GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 19 Feb 2020, 20:01

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

x, y and p are integers, and xyp ≠ 0. If

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 07:09
1
Top Contributor
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:09) correct 52% (02:22) wrong based on 84 sessions

HideShow timer Statistics

x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above

_________________
Test confidently with gmatprepnow.com
Image
Manager
Manager
User avatar
S
Joined: 21 Jun 2019
Posts: 99
Location: Canada
Concentration: Finance, Accounting
GMAT 1: 670 Q48 V34
GPA: 3.78
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post Updated on: 14 Jul 2019, 09:16
Given: P^X<P^Y and XYP different than 0( could be +ve or -ve)

evaluation of choices:
i) x−y<0 for simplicity suppose P=2 x=3 y=4

P^X= 2^3=8< P^Y=2^4=16
x-y= 3-4=-1<0

now suppose P=-2 X=-3 and Y=-4

P^X= -2^-3= = -1/8< P^Y=-2^-4 = 1/16

x-y=-3-(-4)=1>0

statement 1 is excluded since for different values of xpy it gives different answers

ii) x<2y for x=3 and y=4 this equation is true, for x=-3 and y=-4 this equation is not true so we reject it.noting that the stem didnt mention that xyp should be positive integers so they could be both negative or positive

iii) x^p<y^p this one is true for all integer values of x,y,p whether they are positive or negtive

so correct answer is (C)

Originally posted by GeorgeKo111 on 14 Jul 2019, 08:47.
Last edited by GeorgeKo111 on 14 Jul 2019, 09:16, edited 1 time in total.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 09:14
1
Top Contributor
GeorgeKo111 wrote:

P^X= -2^-3= = -1/8< P^Y=-2^-4 = -1/16



Be careful; (-2)^-4 = 1/16 (not -1/16)
_________________
Test confidently with gmatprepnow.com
Image
Manager
Manager
User avatar
S
Joined: 21 Jun 2019
Posts: 99
Location: Canada
Concentration: Finance, Accounting
GMAT 1: 670 Q48 V34
GPA: 3.78
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 09:16
Quote:
Be careful; (-2)^-4 = 1/16 (not -1/16)


a typo man, thanks for pointing that out i will fix it

what do you think of my solution, is it correct? or i missed something?
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 09:17
Top Contributor
GeorgeKo111 wrote:
What do you think of my solution, is it correct? or i missed something?


You missed something.
Keep at it!
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5940
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post Updated on: 14 Jul 2019, 11:55
IMO E;
check with below case
x=1 and y=2 ; p = -3
x=-4 and y=-2 and p = -3
And
P=2 x=3 y=4

condition \(p^x < p^y\)

i) \(x - y < 0\)
yes for +ve integers and yes for -ve integers ; YES
No
ii) \(x < 2y\)
yes for +ve integers and may or may not for -ve integers ; NO

iii) \(x^p < y^p\)
No for +ve case ; yes for -ve integers case

GMATPrepNow ; hope this is correct :|


GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above

Originally posted by Archit3110 on 14 Jul 2019, 09:26.
Last edited by Archit3110 on 14 Jul 2019, 11:55, edited 5 times in total.
Intern
Intern
User avatar
S
Status: Classified
Joined: 19 Jun 2019
Posts: 33
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 09:37
GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above


Given:
  • \(x, y, p \in \mathbb{Z}_{>0}\)
  • \(x*y*z \ne 0\)
  • \(p^x<p^y\)

When inequalities contain integer exponents, one should always check the cases for both positive and negative integers.

If \((x, y, p) = (5, 3, -2)\), statement (i) isn't satisfied.
If \((x, y, p) = (5, 1, -2)\), statement (ii) isn't satisfied.
If \((x, y, p) = (5, 6, -2)\), statement (iii) isn't satisfied.

So, answer is E.
_________________
Best
Palladin
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 11:39
Top Contributor
Archit3110 wrote:
IMO A;
check with below case
x=1 and y=2 ; p = -3
x=-4 and y=-2 and p = -3

condition \(p^x < p^y\)

i) \(x - y < 0\)
yes for +ve integers and yes for -ve integers ; YES
ii) \(x < 2y\)
yes for +ve integers and may or may not for -ve integers ; NO

iii) \(x^p < y^p\)
No for -ve case ; yes for -ve integers case

GMATPrepNow ; hope this is correct :|


GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above


I'll give you a hint: Among the 3 answers given so far (A, C, E), one is correct :)
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5940
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 11:57
GMATPrepNow must say it's a very mind wrecking question.. took over 2 mins coz there was no limit on integers range had it been mentioned that integers are +ve then it would had been a bit easy ..

GMATPrepNow wrote:
Archit3110 wrote:
IMO A;
check with below case
x=1 and y=2 ; p = -3
x=-4 and y=-2 and p = -3

condition \(p^x < p^y\)

i) \(x - y < 0\)
yes for +ve integers and yes for -ve integers ; YES
ii) \(x < 2y\)
yes for +ve integers and may or may not for -ve integers ; NO

iii) \(x^p < y^p\)
No for -ve case ; yes for -ve integers case

GMATPrepNow ; hope this is correct :|


GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above


I'll give you a hint: Among the 3 answers given so far (A, C, E), one is correct :)


Posted from my mobile device
Manager
Manager
avatar
P
Joined: 15 Jul 2018
Posts: 197
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 11:58
Answer is option E?

Posted from my mobile device
Intern
Intern
User avatar
S
Status: Classified
Joined: 19 Jun 2019
Posts: 33
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post Updated on: 14 Jul 2019, 13:37
GMATPrepNow wrote:
Archit3110 wrote:
IMO A;
check with below case
x=1 and y=2 ; p = -3
x=-4 and y=-2 and p = -3

condition \(p^x < p^y\)

i) \(x - y < 0\)
yes for +ve integers and yes for -ve integers ; YES
ii) \(x < 2y\)
yes for +ve integers and may or may not for -ve integers ; NO

iii) \(x^p < y^p\)
No for -ve case ; yes for -ve integers case

GMATPrepNow ; hope this is correct :|



I'll give you a hint: Among the 3 answers given so far (A, C, E), one is correct :)


Look again, GMATPrepNow. Archit3110 changed their answer to E.
_________________
Best
Palladin

Originally posted by Palladin on 14 Jul 2019, 13:32.
Last edited by Palladin on 14 Jul 2019, 13:37, edited 1 time in total.
Intern
Intern
User avatar
S
Status: Classified
Joined: 19 Jun 2019
Posts: 33
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 13:36
Archit3110 wrote:
GMATPrepNow must say it's a very mind wrecking question.. took over 2 mins coz there was no limit on integers range had it been mentioned that integers are +ve then it would had been a bit easy ..



You need to find only one set of integers to eliminate each option. Isn't hard if you know number theory. Can be done within 2:30 minutes.
_________________
Best
Palladin
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5940
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 13:47
Palladin wrote:
Archit3110 wrote:
GMATPrepNow must say it's a very mind wrecking question.. took over 2 mins coz there was no limit on integers range had it been mentioned that integers are +ve then it would had been a bit easy ..



You need to find only one set of integers to eliminate each option. Isn't hard if you know number theory. Can be done within 2:30 minutes.

Palladin GMAT doesn't give luxury of time to solve in 2:30 mins..

Posted from my mobile device
Intern
Intern
User avatar
S
Status: Classified
Joined: 19 Jun 2019
Posts: 33
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 13:58
Archit3110 wrote:
Palladin wrote:
Archit3110 wrote:
GMATPrepNow must say it's a very mind wrecking question.. took over 2 mins coz there was no limit on integers range had it been mentioned that integers are +ve then it would had been a bit easy ..



You need to find only one set of integers to eliminate each option. Isn't hard if you know number theory. Can be done within 2:30 minutes.

Palladin GMAT doesn't give luxury of time to solve in 2:30 mins..



Archit3110, 2 minutes per question is an ideal rule. It cannot always be met. Sometimes you finish a question within a minute. Sometimes it takes longer than 2 minutes. More practical rule is to complete 10 questions in 20 minutes. See the 2 minutes per question as more of an average rate of question completion and less of an explicit deadline for each question.
_________________
Best
Palladin
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 14:28
Top Contributor
Archit3110 wrote:
GMAT doesn't give luxury of time to solve in 2:30 mins..


Surprisingly, the stats (based on 17 sessions) suggest the average time (thus far) is 1:36
100% correct?? Hmmm. :)
_________________
Test confidently with gmatprepnow.com
Image
SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2347
Concentration: Operations, Strategy
Schools: Erasmus '21 (M$)
Reviews Badge
x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 14 Jul 2019, 15:57
GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above


Example 1: Let p =-2, x=5, y=2...........-2^5 < -2^2

i) \(x - y < 0\)

From example 1 above, x >y.............Eliminate A & D

ii) \(x < 2y\)

From example 1 above, x >2y.............Eliminate B

Example 2: Let p =-1, x=3, y=4...........-1^3 < -1^4

iii) \(x^p < y^p\)

From example 1 above......3^-1 > 4^-1.............Eliminate C


Answer: E
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 15 Jul 2019, 06:33
Top Contributor
GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above


Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE

An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
------------------------------------
So, one solution to the inequality \(p^x < p^y\) is \(p = -1\), \(x = 7\) and \(y = 2\)
Plugging those values into the inequality, we get: \((-1)^7 < (-1)^2\)
Simplify to get: \(-1 < 1\), WORKS.

Now plug \(p = -1\), \(x = 7\) and \(y = 2\) into the three statements to get:

i) \(7 - 2 < 0\)
Simplify to get: \(5 < 0\)
NOT true.
So, statement i need not be true.

ii) \(7 < 2(2)\)
Simplify to get: \(7 < 4\)
NOT true.
So, statement ii need not be true.

iii) \(7^{-1} < 2^{-1}\)
Simplify to get: \(\frac{1}{7} < \frac{1}{2}\)
This is TRUE.
So, we can't (yet) conclude that statement iii need not be true.

-------------------------------------
Let's see if any other values will show that statement iii need not be true.

Another solution to the inequality \(p^x < p^y\) is \(p = -1\), \(x = 1\) and \(y = 2\)
Plugging those values into the inequality, we get: \((-1)^1 < (-1)^2\)
Simplify to get: \(-1 < 1\), WORKS.

Now plug \(p = -1\), \(x = 1\) and \(y = 2\) into statement iii to get:
iii) \(1^{-1} < 2^{-1}\)
Simplify to get: \(\frac{1}{1} < \frac{1}{2}\)
NOT true.
So, statement iii need not be true.

Answer: E

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1301
Location: India
Premium Member
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 15 Jul 2019, 15:33
I) is not true, when p<0, and x and y are positive odd integers
x=3 and y=1 and p=-2

II) is not true, when p<0, and x/y>2, where x and y are positive odd integers.
Can consider the same case as in statement I

III) is not true, when p is positive even integer, and x and y are negative integers.
p=4, x=-4 and y=-2



GMATPrepNow wrote:
x, y and p are integers, and xyp ≠ 0. If \(p^x < p^y\), which of the following MUST be true?

i) \(x - y < 0\)

ii) \(x < 2y\)

iii) \(x^p < y^p\)

A) i only
B) ii only
C) iii only
D) i and ii only
E) none of the above
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4331
Location: Canada
Re: x, y and p are integers, and xyp ≠ 0. If  [#permalink]

Show Tags

New post 16 Jul 2019, 05:45
Top Contributor
GMATPrepNow wrote:
Surprisingly, the stats (based on 17 sessions) suggest the average time (thus far) is 1:36
100% correct?? Hmmm. :)


Oops. I just realized that, when I delay the appearance of the official answer by 24 hours, all responses are deemed correct until the correct answer is displayed (now the success rate is 50%)

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: x, y and p are integers, and xyp ≠ 0. If   [#permalink] 16 Jul 2019, 05:45
Display posts from previous: Sort by

x, y and p are integers, and xyp ≠ 0. If

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne