GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Apr 2020, 19:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# For any positive integer n greater than 1, n! denotes the product of a

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Mar 2019
Posts: 909
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

Updated on: 09 Feb 2020, 06:09
1
2
00:00

Difficulty:

95% (hard)

Question Stats:

30% (01:46) correct 70% (03:01) wrong based on 33 sessions

### HideShow timer Statistics

For any positive integer n greater than 1, n! denotes the product of all the integers from 1 to n, inclusive.
If A is a positive integer such that the greatest number that divides both $$A^3$$ and 13! is 448, which of the following can be the value of A?

A. 14
B. 56
C. 140
D. 196
E. 448

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019

Originally posted by lnm87 on 09 Feb 2020, 05:47.
Last edited by lnm87 on 09 Feb 2020, 06:09, edited 1 time in total.
Senior Manager
Joined: 14 Dec 2019
Posts: 496
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 06:05
1
Is that A3 = $$A^3$$ or $$A*3$$??
Director
Joined: 07 Mar 2019
Posts: 909
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 06:10
You are right.
Thanks for pointing the error. Corrected it.
shameekv1989 wrote:
Is that A3 = $$A^3$$ or $$A*3$$??

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Joined: 14 Dec 2019
Posts: 496
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 06:42
1
If $$A^3$$ is divisible by 448 (which is $$2^6$$*7) then A must have atleast one 7 -> $$A^3$$ must have 7^3 = 343

The only value that is greater than 343 is 448 - Answer - E
Director
Joined: 07 Mar 2019
Posts: 909
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 11:00
shameekv1989 wrote:
If $$A^3$$ is divisible by 448 (which is $$2^6$$*7) then A must have atleast one 7 -> $$A^3$$ must have 7^3 = 343

The only value that is greater than 343 is 448 - Answer - E

My friend you were right till halfway. Revisit, i am sure you would find why.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Joined: 15 Jul 2018
Posts: 238
For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

Updated on: 09 Feb 2020, 11:43
Answer would be I think 196 since 448= 2^6 *7
And 196^3 = 7^6*2^6
And it would be divisible by 448

Posted from my mobile device

Originally posted by Apt0810 on 09 Feb 2020, 11:07.
Last edited by Apt0810 on 09 Feb 2020, 11:43, edited 1 time in total.
Senior Manager
Joined: 14 Dec 2019
Posts: 496
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 11:13
1
lnm87 wrote:
shameekv1989 wrote:
If $$A^3$$ is divisible by 448 (which is $$2^6$$*7) then A must have atleast one 7 -> $$A^3$$ must have 7^3 = 343

The only value that is greater than 343 is 448 - Answer - E

My friend you were right till halfway. Revisit, i am sure you would find why.

You are right. That's A^3 not A; Anyways :-

Minimum that A has is one 7 and two 2's. Two 2's is fixed but 7 is flexible. Thus it can be 7^2 * 4 = 196

GMAT Tutor
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Joined: 26 Jun 2014
Posts: 134
GMAT 1: 740 Q51 V39
For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 11:39
1
lnm87 wrote:
For any positive integer n greater than 1, n! denotes the product of all the integers from 1 to n, inclusive.
If A is a positive integer such that the greatest number that divides both $$A^3$$ and 13! is 448, which of the following can be the value of A?

A. 14
B. 56
C. 140
D. 196
E. 448

The greatest common divisor (GCD) of $$A^3$$ and $$13!$$ is 448

$$448 = 4 * 112 = 4 * 4 * 28 = 4 * 4 * 4 * 7 = 2^6 * 7$$

Observe that $$13!$$ has only $$7^1$$ as factor
Also, highest power of $$2$$ in $$13! = [13/2] + [13/4] + [13/8] = 6 + 3 + 1 = 10$$ (where $$[n]$$ denotes the greatest integer less than or equal to $$n$$)

Since $$2^6 * 7$$ is the GCD of $$A^3$$ and $$13!$$, we can conclude that $$2^6 * 7$$ must be a factor of $$A^3$$

Thus, we have:

1. $$A^3$$ must NOT have the power of 2 greater than 6 (since 13! has power of 2 as 10, if $$A^3$$ had a power of 2 greater than 6, the GCD would also have a power of 2 greater than 6) => Highest power of 2 in A must be 2 i.e. A is a multiple of $$2^2$$ (not more than that) ... (i)

2. $$A^3$$ must have $$7^3$$ as a factor as well (it is the cube of a number), implying $$A$$ is a multiple of $$4 * 7$$ i.e. $$28$$ ... (ii)

Working with options:

A. $$A = 14$$ ---- not possible since A should be a multiple of 28 ---> from (ii)

B. $$A = 56 = 2^3 * 7$$ ---- Violates (i)

C. $$A = 140 = 2^2 * 7 * 5$$ ---- If A is a multiple of 5, and since 13! is also a multiple of 5, the GCD would have 5 as a factor ---- Violates given info

D. $$A = 196 = 2^2 * 7^2$$ ---- Satisfies both (i) and (ii). Note: even though A has a factor $$7^2$$, $$13!$$ has a factor only $$7^1$$, hence GCD would still have $$7^1$$ as factor

E. $$A = 448 = 2^6 * 7$$ ---- Violates (i)

_________________
Sujoy Kumar Datta
Director - CUBIX Educational Institute Pvt. Ltd. (https://www.cubixprep.com)
IIT Kharagpur, TU Dresden Germany
GMAT - Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA
_________
Feel free to talk to me about GMAT & GRE | Ask me any question on QA (PS / DS)
Let's converse!
Skype: sk_datta
Alt. Email: sujoy.datta@gmail.com
Director
Joined: 30 Sep 2017
Posts: 786
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 13:10
1
Both A and 13! must have common factors of minimum one 7 and exactly two 2s. No other factors is allowed.

Eliminate choices A, B, E since the number doesn't have exact factors of 2^2.
A. 14=2*7
B. 56=2^3*7
E. 448=2^6*7

Eliminate choice C because it has additional factor 5. If so, A^3 and 13! must have been divisible by 448*5^2
C. 140=2^2*7*5

Both A and 13! must have common factors of minimum one 7 and exactly two 2s.
D. 196=2^2*7^2

Posted from my mobile device
Director
Joined: 07 Mar 2019
Posts: 909
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
For any positive integer n greater than 1, n! denotes the product of a  [#permalink]

### Show Tags

09 Feb 2020, 19:20
Apt0810 wrote:
Answer would be I think 196 since 448= 2^6 *7
And 196^3 = 7^6*2^6
And it would be divisible by 448

Posted from my mobile device

Good that you corrected the mistake made earlier, a mistake that i also made under timed condition. Anyway great learning
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
For any positive integer n greater than 1, n! denotes the product of a   [#permalink] 09 Feb 2020, 19:20
Display posts from previous: Sort by