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amina.shaikh309
- Senior | Next Rank: 100 Posts
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- Joined: Sat Apr 23, 2016 9:06 pm
Range = Highest Balance - Lowest Balanceamina.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.
12 months
Each month Carl either deposited 120 or withdrew 50.
We know what his balance was in May. So, if we know when he stopped depositing and started withdrawing, we can work from the May balance to determine where the balance started the year, what the highest balance was and what the lowest balance was.
Statement 1:
If the April balance is less than 2625 and the May balance is 2600, then he must have deposited in May, because if in May he withdrew 50 from any number less than 2625 he would have ended up with less than 2600.
So we know that he deposited in May, but we don't know when he stopped depositing and started withdrawing.
He could have started withdrawing in June, making the May balance the highest of the year or he could have started withdrawing in a later month, making a higher balance the highest of the year.
From this statement we do know that he started with 2600 - 5 x 120 = 2000.
He could he have continued depositing in the months from June to October making October's the highest balance at 2000 + (10 x 120) = 3200, and the range 3200 - 2000 = 1200.
He could have stopped depositing after May, making the May balance, 2600, the highest of the year and the range, 2600 - 2000 = 600.
Two different possible ranges.
Insufficient.
Statement 2:
If his June balance is less then 2675, then since his May balance is 2600, he must have withdrawn in June, because if in June he had added 120 to 2600, he would have ended up with a balance greater than 2675.
So we know that he withdrew in June, but from this statement alone with don't know when he started withdrawing.
If he started withdrawing in February, for instance, his January ending balance would be 2600 + 50(May) + 50(April) + 50(March) + 50(February) = 2800, the balance at the end of the year would be 2600 - (7 x 50) = 2250, and the range would be 2800 - 2250 = 550.
If he started withdrawing in May, for instance, the April balance would be the high point at 2650, and the range would be 2650 - 2250 = 400.
Two different possible ranges.
Insufficient.
Statements Combined:
From Statement 1 we know that he deposited in May and from Statement 2 we know that he withdrew in June.
So he deposited 120 in January, February, March, April and May, and withdrew 50 in each the remaining seven months of the year.
Given that we know that he had 2600 at the end of May, we could use the deposit and withdrawal information to determine how much was in the account at the end of each month, and from that we could determine the range of the balances.
Sufficient.
The correct answer is C.
