If 4a + 2b m, then which of the following must be tr

Question

If 4a + 2b < n and 4b + 2a > m, then which of the following must be true?

A. b – a < (m – n)/2

B. b – a ≤ (m – n)/2

C. b – a > (m – n)/2

D. b – a ≥ (m – n)/2

E. b – a ≤ (m + n)/2

GMATinsight · Answer

4a + 2b < n and 4b + 2a > m (Multiplying -1 both sides and changing inequality sign) 4a + 2b < n and -4b - 2a < -m CONCEPT: Two inequations may be added if their inequality signs are identical Adding 4a + 2b < n and -4b - 2a < -m (4a + 2b)+ (-4b - 2a) < n -m i.e. 2a - 2b < n-m i.e. a - b < \frac{(n-m)}{2} i.e. b - a > \frac{(m-n)}{2} Answer: Option C

chetan2u · Answer

4a + 2b < n and 4b + 2a > m Add the same sides of inequality 4a+2b+m\frac{m-n}{2} So C is correct. But C also lies within the range of D : b – a ≥ \frac{(m – n)}{2} . Thus D also MUST be true. One of C and D requires to be changed as we cannot have two answers.

chetan2u · Answer

But why not D, as C is within the range of D?

Kinshook · Answer

Asked: If 4a + 2b < n and 4b + 2a > m, then which of the following must be true?

4b + 2a > m
-2b - 4a > -n
2b -2a > (m-n)
b - a > (m-n)/2

IMO C

Posted from my mobile device

GMATinsight · Answer

Then option D needs correction because I agree D also is part of "must be true".

Bunuel · Answer

______________________
Edited the typo. Thank you!

bumpbot · Answer

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If 4a + 2b < n and 4b + 2a > m, then which of the following must be tr

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