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

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Math Expert
Joined: 02 Sep 2009
Posts: 59712
If a > b and c < a, which of the following must be true?  [#permalink]

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07 Sep 2017, 23:09
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Difficulty:

55% (hard)

Question Stats:

54% (01:20) correct 46% (01:25) wrong based on 153 sessions

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

I. a > b > c
II. 2a > b + c
III. a^2 > bc

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

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Joined: 12 Feb 2017
Posts: 70
If a > b and c < a, which of the following must be true?  [#permalink]

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Updated on: 07 Sep 2017, 23:43
1
2
Given
a>b ---(1)
a>c ---(2)

I. a > b > c
lets consider a=5 b=2 and c=3
a>b-- true a>c-- true
but a>b>c -- not always true
Hence I is out.

II. 2a > b + c
a+a>b+c
2a>b+c
hence true

III. a^2 > bc
lets consider (A) a=5 b=2 and c=3
a^2=25 and b*c= 6
(B) a= -6 , b=-7, c=-9
a^2=36 and b*c= 63
Not always true

Hence Answer is only II Option B

Kudos if it helps

Originally posted by pushkarajnjadhav on 07 Sep 2017, 23:19.
Last edited by pushkarajnjadhav on 07 Sep 2017, 23:43, edited 3 times in total.
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Re: If a > b and c < a, which of the following must be true?  [#permalink]

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07 Sep 2017, 23:31
1
Bunuel wrote:
If a > b and c < a, which of the following must be true?

I. a > b > c
II. 2a > b + c
III. a^2 > bc

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

let (a,b,c) be (-5, -6, -6) then
only II follows
B
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Re: If a > b and c < a, which of the following must be true?  [#permalink]

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08 Sep 2017, 00:10
1
Bunuel wrote:
If a > b and c < a, which of the following must be true?

I. a > b > c
II. 2a > b + c
III. a^2 > bc

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

a>b
a>c
b,c not sure which one is bigger
Option I out

Option II is correct

Multiplying inequalities only when both sides are positive. In this case, unclear.
Option III is out.

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

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31 Jul 2019, 17:28
Bunuel wrote:
If a > b and c < a, which of the following must be true?

I. a > b > c
II. 2a > b + c
III. a^2 > bc

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

All we know is that a is greater than b and greater than c. Thus, the only answer choice that must be true is a + a (or 2a) is greater than b + c.

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Re: If a > b and c < a, which of the following must be true?   [#permalink] 31 Jul 2019, 17:28
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