Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
With digit problems, it’s 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 doesn’t 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.