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If m=n and p < q, which of the following must be true?
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Sajjad1994
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If m=n and p < q, which of the following must be true? [#permalink] New post  27 Jan 2020, 09:53
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If \(m=n\) and \(p < q\), which of the following must be true?

(A) \(m - p > n - q\)

(B) \(p - m > q - n\)

(C) \(m - p < n - q\)

(D) \(mp > nq\)

(E) \(m + q < n + p\)

Source: Master GMAT
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BrentGMATPrepNow
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If m=n and p < q, which of the following must be true? [#permalink] New post  27 Jan 2020, 11:32
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SajjadAhmad wrote:
If \(m=n\) and \(p < q\), which of the following must be true?

(A) \(m - p > n - q\)

(B) \(p - m > q - n\)

(C) \(m - p < n - q\)

(D) \(mp > nq\)

(E) \(m + q < n + p\)

Source: Master GMAT


Given: \(p < q\)

Multiply both sides of the inequality by -1 to get: \(-p > -q\) (since we multiplied both sides of the inequality by NEGATIVE value, we REVERSED the direction of the inequality symbol)

Add \(m\) to both sides to get: \(-p + m> -q + m\)

Since we're told that \(m=n\), we can replace the second \(m\) with \(n\) to get: \(-p + m> -q + n\)

Rearrange the terms to get: \(m-p> n-q\)

Answer: A

Cheers,
Brent

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rajatchopra1994
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Re: If m=n and p < q, which of the following must be true? [#permalink] New post  27 Jan 2020, 19:46
Explanation:

Assume some numbers, let m=n=2
P=4 , Q=6
Checking Option A, m−p>n−q
2-4 > 2-6
-2 > -4.. Always true.

You can check with other values also.

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Re: If m=n and p < q, which of the following must be true? [#permalink] New post  17 Mar 2021, 09:43
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Re: If m=n and p < q, which of the following must be true? [#permalink]
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