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# M19-35

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Math Expert
Joined: 02 Sep 2009
Posts: 44352

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16 Sep 2014, 01:07
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5% (low)

Question Stats:

90% (00:34) correct 10% (00:55) wrong based on 160 sessions

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Which of the following numbers is equal to $$8!$$ ?

A. 38910
B. 39340
C. 39980
D. 40320
E. 40450
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44352

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16 Sep 2014, 01:07
Official Solution:

Which of the following numbers is equal to $$8!$$ ?

A. 38910
B. 39340
C. 39980
D. 40320
E. 40450

Backsolve. $$8!$$ has to be divisible by 3. Choices B, C, and E are out for this reason. $$8!$$ has to be divisible by 4. Hence choice A is out. The only viable option is choice D.

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Joined: 12 Aug 2015
Posts: 2500
GRE 1: 323 Q169 V154

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02 Feb 2016, 23:37
2
KUDOS
Bunuel wrote:
Official Solution:

Which of the following numbers is equal to $$8!$$ ?

A. 38910
B. 39340
C. 39980
D. 40320
E. 40450

Backsolve. $$8!$$ has to be divisible by 3. Choices B, C, and E are out for this reason. $$8!$$ has to be divisible by 4. Hence choice A is out. The only viable option is choice D.

no need to backsolve.
no need to check the divisibility.
since 6!=720
8!=720*8*7=> 720*56=> 72*56*10
here the tens digit must must be 2
hence option D
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Intern
Joined: 29 Sep 2015
Posts: 2
Schools: Booth '19, Duke '19
GMAT 1: 660 Q49 V31

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05 Jul 2016, 11:45
How about checking divisibility with 8.(Since 8! will have 8)
Backsolve. 8! has to be divisible by 8

Only (D) satisfies .
Intern
Joined: 28 Apr 2016
Posts: 20

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08 Apr 2017, 01:52
Hi Bunuel,

I did by looking for divisibilty to 8. Is it correct also?
Math Expert
Joined: 02 Sep 2009
Posts: 44352

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08 Apr 2017, 04:16
dyg wrote:
Hi Bunuel,

I did by looking for divisibilty to 8. Is it correct also?

Yes. A number is divisible by 8 if the number formed by the last three digits is divisible by 8. Since only 320 (D) is divisible by 8 then it must be correct.
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Intern
Joined: 31 Jul 2013
Posts: 16
Location: Viet Nam
Concentration: General Management, Entrepreneurship
GMAT 1: 650 Q49 V28
GPA: 3.46
WE: Sales (Computer Software)

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08 Sep 2017, 07:12
stonecold wrote:
Bunuel wrote:
Official Solution:

Which of the following numbers is equal to $$8!$$ ?

A. 38910
B. 39340
C. 39980
D. 40320
E. 40450

Backsolve. $$8!$$ has to be divisible by 3. Choices B, C, and E are out for this reason. $$8!$$ has to be divisible by 4. Hence choice A is out. The only viable option is choice D.

no need to backsolve.
no need to check the divisibility.
since 6!=720
8!=720*8*7=> 720*56=> 72*56*10
here the tens digit must must be 2
hence option D

yes, I also looked for tenth digit unit of answer choices and then recognized they're totally different. So just leave out 5*2=10, multiply unit digit of 7*8 = 56*6=6*4*3=2, only choice D
Manager
Joined: 04 Jul 2017
Posts: 61
Location: India
Concentration: Marketing, General Management
GPA: 1
WE: Analyst (Consulting)

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30 Sep 2017, 03:07
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I did by looking for divisibilty to 8. Is it correct also?

Yes. A number is divisible by 8 if the number formed by the last three digits is divisible by 8. Since only 320 (D) is divisible by 8 then it must be correct.

Hi Bunuel, Does this work with all numbers? Like is a number divisible 4 if its last 3 digits are divisible by 4? Is it a rule? Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 44352

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30 Sep 2017, 04:31
1
KUDOS
Expert's post
aashishagarwal2 wrote:
Bunuel wrote:
dyg wrote:
Hi Bunuel,

I did by looking for divisibilty to 8. Is it correct also?

Yes. A number is divisible by 8 if the number formed by the last three digits is divisible by 8. Since only 320 (D) is divisible by 8 then it must be correct.

Hi Bunuel, Does this work with all numbers? Like is a number divisible 4 if its last 3 digits are divisible by 4? Is it a rule? Thanks.

A number is divisible by 2 if the last digit is divisible by 2.
A number is divisible by 4 if the last 2 digits are divisible by 4.
A number is divisible by 8 if the last 3 digits are divisible by 8.
...
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Re: M19-35   [#permalink] 30 Sep 2017, 04:31
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# M19-35

Moderators: chetan2u, Bunuel

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