GMAT Quantitative :: Data sufficiency:: 02716

[JackH825]

Course: GMAT Practice Questions
Correct Answer: C
Type: D/S

Of the N candies in a bag, some are peppermint and the rest are spearmint. What is the value of N ?

(1) If 1 peppermint candy were removed from the N candies,
1/5 of the remaining candies would be peppermint.
(2) If 2 spearmint candies were removed from the N candies,
1/4 of the remaining candies would be peppermint.


Is there any way to tackle this (in reasonable time) without algebra?

Thanks!

[Sage Pearce-Higgins]

Which source of GMAT practice questions is this from please? Unfortunately we're not allowed to post paid-for copyright resources here.

As a DS question, there's no need to do any algebra. Remember that we're deciding if we have enough information to answer the question; we don't actually need to answer it.

Testing cases is the go-to on DS problems: this strategy can help us see how the statements alone are insufficient. Taking statement (1), I'd think "well, once the single peppermint candy has been removed, there could be 1 peppermint and 4 spearmint, or there could be 2 peppermint and 8 spearmint." Similar logic applies to statement (2).

Most of my time solving this problem would be spent deciding between C and E, and, since the numbers are pretty small and easy to work with, I'd continue testing cases. To find cases that agree with both statements, I might start writing down the possibilities. So, for statement 1, they are:
2 peppermint and 4 spearmint
3 peppermint and 8 spearmint
4 peppermint and 12 spearmint
5 peppermint and 16 spearmint
(I'm finding these by taking the ratio 1:4 and adding one more peppermint)

For statement 2, they are:
1 peppermint and 5 spearmint
2 peppermint and 8 spearmint
3 peppermint and 11 spearmint
4 peppermint and 14 spearmint
5 peppermint and 17 spearmint
6 peppermint and 20 spearmint

I know that there must be at least one case that satisfies the 2 statements (as otherwise the problem wouldn't make sense), so I'd keep on looking. I can see that by extending my first list I'd get 6 peppermint and 20 spearmint. So now I have one possible case, I'd consider if that's the only possible case. I can see from the pattern that the lists aren't going to overlap again, as the spearmint is increasing by 4 for statement 1, and by 3 for statement 2.