Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #100

2

Max has \$125 consisting of bills each worth

Max has \$125 consisting of bills each worth either \$ 5 or \$ 20. How many bills worth \$ 5 does Max have?

1 Explanation

1

Nathan Okorley

Can you make a video explanation for this?

Aug 14, 2018 • Comment

Sam Kinsman

Hi Nathan,

Unfortunately, we don't have explanation videos for every GMAT Official Guide question yet. It is possible that we will make a video for this question in the future - but I cannot be sure whether we will or not.

However, I'm happy to give you a quick explanation of this question!

Here are the statements:

1) Max has fewer than 5 bills worth \$5 each
2) Max has more than 5 bills worth \$20

Let's start with Statement 1 (S1). From S1, we know that he can have either 4, 3, 2, 1, or 0 bills that are worth \$5.

If he has 4 \$5 bills, that's \$20, and \$125 - \$20 = \$105. Since 105 is not divisible by 20, we know that this is not possible.

If he has 3 \$5 bills, that's \$15, and \$125 - \$15 = \$110. Since 110 is not divisible by 20, we know that this is not possible.

If he has 2 \$5 bills, that's \$10, and \$125 - \$10 = \$115. Since 115 is not divisible by 20, we know that this is not possible.

If he has 1 \$5 bill, that's \$5, and \$125 - \$5 = \$120. Since 120 is divisible by 20, we know that this is possible. In other words, he could have 1 \$5 bill and 6 \$20 bills, for a total of \$125.

If he has 0 \$5 bills, that's \$0, and so the entire \$125 would need to be made up of \$20 bills. Since 125 is not divisible by 20, we know that this is not possible.

Thus, from S1, we know he must have 1 \$5 bill, and 6 \$20 bills. So this is sufficient.

Now let's look at S2. We are told that he has more than 5 bills worth \$20. That means he has 6 or more.

Well, 6 \$20 bills is possible, as we found earlier. And 7 is not possible, because that would be \$140. More than 7 is not possible either. So we know from S2 that he has exactly 6 \$20 bills.

So S2 is also sufficient, and the answer is D.