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
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