If 5x + 3y = 17, what is the value of x?

[BTGmoderatorDC]

If 5x + 3y = 17, what is the value of x?

(1) x is a positive integer

(2) y = 4x

OA B

Source: Official Guide

[fskilnik@GMATH]

If 5x + 3y = 17, what is the value of x?

(1) x is a positive integer

(2) y = 4x

OA B

Source: Official Guide

$$5x + 3y = 17\,\,\,\left( * \right)$$
$$? = x$$
$$\left( 1 \right)\,\,x \ge 1\,\,{\mathop{\rm int}} \,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = 4\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,y = 4x\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,5x + 3\left( {4x} \right) = 17\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,\,{\text{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\,\,\,\,$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Brent@GMATPrepNow]

If 5x + 3y = 17, what is the value of x?

(1) x is a positive integer

(2) y = 4x

OA B

Source: Official Guide

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