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If 5x + 3y = 17, what is the value of x? (1) x is a positive integer

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If 5x + 3y = 17, what is the value of x? (1) x is a positive integer  [#permalink]

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New post 23 Sep 2018, 04:17
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

78% (00:40) correct 22% (00:47) wrong based on 55 sessions

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Re: If 5x + 3y = 17, what is the value of x? (1) x is a positive integer  [#permalink]

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New post 23 Sep 2018, 04:21
From statement 1 we dont get any information about y hence not sufficient.
From statement 2 we can arrive at a unique value for x hence sufficient.
IMO B is the correct choice.
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Re: If 5x + 3y = 17, what is the value of x? (1) x is a positive integer  [#permalink]

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New post 23 Sep 2018, 04:34
(1) No info about y. Insufficient.
(2) y = 4x then, 5x + 12x = 17 hence x=1. Sufficient.

B is the correct answer.
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Re: If 5x + 3y = 17, what is the value of x? (1) x is a positive integer  [#permalink]

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New post 23 Sep 2018, 06:00
Top Contributor
Bunuel wrote:
5x + 3y = 17, what is the value of x?

(1) x is a positive integer
(2) y = 4x


Target question: What is the value of x?

Given: 5x + 3y = 17

Statement 1: x is a positive integer
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 4 (these values satisfy the given equation, 5x + 3y = 17). In this case, the answer to the target question is x = 1
Case b: x = 2 and y = 7/3 (these values satisfy the given equation, 5x + 3y = 17). In this case, the answer to the target question is x = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 4x
When we add this equation to the given equation 5x + 3y = 17, we have a system of two linear equations with 2 variables. Since we COULD solve that system for x and y, we COULD answer the target question with certainty.
So, statement 2 is SUFFICIENT

If you're not convinced, take 5x + 3y = 17 and replace y with 4x to get: 5x + 3(4x) = 17
Expand: 5x + 12x = 17
Simplify: 17x = 17
Solve: x = 1
So, the answer to the target question is x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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Re: If 5x + 3y = 17, what is the value of x? (1) x is a positive integer &nbs [#permalink] 23 Sep 2018, 06:00
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