What is the value of x? (1) 310x + 562y = 909 (2) 951x – 626y = 323

What is the value of x?

(1) 310x + 562y = 909
(2) 951x – 626y = 323

Statement 1 -

310x + 562y = 909
each has more than 1 value to solve this equation
not sufficient


Statement 2 -

951x – 626y = 323
each has more than 1 value to solve this equation
not sufficient

both statement are sufficient to find the value of by eliminating method

so answer C

Each Statement is clearly insufficient alone. When we use both, since the equations are linear (i.e. can be written to look like y = mx + b), we just need to check that they're different. If they are, we can solve. Since the x term is positive in both equations, but the y term is positive in one and negative in the other, there is no chance one equation is a multiple of the other, so we must be able to solve, and the answer is C.

I'd assume the source is using a question like this (with these awkward numbers) to illustrate that in DS, we don't need to find the answer to the question, we just need to see that the question can be answered. But this is the kind of question you don't see on the real GMAT, except perhaps at the 300-level, because it rewards test takers who unthinkingly count equations and unknowns without necessarily understanding why that sometimes (but only sometimes) works, or what exceptions one needs to consider.

What is the value of x?

(1) 310x + 562y = 909
The value of x depends on the value of y. Since value of y is not known. Therefore, insufficient.

(2) 951x – 626y = 323
The value of x depends on the value of y. Since value of y is not known. Therefore, insufficient.

Combining (1) and (2)

In the above equations
\(\frac{a1}{a2} ≠ \frac{b1}{b2}\)
Therefore, we have a unique solution.
Sufficent.

Answer C

(1) 310x + 562y = 909

Clearly Insufficient ( No need to Solve )

(2) 951x – 626y = 323

Clearly Insufficient ( No need to Solve )

Combining both 1 and 2

We can find the value of one variable then put the value to find the value of the second variable