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

 It is currently 24 Sep 2018, 02:42

### 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 6^y is a factor of (10!)^2, What is the greatest possible

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 6803
Re: If 6y is a factor of (10!)2 , what is the greatest possible value o  [#permalink]

### Show Tags

12 Feb 2017, 05:25
1
gupta87 wrote:
If
6^y is a factor of (10!)^2, what is the greatest possible value of y?

Ans is 8......kindly explain.........i understood there are 8 3s but there are 14 2s

Hi,

Since you already know there are 8 3s and 14 2s, I'll start from thereon...
Each 6 is composed of 3 and 2...
So it requires equal number of 3 and 2..

But (14-8) that is 6 of 2s do not have a 3 to make a 6..
Therefore the number of 6s will depend on the integer (3or2) with lowest value thus answer is 8..
_________________

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

GMAT online Tutor

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
If 6y is a factor of (10!)2 , what is the greatest possible value o  [#permalink]

### Show Tags

12 Feb 2017, 05:33
gupta87 wrote:
If
6^y is a factor of (10!)^2, what is the greatest possible value of y?

Ans is 8......kindly explain.........i understood there are 8 3s but there are 14 2s

Hey,

PFB the solution.

• $$6^y$$ can be written as $$2^y * 3^y$$

• To find the greatest possible value of y, we need to find out how many $$3$$'s are there in $$(10!)^2$$

• Now $$10! = 1 * 2 *3 * 4 * 5 * 6 * 7 * 8 * 9 * 10$$
• Which can be written as -
o $$10! = 2^8 * 3^4 * 5^2 * 7^1$$

• Therefore $$(10!)^2 = 2^{16} * 3^8 * 5^4 * 7^2$$
• As we can see there are 16 2's but only 8 3's

• But to make a $$6$$ we need both one $$2$$ and one $$3$$.

• Therefore, the maximum number of $$6$$'s that we can make is $$8$$.

Please note: that out of the 16 2's we can use only 8 of them and the rest 8 cannot be clubbed with any 3's, as there aren't any left.

• Hence, the value of y = $$8$$.

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Joined: 27 Jul 2017
Posts: 51
Re: If 6^y is a factor of (10!)^2, What is the greatest possible  [#permalink]

### Show Tags

03 Apr 2018, 07:57
Thanks Bunuel, though I was able to answer the question correctly I was adding the power of 3 twice to get the answer. But your explanation is correct we must square the power of 3 to get the correct answer.
_________________

Ujjwal
Sharing is Gaining!

Intern
Joined: 17 Jul 2018
Posts: 16
Re: If 6^y is a factor of (10!)^2, What is the greatest possible  [#permalink]

### Show Tags

09 Sep 2018, 14:01
Bunuel wrote:
mindmind wrote:
The tricky thing is limiting factor : 3...
Bunuel you made it look simple..
But is it really sub 600?

It's ~700 level question. Tag changed.

Veritas has it as a 600-650 question
Re: If 6^y is a factor of (10!)^2, What is the greatest possible &nbs [#permalink] 09 Sep 2018, 14:01

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

# If 6^y is a factor of (10!)^2, What is the greatest possible

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.