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M21-22

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M21-22  [#permalink]

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New post 16 Sep 2014, 01:11
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

43% (00:56) correct 57% (00:48) wrong based on 152 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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Re M21-22  [#permalink]

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New post 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".

Answer: E
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-22  [#permalink]

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New post 10 Sep 2016, 16:19
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Can be true and Must be true makes all the difference here.
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Re: M21-22  [#permalink]

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New post 29 Mar 2017, 13:19
I should have looked at it more closely.....shouldnt be missing these type of problems because of language.
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M21-22  [#permalink]

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New post 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
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Re: M21-22  [#permalink]

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New post 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".
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-22  [#permalink]

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New post 13 Aug 2018, 00:43
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?
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Re: M21-22 &nbs [#permalink] 13 Aug 2018, 00:43
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M21-22

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