Remainders - LCM Question

Question

Hi Gmat Club Forum members

I recently gave my GMAT and saw a question that read something like this.

'n' Number of cream rolls are to be packed in boxes of 7 or 8. When packed in boxes of 7 there were 6 rolls left over, and when packed in boxes of 8 , there were 3 rolls left over. What value could 'n' be?

I dont really remember the answer choices and I have made up numbers over here.
But I was really stumped on how to approach the question. Someone please help

Im still confused.
Thanks in advance

Im still confused. Thanks in advance

Kinshook · Answer

n = 7x + 6 = 8y + 3

x = (8y - 3)/7 = y + (y-3)/7

If y = 3; x = 3; n = 27
If y = 10; x = 11; n = 83
If y=17; x= 19; n = 139

and so on...

AndrewN · Answer

Hello,  Vvucthcd . As long as the question is not a copy of the one you saw with slightly different numbers, you will not risk disciplinary actions by GMAC™ (if your query somehow made its way back to someone working there). That said, I prefer a logic-based approach for such questions, and I was able to work through the problem comfortably without a rigorous mathematical framework.

Consider the boxes of 7. They could hold 7, 14, 21, 28, or 35 rolls, and so on.
Consider the boxes of 8. They could hold 8, 16, 24, 32, or 40 rolls, and so on.

If we hold one of these constant, relative to the remainder provided for that type of box, we can find a reasonable answer. Consider the 7's. Just add 6 to each number in the above list to represent the leftover rolls for that type of box and check against the 8's:

(7 + 6) or 13 rolls; (13 - 8) = 5 leftover rolls  X  (remember, we are looking for 3)
(14 + 6) or 20 rolls; (20 - 16) = 4 leftover rolls  X 
(21 + 6) or 27 rolls; (27 - 24) = 3 leftover rolls  √

Both remainders check out, so  27 is a valid input for  n  . Of course, there could be any of a number of values for  n , but the GMAT™ typically keeps values fairly low for these types of questions. If it were a PS problem, I would use the given answers and check the numbers in the same way I have outlined above. (I am not afraid to get my hands dirty, especially if I cannot recall a formula in the moment.)

I imagine others will respond with more technical analyses, but this is exactly how I approached the question on my note board.

- Andrew

Remainders - LCM Question

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