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# If x>1, what is the value of integer x? 1) There are x

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If x>1, what is the value of integer x? 1) There are x [#permalink]

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10 Aug 2011, 18:45
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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.

The MGMAT book explains the answer as 1) S, 2) NS. They say that in order for statement one to be true, every integer between 1 and x, inclusive, must be a factor of x. By testing numbers, this holds true for 1 and 2, but not for 3 and 4. (Page 31 of the number properties guide if anyone cares to look).

Can someone please explain to me why this does not hold true for the numbers 3 and 4. Not sure what I am missing here.
[Reveal] Spoiler: OA
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Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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10 Aug 2011, 20:03
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jgonza8 wrote:
If x>1, what is the value of integer x?

x is an integer greater than 1.
What is the value of x ?

1) There are x unique factors of x.
This can happen for 2 only if x>1...because 2 has 2 factors - 1,2
All other values of x do not x unique factors -
example -
3 has only 1 unique factors (1,3) other than 3 itself because$$3 = 1*3$$
4 has only 2 unique factors (1,2) other than 4 itself because $$4 = 1*2^2$$
5 has only 1 unique factors (1,5) other than 5 itself because $$5 = 1*5$$
6 has only 3 unique factors (1,2,3) other than 6 itself because $$6 = 1*2*3$$
So A/D now

2) The sum of x and any prime number larger than x is odd.
Let us substitute...x will only be even value because odd - odd = even
2+5 = 7
4+5 = 9
So multiple values...So B is not sufficient.

So A will be the OA

The MGMAT book explains the answer as 1) S, 2) NS. They say that in order for statement one to be true, every integer between 1 and x, inclusive, must be a factor of x. By testing numbers, this holds true for 1 and 2, but not for 3 and 4. (Page 31 of the number properties guide if anyone cares to look).

Can someone please explain to me why this does not hold true for the numbers 3 and 4. Not sure what I am missing here.
Have explained above.

Tell if you are not clear.
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Last edited by krishp84 on 12 Aug 2011, 18:18, edited 2 times in total.
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Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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11 Aug 2011, 22:06
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the question asks what number is equal to the number of his unique factors. 1 has 1 unique factor so 1 is equal to the number of his unique factors. 2 is equal to the number of his unique factors.
3 has only 2 unique factors , 4 and 5 have 2, 11 only 2 and so on.

so the only numbers equal to their unique fators are 1 and 2 . the condition is that x>1 so only 2 applies.
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Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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11 Aug 2011, 22:15
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Why are you guys not considering the number itself as a factor?

To me:

4 has 3 unique factors (not 2) - 1,2,4
5 has 2 unique factors - 1,5
6 has 4 (not 3) unique factors - 1,2,3,6

It doesn't change the answer or anything, but the number itself is a unique factor. They weren't asking for the prime roots.
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Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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12 Aug 2011, 17:55
I understand it now!...I was reading it differently.
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Re: Odds and Evens - DS - Manhattan GMAT [#permalink]

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12 Aug 2011, 18:11
Sovjet wrote:
Why are you guys not considering the number itself as a factor?

To me:

4 has 3 unique factors (not 2) - 1,2,4
5 has 2 unique factors - 1,5
6 has 4 (not 3) unique factors - 1,2,3,6

It doesn't change the answer or anything, but the number itself is a unique factor. They weren't asking for the prime roots.

Yes - This is correct.....I had missed this...

And why does this not affect the answer ?
Because
Total number of unique factors for any number = 1 + Total number of unique factors other than the number
Adding 1 does not affect the count because we are any way comparing the (actual count - 1)

However my solution will be wrong if applied for larger numbers say 12
$$12 = 3 *2^2$$
Number of unique factors other than $$1 = (1+1)*(2+1) - 1 = 2*3 - 1 = 5$$

You can also calculate and confirm this :
Factors of 12 - 1,2,3,4,6,12
Factors of 12 other than 1 = 2,3,4,6,12
All are unique
Total number of such unique factors other than 1 = 5

So - Substitute smartly because this is a DATA SUFFICIENCY and NOT PROBLEM SOLVING question.
I am editing my post to correct this ....
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Re: Odds and Evens - DS - Manhattan GMAT   [#permalink] 12 Aug 2011, 18:11
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