The positive difference between Sam and Lucyâ€™s ages . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

The positive difference between Sam and Lucyâ€™s ages . . .

by Vincen » Tue Jan 09, 2018 5:53 am

The positive difference between Sam and Lucy's ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy's age?

A. (z - a)/2
B. a - z/2
C. 2a + z
D. (z + a)/2
E. (a - z)/2

The OA is the option D.

I don't know how to set an equation that let me solve this PS question. Experts, can you give me some help, please? Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Jan 09, 2018 5:53 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Jan 09, 2018 6:26 am

Vincen wrote:The positive difference between Sam and Lucy's ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy's age?

A. (z - a)/2
B. a - z/2
C. 2a + z
D. (z + a)/2
E. (a - z)/2

Let Lucy = 5 and Sam = 2.
a = the positive difference between their ages = 5-2 = 3.
z = the sum of their ages = 5+2 = 7.
Since the question stem asks for Lucy's age, the target value is 5.
Now plug a=3 and z=7 into the answers to see which yields the target value of 5.
Only D works:
(z+a)/2 = (7+3)/2 = 5.

The correct answer is D.

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Jan 10, 2018 1:00 am

Vincen wrote:The positive difference between Sam and Lucy's ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy's age?

A. (z - a)/2
B. a - z/2
C. 2a + z
D. (z + a)/2
E. (a - z)/2

The OA is the option D.

I don't know how to set an equation that let me solve this PS question. Experts, can you give me some help, please? Thanks.

Say Lucy's age be L and Suzy's S; where L > S.

Thus, L - S = a and L + S = z.

Adding the two equations, we get 2L = a + z => L = (a + z)/2.

The correct answer: D

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 16, 2018 4:58 pm

Vincen wrote:The positive difference between Sam and Lucy's ages is a, and the sum of their ages is z. If Lucy is older than Sam, then which of the following represents Lucy's age?

A. (z - a)/2
B. a - z/2
C. 2a + z
D. (z + a)/2
E. (a - z)/2

We can let Sam's current age = S and Lucy's current age = L; thus:

L - S = a

and

L + S = z

Adding the two equations together, we have:

2L = a + z

L = (a + z)/2

Answer: D

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