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

Question

What is the value of x?

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

Project DS Butler Data Sufficiency (DS3) 
 For DS butler Questions  Click Here

yashikaaggarwal · Answer

What is the value of x?

(1) 310x + 562y = 909
2 variables one equation,
(Not Sufficient)

(2) 951x – 626y = 323
2 variables one equation,
(Not Sufficient)

Combining Both:
2 variables and 2 equations,
they can be solved using equating rules.
(Sufficient)

exc4libur · Answer

(1) insufic
(2) insufic
(1/2) sufic
equations 1 and 2 have different variables,
thus equating them you can find the first variable,
and by substitution the second variable.

Ans (C)

winterschool · Answer

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

IanStewart · Answer

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.

jhavyom · Answer

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.

Nipungupta9081 · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards