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# The positive difference between Sam and Lucy’s ages is a, and the sum

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
The positive difference between Sam and Lucy’s ages is a, and the sum  [#permalink]

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13 Dec 2015, 04:39
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Difficulty:

35% (medium)

Question Stats:

68% (01:09) correct 33% (01:15) wrong based on 54 sessions

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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

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Posts: 727
Concentration: Strategy, General Management
Re: The positive difference between Sam and Lucy’s ages is a, and the sum  [#permalink]

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13 Dec 2015, 13:17
let Lucy's age be L and sam's age be S
as given,
L-S=a -- 1
L+S=z --2

L= (a+z)/2
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Re: The positive difference between Sam and Lucy’s ages is a, and the sum  [#permalink]

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15 Dec 2015, 17:36
Hi All,

This question can be solved by TESTing VALUES.

We're given three facts about the ages of two people:
1) The positive difference between Sam and Lucy’s ages is a,
2) The sum of their ages is z.
3) Lucy is older than Sam

We're asked which of the following represents Lucy’s age:

IF....
Lucy = 3
Sam = 2
a = 3-2 = 1
z = 3+2 = 5

So we're looking for an answer that equals 3 when a=1 and z=5.

Answer A) (z - a)/2 = (5-1)/2 = 2 NOT a match
Answer B) a - z/2 = 1 - 5/2 = Negative
Answer C) 2a + z = 2+5 = 7 NOT a match
Answer D) (z + a)/2 = (6)/2 = 3 This IS a MATCH
Answer E) (a - z)/2 = (1-5)/2 = Negative

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Re: The positive difference between Sam and Lucy’s ages is a, and the sum  [#permalink]

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15 Dec 2015, 22:53
L > S
L - S = a
L + S = z

2L = a + z
Hence D
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Re: The positive difference between Sam and Lucy’s ages is a, and the sum  [#permalink]

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16 Jan 2018, 17:50
Bunuel 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

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Re: The positive difference between Sam and Lucy’s ages is a, and the sum   [#permalink] 16 Jan 2018, 17:50
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