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2 questions

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Joined: 15 Feb 2009
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2 questions [#permalink]

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New post Updated on: 13 Jun 2009, 00:16
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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

the answer is 75


(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

The correct answer is D


Thank you

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Originally posted by MontrealGirl on 12 Jun 2009, 17:59.
Last edited by bb on 13 Jun 2009, 00:16, edited 1 time in total.
Converted to Math Symbols and hid the answer choices
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Schools: Haas School of Business
Re: 2 questions [#permalink]

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New post 12 Jun 2009, 19:01
1
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
\(\frac{5^2\times3}{5^2\times3}=1\)

\({5^2\times3}=75\)

Hence the answer is D.

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

http://www.math.com/school/subject1/les ... 3L1GL.html

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: 2 questions   [#permalink] 12 Jun 2009, 19:01
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