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

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

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New post 08 Sep 2018, 08:18
2
00:00
A
B
C
D
E

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

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New post 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.
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Re: If a>b and c<d , which of the following MUST be true?   [#permalink] 08 Sep 2018, 10:37
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If a>b and c<d , which of the following MUST be true?

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