$2x + y = 12$
$|y| \le 12$

For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?

Correct answer marked below

Correct

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Comments

IarinaMay 28

Thanks, this one finally clicked for me. The absolute value constraint was the tricky part — I kept forgetting to limit y before counting x values.

NeelakshiJun 3

Same here. Once you realize y has to stay between -12 and 12, the rest is just plugging in and checking divisibility.

AnmolJun 21

Wait, why can't y be 13 if x is a fraction? I think I'm missing why both have to be integers...

VidushiJul 1

Because the question literally says 'x and y both integers.' If y = 13, then from 2x + y = 12 you'd get x = -0.5, which isn't an integer.

RheyaAug 4

Solid 600-level question. Not hard conceptually, but a lot of room for careless mistakes with the inequality and counting.

PravinJul 23

Is there a faster way than listing every pair? I did it by brute force and it took me almost two minutes.

JohnJul 31

Look at 2x = 12 - y. Since 2x is even, 12 - y has to be even, so y must be even. Then just count the even values of y in that range.

What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

2x+y=122x + y = 122x+y=12∣y∣≤12|y| \le 12∣y∣≤12For how many ordered pairs (x, y) that are solutions of the system above are x and y both integers?