Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 May 2017, 08:25

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

2 questions

Author Message
Intern
Joined: 15 Feb 2009
Posts: 12
Followers: 0

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

Show Tags

12 Jun 2009, 17:59
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

I have the answers, but it would be great if some one can explain to me.

If both $$5^2$$ and $$3^3$$ are factors of $$n * 2^5 * 6^2 * 7^3$$, what is the smallest possible positive value of n?

A) 25
B) 27
C) 45
D) 75
E) 125

[Reveal] Spoiler:

(I'm not good in questions asking about facots..does some one have a site of set of questions about factors so i can practice?
*********

How many different ways can 2 students be seated in a row of 4 desks, so that there is alwayes at least one emplty desk between the students?

A)2
B)3
C)4
D)6
E)12

[Reveal] Spoiler:

Thank you

Last edited by bb on 13 Jun 2009, 00:16, edited 1 time in total.
Converted to Math Symbols and hid the answer choices
Current Student
Joined: 03 Aug 2006
Posts: 115
Followers: 4

Kudos [?]: 265 [1] , given: 3

Show Tags

12 Jun 2009, 19:01
1
KUDOS
For the first one
Given
$$5^2$$ and $$3^3$$ are factors of $$n\times 2^5\times6^2\times7^3$$
Need to find the smallest value of n.

As $$5^2$$ and $$3^3$$ are factors of $$n\times 2^5\times6^2\times7^3$$,
$$n\times 2^5\times6^2\times7^3$$ should be either the Least common Multiple of the two or a multiple of the LCM itself. i.e. dividing $$n\times 2^5\times6^2\times7^3$$ by the LCM should result into an integer.

Lets find the LCM of the two:

$$5^2=5\times5$$
$$3^3=3\times3\times3$$

$$\text{LCM}=5\times5\times3\times3\times3=5^2\times3^3$$

Now
$$\frac{n\times 2^5\times6^2\times7^3}{5^2\times3^3}$$
should be an integer
$$=\frac{n\times 2^5\times2^2\times3^2\times7^3}{5^2\times3^3}$$
Reducing it further
$$= \frac{n\times 2^5\times2^2\times7^3}{5^2\times3}$$
for the fraction to be an integer n should be divisible by $${5^2\times3}$$. Ans the smallest value n can have is $${5^2\times3}$$.
As
$$\frac{5^2\times3}{5^2\times3}=1$$

$${5^2\times3}=75$$

Also here is a good overview of the basics of factors.

http://www.math.com/school/subject1/les ... 3L1GL.html
Re: 2 questions   [#permalink] 12 Jun 2009, 19:01
Display posts from previous: Sort by