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Number Theory - Factors

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Number Theory - Factors

by ddg » Thu Apr 09, 2015 9:30 am
Please refer to the image :) Need a little help on this... Also posting my explanation along with it.
QUESTION:

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MY EXPLANATION:


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Please help me out on this..thanks!
Last edited by ddg on Fri Apr 10, 2015 2:49 am, edited 1 time in total.
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by [email protected] » Thu Apr 09, 2015 10:25 am
Hi ddg,

I'd like to know a few things about this question before I offer a solution:

1) What is the source of this question? Did it come from a GMAT book/website/CAT/etc or did it come from a math book(or equivalent)?
2) As a problem solving question, it should include 5 answer choices. What are they?

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by ddg » Thu Apr 09, 2015 9:03 pm
Hi, I am so sorry, I completely forgot to mention the source and the options :)

Source: Book on CAT prep - Demystifying the Number System 1st edition
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Options of the question

A) 39
B) 493
C) 439
D) 593
E) 539
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by ddg » Thu Apr 09, 2015 9:14 pm
Also, the answer is supposed to be 493
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Consider an example: 6 and 36 where 6 = n and 36 = n(square)
then 6 has the factors = 1, 2, 3, 6 (4 in number)
and 36 had the factors = 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 in number)
Now any of the factors of 6 are < 6 and hence we subtract those numbers or remove those numbers from the factors of n(square) -> we get 4, 9, 12, 18, 36 left.
Out of all of these factors, only 4 is < 6 that does NOT divide (specified according to qn to find factors < n that don't divide n).
So in an example such as this, we have only one factor.

Now considering that for this qn, n(square) has 59X35 factors = 2065 factors.
And n has 540 factors. So, subtracting them, the pool of factors we can choose from is = 2065 - 540 = 1525 factors. how do we know how many of these factors are less than n???????
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