Interested to Buy Any Domain ? << Click Here >> for more details...
There are 4 mathematicians - Brahma, Sachin, Prashant and
Nakul - having lunch in a hotel. Suddenly, Brahma thinks of
2 integer numbers greater than 1 and says, "The sum of the
numbers is..." and he whispers the sum to Sachin. Then he
says, "The product of the numbers is..." and he whispers the
product to Prashant. After that following conversation takes
place :
Sachin : Prashant, I don't think that we know the numbers.
Prashant : Aha!, now I know the numbers.
Sachin : Oh, now I also know the numbers.
Nakul : Now, I also know the numbers.
What are the numbers? Explain your answer.
- 1 Answers
- 8726 Views
- I also Faced
- E-Mail Answers
Answer Posted / guest
The numbers are 4 and 13.
As Sachin is initially confident that they (i.e. he and
Prashant) don't know the numbers, we can conclude that -
1) The sum must not be expressible as sum of two primes,
otherwise Sachin could not have been sure in advance that
Prashant did not know the numbers.
2) The product cannot be less than 12, otherwise there would
only be one choice and Prashant would have figured that out
also.
Such possible sum are - 11, 17, 23, 27, 29, 35, 37, 41, 47,
51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97,
101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137,
143, 145, 147, 149, 155, 157, 161, 163, 167, 171, 173, 177,
179, 185, 187, 189, 191, 197, ....
Let's examine them one by one.
If the sum of two numbers is 11, Sachin will think that the
numbers would be (2,9), (3,8), (4,7) or (5,6).
Sachin : "As 11 is not expressible as sum of two primes,
Prashant can't know the numbers."
Here, the product would be 18(2*9), 24(3*8), 28(4*7) or
30(5*6). In all the cases except for product 30, Prashant
would know the numbers.
- if product of two numbers is 18:
Prashant : "Since the product is 18, the sum could be either
11(2,9) or 9(3,6). But if the sum was 9, Sachin would have
deduced that I might know the numbers as (2,7) is the
possible prime numbers pair. Hence, the numbers must be 2
and 9." (OR in otherwords, 9 is not in the Possible Sum List)
- if product of two numbers is 24:
Prashant : "Since the product is 24, the sum could be either
14(2,12), 11(3,8) or 10(4,6). But 14 and 10 are not in the
Possible Sum List. Hence, the numbers must be 3 and 8."
- if product of two numbers is 28:
Prashant : "Since the product is 28, the sum could be either
16(2,14) or 11(4,7). But 16 is not in the Possible Sum List.
Hence, the numbers must be 4 and 7."
- if product of two numbers is 30:
Prashant : "Since the product is 30, the sum could be either
17(2,15), 13(3,10) or 11(5,6). But 13 is not in the Possible
Sum List. Hence, the numbers must be either (2,15) or
(5,6)." Here, Prashant won't be sure of the numbers.
Hence, Prashant will be sure of the numbers if product is
either 18, 24 or 28.
Sachin : "Since Prashant knows the numbers, they must be
either (3,8), (4,7) or (5,6)." But he won't be sure. Hence,
the sum is not 11.
Summerising data for sum 11:
Possible Sum PRODUCT Possible Sum
2+9 18 2+9=11 (possible)
3+6=9
3+8 24 2+12=14
3+8=11 (possible)
4+6=10
4+7 28 2+12=14
3+8=11 (possible)
4+6=10
5+6 30 2+15=17 (possible)
3+10=13
5+6=11 (possible)
Following the same procedure for 17:
Possible Sum PRODUCT Possible Sum
2+15 30 2+15=17 (possible)
3+10= 13
5+6=11 (possible)
3+14 42 2+21=23 (possible)
3+14=17 (possible)
6+7=13
4+13 52 2+26=28
4+13=17 (possible)
5+12 60 2+30=32
3+20=23 (possible)
4+15=19
5+12=17 (possible)
6+10=16
6+11 66 2+33=35 (possible)
3+22=25
6+11=17 (possible)
7+10 70 2+35=37 (possible)
5+14=19
7+10=17 (possible)
8+9 72 2+36=38
3+24=27 (possible)
4+18=22
6+12=18
8+9=17 (possible)
Here, Prashant will be sure of the numbers if the product is
52.
Sachin : "Since Prashant knows the numbers, they must be
(4,13)."
For all other numbers in the Possible Sum List, Prashant
might be sure of the numbers but Sachin won't.
Here is the step by step explaination:
Sachin : "As the sum is 17, two numbers can be either
(2,15), (3,14), (4,13), (5,12), (6,11), (7,10) or (8,9).
Also, as none of them is a prime numbers pair, Prashant
won't be knowing numbers either."
Prashant : "Since Sachin is sure that both of us don't know
the numbers, the sum must be one of the Possible Sum List.
Further, as the product is 52, two numbers can be either
(2,26) or (4,13). But if they were (2,26), Sachin would not
have been sure in advance that I don't know the numbers as
28 (2+26) is not in the Possible Sum List. Hence, two
numbers are 4 and 13."
Sachin : "As Prashant now knows both the numbers, out of all
possible products - 30(2,15), 42(3,14), 52(4,13), 60(5,12),
66(6,11), 70(7,10), 72(8,9) - there is one product for which
list of all possible sum contains ONLY ONE sum from the
Possible Sum List. And also, no such two lists exist. [see
table above for 17] Hence, two numbers are 4 and 13."
Nakul figured out both the numbers just as we did by
observing the conversation between Sachin and Prashant.
It is interesting to note that there are no other such two
numbers. We checked all the possible sums till 500 !!!
| Is This Answer Correct ? | 7 Yes | 2 No |
Post New Answer View All Answers
plz send me aptitude test questions on my email id bpraichur@gmail.com
4 cards are placed on a table, each card has two colors. U don't know the color of the back side of eachcard.4 persons A B C and D are sitting on the table before the cards. They can see Red, Green Red and blue.Out of the 4 poeple 2 always lie. They see the color on the reverse side and give the following comment A: Yello/green B: Neither Blue/nor Green c: Blue/Yello D: Blue/ Yello find out the color on the other side of the 4 cards. No. of animals is 11 more than the no. of birds. If the no. of birds were the no. of animals and no. of animals were the no. of birds( ie., interchanging no.s of animals and birds.), the total no. of legs get reduced by one fifth (1/5). How many no. of birds and animals were there?
Ship is 180 miles away from shore. At that time a plane started from shore to pass some information to the ship with 10 times velocity of ship's velocity. At what distance from shore they will meat?
What is the syllabus for numerical aptitude exam to be held by the United bank of India. Plz inform me through email. Thanking You!
In a soap company a soap is manufactured with 11 parts. For making one soap you will get 1 part as crap. At the end of the day u have 251 such scraps. From that how many soaps can be manufactured?
how soon can you travel down to start your new job?
foot is related to man in the same way hoof is related to...........
sir i need catholic syrian bank previous question papers fully. it will be helpful for me to greater extend .please do the needful to me.
what three specific job positions do you target from qatar airways group u.k?
Three members are hunting in a forest.While crossing a streem cartridges of two of them gets wetted up.Then the third person decides his cartidges equally. After 4 shots of each person, total cartridges remaining are equal to what each had initially after sharing.How many total cartridges they initially they shared?
what job position/s are you currently holding with your current employer?
sir i need generalKnowledge previous questions for rrb secunderabad goods guard exam
At 6o'clock ,a watch strokes 6 times.The time between first and last is 30secs.At midnight 12o' clock how much time for all strokes?
Wo kay chej hi jo saal may 1 baar aata hai months may 2 baar aata hai weeks may 4 baar aata hai or din may 6 baar
Three neighbours are there. 1st one lends 2nd and 3rd that many no.of tractors that then already each had.After few months , 2nd lends to 1st and 3rd that many tractors then they had. After a few months 3rd lends to 1st and 2nd that many tractors then they had.Now each of them got 24. Find howmany they had initially?
