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The positive difference between Sam and Lucy’s ages . . .

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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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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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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!

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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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by DrMaths » Wed Jan 17, 2018 9:28 am
a=L-S
z =L+S
Add these 2 equations together
a+z = 2L
so L=(a+z)/2
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