Question

Max has $125consistingofbillseachwortheither$5 or $20.Howmanybillsworth$5 does Max have?
(1) Max has fewer than 5 bills worth $5 each.
(2) Max has more than 5 bills worth $20 each.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (D)

Each statement alone is sufficient.

Let the integer x be the number of bills worth $5eachandlettheintegerybethenumberofbillsworth$20 each. Then 5x + 20y = 125. Determine the value of x.

1. Given that x < 5, then x = 0,1,2,3 or 4. If x is even, then 5x+ 20y is even and therefore cannot equal 125. If x = 3, then 15 + 20y = 125 from which it follows that 20y = 110. But, is not an integer and x not equal 3. Thus, x = 1, thus, sufficient.
2. Given that y > 5 then . If , then and so . Therefore, y = 6 and 5x + 20(6) = 125. So, x = 1. Thus, sufficient. The correct answer is D; each statement alone is sufficient.