M13-15

Question

Money is deposited into an account in increments of $500 and withdrawn in increments of $300. If the account balance increases by $1,200 after a month, what is the minimum number of transactions that could have occurred?

A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

Bunuel · Answer

Official Solution:

Money is deposited into an account in increments of $500 and withdrawn in increments of $300. If the account balance increases by $1,200 after a month, what is the minimum number of transactions that could have occurred?

A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

Essentially, the question asks us to find the minimum possible value of  x + y  such that  500x - 300y = 1,200 . By trial and error, it's easy to find that the minimum value of  x + y  occurs when  x = 3  and  y = 1 . In this case,  500*3 - 300*1 = 1,200 .

Answer: B

Showmeyaa · Answer

Basically, money paid into account is money getting added. Let's represent that with x
Money paid out is money getting deducted. Let's represent that with y.

500x - 300y = 1200
Try plugging in, as we are asked the lowest number of transactions:
x = 3, y = 1
So, minimum number of transaction = x + y = 3 + 1 = 4
IMO, (B)!

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

kingbucky · Answer

I think this is a  poor-quality  question and I don't agree with the explanation. Why cant it be assumed that, the money deposited is as per the series {500,1000,1500....} and withdrawan as per the series {300,600,900} ? each time the amount deposited increases ?

Bunuel · Answer

The phrase "Money is deposited into an account in increments of $500 and withdrawn in increments of $300" means that each deposit is exactly $500, and each withdrawal is exactly $300. It does not mean the amounts were deposited or withdrawn in multiples of $500 or $300.

KRNSW · Answer

When the question states that amounts are either deposited or withdrwan in increments. 
What I assumed was that 1st deposit would be of $500, then it will keep increasing by $500, and the same for withdrawl.
Therefor, 1st deposit = $500, 2nd deposit = $1000 and one withdrawl of $300, making acount balance of $(500+1000-300)=$1200
Basis this I selected 3 as the min. no. of trnsactions...
Have I misinterpreted the questions wordings?

Bunuel · Answer

This has been addressed here: https://gmatclub.com/forum/m13-183971.html#p3467151 You’re mixing up two meanings of increment. Here, “in increments of 500” means the unit size of each transaction is 500. It does not mean the next deposit is 500 more than the previous one. Likewise, “in increments of 300” means each withdrawal is 300. It does not mean withdrawals increase from one transaction to the next. So you should count each 500 and each 300 as separate transactions. The word increment refers to the per-transaction step size, not a growing sequence.

M13-15

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards