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Math Expert V
Joined: 02 Sep 2009
Posts: 58414

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Difficulty:   55% (hard)

Question Stats: 56% (01:28) correct 44% (01:34) wrong based on 122 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 V
Joined: 02 Sep 2009
Posts: 58414

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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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Intern  B
Joined: 18 Jun 2015
Posts: 38

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

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I should have looked at it more closely.....shouldnt be missing these type of problems because of language.
Intern  B
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
WE: Business Development (Consulting)

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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 V
Joined: 02 Sep 2009
Posts: 58414

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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".
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Intern  B
Joined: 13 Aug 2017
Posts: 1

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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  B
Joined: 03 Feb 2018
Posts: 91

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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 V
Joined: 02 Sep 2009
Posts: 58414

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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.
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Manager  B
Joined: 11 Sep 2019
Posts: 53
Schools: Great Lakes '21

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I tried with a very different approach.
Tough, I was a victim of Must Be true or Can be true trap, have a look at my approach.
Refer to snapshot by Aadi01 in forum discussion link
Hit Kudos and let me know you find this helpful...
>> !!!

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Check out the Special RC Collection- https://gmatclub.com/forum/trouble-in-rc-listen-to-your-rc-friend-15-days-rc-challenge-day-305898.html M21-22   [#permalink] 24 Sep 2019, 11:01
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