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Preptest Maths DS

by kvcpk » Thu Jun 10, 2010 8:35 am
If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors

(2)The difference of any two positive factors of n is odd.

OA is B

Please explain me how second statement alone is sufficient?

Let n be 12. it has 3,4 as factors. difference of 3,4 is odd.
Let n be 2, it has two factors 2,1.
2-1 =1 is also odd.
So for the same premise we are getting 2 answers(yes and No). Hence it is insufficient.

What is the mistake i am making?
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by albatross86 » Thu Jun 10, 2010 8:55 am
"The difference of ANY two positive factors of n is odd"

Remember, any two.

This means that if you were testing, say 12:

12 has the factors : 1, 2, 3, 4, 6, and 12

If you pick 1 and 3, or 3 and 12, you will get even differences. So (2) is violated.

Only an ( Even - Odd ) or ( Odd - Even ) can give you an Odd difference. This is an important number property for you to know.

This means that n has only 1 even and 1 odd factor, since if it had more than 1 of either of them you could pick 2 of the kind and get an even difference.

This is only true of the number 2 which has factors 1 and 2. Difference = 1

Hope that clears your doubt!
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by Patrick_GMATFix » Thu Jun 10, 2010 11:01 am
Hi kvcpk,

Is n=2?

1) exactly 2 factors --> n is prime. Could be 2, but could also be 3. NOT SUFFICIENT
2) Any two factors of n must have an odd difference:
  • n cannot be odd because two of its factors (n and 1) would have an even difference.
  • n cannot be an even greater than 2 because two if its factors (n and 2) would have an even difference.
  • n must be 2, because the difference between its only 2 factors (2 and 1) would be odd.
n=2. SUFFICIENT
[spoiler]
The answer is B[/spoiler]. A more detailed solution as well as a step by step video solution can be found at GMATPrep question 1017. Use the Drill Engine to generate similar questions in a timed drill. Set topic='Number Properties' and difficulty='700+'
  • Ask me about tutoring.
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by kvcpk » Thu Jun 10, 2010 1:07 pm
Patrick & albatross86

Thanks for the explanation. I understand it now. Was looking at the seond premise in a wrong way.

Praveen
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