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, Magoosh Tutor

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

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Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 6.3 Data Sufficiency

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