If x is a factor of positive integer y, then which of the following mu

Question

If x is a factor of positive integer y, then which of the following must be positive?

A. x – y
B. y – x
C. 2x – y
D. x − 2y
E. y – x + 1

mikemcgarry · Accepted Answer

Dear SajjadAhmad , I'm happy to respond. :-)

This is an interesting question. Here, it's important to understand that, if P is a positive number, all the factors of P are less than P except for P itself. Every positive integer is a factor of itself and a multiple of itself. That's very important to understand. Here's a blog article: GMAT Math: Factors Here's a free lesson: Multiples For example, suppose y = 12. Then it could be true that x = 3 or that x = 12. Since the factor is sometimes smaller than the number, subtracting factor minus number would be negative. With the examples x = 3 and y = 12, we get (A) negative (B) positive (C) negative (D) negative (E) positive We eliminated three answer choices with that. Now, use x = 12 and y = 12. (B) negative (E) positive By POE, the answer must be (E). Does all this make sense? Mike :-)

Shiv2016 · Answer

(1) There is no mention in the question that the two integers are DISTINCT. That means they can be equal and thus resulting in zero (such as in option A and B) which is neither positive nor negative.

(2) This is true because every integer is a factor of itself and a multiple of itself (e.g. 2 is a factor of 2 and 2 is a multiple of 2 (2*1)).

(3) Also 1 is a factor of every integer and thus would yield a negative result in option C and D.

Thus the answer is option E.

pineapple123456 · Answer

I used substitution to solve the problem. Take x=3 and y=6. Take x=6 and y=6.

Either case, only e is positive.

fskilnik · Answer

y \ge 1\,\,{\mathop{m int}}

x\,\,{\mathop{m int}} \,\,\,,\,\,\,{y \over x} = {\mathop{m int}} \,\,\,\left( * ight)

?\,\,\,:\,\,\,{m{positive}}\,\,\left( {{m{always}}} ight)

\left( {m{A}} ight)\,\,\,{m{Take}}\,\,\left( {x,y} ight) = \left( {1,1} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{alternative}}\,\,{m{refuted}}

\left( {m{B}} ight)\,\,\,\left( {{\mathop{m Re}
olimits} } ight){m{Take}}\,\,\left( {x,y} ight) = \left( {1,1} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{alternative}}\,\,{m{refuted}}

\left( {m{C}} ight)\,\,\,{m{Take}}\,\,\left( {x,y} ight) = \left( { - 1,1} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{alternative}}\,\,{m{refuted}}

\left( {m{D}} ight)\,\,\,\left( {{\mathop{m Re}
olimits} } ight){m{Take}}\,\,\left( {x,y} ight) = \left( {1,1} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{m{alternative}}\,\,{m{refuted}}

The correct answer is (E), by exclusion.

POST-MORTEM:

\left( {m{E}} ight)\,\,\,\left\{ \matrix{
 \,x < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y - x + 1\,\,\, > \,\,\,0 \hfill \cr 
 \,x > 0\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * ight)} \,\,\,\,\,{y \over x} = {\mathop{m int}} \,\, \ge 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,y \ge x\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,y - x + 1\,\,\, > 0 \hfill \cr} ight.

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Basshead · Answer

The key here is that a factor is a factor of itself.

For example, 20 is a factor of 20.

Knowing this, we can quickly arrive at the  answer E.

If x is a factor of positive integer y, then which of the following mu

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GMAT Problem Solving (PS) Questions

If x is a factor of positive integer y, then which of the following mu

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