Manhattan GMAT Challenge Problem of the Week – 17 Jan 2011

by Manhattan Prep, Jan 17, 2011

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Question

What is the units digit of the three-digit integer N ?

1. When N is rounded to the nearest hundred, the result is 50 less than the result when N is rounded to the nearest ten.
2. N is divisible by 4.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are not sufficient.

Answer

With digit problems, its generally a good idea to rephrase the given statements into lists of possibilities. If possible, you should make an exhaustive list.

(1) INSUFFICIENT: When N is rounded to the nearest hundred, the result ends with 00. Therefore, according to this statement, N rounded to the nearest ten yields a number ending with 50. Furthermore, since the value rounded to the nearest hundred is lower, N must round down to the nearest hundred. Using basic facts about rounding, we can deduce from these two facts that the last two digits of N are somewhere between 45 and 49(inclusive). This range includes five possible units digits (5 through 9), so this statement is INSUFFICIENT.

(2) INSUFFICIENT: This statement tells us only that N is a three-digit multiple of 4. This is not enough information to determine the units digit of N.

(1) and (2): SUFFICIENT: An integer is divisible by 4 if its last two digits are divisible by 4. (The hundreds digit doesnt matter, since 100 is a multiple of 4.) Of the options allowed by statement (1) for the last two digits 45, 46, 47, 48, and 49 only 48 is divisible by 4. Therefore, the last two digits of N are 48. Therefore, the units digit of N is 8; SUFFICIENT.

The correct answer is C.

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