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

It is currently 19 Oct 2018, 21:28

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

For real numbers a and b, is it true that a = b?

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

Hide Tags

Current Student
avatar
B
Joined: 24 Jul 2016
Posts: 2
GMAT 1: 730 Q48 V42
GPA: 3.69
Reviews Badge
For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 25 Jul 2016, 18:25
6
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (00:20) correct 19% (00:28) wrong based on 172 sessions

HideShow timer Statistics

For real numbers a and b, is it true that a = b?

(1) a^4 = b^4
(2) a^5 = b^5
Manager
Manager
User avatar
Joined: 24 Apr 2014
Posts: 102
Location: India
Concentration: Strategy, Operations
GMAT 1: 730 Q50 V38
GMAT 2: 750 Q48 V45
GPA: 4
WE: Information Technology (Computer Software)
Reviews Badge
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post Updated on: 25 Jul 2016, 18:38
Real numbers are any number ....

By using both statements we can say c can be .. the answer

Bcz in B , a^5 = b^5

A can be 2^ 4/5. And b can be 4^ 2/5

But both ans will be same .


Thus we need both 1 and 2 to solve this question

C
Sent from my Le X507 using GMAT Club Forum mobile app
_________________

way to victory .....


Originally posted by Nick90 on 25 Jul 2016, 18:32.
Last edited by Nick90 on 25 Jul 2016, 18:38, edited 1 time in total.
Current Student
avatar
B
Joined: 24 Jul 2016
Posts: 2
GMAT 1: 730 Q48 V42
GPA: 3.69
Reviews Badge
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 25 Jul 2016, 18:33
Yes it is B. However I don't understand why.
Intern
Intern
avatar
Joined: 10 Jul 2016
Posts: 1
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 25 Jul 2016, 20:48
1) Since a and b are both raised to the fourth power, the answers will be positive. But, a could equal negative b. For example, a = 2, b = -2.
2) Since both are raised to the 5th power, a = b. For example, a = b = 2 OR a = b = -2.

Hope this is correct!
Senior Manager
Senior Manager
User avatar
V
Joined: 06 Jan 2015
Posts: 488
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 26 Jul 2016, 22:16
yudiwan wrote:
For real numbers a and b, is it true that a = b?

(1) a^4 = b^4
(2) a^5 = b^5


Bunuel Could you please explain it?
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 27 Jul 2016, 00:20
Senior Manager
Senior Manager
User avatar
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 270
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
GMAT ToolKit User Premium Member
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 27 Jul 2016, 02:27
1
Top Contributor
1
Nick90 wrote:
Real numbers are any number ....

By using both statements we can say c can be .. the answer

Bcz in B , a^5 = b^5

A can be 2^ 4/5. And b can be 4^ 2/5

But both ans will be same .


Thus we need both 1 and 2 to solve this question

C
Sent from my Le X507 using GMAT Club Forum mobile app


Nahh! not true. For example, by plugging in numbers.

St1: a^4 = b^4 --> if we plugin a = 2 & b =2 --> 2^4 = 2^4 --> 16 = 16 so right whenever a^4 is equal to b^4 then a will be equal to b .... but if one of them is negative number while other is positive, they yield the same result but in that case a is not equal to b --> a = 2, b = -2 --> 2^4 = (-2)^4 --> 16 = 16 hence a^4 = b^4 but a is not equal to b. Same result can be yielded for a^4 = b^4 whether +ve & -ve or +ve & +ve or -ve & -ve same numbers are plugged in which case either a can be equal to b or cannot be.

St1 alone Insufficient


St2: both a & b need to be same +ve numbers for a^5 to be equal to b^5 or both a & b be -ve numbers for a^5 to be equal to b^5. If one is +ve whereas the other is -ve then a^5 won't be equal to b^5 that's why for a^5 = b^5 either both a & b have to be +ve or -ve.

a^5 = b^5 --> plugin both +ve yet same number by having a = 2 , b = -2 --> 2^5 = 2^5 --> 32 = 32 hence a^5 = b^5.

And, now --> a^5 = b^5 --> plugin both -ve yet same numbers by having a = -2 , b = -2 --> (-2)^5 = (-2)^5 --> -32 = -32 hence a^5 = b^5.

What if a = 2 & b = -2 in which case they are not same then for a^5 = b^5 --> 2^5 = (-2)^5 --> 32 = -32 which can't be true hence a^5 can't be equal to b^5. Hence to get a^5 = b^5 we must have a = b.

St2 alone Sufficient

So, answer should be B

It is an easy question and I went into the detail so that it may be easy for others, who may be new to the forum, to understand otherwise answer provided by Bunuel was enough. :)
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 856
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 27 Jul 2016, 18:13
yudiwan wrote:
For real numbers a and b, is it true that a = b?

(1) a^4 = b^4
(2) a^5 = b^5


(1) a^4 = b^4
Four possible conditions:-
1) a=b=0
2) a=b
3) a= -b (even powers give +ve numbers)
4) -a=b
Not sufficient

(2) a^5 = b^5
three possible conditions:-

a=b=0
a=b
-a=-b
Sufficient

B is the answer
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Manager
Manager
avatar
B
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 27 Jul 2016, 20:34
The first thing to notice is that this is a yes/no question. We don't need to know exact values for a and b. We just need enough information to prove that a and be are the same.

Next, a very important difference between odd powers and even powers:

For every positive number, there are two numbers that can be raised to an EVEN power to yield that number. For example both 2 and -2 can can be squared to get 4. Similarly, both the positive 6th root of 732 and the negative 6th root of 732 can be raised to the 6th power to get 732.

However, for every number (both pos and neg), there is only one number that can be raised to an odd power to yield that number. For example, the only number we can raise to the 3rd power to get 27 is 3.

It's worth noting what this means for algebra. You CAN take an odd root of both sides of an equation. But you cannot reliably take an even root of both sides of an equation.

So the statements:

Statement 1) so both a and be lead to the same number when they are raised to an EVEN power. But a and b aren't necessarily the same number since one might be pos and the other might be neg. For example a could be 2 and b could be -2, but they also might both be 2. Insufficient.

Statement 2) both a and b yield the same number when they are raised to an ODD power. The only way this is possible is for a and b to be the same number. Sufficient.
Intern
Intern
avatar
B
Joined: 15 Jul 2018
Posts: 8
GMAT 1: 700 Q47 V39
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 28 Sep 2018, 02:47
Bunuel,

Could you please let me understand why in statement 2 we assume only the case when a=b like(+-1, +-1/2 and so on), what if a = 5th√(32^5), which gives us 32 and b = 2^5 which gives us again 32, thus a^5=b^5, while a=√(32^5) and b=2?

Thanks a lot
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 28 Sep 2018, 02:51
Gayluk wrote:
For real numbers a and b, is it true that a = b?

(1) a^4 = b^4 --> |a| = |b| --> a = b or a = -b. Nor sufficient.

(2) a^5 = b^5 --> a = b. Sufficient.

Answer: B.

Bunuel,

Could you please let me understand why in statement 2 we assume only the case when a=b like(+-1, +-1/2 and so on), what if a = 5th√(32^5), which gives us 32 and b = 2^5 which gives us again 32, thus a^5=b^5, while a=√(32^5) and b=2?

Thanks a lot


\(a=\sqrt[5]{32^5}=32\)
\(b=2^5=32\)

Doesn't a = b?
_________________

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

BSchool Forum Moderator
User avatar
S
Joined: 23 May 2018
Posts: 251
Location: Pakistan
GMAT 1: 770 Q48 V50
GPA: 3.4
Premium Member CAT Tests
For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 28 Sep 2018, 03:02
As real numbers could be both positive and negative,

(1) will be true even if the sign of both the numbers is different as it has an even power - INSUFFICIENT

(2) will be true only if the numbers have the same sign - SUFFICIENT

Answer is B
_________________

If you can dream it, you can do it.

Practice makes you perfect.

Kudos are appreciated.

Intern
Intern
avatar
B
Joined: 15 Jul 2018
Posts: 8
GMAT 1: 700 Q47 V39
Re: For real numbers a and b, is it true that a = b?  [#permalink]

Show Tags

New post 28 Sep 2018, 03:12
Bunuel,

yes, that is true. Sorry, don't know why I made this simple question look overcomplecated for me. I was thinking like what if a=√(32^5) (which is 32^5/2), and when we have a^5 we actually have (√(32^5))^5 (which is 32^25/2) here is my mistake, I thought (√(32^5))^5 = just 32 , which can be rewritten as 2^5 (then I have a =√(32^5) and b=2, whcih is not equal to a)

Thank you!
GMAT Club Bot
Re: For real numbers a and b, is it true that a = b? &nbs [#permalink] 28 Sep 2018, 03:12
Display posts from previous: Sort by

For real numbers a and b, is it true that a = b?

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


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®.