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If Ron's age is exactly twice Will's age, what is Ron's age?

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If Ron's age is exactly twice Will's age, what is Ron's age? [#permalink]

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New post 04 Apr 2017, 07:19
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If Ron's age is exactly twice Will's age, what is Ron's age?

(1) Five years ago, Ron's age was exactly 3 times Will's age
(2) Ten years from now, Ron's age will be exactly 1.5 times Will's age

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Re: If Ron's age is exactly twice Will's age, what is Ron's age? [#permalink]

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New post 04 Apr 2017, 07:38
R = 2w

1)
R - 5 = 3(w-5)
R = 3w - 10
2w = 3w - 10
w = 10
R = 20

2)
R + 10 = 3/2(w + 10)
R = 3/2w + 5
w/2 = 5
w = 10
R = 20

D


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Re: If Ron's age is exactly twice Will's age, what is Ron's age? [#permalink]

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New post 04 Apr 2017, 10:33
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Bunuel wrote:
If Ron's age is exactly twice Will's age, what is Ron's age?

(1) Five years ago, Ron's age was exactly 3 times Will's age
(2) Ten years from now, Ron's age will be exactly 1.5 times Will's age


Let R = Ron's PRESENT age
Let W = Will's PRESENT age

Target question: What is the value of R?

Given: Ron's age is exactly twice Will's age
We can write: R = 2W
Or we can rewrite as: R - 2W = 0

Statement 1: Five years ago, Ron's age was exactly 3 times Will's age
Ron's age 5 years ago: R - 5
Bill's age 5 years ago: W - 5

Ron's age was exactly 3 times Will's age
R - 5 = 3(W - 5)
Expand: R - 5 = 3W - 15
Rewrite as: R - 3W = -10

We now have a system of 2 equations with 2 variables:
R - 2W = 0
R - 3W = -10

Since we COULD solve this system, we COULD determine the value of R
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Ten years from now, Ron's age will be exactly 1.5 times Will's age
Ron's age in 10 years: R + 10
Bill's age in 10 years: W + 10

Ron's age will be exactly 1.5 times Will's age
R + 10 = 1.5(W + 10)
Expand: R + 10 = 1.5W + 15
Rewrite as: R - 1.5W = 5

We now have a system of 2 equations with 2 variables:
R - 2W = 0
R - 1.5W = 5

Since we COULD solve this system, we COULD determine the value of R
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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Re: If Ron's age is exactly twice Will's age, what is Ron's age? [#permalink]

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New post 04 Apr 2017, 10:45
stem says R= 2W
stat 1 : R-5 = 3(W-5)
suff..
stat 2 : R+10 = 1.5 W ,,suff

hence ans D
Re: If Ron's age is exactly twice Will's age, what is Ron's age?   [#permalink] 04 Apr 2017, 10:45
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If Ron's age is exactly twice Will's age, what is Ron's age?

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