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# If a>b and c<d , which of the following MUST be true?

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Manager
Joined: 31 Aug 2016
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If a>b and c<d , which of the following MUST be true?  [#permalink]

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08 Sep 2018, 08:18
2
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:57) correct 49% (01:44) wrong based on 52 sessions

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If $$a>b$$ and $$c<d$$, which of the following MUST be true?

A. $$a−d>c−b$$
B. $$a+d>b$$
C. $$b+c>a−d$$
D. $$b−d<a−c$$
E. $$a^2+d^2>b^2+c^2$$

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Re: If a>b and c<d , which of the following MUST be true?  [#permalink]

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08 Sep 2018, 09:32
1
PeepalTree wrote:
If$$a>b$$ and $$c<d$$, which of the following MUST be true?

A. $$a−d>c−b$$
B. $$a+d>b$$
C. $$b+c>a−d$$
D. $$b−d<a−c$$
E. $$a^2+d^2>b^2+c^2$$

Note:- You can only apply subtraction when the inequality signs are in the opposite directions. (take the sign of the inequality you subtract from)
We can write $$a>b$$ as $$b<a$$----(1)
Also, we can write $$c<d$$ as $$d>c$$ ---------(2)
Since (1) and (2) bear opposite sign of inequality, hence we can subtract (2) from (1),
$$b-d < a-c$$

Ans. (D)
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Re: If a>b and c<d , which of the following MUST be true?  [#permalink]

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08 Sep 2018, 09:45
1
PeepalTree wrote:
If$$a>b$$ and $$c<d$$, which of the following MUST be true?

A. $$a−d>c−b$$
B. $$a+d>b$$
C. $$b+c>a−d$$
D. $$b−d<a−c$$
E. $$a^2+d^2>b^2+c^2$$

a>b and d>c
We can add the inequalities in same direction
a+d>b+c
Checking the options
Answer choice D is the same as above
b-d<a-c
OR a+d>b+c
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Re: If a>b and c<d , which of the following MUST be true?  [#permalink]

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08 Sep 2018, 10:37
Popular choice seems to be option E. It would've been correct if the question stated that they are positive integers.

a = -2 , b = -5 , c = 4 , d = 5. Option E will fail.
Re: If a>b and c<d , which of the following MUST be true?   [#permalink] 08 Sep 2018, 10:37
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