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If a is divisible by 9!, then a/6 must be

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If a is divisible by 9!, then a/6 must be [#permalink]

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New post 02 Dec 2016, 06:57
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If a is divisible by 9!, then a/6 must be

I. divisible by 3
II. divisible by 14
III. a multiple of 100

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III
[Reveal] Spoiler: OA

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If a is divisible by 9!, then a/6 must be [#permalink]

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New post 02 Dec 2016, 07:31
Bunuel wrote:
If a is divisible by 9!, then a/6 must be

I. divisible by 3
II. divisible by 14
III. a multiple of 100

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


\(\frac{a}{6}=\frac{2\times 3 \times ... \times 8 \times 9}{6}=4 \times 5 \times 6 \times 7 \times 8 \times 9\)

(I) \(\frac{a}{6}\) has factor \(6=2 \times 3\) so \(a/6\) is divisible by 3. True

(II) \(\frac{a}{6}\) has factor \(7 \times 4=2\times 14\) is divisible by 14. True.

(III) \(100=2^2\times 5^2\). However \(\frac{a}{6}\) isn't divisible by \(5^2\) so (III) is not true.

The answer is D.
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Last edited by broall on 02 Dec 2016, 09:57, edited 1 time in total.

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Re: If a is divisible by 9!, then a/6 must be [#permalink]

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New post 02 Dec 2016, 08:15
Let's say a has minimum value as 9!, then

a/6 = 9*8*7*5*4*3*2*1. Let go to answer choice now,

I. divisible by 3 = Yes. possible. As a/6 is divisible by 3.
II. divisible by 14 = Yes. Again Possible. As a/6 is divisible by 7*2.
III. a multiple of 100 = Not possible. does not have number which makes it to 100.

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Kudos [?]: 135185 [0], given: 12671

Re: If a is divisible by 9!, then a/6 must be [#permalink]

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New post 03 Dec 2017, 08:22
Bunuel wrote:
If a is divisible by 9!, then a/6 must be

I. divisible by 3
II. divisible by 14
III. a multiple of 100

A. None
B. II only
C. III only
D. I and II only
E. I, II, and III


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_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135185 [0], given: 12671

Re: If a is divisible by 9!, then a/6 must be   [#permalink] 03 Dec 2017, 08:22
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