runningguy wrote:When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35?

A) 3
B) 4
C) 12
D) 32
E) 35

I got the answer by plugging in numbers for n until I found the number (31) that met the remainder requirements, but I feel like I won't have the time and it is a risky method for the test. What is the easiest way to tackle a problem like this in under 2 minutes without guessing numbers? The explanation in the guide is difficult for me to understand.

One more question, how many questions can we post up at one time? I have a lot more questions but I don't want to flood the forum. Thanks!

I'm not sure what you mean by "plugging in numbers," but there is a systematic approach to listing possible values.

There's a nice rule that says, If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

When n is divided by 5, the remainder is 1.
So, possible values of n are 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, etc.

When n is divided by 7, the remainder is 3.
So, possible values of n are 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, etc.

So, we can see that n could equal 31, or 66, or an infinite number of other values.

Important: Since the Least Common Multiple of 7 and 5 is 35, we can conclude that if we list the possible values of n, each value will be 35 greater than the last value.

So, n could equal 31, 66, 101, 136, and so on.

Answer choice A: If we add 3 to any of these possible n-values, the sum is NOT a multiple of 35.
ELIMINATE A

Answer choice B: if we take any of these possible n-values, and add 4, the sum will be a multiple of 35.

So, the smallest value of k is 4 such that k+n is a multiple of 35.

Answer = B

Cheers,
Brent

Your method looks great.
Once you become fast at listing possible values, you can solve a question like this in under 1 minute.

Cheers,
Brent

Hi runningguy,

The approach that Brent showed you is a great way to solve this type of question; it's exactly the way that I'd approach it. For all intents and purposes, it's the best/fastest way to approach this question.

You mentioned one other thing in your original post, which I think needs to be addressed. While the AVERAGE amount of time per Quant question is about 2 minutes (75 minutes/37 questions = about 2 minutes per question), you should NOT expect to spend 2 minutes on each question. Certain questions can be answered relatively quickly (in under a minute), others require 3 minutes (even if you know the shortcuts). So make sure to be flexible with how much time you spend on a given question.

GMAT assassins aren't born, they're made,
Rich