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Number Properties

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Source: — Data Sufficiency |
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by adthedaddy » Sat Aug 25, 2012 5:20 am
Case-1:
We get x=-2 or x=3

5x-25 = 5(x-5) i.e. ODD x ______
We do not get a unique ans when we take the above solutions. So this is NOT SUFFICIENT

Case-2:
We do not get a unique value as there are odd as well even nos which are not a factor of 10.
NOT SUFFICIENT

Combined

As '2' is a factor of 10, take only x=3 as the solution.
Substituting x=3 in 5x-25 we get a confirmed reply as 'NO'.
Thus, SUFFICIENT

Ans: Option C

Plz confirm OA.
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by neelgandham » Sat Aug 25, 2012 5:44 am
As '2' is a factor of 10, take only x=3 as the solution.

2 is a factor of 10 but -2 isn't. So, I think the answer to the question is E and not C.
What is the answer to the question ? 'What are the factors of 10?"
Is it '1,2,5,10' or '-10,-5,-2,-1,1,2,5,10' ? For me it is the former.

Please correct me if I am wrong!

p.s: Post # 900!
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by Brent@GMATPrepNow » Sat Aug 25, 2012 7:34 am
shivanigs wrote: Is 5x -25 odd?
(1)(x+2)(x-3)= 0
(2)x is not a factor of 10.
Target question: Is 5x -25 odd?
Notice that, for 5x-25 to be odd, 5x must be even (since even-odd=odd)
So, we can reword our target question as: Is 5x even?

Statement 1: (x+2)(x-3)= 0
From this we can conclude that x=-2 or x=3
If x = -2, then 5x is even.
If x = 3, then 5x is not even.
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is not a factor of 10.
Well, there are lots of possible values of x that satisfy this condition. Here are two:
case a: x = 4, in which case 5x is even
case b: x = 3, in which case 5x is not even
Since we can't answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 + 2:
Statement 1 tells us that x = -2 or 3.
Statement 2 tells us that is not a factor of 10. This rules out the possibility that x= -2 (since -2 is a factor of 10), which means that x must equal 3.
If we know that x must equal 3, we can now answer the target question with certainty (no, 5x is definitely not even)
As such the combined statements are SUFFICIENT, and the answer is C

Cheers,
Brent
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by Brent@GMATPrepNow » Sat Aug 25, 2012 7:39 am
neelgandham wrote:
2 is a factor of 10 but -2 isn't.
What is the answer to the question ? 'What are the factors of 10?"
Is it '1,2,5,10' or '-10,-5,-2,-1,1,2,5,10' ? For me it is the former.

Please correct me if I am wrong!
Factors can be either positive or negative.

From the OG13:

If x and y are integers and x does not equal 0, then x is a divisor (factor) of y provided that y = xn for some integer n.

From this definition, we can see that -2 is a factor of 10, since we can express 10 as the product of -2 and some integer. That is 10 = (-2)(-5)

Having said that, most GMAT questions add language that restricts the factors (divisors) to positive values.

Cheers,
Brent
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