A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?
(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
Question stem: What is the value of Y-R?
Statement 1: To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
Implication:
It is possible to remove 13 NON-RED marbles, with the result that AT LEAST 14 marbles must be removed to guarantee that a red marble is removed.
Since there are 13 non-red marbles, we get:
Y+B = 13.
No way to determine the value of Y-R.
INSUFFICIENT.
Statement 2: To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
Implication:
It is possible to remove 7 NON-YELLOW marbles, with the result that AT LEAST 8 marbles must be removed to guarantee that a yellow marble is removed.
Since there are 7 non-yellow marbles, we get:
B+R = 7.
No way to determine the value of Y-R.
INSUFFICIENT.
Statements combined:
Subtracting B+R=7 from Y+B=13, we get:
(Y+B) - (B+R) = 13-7
Y-R = 6.
SUFFICIENT.
The correct answer is
C.
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