Max has $125 consisting of bills each worth

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.

Aug 16, 2018 • Reply