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# Rey is 12 years younger than Sebastian. Five years ago, Rey

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Rey is 12 years younger than Sebastian. Five years ago, Rey [#permalink]  14 Jun 2018, 14:14
Expert's post
00:00

Question Stats:

77% (01:02) correct 22% (02:06) wrong based on 22 sessions
Rey is 12 years younger than Sebastian. Five years ago, Rey was half Sebastian’s age. How old will Sebastian be next year?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
[Reveal] Spoiler: OA

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Re: Rey is 12 years younger than Sebastian. Five years ago, Rey [#permalink]  03 Jul 2018, 07:27
sandy wrote:
Rey is 12 years younger than Sebastian. Five years ago, Rey was half Sebastian’s age. How old will Sebastian be next year?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 35

Let Ray present age = R

and Sebastian age = S

From Statement we have;

R = S - 12

and

R - 5 = 1/2*(S - 5)

or 2R - 10 = S - 5

or 2S - 24 - 10 = S - 5

or S = 29

Therefore Sebastian's age in next year will be = 29 + 1 = 30 years
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 [0], given: 394

Re: Rey is 12 years younger than Sebastian. Five years ago, Rey [#permalink]  05 Jul 2018, 01:53
Expert's post
Explanation

Assign variables and translate equations from the given information:

r = Rey’s age NOW

s = Sebastian’s age NOW

$$r = s - 12$$

$$(r - 5) = \frac{1}{2}(s - 5)$$

Multiply the second equation by 2 to eliminate the fraction and simplify:

$$2r - 10 = s - 5$$

$$2r = s + 5$$

Since the question asks for Sebastian’s age next year and r is already isolated in the first equation, substitute for r in the adjusted second equation and solve:

$$2(s - 12) = s + 5$$

$$2s - 24 = s + 5$$

$$2s = s + 29$$

$$s = 29$$

If Sebastian is 29 now, he will be 30 next year.

Check the answer. If Sebastian is 29 now, Rey is 17 now. Five years ago, they were 24 and 12, respectively, and 12 is half of 24.

Hence option D is correct!

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Sandy
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Re: Rey is 12 years younger than Sebastian. Five years ago, Rey   [#permalink] 05 Jul 2018, 01:53
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