Last Updated on May 8, 2023
GMAT OFFICIAL GUIDE DS
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.
Answer: D
