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

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

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

(1) x is a positive integer
Since value of y is unknown
NOT SUFFICIENT

(2) y = 4x
5x + 12x = 17
x = 1
SUFFICIENT

IMO B

nowhere it's mentioned that x and y are integers - so special case isn't applicable here -

from choice a =

take x = 1 and y=4, satisfying the equation -> here x = 1

take x = 2 and y = 7/3 , satisfying the equation -> here x = 2 | So statement one isn't sufficient

Statement 2 explicitly mention that y = 4x, can be only one answer to this - so Answer is B

Question Stem Analysis:

We are told that 5x + 3y = 17 and we need to determine the value of x. No other information is given in the question stem.

Statement One Alone:

\(\Rightarrow\) x is a positive integer

It is important to notice that although x is required to be a positive integer, there are no restrictions on y. The value of x could be 1 (which would mean y = 4), or the value of x could be 2 (which would mean y = 7/3). Since more than one value of x is possible, statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

\(\Rightarrow\) y = 4x

Let's substitute y = 4x in 5x + 3y = 17:

\(\Rightarrow\) 5x + 3y = 17

\(\Rightarrow\) 5x + 3(4x) = 17

\(\Rightarrow\) 5x + 12x = 17

\(\Rightarrow\) 17x = 17 \(\rightarrow\) x = 1

Statement two alone is sufficient.

Answer: B