Maximum value of m for the expression to yield integer value

Expert replies

rohitacmilan: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri Apr 09, 2010 6:30 pmFollowed by: 1 member

by rohitacmilan » Tue Oct 15, 2013 11:32 pm

N is the product of multiples of 3 lying between 1 and 100. What is the maximum value of m for which the following expression N/(10^m) is an integer?

I really don't remember the answer choices. Apologies for that.

Source: Economist GMAT Tutor Simulation Test
It would be great if someone can help me with how to approach such questions and solve it in less than 2 mins.

Like this post

Source: Beat The GMAT — Problem Solving | Tue Oct 15, 2013 11:32 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Oct 16, 2013 12:02 am

N = 3 x 6 x 9 .... 99
= 3 ( 1x2x3...33) ==> 3.33!

Basically question is asking for the power of 10 in 33! .. so .

33/5 = 6
6/5 = 1

Answer {7}

Is m = 7?

R A H U L

Like this post

rohitacmilan: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri Apr 09, 2010 6:30 pmFollowed by: 1 member

by rohitacmilan » Wed Oct 16, 2013 12:20 am

I am not sure about the correct answer - you are right.
Now I recollect this approach that from one of Brent's post.

Thanks a ton

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Oct 16, 2013 12:22 am

rohitacmilan wrote:I am not sure about the correct answer - you are right.
Now I recollect this approach that from one of Brent's post.

Thanks a ton

you are welcome!

R A H U L

Like this post

Premalatha Anand: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Sep 25, 2013 9:38 am

by Premalatha Anand » Wed Oct 16, 2013 2:21 pm

theCodeToGMAT wrote:N = 3 x 6 x 9 .... 99
= 3 ( 1x2x3...33) ==> 3.33!

Basically question is asking for the power of 10 in 33! .. so .

33/5 = 6
6/5 = 1

Answer {7}

Is m = 7?

Didn't get it from 33/5 step.
Can you explain pls!

Regards
Premalatha

Like this post

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Oct 16, 2013 6:09 pm

Premalatha Anand wrote: Didn't get it from 33/5 step.
Can you explain pls!

To find power of the smallest factor in a number divide the number (without factorial) with that number.

In this question we want to find the power of 10 in 33!... 10 = 2 x 5 .. so by finding power of "5" we can conclude..

To find power of "5" in 33!.. keep on dividing 33 untill further division is not possible.

33/5 = 6 [we took 33 and not 33!]
6/5 = 1
1/5 = 0 [division not possible]

So, 6+1 = 7

R A H U L

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Oct 16, 2013 7:15 pm

Hi rohitacmilan,

This questions asks us for the MAXIMUM M for which N/(10^M) is an integer, so we're looking for the "powers of 10" that can be found by multiplying all of the multiples of 3 from 3 to 99: 3 x 6 x 9 x ......96 x 99. Sometimes a bit of "brute force" math is the easiest way to answer a Quant question.

We need to find all the multiples of 10 in that multiplication string.

The immediate multiples of 10: 30, 60, 90 that's three 0s

When you multiply a number that ends in 5 by an even number, you get a number that ends in a 0, so we have to factor those in as well:
15, 45 and 75
15 x 2 = 30
45 x 2 = 90
75 x 2 x 2 = 300
Here we have another four 0s.

Total = 3 + 4 = seven 0s.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review