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

 It is currently 23 Feb 2019, 15:07

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x  [#permalink]

### Show Tags

09 Oct 2018, 01:56
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:05) correct 36% (01:39) wrong based on 34 sessions

### HideShow timer Statistics

If x, y and z are positive integers, is y − x > 0?

(1) y/x = z/y

(2) z > x

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 890
Re: If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x  [#permalink]

### Show Tags

09 Oct 2018, 02:16

1) let's use numbers to see the logic: say y=2. let's see if a "yes" answer is possible - that is, if y is larger than x: say x=1. This means 2/1=4/2 (z=4). definitely possible! now, is a "no" answer possible - can y-x<0? let's try: x=4. This means 2/4=1/2 (z=1). also possible!
we have found two contradicting answers, thus this data is insufficient - . eliminate answers A and D.
2) this tells us nothing about y, and thus nothing about the relationship between x and y, clearly insufficient - eliminate B

Combined: if z > x, then the second scenario we checked before (where y-x<o) is impossible, since it had z=1 and x=2. In fact, we can now see that any "no" answer will be impossible: if z>x, this means that z/x > 1, which means that the left side of the equation - y/x, must also be larger than 1: if y/x>1 ==> y - x >0 - sufficient! answer C.
_________________
VP
Joined: 31 Oct 2013
Posts: 1163
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x  [#permalink]

### Show Tags

09 Oct 2018, 02:18
Bunuel wrote:
If x, y and z are positive integers, is y − x > 0?

(1) y/x = z/y

(2) z > x

we are looking for the positive difference between y and x.

Statement 1: As we don't the order of these integers it is not possible to determine the difference. NOT sufficient.

Statement : z>x. but information about y. NOT sufficient.

Combining 1 and 2:

y/x = z/y

$$z= y^2 / x.$$

z>x

$$y^2/x >x$$
$$y^2>x^2.$$

we already know all these are integers.

thus, y -x >0.

Manager
Joined: 10 Jan 2013
Posts: 172
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
GPA: 3.95
Re: If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x  [#permalink]

### Show Tags

09 Oct 2018, 20:48
Bunuel wrote:
If x, y and z are positive integers, is y − x > 0?

(1) y/x = z/y

(2) z > x

Math Expert
Joined: 02 Aug 2009
Posts: 7335
If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x  [#permalink]

### Show Tags

09 Oct 2018, 21:09
1
saurabh9gupta wrote:
Bunuel wrote:
If x, y and z are positive integers, is y − x > 0?

(1) y/x = z/y

(2) z > x

Hi..

Info given
a) x, y and z are positive integers. SO you can cross multiply
b) is y-x>0..... or Is y>x?

(1) y/x = z/y..
$$\frac{y}{x} =\frac{z}{y}.........y^2=xz$$..
case I : if $$x<z$$, so $$z=x+a$$, where a is a positive number....
$$y^2=x(x+a)=x^2+ax$$.... now ax is positive, so $$y^2>x^2.......y>x$$ as y and x are positive
case II : if $$x>z$$, so $$z=x-a$$, where a is a positive number....
$$y^2=x(x-a)=x^2-ax$$.... now ax is positive, so $$y^2<x^2.......y<x$$ as y and x are positive
insuff

(2) z > x
insuff

combined..
case I of statement 1 is left
case I : if x<z, so z=x+a, where a is a positive number....$$y^2=x(x+a)=x^2+ax$$.... now ax is positive, so $$y^2>x^2.......y>x$$ as y and x are positive
so y>x....y-x>0
sufficient

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

If x, y and z are positive integers, is y−x>0? (1) y/x = z/y (2) z > x   [#permalink] 09 Oct 2018, 21:09
Display posts from previous: Sort by