It is currently 26 Nov 2020, 21:07

### 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

# 10! is divisible by 3x5y, where x and y are positive integer

Author Message
TAGS:
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3035 [0], given: 394

10! is divisible by 3x5y, where x and y are positive integer [#permalink]  12 Aug 2018, 16:00
Expert's post
00:00

Question Stats:

61% (01:00) correct 38% (01:03) wrong based on 52 sessions
10! is divisible by $$3^x5^y$$, where x and y are positive integers.

 Quantity A Quantity B The greatest possible value for x Twice the greatest possible value for y

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3035 [2] , given: 394

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  17 Aug 2018, 16:09
2
KUDOS
Expert's post
Explanation

First, expand 10! as 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

(Do not multiply all of those numbers together to get 3,628,800—it’s true that 3,628,800 is the value of 10!, but analysis of the prime factors of 10! is easier in the current form.)

Note that 10! is divisible by 3x5y, and the question asks for the greatest possible values of x and y, which is equivalent to asking, “What is the maximum number of times you can divide 3 and 5, respectively, out of 10! while still getting an integer answer?”

In the product 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, only the multiples of 3 have 3 in their prime factors, and only the multiples of 5 have 5 in their prime factors. Here are all the primes contained in 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and therefore in 10!:

10 = 5 × 2
9 = 3 × 3
8 = 2 × 2 × 2
7 = 7
6 = 2 × 3
5 = 5
4 = 2 × 2
3 = 3
2 = 2
1 = no primes

There are four 3’s and two 5’s total. The maximum values are x = 4 and y = 2. Therefore, the two quantities are equal.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 20 Dec 2018
Posts: 3
Followers: 0

Kudos [?]: 3 [0], given: 78

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  09 Mar 2019, 03:24
As the maximum values are x = 4 and y = 2, should not be A greater?
Founder
Joined: 18 Apr 2015
Posts: 13908
GRE 1: Q160 V160
Followers: 314

Kudos [?]: 3680 [1] , given: 12931

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  09 Mar 2019, 04:05
1
KUDOS
Expert's post
$$10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1$$

$$(2*5) * (3^2) * (2^3) * 7 * (2*3) * 5 * 3 * (2^2) * 1$$

$$\frac{7 * 5^2 * 3^4 * 2^7 * 1}{3^x 5^y}$$

As you clearly see the quantity must be divided by $$3^x$$ and $$5^y$$.

In the numerator $$3^4$$ and $$5^2$$ , which means that the exponent of 3 is $$4 = x$$ and the exponent of 5 is $$2=y$$

A > B

I think also the answer should be A

Hope this helps.

Regards
_________________

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

GRE Instructor
Joined: 10 Apr 2015
Posts: 3907
Followers: 164

Kudos [?]: 4769 [1] , given: 70

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  09 Mar 2019, 07:06
1
KUDOS
Expert's post
Carcass wrote:
$$10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1$$

$$(2*5) * (3^2) * (2^3) * 7 * (2*3) * 5 * 3 * (2^2) * 1$$

$$\frac{7 * 5^2 * 3^4 * 2^7 * 1}{3^x 5^y}$$

As you clearly see the quantity must be divided by $$3^x$$ and $$5^y$$.

In the numerator $$3^4$$ and $$5^2$$ , which means that the exponent of 3 is $$4 = x$$ and the exponent of 5 is $$2=y$$

A > B

I think also the answer should be A

Hope this helps.

Regards

Be careful.
Quantity B = TWICE the greatest possible value for y

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 20 Dec 2018
Posts: 3
Followers: 0

Kudos [?]: 3 [1] , given: 78

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  09 Mar 2019, 09:55
1
KUDOS
Thanks to both of you, it is clear now.

I often make this kind of silly mistakes, I need to read more carefully.

Thanks again!
Founder
Joined: 18 Apr 2015
Posts: 13908
GRE 1: Q160 V160
Followers: 314

Kudos [?]: 3680 [0], given: 12931

Re: 10! is divisible by 3x5y, where x and y are positive integer [#permalink]  09 Mar 2019, 09:56
Expert's post
Re: 10! is divisible by 3x5y, where x and y are positive integer   [#permalink] 09 Mar 2019, 09:56
Display posts from previous: Sort by