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Age problem (m03q13)

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Re: Age problem (m03q13) [#permalink] New post 11 Apr 2014, 11:39
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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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Re: Age problem (m03q13) [#permalink] New post 12 Apr 2014, 02:10
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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.
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Re: Age problem (m03q13) [#permalink] New post 06 May 2014, 04:15
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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.

Check answer choice C first:

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.

Check answer choice B:

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.

Answer: B.


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_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Age problem (m03q13) [#permalink] New post 06 May 2014, 07:46
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)
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
Re: Age problem (m03q13)   [#permalink] 06 May 2014, 07:46
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