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Data Sufficiency

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by shanice » Sat Apr 07, 2012 10:15 am
Hi all,

Please help me with the below data sufficiency question(Sources - Manhattan Gmat).

If x>1, what is the value of integer x?

(1)There are x unique factors of x.
(2)The sum of x and any prime number larger than x is odd.

Answer - A - Statement (1) is sufficient and Statement (2) is insufficient.

I'm having problem in understanding the first statement. What does it mean by "unique factors" in mathematical term?

Thank you.
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by rijul007 » Sat Apr 07, 2012 11:12 am
shanice wrote:Hi all,

Please help me with the below data sufficiency question(Sources - Manhattan Gmat).

If x>1, what is the value of integer x?

(1)There are x unique factors of x.
(2)The sum of x and any prime number larger than x is odd.

Answer - A - Statement (1) is sufficient and Statement (2) is insufficient.

I'm having problem in understanding the first statement. What does it mean by "unique factors" in mathematical term?

Thank you.

Unique factors of x refer to numbers that divide x with 0 as remainder rmainder..

For example..
4 has 3 unique factors => 1,2,4
12 has 6 unique factors=> 1,2,3,4,6,12

How to find the number of Unique factors of a number--
1)expand the given number into multiples of prime factors
12 = 2*2*3
2)increment the power on each prime factor by one
3)find the product of the values

eg.. 56
56 = 2^3 * 7^1
Number of unique factors = (3+1)(1+1) = 8


In this particualr question..
Statement 1-
implies taht value of x is 2

Statement 2-
Not sufficient

Option A
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by shanice » Sat Apr 07, 2012 8:21 pm
Thank you, Rijul. So, can I conclude that "unique factors" are generally division of two integers with zero remainder?
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by rijul007 » Sat Apr 07, 2012 9:05 pm
Unique factors are just factors which are different from each other. :-)
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by Shalabh's Quants » Sun Apr 08, 2012 4:11 am
Take Away--

If N is a composite no.,so it can be expressed as

N=a^x*b^y*c^z; where a, b& c are prime factors & x,y,z are +ive integers..

Then,Number of unique factors=(x+1)*(y+1)*(z+1).
Shalabh Jain,
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by shanice » Sun Apr 08, 2012 9:31 pm
What does this sentence mean then?

Every integer larger than 1 has a unique prime factorization
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by Anurag@Gurome » Sun Apr 08, 2012 9:43 pm
shanice wrote:What does this sentence mean then?

Every integer larger than 1 has a unique prime factorization
This is the fundamental theorem of arithmetic (or the unique-prime-factorization theorem). Let us take examples on this:
56 = 2^3 * 7, so here 56 is written as the product of prime numbers.
Similarly, 3,146 = 2 * 11^2 * 13. Here 3,146 is written as the product of prime numbers.

So, we can write any number greater than 1 as the product of prime numbers.
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by shanice » Mon Apr 09, 2012 4:11 am
Thank you, Sir. I understand it now.
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by Anurag@Gurome » Mon Apr 09, 2012 4:13 am
shanice wrote:Thank you, Sir. I understand it now.
You are welcome, Shanice.
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