Data Sufficiency

Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account for April was less than $2,625
(2) Last year the closing balance of Carl's account for June was less than $2,675

Marty Murray wrote:

amina.shaikh309 wrote:Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account for April was less than $2,625.

(2) Last year the closing balance of Carl's account for June was less than $2,675.

We are given that in January Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. We also given that the closing balance of Carl's account for May was $2,600. We must determine the range of monthly closing balances of Carl's account last year.

Statement One Alone:

Last year the closing balance of Carl's account for April was less than $2,625.

From the given information we know that the closing balance of Carl's account for May was $2,600. The question is whether he deposited $120 or withdrew $50 on May 15. From statement one we know that the closing balance of Carl's account for April was less than $2,625; therefore, there is no way he could have made a withdrawal of $50 on May 15 (when the balance was less than $2,625) and ended up with $2,600 at the end of May. Thus, we know that Carl must have made a deposit on May 15. However, we still have no idea as to when Carl began making withdrawals. Thus, we cannot determine the range of monthly closing balances of Carl's account last year.

Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Last year the closing balance of Carl's account for June was less than $2,675.

From the given information we know that the closing balance of Carl's account for May was $2,600, and from statement two we know that the closing balance of Carl's account for June was less than $2,675. Since the difference between $2,675 and $2,600 is less than $120, we know that Carl could not have made a deposit of $120 on June 15 and thus must have made a withdrawal in June. However, because we still do not know when Carl actually started making withdrawals we do not have enough information about the range of monthly closing balances of Carl's account last year.

Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using our given information and statements together we know that that Carl must have made a deposit on May 15 and made a withdrawal on June 15. Thus, we know that he must have been making deposits on the 15th of each month from January to May and he must have been making withdrawals on the 15th of each month from June to December. Because we know his closing balance in May, we can determine the closing balances for all months from January to December. This is enough information to determine the range of monthly closing balances of Carl's account last year.

Note that it would be tedious to actually calculate the range of monthly closing balances of Carl's account last year. It is not necessary to perform the calculations! It is sufficient to know that there is enough information provided in the two statements together to be able to determine the range.

The answer is C.