GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Mar 2019, 15:59

### 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

# If a = n!, what is value of n ?

Author Message
TAGS:

### Hide Tags

Director
Joined: 02 Oct 2017
Posts: 731
If a = n!, what is value of n ?  [#permalink]

### Show Tags

08 Nov 2018, 10:49
1
3
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:29) correct 28% (01:23) wrong based on 102 sessions

### HideShow timer Statistics

If a = n!, what is value of n ?

(1) The highest prime factor of a is 7

(2) a is divisible by 100

_________________

Give kudos if you like the post

Math Expert
Joined: 02 Aug 2009
Posts: 7431
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

09 Nov 2018, 11:47
4
If a=n! , what is value of n ?

i) The highest prime factor of a is 7
It can be 7! or 8!,9!,10!
Insufficient

ii) a is divisible by 100
Clearly insufficient..
When n is equal to or greater than 10, A will be divisible by 100, as n! will contain atleast two 5s and thus atleast two 0s..

Combined only 10! Is possible
Sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 910
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

09 Nov 2018, 12:08
1
1
push12345 wrote:
If a=n! , what is value of n ?

i) The highest prime factor of a is 7

ii) a is divisible by 100

$$a = n!\,\,\,\,\,\left( {n \geqslant 0\,\,\operatorname{int} } \right)$$

$$? = n$$

$$\left( 1 \right)\,\,\, \Rightarrow \,\,n \in \left\{ {7,8,9,10} \right\}\,\,\,\,\left( {11\,\,{\text{is}}\,\,{\text{prime}}} \right)\,\,\,;\,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,a = 7!\,\,\,\,\,\, \Rightarrow \,\,\,\,n\, = \,7\, \hfill \\ \,{\text{Take}}\,\,a = 8!\,\,\,\,\,\, \Rightarrow \,\,\,\,n\, = \,8\,\, \hfill \\ \end{gathered} \right.\,$$

$$\left( 2 \right)\,\,100 = {2^2} \cdot \boxed{{5^2}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,n \geqslant 10\,\,\,\,\left( {10\,\,{\text{offers}}\,\,{\text{the}}\,\,{\text{2nd}}\,\,{\text{factor}}\,\,{\text{5}}} \right)\,\,\,\,\,;\,\,\,\,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,a = 10!\,\,\,\,\,\, \Rightarrow \,\,\,\,n\, = \,10\, \hfill \\ \,{\text{Take}}\,\,a = 11!\,\,\,\,\,\, \Rightarrow \,\,\,\,n\, = \,11\,\, \hfill \\ \end{gathered} \right.\,$$

$$\left( {1 + 2} \right)\,\,\left\{ \begin{gathered} \,n \in \left\{ {7,8,9,10} \right\}\, \hfill \\ \,n \geqslant 10 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,n = 10$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

15 Nov 2018, 03:47
1
push12345 wrote:
If a=n! , what is value of n ?

i) The highest prime factor of a is 7

ii) a is divisible by 100

from stmn1 : n= could be 8!,9 ! ,10!so on
not sufficient

Stmnt 2: not sufficient

Combing both stmtns : n has to be 10!...
C
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

02 Jan 2019, 03:09
1
If a = n!, what is the value of n?

(1) The highest prime factor of a is 7.

(2) a is divisible by 100
Manager
Joined: 01 May 2017
Posts: 69
Location: India
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

02 Jan 2019, 03:23
1
If a = n!, what is the value of n?

(1) The highest prime factor of a is 7.
if highest prime factor is 7
then it can be any 8! OR 9! OR 10!
Insufficient

(2) a is divisible by 100
for a number to be divisible by 100 it should be a multiple of 25
it cab be 10! OR 15! or 20!... and so on since 5! has only one 5 it can be divisible by 100
Insufficient

(1) and (2) together
Highest prime factor is 7 and divisible by 100
10! is the only possibility
implies a = 10!
Sufficient

Option C is correct
Manager
Joined: 15 Jan 2018
Posts: 179
Location: India
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
WE: Information Technology (Computer Software)
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

02 Jan 2019, 03:27
If a = n!, what is the value of n?

Statement 1: The highest prime factor of a is 7.
Values of n that satisfy this condition are 7, 8, 9, & 10

Since there's no unique value of n, Statement 1 is NOT Sufficient

Statement 2: a is divisible by 100
Values of n that satisfy this condition are 10, 11, 12, ........

Since there's no unique value of n, Statement 2 is NOT Sufficient

Combining Statement 1 & Statement 2, we get only one unique value of n that satisfies both the conditions, i.e. n = 10. Therefore, Statement 1 & Statement 2 together is sufficient to answer the question.

Hence, the Correct Answer of C.

_________________

Please provide me with kudos in case you like my post. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 53792
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

02 Jan 2019, 09:43
akurathi12 wrote:
If a = n!, what is the value of n?

(1) The highest prime factor of a is 7.

(2) a is divisible by 100

___________________
Merging topics.
_________________
SVP
Joined: 18 Aug 2017
Posts: 2448
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a = n!, what is value of n ?  [#permalink]

### Show Tags

02 Jan 2019, 16:53
push12345 wrote:
If a = n!, what is value of n ?

(1) The highest prime factor of a is 7

(2) a is divisible by 100

#1: a could be 14,35,.. in sufficient

#2:
a can be any value ; 100,200,300.. in sufficient

from 1&2::
n has to be 10! so as to be divisible by 100 and also have 7 as the highest prime factor...
IMO C
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Re: If a = n!, what is value of n ?   [#permalink] 02 Jan 2019, 16:53
Display posts from previous: Sort by