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For the integers m, n, r, and s, if m + n = 250 and m > n, is (m – r) > (s – n)?
(1) 250 > r + s
(2) m + r + s= 375
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.
(D) Statement (1) tells us that 250 > r + s. Since the question statement tells us that m + n = 250, we can determine that m + n > r + s.
Now, let us manipulate this inequality to see whether it is equivalent to the inequality in the question:
(m + n) > (r + s)
m > (r + s) – n
(m – r) > (s – n)
This is exactly what we were looking for. We can answer the question using Statement (1), hence it is sufficient.
Statement (2) tells us that m + r + s = 375.
Because we know that m + n = 250 and m > n, m must be greater than 125. Subtracting 125 from 375 yields 250, so if m is greater than 125, then r + s must be smaller than 250. We are now left with the same inequality that we were given in Statement (1), which can be manipulated to show that (m – r) > (s – n). So Statement (2) is also sufficient.
Since both statements are sufficient alone, the correct answer is choice (D).
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The two statements should never contradict themselves:
1) 250 > r + s
2) We know m > 125
If I substitute 126 for m in the stament (2) then r + s = 249
I thought r + s were greater than 250.
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