Official Guide Explanation:
Data Sufficiency #161




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Solution and Metadata

Question: 161
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Other >

Explanation: This question is very wordy, but it's important not to get bogged down in the details. The concept is simple. At the end of May, the balance was $2,600. For some number of months after the start of the year (those months might or might not include May), he made a $120 deposit every month. After the months in which he made deposits, he made a monthly withdrawal of $50.

Statement (1) is insufficient. We know that the balance at the end of May was $2,600. If Carl made a deposit in May, the balance at the end of April must have been $120 less--$2,480. That's possible. If Carl made a withdrawal in May, the balance at the end of April must have been $2,650. This statement contradicts that. Thus, he must have made a deposit in May, meaning that he made a deposit in each month up to May. Thus, his month - end balances up to that point were:

April: $2,480

March: $2,360

February: $2,240

January: $2,120

(You don't need to figure all of this out--the important thing is that this question tells you the month - end balances for the first four months.) We don't know how much longer Carl keeps making deposits, though, so we don't know what the range turns out to be for the entire year.

Statement (2) is also insfficient. By the same reasoning as in (1), we can figure out the two possible balances for the end of June, based on the May - end balance of $2,600. If he made a deposit in June, the June - end balance would be $2,720. That's impossible, according to this statement. Thus, he must have made a withdrawal, meaning that the June - end balance was $2,550. We know that he made a withdrawal for every month after that, so we can figure out the month - end balances from May through December. However, this statement doesn't give us enough information to determine when he started making withdrawals.

Taken together, the statements are sufficient. (1) told us that Carl made deposits from January until May, then (2) indicates that he made withdrawals from June to December. As we saw in (1), we could determine his opening balance, and if we subtract $50 for each month starting in June, we can determine the rest. That gives us the information we need to find the range of the monthly closing balances. Choice (C) is correct.

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