ivonneqf wrote:Hi guys,
help me with this one:
Q: How many more men than women are in the room?
(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.
Statement 1: M+W = 20.
No way to determine the value of M-W.
Statement 2: M = W².
No way to determine the value of M-W.
Statements combined:
Substituting M=W² into M+W=20, we get:
W² + W = 20.
Make a list of possible values for W and W² and look for a combination with a sum of 20:
W=1, W²=1
W=2, W²=4
W=3, W²=9
W=4, W²=16.
Since 4+16 = 20, W=4, implying that M=W²=4²=16.
Thus, M-W = 16-4 = 12.
SUFFICIENT.
The correct answer is
C.
When the statements are combined, we could also use algebra:
W² + W = 20
W² + W - 20 = 0
(W+5)(W-4) = 0
W=-5 or W=4.
Since the number of women must be positive, W=4.
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