GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Nov 2019, 19:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4357
GPA: 3.39
If x is a factor of positive integer y, then which of the following mu  [#permalink]

### Show Tags

17 Mar 2017, 02:35
6
00:00

Difficulty:

35% (medium)

Question Stats:

58% (01:06) correct 42% (01:01) wrong based on 217 sessions

### HideShow timer Statistics

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

_________________
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4468
Re: If x is a factor of positive integer y, then which of the following mu  [#permalink]

### Show Tags

17 Mar 2017, 11:05
4
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

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
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Director
Joined: 02 Sep 2016
Posts: 643
Re: If x is a factor of positive integer y, then which of the following mu  [#permalink]

### Show Tags

03 Apr 2017, 00:27
1
(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.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Manager
Joined: 26 Sep 2018
Posts: 56
Location: Sweden
Re: If x is a factor of positive integer y, then which of the following mu  [#permalink]

### Show Tags

27 Nov 2018, 07:49
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.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If x is a factor of positive integer y, then which of the following mu  [#permalink]

### Show Tags

26 Dec 2018, 06:32
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

$$y \ge 1\,\,{\mathop{\rm int}}$$

$$x\,\,{\mathop{\rm int}} \,\,\,,\,\,\,{y \over x} = {\mathop{\rm int}} \,\,\,\left( * \right)$$

$$?\,\,\,:\,\,\,{\rm{positive}}\,\,\left( {{\rm{always}}} \right)$$

$$\left( {\rm{A}} \right)\,\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{alternative}}\,\,{\rm{refuted}}$$

$$\left( {\rm{B}} \right)\,\,\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{alternative}}\,\,{\rm{refuted}}$$

$$\left( {\rm{C}} \right)\,\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 1,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{alternative}}\,\,{\rm{refuted}}$$

$$\left( {\rm{D}} \right)\,\,\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{alternative}}\,\,{\rm{refuted}}$$

The correct answer is (E), by exclusion.

POST-MORTEM:

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

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If x is a factor of positive integer y, then which of the following mu   [#permalink] 26 Dec 2018, 06:32
Display posts from previous: Sort by