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Three years from now, Dathan will be three times as old as E

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Three years from now, Dathan will be three times as old as E [#permalink] New post 22 Oct 2013, 19:00
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Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Oct 2013, 23:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Three years from now, Dathan will be three times as old as E [#permalink] New post 22 Oct 2013, 23:57
Expert's post
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow


Three years from now, Dathan will be three times as old as Ellen: D + 3 = 3(E+3) --> D = 3E + 6.

Three years from now, Ellen will be six years younger than Famke: E +3 = (F + 3) - 6 --> E = F - 6.

Dathan's age (now) is three years less than twice Famke's age: D = 2F - 3.

From (I) and (III): 3E + 6 = 2F - 3 --> 3E = 2F - 9.
Since from (II) E = F - 6, then 3(F - 6) = 2F - 9 --> F = 9.

Answer: A.
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Re: Three years from now, Dathan will be three times as old as E [#permalink] New post 23 Oct 2013, 00:14
Expert's post
Bunuel wrote:
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow


Three years from now, Dathan will be three times as old as Ellen: D + 3 = 3(E+3) --> D = 3E + 6.

Three years from now, Ellen will be six years younger than Famke: E +3 = (F + 3) - 6 --> E = F - 6.

Dathan's age (now) is three years less than twice Famke's age: D = 2F - 3.

From (I) and (III): 3E + 6 = 2F - 3 --> 3E = 2F - 9.
Since from (II) E = F - 6, then 3(F - 6) = 2F - 9 --> F = 9.

Answer: A.


Similar "age" problems to practice:
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roy-is-now-4-years-older-than-erik-and-half-of-that-amount-90386.html

Hope it helps.
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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: Three years from now, Dathan will be three times... [#permalink] New post 23 Oct 2013, 06:44
Official Explanation

Answer: A
Three years from now, Dathan's age will be d + 3, Ellen's will be e + 3, and Famke will be f + 3. Thus, three years from now, (d + 3) = 3(e + 3), and (e + 3) = (f + 3) - 6. We also know that d = 2f - 3 from the last sentence. Line up and simplify the equations:

d + 3 = 3e + 9, or d = 3e + 6 -----> e + 3 = f - 3 ------> d = 2f - 3

Since the first and third equations are set equal to d, combine them: 3e + 6 = 2f - 3

Now there are two equations, each of which has the same two variables, e and f: e + 3 = f - 3, or e = f - 6 ----> 3e + 6 = 2f - 3

Substitute the value of e from the first equation into the second:
3(f - 6) + 6 = 2f - 3 ----> 3f - 18 + 6 = 2f - 3 -----> 3f - 9 = 2f -----> f = 9, choice (A).

Hope it helps
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Re: Three years from now, Dathan will be three times as old as E [#permalink] New post 25 Feb 2014, 02:18
avohden wrote:
Three years from now, Dathan will be three times as old as Ellen and Ellen will be six years younger than Famke. If Dathan's age is three years less than twice Famke's age, how old is Famke?

(A) 9
(B) 15
(C) 21
(D) 27
(E) 33

GH-10.18.13 -OE to follow


Let the present ages of Dathan, Ellen & Famke be d , e & f

So from the information given in the question, we get the following 3 equations:

d+3 = 3(e+3)
e = f-6
d = 2f - 3

Solving the above 3 equations, we get Famke = 9 yrs = Answer = A
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Re: Three years from now, Dathan will be three times as old as E   [#permalink] 25 Feb 2014, 02:18
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