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

 It is currently 16 Dec 2018, 19:26

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

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• 10 Keys to nail DS and CR questions

December 17, 2018

December 17, 2018

06:00 PM PST

07:00 PM PST

Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
• FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

x and y are two integers greater than 1. Is x^y greater than

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

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51229
x and y are two integers greater than 1. Is x^y greater than  [#permalink]

Show Tags

14 Feb 2014, 01:14
00:00

Difficulty:

95% (hard)

Question Stats:

44% (02:45) correct 56% (02:32) wrong based on 157 sessions

HideShow timer Statistics

$$x$$ and $$y$$ are two integers greater than 1. Is $$x^y$$ greater than 8?

(1) The sum of ANY two factors of $$x^2$$ is even.

(2) The product of ANY two factors of $$y^3$$ is odd.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51229
Re: x and y are two integers greater than 1. Is x^y greater than  [#permalink]

Show Tags

14 Feb 2014, 01:15
$$x$$ and $$y$$ are two integers greater than 1. Is $$x^y$$ greater than 8?

(1) The sum of ANY two factors of $$x^2$$ is even.

From this statement it follows that each factor of $$x^2$$ is odd: if even one factor were even, the sum of at least one pair of factors, 1 and that even factor, would be odd. Next, if all the factors of $$x^2$$ are odd, then $$x^2$$ is odd. For $$x^2$$ to be odd, $$x$$ must also be odd. The least value of $$x$$ is therefore 3 and since $$y$$ is greater than 1, then the least value of $$y$$ is 2. Thus the least value of $$x^y=3^2=9>8$$. Sufficient.

(2) The product of ANY two factors of $$y^3$$ is odd.

From this statement it follows that each factor of $$y^3$$ is odd: if even one factor were even, the product of at least one pair of factors would be even. Next, if all the factors of $$y^3$$ are odd, then $$y^3$$ is odd. For $$y^3$$ to be odd, $$y$$ must also be odd. The least value of $$y$$ is therefore 3 and since $$x$$ is greater than 1, then the least value of $$x$$ is 2. Thus the least value of $$x^y=2^3=8$$, but if $$y=odd>3$$, then $$x^y>8$$. Not sufficient.

Answer: A.
_________________
Manager
Joined: 04 Jan 2014
Posts: 117
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: x and y are two integers greater than 1. Is x^y greater than  [#permalink]

Show Tags

14 Feb 2014, 03:57
1
St1: The sum of ANY two factors of x^2 is even.

This means x is an odd integer. You can try by having x = 3, 5, 7, 9 etc. From stem, y can be 2 at a minimum. If x = 3 and y = 2, x^y = 3^2 = 9 so answer is yes to the stem question. Further, any combination of x and y will always have x^y > 8. Sufficient.

St2: The product of ANY two factors of y^3 is odd.

This means y is an odd integer. You can try by having y = 3, 5, 7, 9 etc. From stem, x can be 2 at a minimum. If x = 2 and y = 3, x^y = 2^3 = 8 so answer is no to the stem question. If x = 3 and y = 3, x^y = 3^3 = 27 so answer is yes to the stem question. Not sufficient.

Answer (C).

Answer (A). I hope I'm right.

p.s. I have edited my original answer.
Manager
Joined: 20 Dec 2013
Posts: 230
Location: India
Re: x and y are two integers greater than 1. Is x^y greater than  [#permalink]

Show Tags

03 Mar 2014, 21:41
Got A but took 5 minutes to get there!
S1 is basically saying x will be odd.Since x>1 and odd,x=3,5,7,9...
And least y=2
So x^y=9 (least value).Sufficient.

S2 is saying y is odd.This is not sufficient since x=2 or x=3 would give diff answers to the question.
Senior Manager
Joined: 06 Jul 2016
Posts: 368
Location: Singapore
Concentration: Strategy, Finance
Re: x and y are two integers greater than 1. Is x^y greater than  [#permalink]

Show Tags

21 Nov 2017, 11:50
Bunuel wrote:
$$x$$ and $$y$$ are two integers greater than 1. Is $$x^y$$ greater than 8?

(1) The sum of ANY two factors of $$x^2$$ is even.

S1) This statement means that x = odd
x = 3
$$x^2$$ = 9
Factors of 9 = 1,3,9
Sum of any factor is even.

=> Minimum value of x can be 3.
=> As per the question stem, minimum value of y can be 2.

$$x^y$$ = $$3^2$$ = 9 > 8

Sufficient.

Quote:
(2) The product of ANY two factors of $$y^3$$ is odd.

This statement means that y = odd
y = 3
$$y^3$$ = 27
Factors of 27 are 1,3,9,27. Product of any 2 factors is odd.

=> Minimum value of y can be 3.
If x = 2, then
$$x^y$$ = $$2^3$$ = 8
$$x^y$$ = 8

if x = 3, then
$$x^y$$ = $$3^3$$ = 27
$$x^y$$ > 8
Insufficient.

A is the answer.
_________________

Put in the work, and that dream score is yours!

Re: x and y are two integers greater than 1. Is x^y greater than &nbs [#permalink] 21 Nov 2017, 11:50
Display posts from previous: Sort by

x and y are two integers greater than 1. Is x^y greater than

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.