Infosys Aptitude Tests

Below are three numeric puzzles dealing with some basic arithmetic calculations.

Question 1

Find X's age which equals the number of grand children of a man who has 4 sons and 4 daughters. Each daughter of the man's wife have 3 sons and 4 daughters and each son of the man's wife have 4 sons and 3 daughters.

a) 40
b) 56
c) 64
d) none of these

Answer : b) 56

Solution :

We have to find the number of grand children of the man.
Given that, he had 4 sons and 4 daughters.
Each son has 4 sons and 3 daughters and each daughter has 3 sons and 4 daughters.
Therefore total number of grandsons = 4x4 + 4x3 = 16 + 12 = 28
And total number of grand daughters = 4x3 + 4x4 = 28
Total number of grandchildren is 28+28 = 56.
Hence the required age is 56.

Question 2

A man have many daughters, each daughter have as many sons as her sisters. The product of the number of daughters and grandsons of the man lies between 40 and 50. Find the number of daughters of the man.

a) 6
b) 4
c) 3
d) 8

Answer : b) 4

Solution:

Let N be the number of daughters of the man.
Then each daughter has N-1 sisters.
Given that, each daughter has as many sons as her sisters.
That is, each of them has N-1 sons.

Number of grandsons of the man = N(N-1)
And the required product = N(N-1) x N = N x N(N-1) which lies between 40 and 50.
If N = 1 then N x N(N-1) = 0.
f N = 2 then N x N(N-1) = 2 x 2(1) = 4
If N = 3 then N x N(N-1) = 3 x 3 x 2 = 18
If N = 4 then N x N(N-1) = 4 x 4 x 3 = 48
If N = 5 then N x N(N-1) = 5 x 5 x 4 = 100
Therefore the possible value of N is 4.
Hence the man has 4 daughters.

Question 3

Two men A and B have equal number of daughters and A have 1 more son than B. Each son and daughter of A have 2 sons and 2 daughters and each son and daughter of B have 3 sons and 3 daughters. If A and B have equal number of grandchildren then find the number of sons of B.

a) 3
b) 4
c) 5
d) none of these.

Answer : d) none of these

Solution :

Let D be the number of daughters of A and B.
Let S be the number of sons of A.
Then S-1 be the number of sons of B.

Now, number of grandsons of A = 2S + 2D.
Number of granddaughters of A = 2S + 2D
Number of grand children of A = 2S + 2D + 2S + 2D = 4S + 4D.

Number of grandsons of B = 3(S-1) + 3D = 3S + 3D - 3
Number of granddaughters of B = 3(S-1) + 3D = 3S + 3D - 3
Number of grand children of A = 3S + 3D - 3 + 3S + 3D - 3 = 6S + 6D - 6

And, 4S + 4D = 6S + 6D - 6
2S + 2D = 6
S + D = 3

Then the possibilities of (S,D) are (1,2), (2,1), (0,3), (3,0)
We have to find the value of S-1.
S-1 cannot be a negative number, so (0,3) is not possible.

Therefore, possible S-1 values are 0,1,2.
Hence the answer is option d.