If the sum of two different numbers, x and y, is 24 and x is the larger of the numbers, is the sum of the two numbers greater than the sum of x and a third number, c?
(1) -c > -y
(2) 46 > 2x + 2c + 22
The OA is D.
How can I conclude that statement (1) is sufficient?
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If the sum of two different numbers. . .
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This question asks whether x + y > x + c (or whether 24 > x + c).
Statement 1 tells us that -y is more negative than -c. For example, -c > -y could be:
This means that y has a greater magnitude than c. In other words, if -c > -y, y > c.
We can see this with a couple examples:
If c = 1 and y = 2, -1 > -2 and 2 >1.
If c = 2 and y = 500, -2 > -500 and 500 > 2.
If c = 3.3 and y = 3.4, -3.3 > -3.4 and 3.4 > 3.3.
So we know that y > c. Since y will always be greater than c, x + y will always be greater than x + c. SUFFICIENT
Statement 1 tells us that -y is more negative than -c. For example, -c > -y could be:
This means that y has a greater magnitude than c. In other words, if -c > -y, y > c.
We can see this with a couple examples:
If c = 1 and y = 2, -1 > -2 and 2 >1.
If c = 2 and y = 500, -2 > -500 and 500 > 2.
If c = 3.3 and y = 3.4, -3.3 > -3.4 and 3.4 > 3.3.
So we know that y > c. Since y will always be greater than c, x + y will always be greater than x + c. SUFFICIENT
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