vksunder wrote:

This year, the sum of ages of the Perkins family members is 78. Currently, there are 4 members: husband, wife, daughter, and son. The husband is 4 years older than the wife. The daughter is two years older than the son. If the husband is 7 times as old as the son, how old is the daughter?

(A) 5

(B) 7

(C) 10

(D) 13

(E) 14

Source: GMAT Club Tests - hardest GMAT questions

Let

H= Husband

W= Wife

D= Daughter

S= Son

According to the question Sum of H, W, D and S is 78

It means

H+W+D+S=78............................................(i)

Question asked is D's age

Again it is given in the question

H= W+4

=> W= H-4 ..............................................................(ii)

D= S+2....................................................................(iii)

H=7S........................................................................(iv)

Now substitute the value of W, and D, from equation (ii), and (iii)

H+ (H-4)+(S+2)+S=78

=> 2H+2S-2=78

=> 2H+2S=80

=> H+S=40

Now substitute the value of from equation (iv)

7S+S=40

=> 8S=40

=> S=5

Now substitute the value of S into equation (iii)

D=5+2

D=7

Hence B is the answer