When is divided by 4, the quotient is and the remainder is 1. When is divided by 7, the quotient is and the remainder is 6. Which of the following is the value of in terms of ?
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
This one tripped me up at first but then I realized I could just write x two different ways and set them equal. Once you do that the algebra is pretty clean.
Exactly, that's the move. Took me a second to see it too.
Wait, how do we know which equation to substitute into? I set them equal but then got stuck rearranging.
You just need to isolate y. Since you have x = 4y + 1, solve for y after substituting the other expression for x.
Ah got it, thanks. The rearranging was the part I was fumbling.
Solid 500-level question. Not hard once you set it up, but the answer choices look similar enough that a careless step will send you to the wrong one.
Yeah the distractors are sneaky, especially B and D.
Can someone explain why we can't just plug in a number for x? I tried x = 13 and it worked, but I want to be sure that's valid.
Plugging in is fine here since the relationship holds for any valid x. Just make sure your number satisfies both conditions.
What it tests
Your understanding of divisibility rules, least common multiples, and greatest common factors.
Common trap
Forgetting that 1 is not prime and that every integer divides 0.