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

 It is currently 10 Dec 2018, 22:54

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# If x, y, and z are all distinct positive integers and the percent

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 01 Nov 2013
Posts: 293
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

27 Mar 2016, 12:36
3
21
00:00

Difficulty:

95% (hard)

Question Stats:

19% (02:39) correct 81% (02:22) wrong based on 366 sessions

### HideShow timer Statistics

If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x?

(1) y is prime

(2) z = 9

_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

Math Expert
Joined: 02 Sep 2009
Posts: 51073
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

27 Mar 2016, 13:08
8
9
If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x?

The percent increase from x to y is equal to the percent increase from y to z: $$\frac{(y-x)}{x}*100 = \frac{(z-y)}{y}*100$$ --> $$xz = y^2$$ ($$0 < x < y < z$$)

(1) y is prime:

y = 2, then $$xz = 4$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 4.
y = 3, then $$xz = 9$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 9.
y = 5, then $$xz = 25$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 25.
y = 7, then $$xz = 49$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 49.
...

We can see a pattern there, in all cases x = 1. Sufficient.

(2) z = 9 --> $$9x = y^2$$. Case 1: x = 1 and y = 3; case 2: x = 4 and y = 6. Not sufficient.

_________________
##### General Discussion
Intern
Joined: 16 Mar 2015
Posts: 3
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

08 Jun 2016, 07:48
Hello Bunuel,

I couldnt understand why (0<x<y<z). We could have selected the values of x,y and z as 4,2 and 1 or 9,3 and 1. The percentage changes for the above 2 cases would be negative but the changes would be equal. It was based on these 2 different sets that I ruled out option A as a possibility.

Could you please suggest where I might be going wring?

Regards,
Amit
Math Expert
Joined: 02 Aug 2009
Posts: 7100
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

08 Jun 2016, 08:01
gmat_for_life wrote:
Hello Bunuel,

I couldnt understand why (0<x<y<z). We could have selected the values of x,y and z as 4,2 and 1 or 9,3 and 1. The percentage changes for the above 2 cases would be negative but the changes would be equal. It was based on these 2 different sets that I ruled out option A as a possibility.

Could you please suggest where I might be going wring?

Regards,
Amit

hi anit,

the Q stem talks of % increase - "the percent increase from x to y", so we cannot take % decrease by taking x>y>z....
_________________

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

GMAT online Tutor

Intern
Joined: 16 Mar 2015
Posts: 3
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

08 Jun 2016, 08:21
Oh right! My mistake! thanks a lot Chetan!
Math Expert
Joined: 02 Aug 2009
Posts: 7100
If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

04 Jul 2017, 16:52
3
sahilkak007@gmail.com wrote:
If x, y, z are all distinct positive integers and percent increase from x to y is equal to the percent increase from y to z , what is x?

1) y is a prime
2) z=9

Hi..

I would simplify for myself by taking same % increase as multiplication by same number

Although Q becomes a bit easier with finding value of x, I'll answer it if say we were to find value of y as it would be a bit more challenging.
For finding x as the Q presently states, statement I is sufficient as shown below. x will always be 1.
A

Say we were to find value of y
1) y is prime..
Starting with 1, I can find various combinations.
Say y is 2.... 1, 1*2, 2*2......1,2,4
Say y is 3.....1, 1*3, 3*3...... 1,3,9
Say y is 5......1,1*5,5*5.....1,5,25
Insufficient
2) z=9
Possible values..
1,3,9.....1,1*3,3*3
4,6,9....4,4*(1.5),6*(1.5)
Two possible ways..
Insuff

Combined..
ONLY 1,3,9 remains.
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

GMAT online Tutor

VP
Joined: 05 Mar 2015
Posts: 1004
Re: If x, y, z are all distinct positive integers and percent increase  [#permalink]

### Show Tags

04 Jul 2017, 18:10
sahilkak007@gmail.com wrote:
If x, y, z are all distinct positive integers and percent increase from x to y is equal to the percent increase from y to z , what is x?

1) y is a prime
2) z=9

simplifying the stem
as percent increase from x to y is equal to the percent increase from y to z

(y-x)/x = (z-y)/y
y^2-xy = xz-xy
y^2 = xz-------(given in stem)
so x=??

(1) if y =3
then x=1,z=9 or x=9 ,z=1
Not suff

(2) no info of other integers
clearly insuff..

Combined
z=9 and y is prime then,

y^2= x*9
as 9 = 3^2 = Prime ^2, then for x,any value but 1 leaves y not anymore a prime number
rather x=1 leaves y =3
i.e Y^2(3^2) = x(1) * 9(z)
thus x=1,y=3 ,z=9
suff

Ans C

sahilkak007@gmail.com
Intern
Joined: 06 Feb 2016
Posts: 3
Re: If x, y, z are all distinct positive integers and percent increase  [#permalink]

### Show Tags

04 Jul 2017, 20:10
Wrong;
Y= %increase* x= prime
Prime= no. itself * 1
Comparing both, since x and y are distinct, x can only be 1, hence statement 1 is sufficient
Current Student
Joined: 22 Sep 2016
Posts: 175
Location: India
GMAT 1: 710 Q50 V35
GPA: 4
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

05 Jul 2017, 02:53
Bunuel wrote:
If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x?

The percent increase from x to y is equal to the percent increase from y to z: $$\frac{(y-x)}{x}*100 = \frac{(z-y)}{y}*100$$ --> $$xz = y^2$$ ($$0 < x < y < z$$)

(1) y is prime:

y = 2, then $$xz = 4$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 4.
y = 3, then $$xz = 9$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 9.
y = 5, then $$xz = 25$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 25.
y = 7, then $$xz = 49$$, and since $$0 < x < y < z$$ and all of them are positive integers, then x = 1 and z = 49.
...

We can see a pattern there, in all cases x = 1. Sufficient.

(2) z = 9 --> $$9x = y^2$$. Case 1: x = 1 and y = 3; case 2: x = 4 and y = 6. Not sufficient.

Great approach, Bunuel
I have learnt so much from you!!
_________________

Desperately need 'KUDOS' !!

Intern
Joined: 16 Aug 2018
Posts: 28
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

### Show Tags

19 Aug 2018, 21:00
(y-x)/x=(z-y)/y
>> y^2=x*z
1. if y is prime, y^2 has only 3 factors 1,y,y^2.
since x<y<z, x must be 1
2. 3^2=1*9
3^6=3^4*3^2
Re: If x, y, and z are all distinct positive integers and the percent &nbs [#permalink] 19 Aug 2018, 21:00
Display posts from previous: Sort by