mrinal2100 wrote:

When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12

(B) 24

(C) 35

(D) 16

(E) 30

i used the numbers and reached at two numbers 18 and 53 and 53-18 gives 35.is there any better way to solve this question

If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:

n = 5a + 3

n = 7b + 4

I will need to check for the smallest such number.

I put b = 1. n = 11. Is it of the form 5a + 3? No.

Put b = 2. n = 18. Is it of the form 5a + 3? Yes.

When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.

Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder

Next will be 35*2 + 18

and so on...

Difference between such numbers will be a multiple of 35 so your answer is 35.

Note: Actually, because of this reasoning, you just had to take the LCM. You didn't even need to find the first such number!I have discussed this topic a little more in detail here:

http://gmatclub.com/forum/good-problem-90442-20.html#p814507
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