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Of the N candies in a bag, some are peppermint and the rest

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Of the N candies in a bag, some are peppermint and the rest

by BTGmoderatorLU » Tue Feb 05, 2019 2:45 pm

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Source: GMAT Prep

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 was 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.

The OA is C
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by Jay@ManhattanReview » Tue Feb 05, 2019 10:01 pm

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BTGmoderatorLU wrote:Source: GMAT Prep

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 was 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.

The OA is C
Say there are P numbers of peppermints and S numbers of spearmints.

Thus, we have P + S = N.

We have to get the value of N.

Let's take each statement one by one.

1) If 1 peppermint candy was removed from the N candies, 1/5 of the remaining candies would be peppermint.

=> P - 1 = (N - 1)/5

P = 1 + (N - 1)/5 ---(1)

Can't get the value of N. Insufficient.

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

=> P = (N - 2)/4 ---(2)

Can't get the value of N. Insufficient.

(1) and (2) together

From (1) and (2), we have

1 + (N - 1)/5 = (N - 2)/4

N = 26. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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