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# M21-22

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Math Expert
Joined: 02 Sep 2009
Posts: 47184

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16 Sep 2014, 01:11
1
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Difficulty:

65% (hard)

Question Stats:

41% (00:51) correct 59% (00:46) wrong based on 148 sessions

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If $$a$$, $$b$$, and $$c$$ are consecutive integers, which of the following can be true?

I. $$abc$$ is divisible by 6

II. $$a + c - b$$ is odd

III. $$\frac{c}{a} \gt b$$

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

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Math Expert
Joined: 02 Sep 2009
Posts: 47184

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16 Sep 2014, 01:11
Official Solution:

If $$a$$, $$b$$, and $$c$$ are consecutive integers, which of the following can be true?

I. $$abc$$ is divisible by 6

II. $$a + c - b$$ is odd

III. $$\frac{c}{a} \gt b$$

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

All the three scenarios are possible. Consider $$a = -8$$, $$b = -7$$, $$c = -6$$. Note that the question asks "what 'can' be true" rather than "what 'must' be true".

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Current Student
Joined: 18 Jun 2015
Posts: 41

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10 Sep 2016, 16:19
1
Can be true and Must be true makes all the difference here.
Intern
Joined: 07 Mar 2017
Posts: 7
Location: United States
GMAT 1: 580 Q40 V30
GPA: 3.6

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29 Mar 2017, 13:19
I should have looked at it more closely.....shouldnt be missing these type of problems because of language.
Intern
Joined: 07 Oct 2016
Posts: 14
Location: India
Concentration: Sustainability, General Management
GMAT 1: 640 Q47 V30
GMAT 2: 700 Q47 V40
GPA: 3.5

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25 Nov 2017, 08:12
Hi,

Can't we take -1, 0 & +1 ----> the answers in this case might be different ?

Also, if you could explain the difference b/w "must be true" & "can be true", I think i am missing a point here.

Thx
Math Expert
Joined: 02 Sep 2009
Posts: 47184

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25 Nov 2017, 08:15
quest800 wrote:
Hi,

Can't we take -1, 0 & +1 ----> the answers in this case might be different ?

Also, if you could explain the difference b/w "must be true" & "can be true", I think i am missing a point here.

Thx

Look at the highlighted part of the solution:
All the three scenarios are possible. Consider $$a = -8$$, $$b = -7$$, $$c = -6$$. Note that the question asks "what 'can' be true" rather than "what 'must' be true".
_________________
Re: M21-22 &nbs [#permalink] 25 Nov 2017, 08:15
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# M21-22

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