a-2e 3e=4a 3(35-a)=4a
105-3a=4a a=15 hence e=20 Pattern 33 Q)20 men handshake with each other
without repetition. What is the total number of handshakes made? a)190
b)210 c)150 d)250
Sol: 20th man = 19 handshakes 19th man = 18 ....1st man = 0 so we get a
series from 1 to 19 handshakes where n = 19 a = 1 d =1 So total handshakes
= sum of the series = n/2(2a+(n-1)d) = 190
Q)10 people are there, they are shaking hands together, how many hand
shakes possible, if they are in no pair of cyclic sequence. a)45 b)9 c)12
d)10 Sol: 10th man = 9 handshakes
9th man = 8
….1st man =0
So we get a series from 1 to 9 handshakes where n=9 a=1 d=1
So, total handshakes = sum of the series = n/2(2a+(n-1)d) = 45
Pattern 34 Q)If there are 2 wheelers and 4 wheelers parked in a school
located at the heart of the city, find the number of 4 wheelers parked
there if there were 20 two wheelers parked there a)48 b)50 c)52 d)64
Sol: Question incomplete
Q)If there are 2 wheelers and 4 wheelers parked in a school located at the
heart of the city, find the number of 4 wheelers parked there if there were
58 wheels are parked there a)10 b)33 c)22 d)none Sol: no of 4 wheelers are
10.i.e. 10*4=40 wheels. no. of wheels left = 58-40=18 hence no. of 2
wheelers=18/2=9 22 and 33 cant be ans bcz it will make no. of wheels
greater than 58 Pattern 35 Q)A man whose age is 45 yrs has 3 sons named
John, Jill, jack. He went to a park weekly twice. He loves his sons very
much. On a certain day he found the shop keepers selling different things.
An apple cost 1penny, 2chocalate costs 1penny & 3 bananas cost 1 penny. He
has bought equal number of apple, chocolate & banana for each son. If the
total amount he invest is 7 penny then how many he has bought from each
piece for his son? a)1app,1cho,1 banana b)1 app,2cho,3 banana
c)1app,2cho,1banana Q)One person had three children. He had 7 pennies. Find
the distribution of the fruits among the three children. A melon costs 1
penny, 2 oranges cost 1 penny and 3 grapes cost 1 penny a)2 melons, 1
orange, 1 grape b) 2 melons, 2 orange, 1 grape c) 1 melons, 2 orange, 1
grape. PATTERN 36 Q)The age of the two friends were in the ration of 6:5.If
the sum of their ages is 55.Then after how many years their ratio will
become 8:7? a)11 b)7 c)10 d)12 Sol: 6x+5x = 55 x = 5 so ages 30 and 25 So
after 10 yrs 40 and 35 so ratio is 8:7 Q)The age of the two friends were in
the ration of 6:5.If the sum of their ages is 66.Then after how many years
their ratio will become 7:6? a)11 b)6 c)10 d)12 Sol: 6x+5x=66
X=6
So ages 36 and 30
So after 6 years 42 and 36
So ratio is 7:6 Q)The age of the two friends were in the ration of 2:3.If
the sum of their ages is 55.Then after how many years their ratio will
become 4:5? a)11 b)33 c)22 d)44 Sol: 2x+3x=55
X=11
So ages 22 and 33
So after 22 years 44 and 55
So ratio is 4:5 PATTERN 37 Q)A volume of 10936 l water is in a container of
sphere. How many semi sphere of volume 4l each will be required to transfer
all the water into the small semi spheres? a)2812 b)8231 c)2734 d)4222 Sol:
ans = 10936/4 = 2734 PATTERN 38 Q)A person is manufacturing a house. He
bought 20 ropes of wire which has a density of 300 Kg/m3.The height of the
building to be constructed is 40 m. If the capacity of the current passed
in the wire is 20 A and the voltage capacity is 80 Volts.Then what will be
the opposing force to the current if the wire is used ? a)2 b)4 c)8 d)1600
Sol: by ohms law v = ir so r = v/i so r = 80/20 = 4 PATTERN 39 Q)A horse
chases a pony 2 hours after the pony runs. Horse takes 3 hours to reach the
pony. If the average speed of the horse is
81Kmph.Then what is the average speed of the pony? a)46.4 b)51 c)53.4
d)48.6 Sol: pony = 2 hours + 3 hours= 5 hours.
horse= 3 hours= 3 hours.
3*81=243
243/5=48.6=>average speed of pony.
Q)A horse chases a pony 3 hours after the pony runs. Horse takes 4 hours to
reach the pony. If the average speed of the horse is 35 kmph, what s the
average speed of the pony? Sol: pony = 3 hours + 4 hours= 7 hours.
horse= 4 hours= 4 hours.
3*35=105
105/7=15=>average speed of pony.
PATTERN 40 Q)The difference between two no is 9 and the product of the two
is 14.What is the square of their sum? a)120 b)130 c)137 d)145 Sol: x-y=9
xy=14
(x+y)2-(x-y)2 = 4xy
(x+y)2= 4xy + (x-y)2
(x+y)2= 4*14 + 81
=137
Q)The sum of two no is 5 and the product of the two is 14.What is the sum
of their squares? Q) The sum of the squares of two no is 12 and their sum
is 15.Find the product of the two no? PATTERN 41 Q)On planet korba, a solar
blast has melted the ice caps on its equator. 9 years after the ice melts,
tiny planetoids called echina start growing on the rocks. Echina grows in
the form of circle, and the relationship between the diameter of this
circle and the age of echina is given by the formula d = 4*√ (t-9) for t ≥
9 where d represents the diameter in mm and t the number of years since the
solar blast.Jagan recorded the radius of some echina at a particular spot
as 7mm. How many years back did the solar blast occur? a) 17 b)21.25
c)12.25 d)14.05
Q)On planet korba, a solar blast has melted the ice caps on its equator. 9
years after the ice melts, tiny planetoids called echina start growing on
the rocks. Echina grows in the form of circle, and the relationship between
the diameter of this circle and the age of echina is given by the formula d
= 4* sqrt(t-9) for t ≥ 9 Where d represents the diameter in mm and t the
number of years since the solar blast. Jagan recorded the radius of some
echina at a particular spot as 12mm. How many years back did the solar
blast occur
Sol: so d=24 = 12*2 now 24=4*sqrt(t-9) 6^2=t-9 36+9=t t=42 PATTERN 42
Q)A man goes 50Km north , then turned left walked 40Km, then turned right ?
In which direction he is? a)North b)South c)East d)West PATTERN 43 Q)In
T.Nagar the building were numbered from 1 to 100.Then how many 4‟s will be
present in the numbers? a)18 b)19 c)20 d)21
Q)In T.Nagar the building were numbered from 1 to 100.Then how many 6‟s
will be present in the numbers? a)18 b)19 c)20 d)21 Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 1‟s will be present in
the numbers? a)18 b)19 c)20 d)21
Q)In T.Nagar the building were numbered from 1 to 100.Then how many 0‟s
will be present in the numbers? a)18 b)19 c)20 d)11 PATTERN 44 Q)A number
when divided by D leaves a remainder of 8 and when divided by 3D leaves a
remainder of 21. What is the remainder left, when twice the number is
divided by 3D? 13 b) cannot be determined c) 3 d) 42
Sol: suppose the no. is a a = Dx +8 ...1 a = 3Dy + 21 ...2 So from 1 & 2 we
get D(x-3y) = 13 13 is prime so x-3y has to be 1 let x = 4 and y = 1 We get
a = 60 2a = 120 So 120 when divided by 3D = 39 we get remainder as 3 So
answer is 3
PATTERN 45 Q)Ferrari S.P.A is an Italian sports car manufacturer based in
Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the
company sponsored drivers and manufactured race cars before moving into
production of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout
its history, the company has been noted for its continued participation in
racing, especially in Formula One where it has employed great success
.Rohit once bought a Ferrari. It could go 4 times as fast as Mohan's old
Mercedes. If the speed of Mohan's Mercedes is 35 km/hr and the distance
traveled by the Ferrari is 490 km, find the total time taken for Rohit to
drive that distance. 20.72 b) 5.18 c) 238.25 d) 6.18
Q)Ferrari S.P.A is an Italian sports car manufacturer based in Maranello,
Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company
sponsored drivers and manufactured race cars before moving into production
of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history,
the company has been noted for its continued participation in racing,
especially in Formula One where it has employed great success .Rohit once
bought a Ferrari. It could go 4 times as fast as Mohan's old Mercedes. If
the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the
Ferrari is 953 km, find the total time taken for Rohit to drive that
distance. 20.72 b) 5.18 c) 238.25 d) 6.18
PATTERN 46 Q)A sheet of paper has statements numbered from 1 to 70. For all
values of n from 1 to 70. Statement n says ' At least n of the statements
on this sheet are false. „Which statements are true and which are false? a)
The even numbered statements are true and the odd numbered are false. b)
The odd numbered statements are true and the even numbered are false. c)
The first 35 statements are true and the last 35 are false. d) The first 35
statements are false and the last 35 are false.
Sol: Suppose the first 35 statements are true! Statement 1: At least 1
statement is false [TRUE] Statement 2: At least 2 statements are false
[TRUE] ... Statement 35: At least 35 statements are false [TRUE]
--------------------------------------------------------------------
Statement 36: At least 36 statements are false [FALSE] .. Statement 40: At
least 40 statements are false [FALSE]
-------------------------------------------------------------------- AT
LEAST puts the minimum tag or the floor tag on the statements So, if the
first 35 statements are true and the rest are false, everything fits into
place!
PATTERN 47 Q)A man goes north 37km.turns left goes 2km.turns right goes
17km.turns right goes 2km. find distance b/w starting ending point. a) 54
b) 27 c) 81 d) 67
Try representing the statement as a pictoral representation. The 2 Km turns
becomes reversed in the second 2 Km turn. The total distance travelled
therefore is 17+37 = 54 Km
Q)If a person moves 15km straight and turns 45 km right and moves 15Km
staright then how much distance he needs to walk to reach starting point?
PATTERN 48 Q)If there are 30 cans out of them one is poisoned if a person
tastes very little he will die within 14 hours so if there are mice to test
and 24 hours to test, how many mices are required to find the poisoned can?
a) 3 b) 2 c) 6 d) 1
Sol: Have 6 mice for testing, Give each mice contents from 5 cans each 5 5
5 5 5 5 After 14 hours, one of the mice will die So, we will know which 5
cans must have the poison Then , take the contents of these 5 cans and give
to the remaining 5 mice each. We will know in due time which can is poisoned.
PATTERN 49 Q)If a and b are mixed in 3:5 ration and b and c are mixed in
8:5 ration if the final mixture is 35 liters, find the amount of b? A)
13.34 b) 15.73 c) 16.73 d) 9.45
Sol: total ratio = 24:40:25 sso b in 35 lts = 40/89 * 35 which is 15.73
PATTERN 50 Q)If we subtract a number with y, we get 4 increase of number,
once it got divided by y itself... Find that number?? A) 13 b) 12 c) 14 d) 11
Sol: Let number be x then x - y = x/y + 4 => xy - y^2 = x + 4 now we need
options to solve , one pair can be x = 12 and y = 6 options are incorrect
PATTERN 51 Q)It is the class with the seating arrangement in 4 rows and 8
columns. When the teacher says 'start' the girl who is sitting in first row
and first column will say 1, then the next girl sitting behind her will say
4, the next girl sitting behind that girl will say 7, in a particular order
each girl is telling a number, the following girls told 10, 13 next turn is
yours what u will say? a) 15 b) 17 c) 14 d) 16
Sol: 1 4 7 10 13 16 this is the series
PATTERN 52 Q)It is dark in my bedroom and I want to get two socks of the
same color from my drawer, which contains 24 red and 24 blue socks. How
many socks do I have to take from the drawer to get at least two socks of
the same color? A) 2 b) 3 c) 48 d) 25
Sol: 3 socks are only reqd to get socks of the same color
Q)Lady has 2 select gloves & hat from a basket. In the dark, she can
distinguish hat&gloves.14red, 20blue, 18green r there. Find probability
that any selected glove pair has same color.
Sol: SAME AS PATTERN 23
Q)A lady had fine gloves and hats. 25 blue, 7 red and 9grey. She had to
select a pair among them. But there was no light so she had to select in
darkness the correct pair with a glove and a hat. Therefore how many
combinations of same color she can select?
PATTERN 53 Q)If the Valentine‟s Day in 2005 falls on Monday, then on which
day will the Valentine‟s Day fall on 2010? A) Saturday b) Thursday c)
Wednesday d) Sunday
Sol: 14/2/2005 is a Monday So, from 1/1/2005, days till 14/2/2005 = 31 + 14
= 45 45 mod 7 = 3 Let us say Saturday = 1 Sunday = 2 Monday = 3 Tuesday = 4
.. Friday = 7 Now, 14/2/2010 is 365*5(1/1/2005 to 31/12/2009) + 1(as 2008
is a leap year) + 31(jan 2010)+14(feb 2010) = 1871 days from 1/1/2005 1871
mod 7 = 2 So, if 3 = Monday, 2 = Sunday So, 14/2/2010 is a Sunday!
PATTERN 54 Q)A person run from A to B.He took ¼ of the time less to reach B
when compare to run at normal Speed.Then how many percentage he has
increased his speed? a)40 b)44.4 c)33.3 d)22.2
Sol: We proceed as follows d=s*t when t1=(3/4)t then d=s1'*t1
s*t=s'1*(3/4)t then s1/s=4/3 Therefore increase in speed=s1/s-1=1/3or100/3
%=33.33% So answer is option 3 Q)An athlete decides to run the same
distance in 1/4th less time that she usually took. By how much percent will
she have to increase her average speed? a)40 b)44.4 c)33.3 d)22.2 Sol: let
he takes time t at speed s now new time is 3/4t , so speed will become 4/3s
so speed is 1.33s , that is speed increases by 33.3% hence option 3 PATTERN
55 Q)In a building there are 5 rooms. Each having a equal area .The length
of the room is 4m and breadth is 5 m. The height of the rooms is 2m. If 17
bricks are needed to make a square meter then how many bricks are needed to
make the floor of a particular room? a) 320 b) 380 c) 340 d) 300
Sol: 340 bricks for 1 room considering height of brick as 1 as it is not
given As 17 bricks for 1 sq m So l*b for room = 5*4 = 20 sq m So bricks =
20*17= 340
PATTERN 56 Q)One man want to build a wall .The length and breadth of the
wall are 20 and 30 respectively. He need 35 bricks for one square
centimeter then how many bricks he need? a)21,500 b)30,000 c)21,000
d)20,000 Sol: total area = 20 * 30 =600 so bricks reqd = 600 * 35 = 21000
PATTERN 57 Q)In a hotel we can order two types of varities,but we can make
6 more variteis in home.One can choose the four varities with two from
hotel as must.Find how many ways one can order. a)14 b)15 c)56 d)28 Sol: we
have to choose 2 out of 6 so answer = 6C 2 =15
PATTERN 58 Q)If a pipe can fill the tank within 6hrs.But due to leak it
takes 30 min more. Now the tank is full then how much time will it take to
empty the tank throught the leak.? a)78 b)56 c)66 d)59 Sol: let the leak
per hour be 1/x. ((1/6)-(1/x)=1/6.5 so,1/x=1/78 x=78 PATTERN 59 Q)The
bacteria has the probability of split into 3 and probability to die is
1/3rd of the total bacteria.Let the probability is P.Some of them survived
with probability 1/5.Then which among the following relation is true?
a)P=1/3+1/5*3 b)P=1/5*(1/8-3) Sol: First option is correct as , prob to die
is 1/3 and surviving is remaining which is 1/5 *3 as it becomes 3 times
hence option 1 Q)There is a bacteria which has the probability of die 1/3
of its total number or it may tripled. Find out the probability A.
P=1/3+(2/3*p^3) B. P=2/3+(2/3*p^3) C. P=2/3+(1/3*p^3) D P=2/3+(2/3*p^3)
Sol: probability of die is 1/3 or its get tripled the probability of
tripled is 2/3*p*p*p thats 2/3*p^3 so both the probability combined as
P=1/3+(2/3*p^3) PATTERN 60 Q)There was a grand mother in a village who had
a grand child. Upon asking her grand Childs age she told that she is as
older as many days old as her daughters age in weeks and as many days as
her own age in years. The sum of the three is 130.then how old is the child.?
Sol: as per ur logic , the baby is 127 days old... her mother 2 years
old... and tat old lady is 127 years old.. PATTERN 61 Q)In T.Nagar the
building were numbered from 1 to 100.Then how many 4‟s will be present in
the numbers? a)18 b)19 c)20 d)21 Sol: 10 4s in units place 10 in 10s place
so answer is 20 Q)In Tnagar many buildings were under residential category.
For buildings they number as 1 to 100. For shops, corporation numbered
between 150 and 200 only prime numbers. how many time 6 will appear in
building numbering? PATTERN 62 Q)Amrith told to Anand in front of a Photo
that “He is the son of my father‟s son”. Find who is in the picture if
amrith have no brothers and sisters. a)Amrith himself b)Amrith‟s Uncle
c)Amrith‟s Father d)Amrith‟s son Q)One person has no siblings and says,”
the guy in the photo is the only son of my father „s son”. What is the
relation of the guy to the person? PATTERN 63 Q)One grand father has 3
grand children two of the age difference is 3.Eldest child age is 3 times
the youngest childs age and the eldest child age is two year more than the
sum of other two children. Find what is the age of the elders child? a)18
b)22 c)30 d)10. Sol: let say, a,b, & c are the children, where a is eldest.
a=3C.......(1) b+c+2=a...........(2) jst check all the options which are
dividable by 3. (18 & 30) a=18 => c=6 put this value in (2) => b=10. which
is not satisfied the condition (two of the age difference is 3). if we take
a=30, then we get c=10 & b=18. which also not satisfied the condition.
so i think there is a problem with que. or in my understanding. please help
if there is any mistake in my calculations. Q)One grandfather has three
grandchildren, two of their age difference is 3, eldest child age is 3
times youngest child‟s age and eldest child‟s age is two times of sum of
other two children. What is the age of eldest child? Sol: consider that the
grand child are x,y,z then based on the conditions we have, 'two of their
age difference is 3' this leads to 3 possibilities x-y=3 y-z=3 x-z=3 but
only one will be correct 'eldest child age is 3 times youngest child's age'
x=3z 'eldest child's age is two times of sum of other two children' x=y+z+2
but since x=3z, x-z=3 is not feasible and again x-y=3 is also not
feasible.. so we got, y-z=3 x=3z x=y+z+2 we got three equations, 3
unknowns.. this lead to one possibility.. x=15 y=8 z=5 PATTERN 64 Q)In a
school, for a student out of 100 he got 74 of average for 7 subjects and he
got 79 marks in the 8th subject. what is the average of all the subject?
a)76.251 b)80.25 c)74.265 d)74.625 Sol: total marks of 8 subjects = 74*7 +
79 = 597 average = 597/8 = 74.625 PATTERN 65 Q)3 persons a,b,c were there A
always says truth,B lies on Monday,tusday,& Wednesday.but C lies on
thrusday,Friday & saturday .one day A said”that B & C said to A that” B
said “yesterday way one of the days when I lies”,C said that”yesterday way
one of the days when I lies too”.then which day was that? a)Sunday
b)Thursday c)Saturday d)Tuesday Sol: If today is Monday, Yesterday was
Sunday. Now B should lie on monday so Sunday was NOT one of the days he
lies on...Correct. And C shouldn't lie on monday so sunday was one of the
days he lies on....Incorrect. So it's not Monday. If today is Tuesday,
Yesterday was Monday. Now B should lie on Tuesday so Monday was NOT one of
the days he lies on...Incorrect. So it's not Tuesday. If today is Weds,
Yesterday was Tue. Now B should lie on Weds so Tues was NOT one of the days
he lies on...Incorrect. So it's not Weds. If today is Thurs, yesterday was
Weds. Now B should NOT lie on Thurs so Weds was one of the days he lies
on....Correct. And C should lie on Thurs so Weds was NOT one of the days he
lies on...Correct. So It's THURSDAY. If today is Fri, yesterday was Thurs.
Now B should NOT lie on Fri so Thursday was one of the days he lies
on...Incorrect. So It's Not Friday
If today is Sat, yeterday was Fri. Now B should NOT lie on Sat so Fri was
was one of the days he lies on...Incorrect. So it's Not Saturday. If today
is Sun, yesterday was Sat. Now B should NOT lie on Sun so Sat was one of
the days he lies on...Incorrect. So it's NOT Sunday. Answer: It was on a
Thurday PATTERN 66 Q)Which is the smallest no which divides 2880 and gives
a perfect square? a)4 b)9 c)3 d)5 Sol: ans d PATTERN 67 Q)How many 9 digit
numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4
if the repetition is allowed? a)57 b)56 c)59 d)58 Q)how many 13 digit
numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4
if repetition of digits is allowed? Q)By using 1,2,3,4,5,how many 5 digit
no. can be formed which is divisible by 4,repetation of no. is allowed??
Q)Form 8 digit numbers from by using 1, 2,3,4,5 with repetition is allowed
and must be divisible by4? Q)How many of 14 digit numbers we can make with
1,2,3,4,5 that are divisible by 4. Repetitions allowed.
PATTERN 68 Q)Consider two tumblers, the first containing Water and next
contains coffee. Suppose you take one spoon of water out of the first
tumbler and pour it into the second tumbler. After moving you take one
spoon of the mixture from the second tumbler and pour it back into the
first tumbler . Which one of the following statement holds now? a) There is
less coffee in the first tumbler than water in the second tumblers b) There
is more coffee in the firs tumbler than water in the second tumbler c)
There is as much coffee in the first tumbler as there is water in the
second tumbler d)None of the statements holds true Sol: Consider 100 mls
volume of cup First 100 mls of ink goes in cola total mixture in 2nd cup
1100 mls where 100 ink so ink concentration is 1/11 Now in 100 mls of
mixture 1/11 * 100 mls is ink and 10/11 * 100 mls is cola 10/11 * 100 mls
of ink is left in cola cup whereas we see 10/11 * 100 cola goin in ink cup
So same amount in both cups Q)Two bowls are taken, one contains water and
another contains tea.one spoon of water is added to second bowl and mixed
well, and a spoon of mixture is taken from second bowl and added to the
second bowl. Which statement will hold good for the above? PATTERN 69 Q)Six
friends decide to share a big cake. Since all of them like the cake, they
begin quarreling who gets to first cut and have a piece of the cake. One
friend suggests that they have a blindfold friend choose from well shuffled
set of cards numbered one to six. You check and find that this method works
as it should simulating a fair throw of a die. You check by performing
multiple simultaneous trials of picking the cards blindfold and throwing a
die. You note that the number shown by the method of picking up a card and
throwing a real world die, sums to a number between 2 and 12. Which total
would be likely to appear more often – 8,9 or 10? a) 8 b)All are equally
likely c)9 d)10 Sol: 8 will have higher probability as for 8 (2,6) (6,2)
(3,5) (5,3) and (4,4) which is greater than 9 or 10 so answer is 8 PATTERN
70 Q)Given a collection of points P in the plane , a 1-set is a point in P
that can be separated from the rest by a line, .i.e the point lies on one
side of the line while the others lie on the other side. The number of
1-sets of P is denoted by n1(P). The minimum value of n1(P) over all
configurations P of 5 points in the plane in general position (.i.e no
three points in P lie on a line) is a) 3 b)5 c)2 d)8
Sol:
Arrange points in a circle..so answer is 5
PATTERN 71
Q)Anoop managed to draw 7 circles of equal radii with their centres on the
diagonal of a square such that the two extreme circles touch two sides of
the square and each middle circle touches two circles on either side. Find
the ratio of the radius of the circles to the side of the square.
a)1:(2+ 7√2)
b)(2+ 7√2):1
c)1:(4+ 7√3)
d)1:(2+ 6√2)
Sol: The extreme circles will have radius perpendicular to sides..so the
part of diagonal till the centre of cirlce will be sqrt(2)r [Make diagram
and it will be clear]..now remaining portion is r , 5 more circles will
contribute 10r and last circle will contribute sqrt(2)r + r. total 12r +
2sqrt(2)r = sqrt(2) side so ratio of r:s = 1/2+6sqrt(2)
Q)An orange glass has orange juice. and white glass has apple juice. Both
equal volume 50ml of the orange juice is taken and poured into the apple
juice. 50ml from the white glass is poured into the orange glass. Of the
two quantities, calculate the amount of apple juice in the orange glass and
the amount of orange juice in the white glass Sol: To look simple assume
both glasses have 200ml juice.50ml orange from glass1 added to apple in
glass2. So glass1 have 150ml orange and glass2 have 250ml (200ml apple+50ml
orange). In glass2 clearly, for every 1 ml of orange,there is 4 ml of
apple. So if you take 50ml,there will be [40ml apple + 10ml orange].It is
added to glass1. Now glass1 has [160ml org + 40ml app]. Subtract the same
amount from glass2, it will have[160ml app+ 40ml org].But see the question,
apple in orange glass= 40ml and orange in white glass=40ml.So both are equal.
Q)Alok and Bhanu play the following min-max game. Given the expression
N=40+X+Y-Z, where X, Y and Z are variables representing single digits (0 to
9), Alok would like to maximize N while Bhanu would like to minimize it.
Towards this end, Alok chooses a single digit number and Bhanu substitutes
this for a variable of her choice (X, Y or Z). Alok then chooses the next
value and Bhanu, the variable to substitute the value. Finally Alok
proposes the value for the remaining variable: Assuming both play to their
optimal strategies,the value ofN at the end of the game would be:
Sol: Numbers from 0 to 9 [0 1 2 3 4 5 6 7 8 9]
1)Let alok choose 0, without thinking bhanu will place it in X or Y. (Since
0 is part of lower values, see above)
2)So the expression becomes 40+X-Z. Now if alok chose 9 bhanu will keep in
Z. So it becomes 31+X.Now alok will choose 9 in order to maximise. Now sum
becomes 40. (Now Continued from step 2 only i.e after the expression became
40+X-Z. Don't think of step 1. It is explained later below. ) But alok has
better way. He chose 5, then bhanu places it in Z (because 5 is a part of
higher value). Expression becomes 35+X. Now alok will choose 9. So final
value =44. Remember that the max value and min value for the expression
(X-Z) will always be 4 if they play optimal strategies.Try keeping
different values, you can get upto max of 44 only if they play optimal
strategies.
3)Now see step 1. Alok can increase the value of Y upto 4.(Bhanu still
places it in Y as it is lower value) So he can get upto 48.
4)Now first let alok chose 5,
case i)Bhanu places it in Z. Expression becomes 35+X+Y. Alok must choose
two 9's to maximize. So it is 35+18=53
case ii)Bhanu places it in Y or X(doesn't matter). Now the expression
becomes 45+X-Z. Remember max or min value of (X-Z) can be 4 only. So value
of expression = 45+4=49. Clearly (case ii) is lower. So if alok chose 5
bhanu should place in X or Y.
5)But alok is clever. He chose 6 as first number. Follow step 4 again. You
get 2 cases. Now max value is 50.
6)Alok choses 7 as first number. Now see that the value becomes 51 in both
cases of step 4. So here bhanu can place it in any variable, it doesn't matter.
7)But if alok chose 8 as his first number. (case i) of step 4 becomes
40+18-8 =50.So alok does not use 8 at all. So 51 remains max value for alok
and min value for bhanu.
Q) Alice and Bob play the following coins-on-a-stack game. 50 coins are
stacked one above the other. One of them is a special (gold) coin and the
rest are ordinary coins. The goal is to bring the gold coin to the top by
repeatedly moving the topmost coin to another position in the stack. Alice
starts and the players take turns. A turn consists of moving the coin on
the top to a position i below the top coin. We will call this an i-move
(thus a 0-move implies doing nothing). The proviso is that an i-move cannot
be repeated; for example once a player makes a 2-move, on subsequent turns
neither player can make a 2-move. If the gold coin happens to be on top
when it's a player's turn then the player wins the game. Initially, the
gold coins the third coin from the top. Then a) In order to win, Alice
first move should be a 0-move. b) In order to win, Alice first move should
be a 1-move. c) Alice has no winning strategy. d) In order to win, Alice
first move can be a 0-move or a 1-move
Sol:
Look at the figures and understand moves. All the moves shown here are with
respect to initial position onlySee that 0-move does nothing. Let O stand
for an ordinary coin and G stand for the gold coin Initially,
O1-O2-G-O3-O4-..-O20 Suppose Alice does the 1-move. Then,
O2-O1-G-O3-O4-..-O20 Then Bob can follow two paths 1. Bob does a 0-move 2.
Bob does a 2-move or a higher move 1. If Bob does a 0-move, A cannot do a
1-move or 0-move. So, A would do a 2-move or a higher move. Then,
O1-G-O3-..-O20 Bob then cannot do a 0-move. So A wins 2. If Bob does a
2-move or higher, A would do a 0-move and win! So, for A to win, 1-move is
the best strategy! Q)A circular dashboard of radius 2.0 foot is at a
distance of 20 feet from you. You throw a dart at it and it hits the
dartboard at some point Q in the circle. What is the probability that Q is
closer to the center of the circle than the periphery?
Sol: Here the distance 20 feet is irrelevant. Don't think of it. Now see
the diagram below:
Consider the general situation i.e radius = r. Now we divide the dart board
into two halves. Any point in the inner circle is clearly closer to the
center than perifery since we have divided the circle as r/2 and r/2. The
dart can hit at
any point in the circle. So total sample space is whole area of the circle
= (pi)(r2)----------eq(1). Now we need to find area of the inner circle.
Its (pi)*(r/2)2= (pi)*(r2/4)-----------eq(2). Probability is (required
event)/(sample space) = eq(2)/eq(1) = 1/4=0.25.

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tcs placement papers..

Answer / divya

avg age of 4 members before 4 yrs is....let the avg age of 4mem at present is x. before 4yrs it is (x-8)/4=55 therefore x=228.
(x+age of 5th person)/5=avg i.e; (228+45)/5=54.6 (hence k.)

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