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# M21-22

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Math Expert
Joined: 02 Sep 2009
Posts: 52296

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16 Sep 2014, 00:11
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

45% (00:55) correct 55% (00:49) wrong based on 174 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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52296

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16 Sep 2014, 00:11
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".

_________________
Intern
Joined: 18 Jun 2015
Posts: 41

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10 Sep 2016, 15:19
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, 12:19
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, 07:12
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: 52296

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25 Nov 2017, 07:15
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".
_________________
Intern
Joined: 13 Aug 2017
Posts: 1

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12 Aug 2018, 23:43
I understand the difference between 'can be' true and 'must be' true here. Were this question to come in the exam, I would basically need to test multiple consecutive number options till I get an option i.e (-8, -7, -6) that satisfies all three? (-8, -7, -6) this combination is rather unusual to test as the first thing that comes to one's mind. Is there a shorter way to address this?
Manager
Joined: 03 Feb 2018
Posts: 77

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08 Dec 2018, 19:14
Bunuel wrote:
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".

hi Bunel,

If it is given in the question that a,b,c, are consecutive numbers, then we can by default assume that the order is a<b<c ??
Math Expert
Joined: 02 Sep 2009
Posts: 52296

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08 Dec 2018, 23:11
kanthaliya wrote:
Bunuel wrote:
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".

hi Bunel,

If it is given in the question that a,b,c, are consecutive numbers, then we can by default assume that the order is a<b<c ??

No. On the GMAT a, b, c are consecutive integers does not necessarily mean that a < b < c.
_________________
Re: M21-22 &nbs [#permalink] 08 Dec 2018, 23:11
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# M21-22

Moderators: chetan2u, Bunuel

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