A charity planned to distribute 'n' pens (n

Question

A charity planned to distribute 'n' pens (n<300) to students such that the 1st student gets 4 pens, 2nd gets 8, 3rd gets 12 and so on. However, it realized the pens were shrink wrapped in sets of five. So, it was decided that every student will receive pens in multiples of 5 closest to the original allocation. What is the total number of students?

(1) n is divisible by 9
(2) n>250

Source: Gmat class- 4Gmat

(1) n is divisible by 9
(2) n>250

Source: Gmat class- 4Gmat

neel90 · Answer

observe the pattern in the no of pens given to the students
 5,10,10,15,20,25,30,30,35,40,... 
observe the sum of first sum of first 10 term is 220, sum of first 11 terms is 265 and the sum of first 12 terms is 315. Therefore if n>250, the number of students can be 10 or 11.

if n is divisible by 9, the only possible value of n is 270 thich means the no. of student is 11.

IanStewart · Answer

As written, the question doesn't make sense. If we assume that, under the original plan, the pens would all be distributed (that no pens would be left over), then the total number of pens clearly needs to be a multiple of 4. And if, under the new plan, the pens can also all be distributed, the total number of pens needs to be a multiple of 5. So if Statement 1 is true, and our assumptions are correct, then n must be divisible by 4, 5, and 9, so must be divisible by 180. But then Statement 2 cannot possibly be true (there are no multiples of 180 between 250 and 300).

So if you assume no pens can be left over under either plan, there is no possible answer to the question, because the numbers don't make sense. But if you assume pens can be left over, then the number of students can be any small number. We might have 270 pens, and 1 student, and have 265 pens left over under the second plan, for example. The only way you might be able to get an answer here is if you assume that all the pens are distributed under one plan but not under the other, and there's no way to guess which assumption to make, so it's not a good question.

A charity planned to distribute 'n' pens (n<300) to students

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