# GMAT OFFICIAL GUIDE DS – Max has \$125 consisting…

## Solution:

We are given that Max has \$125 consisting of \$5 or \$20 dollar bills and we need to determine the number of \$5 bills he has. Let’s define some variables for the number of \$5 and \$20 bills.

x = the number of \$5 bills

y = the number of \$20 bills

Thus, we can say:

125 = 5x + 20y

Divide both sides by 5:

25 = x + 4y

We need to determine the value of x.

Statement One Alone:

Max has fewer than 5 bills worth \$5 each.

From the given information we have:

25 = x + 4y

25 – x = 4y

(25 – x)/4 = y

Since y is an integer, 25 – x must be a multiple of 4.

From statement one, we know that x can be 4, 3, 2, or 1. However, of these values, only when x = 1, will 25 – x be a multiple of 4. Thus, x = 1. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

Max has more than 5 bills worth \$20 each.

From statement two we know that y > 5. We also have the equation:

25 = x + 4y

Since the smallest integer value for y is 6, let’s substitute that into the above equation for y.

25 = x + 4(6)

25 = x + 24

x = 1

We see that if y were any integer larger than 6, x would be a negative value. Since the number of bills cannot be negative, y = 6 and x = 1. Statement two is also sufficient to answer the question.