When 15 is divided by y, the remainder is . If y must be an integer, what are all the possible values of y?
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This one got me for a minute because I forgot the remainder has to be less than y. Once I set up y - 3 < y it was basically automatic, but the y > 3 part still feels like a trap.
Same. The remainder being less than the divisor is the whole game here.
Yeah I always have to remind myself that the remainder can't be negative either.
How do you know to plug in the choices instead of solving algebraically? I set up 15 = qy + (y - 3) and then got stuck.
Rewrite as 15 = y(q+1) - 3, so 18 = y(q+1). That means y is a divisor of 18 greater than 3.
Oh that's clean. I was trying random numbers like an idiot.
A bit tricky for a 655-705. The wording "all possible values" makes you want to rush, but you have to test the remainder condition on each choice.
Got 18 at first but then realized I needed to double check whether y - 3 is actually less than y. It always is, but the remainder also has to be non-negative, which kills the small values.
What it tests
Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.
Common trap
Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.