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.


Answer is (C). Both statements together are sufficient to answer the question.


Explanation:

Carl deposits/withdraws once in a month.

Deposits consecutively worth of 120$

Jan - 120$
Feb - 240$
Mar - 360$
APR - 480$
May - 600$

But as per the question Carl's account for May of last year
was $2,600 => 2000$(Initial account balance) + 600$ (120 $'s deposit each month)

Now, look at first choice. Statement 1 Say's Carl's account for April was less than $2,625.
This alone might not help us to derive anything.


Now, look at Second choice. Statement 2 say's Carl's account for June was less than $2,675

For May, it is 2600$ and for June 15th it should be 2550 ( Since, 2600$ +120$ = 2720 $ which is greater than $ 2,675 given in statement B and As per the question, withdrawals of $50 from the account on the 15th of each of the remaining months of the year)

For Jul 15th it is 2550 - 50 = 2500 etc...

This was you can find the closing balance of each month till December.

But, second option Alone can't help us find the monthly closing because Statement 1 will help us understand that deduction of 50$ has not happened before April.

Correct Answer is Option (c) (Both statement 1 and statement 2 are used to answer the question)

hi,

The solution is as below.

Given info deposits of $120 and withdrawls of $50 can be done. First Deposits and then withdrawls.
May balance is 2600

Given in A : balance of April was less than $2,625.

Case 1
1. Consider deposits of 120 till may: total deposit = 120*5 = 600 so initial balance =2000. In this case no withdrawl was done and we don't know when in the future the withdrawls have started.
2. For combinations of DWW DDD DDW for Jan,feb,march(D = deposit and W = withdrawl)the balance of April will be less than 2625. Therefore we cannot exaclty calcualte the balances.

Given in B. Balance of June was less than $2,675

Since may balance is 2600 if the amount was deposited in Jun it would be 2720 so deposit was not done in June. therefore withdrawl has started. if Withdral was done in JUNE the balance of june would be 2550 which is less than 2675.Hence the withdrawls started from June.But balances cannot be calculated.2550 balance in may can be achieved in two possible ways an account balance of
$2,680 on January 1, made one $120 deposit on January 15, and then made a $50 withdrawal in each of the remaining 11 months of the year or having an account balance of $2,510 on January 1, made $120
deposits on January 15 and on February 15, and then made a $50 withdrawal in each of the remaining 10 months of the year

Therefore using both A and B we can get the balances.

C

kullayappayenugula wrote:hi,

The solution is as below.

Given info deposits of $120 and withdrawls of $50 can be done. First Deposits and then withdrawls.
May balance is 2600

Given in A : balance of April was less than $2,625.

Case 1
1. Consider deposits of 120 till may: total deposit = 120*5 = 600 so initial balance =2000. In this case no withdrawl was done and we don't know when in the future the withdrawls have started.
2. For combinations of DWW DDD DDW for Jan,feb,march(D = deposit and W = withdrawl)the balance of April will be less than 2625. Therefore we cannot exaclty calcualte the balances.

Given in B. Balance of June was less than $2,675

Since may balance is 2600 if the amount was deposited in Jun it would be 2720 so deposit was not done in June. therefore withdrawl has started. if Withdral was done in JUNE the balance of june would be 2550 which is less than 2675. hence the withdrawls started from June and we cal calculate the rest.


B

What if Carl has account balance of $2800 on Jan 1st .
Imagine that he deposited 120$ in Feb and performed withdrawal of 50$ next 11 months.
Then the closing balance will be 2600$ end of May. Then deduction of $ 50 more in June which is 2550 which is less than 2675 as per statement B. So, we need statement 1 as well to say concretely that actual deduction has started in June 15th.

FLUID added the remaining part of the solution. Sorry it got posted by mistake while I was still editing.

[email protected] 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.

Did nt understand the question and the explanation given in OG. Please help

May = 2600.

Statement 1: Last year the closing balance of Carl's account
for April was less than $2,625.
If 120 was deposited in May, then April = 2600-120 = 2480.
If 50 was withdrawn in May, then April = 2600+50 = 2650.
Since April < 2625, we know that a deposit of 120 was made in May, implying that 120 was deposited every month January through at least May.
Thus, we can determine the balance of every month January - April:
April = 2480, March = 2480-120 = 2360, etc.
No information about June - December.
Insufficient.

Statement 2: Last year the closing balance of Carl's account
for June was less than $2,675.
If 120 was deposited in June, then June = 2600+120 = 2720.
If 50 was withdrawn in June, then June = 2600-50 = 2550.
Since June < 2675, we know that a withdrawal of 50 was made in June, implying that 50 was withdrawn every month June - December.
Thus, we can determine the balance of every month June - December:
June = 2550, July = 2550-50 = 2500, etc.
No information about January - April.
Insufficient.

Statements 1 and 2 combined:
Statement 1 tells us the closing balances January - April.
The question stem tells us the closing balance in May.
Statement 2 tells us the closing balances June - December.
Combining the information above, we can determine the closing balance of every month and determine the range for the whole year.
Sufficient.

The correct answer is C.