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

It is currently 24 Sep 2018, 00:45

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

If wxy ≠ 0, does x = y ?

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

Hide Tags

Intern
Intern
avatar
Joined: 17 Jun 2013
Posts: 24
If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post Updated on: 08 Dec 2013, 06:40
5
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (01:17) correct 70% (01:01) wrong based on 236 sessions

HideShow timer Statistics

If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy

Originally posted by gmatgambler on 08 Dec 2013, 00:08.
Last edited by Bunuel on 08 Dec 2013, 06:40, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49364
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 08 Dec 2013, 06:40
4
3
If wxy ≠ 0, does x = y ?

wxy ≠ 0, means that neither of three is 0. The question asks whether x-y=0.

(1) w^x = w^y --> \(w^{x-y}=1\). Three cases:

\(w=1\) and \(x-y\) is any number;
\(w=-1\) and \(x-y=even\).
\(x-y=0\) and w is any number

Not sufficient.

(2) wxy ≠ xy --> since we know that \(xy\neq{0}\), then this statement implies that \(w\neq{1}\). Not sufficient.

(1)+(2) Since from (2) \(w\neq{1}\), then from (1) we are left with second and third cases. Not sufficient.

Answer: E.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 698
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 08 Dec 2013, 23:14
gmatgambler wrote:
If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy


Hello,

Given that w,x and y ≠ 0. we need to find whether x=y

From st 1, we have W^x=W^y

If W = 2 then x=y=2 then yes because different values of x=y will prove st1 to be insufficient in this case
Consider w=1, then x and y can have any values as 1^(Some Power) = 1 Hence no St 1 is not sufficient.
Consider w= -1 then x and y have same values for ex x=y=-3 or or x=-3 and y = -5.

Hence A and D ruled out

Consider st 2, we get w ≠1 still not sufficent....

Combining the 2 statements we get that there are still cases possible for w=-1 for which x ≠y and x=y

Ans E.

Actually if you look at st 2, it gives you ample hint to check for what values of w
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Manager
avatar
Status: Student
Joined: 26 Aug 2013
Posts: 207
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 26 Dec 2013, 02:13
The main example here is if you use W= -1

Than you will see that X=2 and Y=4 could be correct

Ans E
_________________

Think outside the box

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12444
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 31 Jan 2015, 13:37
1
Hi All,

This DS question can be solved by TESTing VALUES (although recognizing the built-in Number Properties would help make solving this problem easier).

We're told that WXY is not = 0, so NONE of those variables can = 0. We're asked if X = Y. This is a YES/NO question.

To start, it's interesting that this prompt has 3 variables, but the question focuses on just 2 of them. That almost always means that the third variable (in this case, the W) will play a role in defining the other two variables.

Fact 1: W^X = W^Y

Since the 'base' on both sides of this equation are Ws, it might be tempting to think that this X = Y. However, you have to be thorough with your thinking....

IF...
W = 2
X = 3
Y = 3
2^3 = 2^3 and the answer to the question is YES.

But what happens if W = 1 or W = -1? Do the exponents even matter at that point?

IF...
W = 1
X = 1
Y = 5
1^1 = 1^5 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: WXY is NOT = XY

This pinpoints one specific restriction about W....W CANNOT = 1. Unfortunately, it doesn't tell us anything about X and Y

IF....
W =2
X = 1
Y = 1
The answer to the questions is YES.

IF...
W = 2
X = 1
Y = 3
The answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
W^X = W^Y
W CANNOT = 1

IF....
W = 2
X = 3
Y = 3
2^3 = 2^3 and the answer to the question is YES.

IF....
W = -1
X = 1
Y = 3
(-1)^1 = (-1)^3 and the answer to the question is NO.
Combined, INSUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2889
Location: Canada
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 23 May 2018, 06:54
2
Top Contributor
gmatgambler wrote:
If wxy ≠ 0, does x = y ?

(1) w^x = w^y

(2) wxy ≠ xy


Target question: Does x = y?

Given: wxy ≠ 0

IMPORTANT: When I scan the two statements, I can see that this question is testing us on our knowledge about when we can conclude that two exponents are equal.
For statement 1, many students will conclude that, if w^x = w^y, then it must be true that x = y.
HOWEVER, this is true only if w does NOT equal 0, 1 or -1
For example, if 1^x = 1^y, we can't then conclude that x = y
Given all of this, we can jump straight to .....

Statements 1 and 2 combined
There are many values of w, x and y that satisfy BOTH statements. Here are two:
Case a: w = -1, x = 2 and y = 2. These values work because (-1)^2 = (-1)^2. In this case, the answer to the target question is YES, x = y
Case b: w = -1, x = 2 and y = 4. These values work because (-1)^2 = (-1)^4. In this case, the answer to the target question is NO, x does NOT equal y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Intern
Intern
avatar
B
Joined: 09 Mar 2018
Posts: 2
Location: India
Schools: Stern '21
GMAT 1: 650 Q47 V34
GPA: 3.2
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 23 May 2018, 20:48
Please explain where i am wrong:

According to condition 1:
=> w^(x-y) = 1
=> w^(x-y) * w = 1* w
=> w^(x-y+1) = w^1
=> x-y+1 = 1------ Comparing the powers as bases are same
Hence x=y

Can't we find the answer using condition 1 only?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12444
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If wxy ≠ 0, does x = y ?  [#permalink]

Show Tags

New post 23 May 2018, 21:05
1
Hi pushkar633,

Data Sufficiency questions 'test' a number of different skills (more than just 'math' skills), so you have to be thorough with your thinking - and make sure that you're considering all of the possibilities. When dealing with Fact 1 in this particular prompt, what if W = 1? In THAT situations, couldn't each of X and Y be almost anything (and by extension, is it possible that X and Y are NOT equal?)?

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

GMAT Club Bot
Re: If wxy ≠ 0, does x = y ? &nbs [#permalink] 23 May 2018, 21:05
Display posts from previous: Sort by

If wxy ≠ 0, does x = y ?

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.