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# Age problem (m03q13)

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Intern
Joined: 10 Apr 2014
Posts: 33

Kudos [?]: 22 [1], given: 3

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11 Apr 2014, 12:39
1
KUDOS
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 older than the son, how old is the daughter?

(A) 5
(B) 7
(C) 10
(D) 13
(E) 14

[Reveal] Spoiler: OA
B

I think the question needs correction - it should say husband is 7 times as old as the son and not 7 times older than the son.

----------------------
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Math Expert
Joined: 02 Sep 2009
Posts: 42560

Kudos [?]: 135317 [1], given: 12686

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12 Apr 2014, 03:10
1
KUDOS
Expert's post
ind23 wrote:
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 older than the son, how old is the daughter?

(A) 5
(B) 7
(C) 10
(D) 13
(E) 14

[Reveal] Spoiler: OA
B

I think the question needs correction - it should say husband is 7 times as old as the son and not 7 times older than the son.

----------------------
Kudos if the post helped

The original post has a typo. Edited.
_________________

Kudos [?]: 135317 [1], given: 12686

Math Expert
Joined: 02 Sep 2009
Posts: 42560

Kudos [?]: 135317 [1], given: 12686

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06 May 2014, 05:15
1
KUDOS
Expert's post
Bunuel 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

Plug-in method would be the fastest for this question.

If the daughter is 10 years old then: the son is 10-2=8 years old, the husband is 7*8=56 years old and the wife is 56-4=52 years old. Total: 10+8+56+52=126>78. So, the daughter must be less than 10 years old: eliminate D and E too.

If the daughter is 7 years old then: the son is 7-2=5 years old, the husband is 7*5=35 years old and the wife is 35-4=31 years old. Total: 7+5+35+31=78. Correct answer.

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Kudos [?]: 135317 [1], given: 12686

Senior Manager
Status: You have to have the darkness for the dawn to come
Joined: 09 Nov 2012
Posts: 319

Kudos [?]: 223 [0], given: 159

Daboo: Sonu
GMAT 1: 590 Q49 V20
GMAT 2: 730 Q50 V38

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06 May 2014, 08:46
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

[Reveal] Spoiler: OA
B

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)
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
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Re: Age problem (m03q13)   [#permalink] 06 May 2014, 08:46

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# Age problem (m03q13)

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