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

It is currently 17 Feb 2019, 10:03

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52906
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 10 Aug 2018, 00:23
2
20
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:40) correct 36% (02:04) wrong based on 420 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 10 Aug 2018, 01:03
2
1
1
What is the value of 2^x + 2^(-x) ?

\(2^x+2^{-x}=2^x+\frac{1}{2^x}\)
Square both sides..
\(2^{2x}+2^{-2x}+2=4^x+4^{-x}+2\)

(1) x < 0
Does not effect the equation at all..
Insufficient

(2) 4^x + 4^(−x) = 23
So \(4^x+4^{-x}+2=23+2=25\)
Our answer is √25=5
Sufficient

B
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

General Discussion
Intern
Intern
avatar
B
Joined: 17 Feb 2018
Posts: 1
Concentration: Finance, International Business
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 10 Aug 2018, 00:47
(1) Insufficient
(2)
4^x + 4^(-x) = 23
<=> [4^x + 4^(-x) + 2*2^x*2^(-x)] - 2*2^x*2^(-x) = 23
<=> (2^x + 2^(-x))^2 - 2*2^x*2^(-x) = 23
<=> (2^x + 2^(-x))^2 = 25 (Because 2^x*2^(-x) = 1)
<=> 2^x + 2^(-x) = 5
=> Sufficient
B
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
Premium Member
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post Updated on: 10 Aug 2018, 01:04
2
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)


St1:- x < 0

a) when x = -1, then \(2^x+2^{-x}=2^{-1}+2^{1}=\frac{1}{2}+2=\frac{5}{2}\)
b) when x=-2, then \(2^x+2^{-x}=2^{-2}+2^{2}=\frac{1}{4}+4=\frac{17}{4}\)

Insufficient.

St2:- \(4^x + 4^{−x} = 23\)
Now we have to find out a relation between question stem and statement(2), otherwise it is hard to determine question stem.
\((2^x+2^{-x})^2=2^{2x}+2*2^x*2^{-x}+2^{-2x}=(2^2)^x+2^{x+(-x)+1}+(2^2)^{-x}=4^x+2^1+4^{-x}=4^x+4^{-x}+2\)

So, \((2^x+2^{-x})^2=23+2=25\)
Or, \(2^x+2^{-x}=\sqrt{25}=5\)

N.B:- \(2^x+2^{-x}\) is always positive for all value of x. So, -5 is not acceptable.

Sufficient.

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine


Originally posted by PKN on 10 Aug 2018, 01:02.
Last edited by PKN on 10 Aug 2018, 01:04, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
P
Joined: 18 Jun 2018
Posts: 262
Premium Member CAT Tests
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 10 Aug 2018, 01:04
1
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)


OA: B
What is the value of \(2^x + 2^{-x}\) ?
or What is value of \(x\)?

(1) : \(x < 0\)
plugging \(x =-1\)
\(2^x + 2^{-x} = 2^{-1}+2^{1}= 0.5 + 2 =2.5\)
plugging \(x =-2\)
\(2^x + 2^{-x} = 2^{-2}+2^{2}= \frac{1}{4} + 4 = 0.25 + 4 = 4.25\)
We are not getting a unique value of \(2^x + 2^{-x}\)
So Statement 1 alone is not sufficient

(2) \(4^x + 4^{−x} = 23\)
Let \(2^x + 2^{-x}=y\)
Squaring both sides, we get
\((2^x + 2^{-x})^2=y^2\)
\((2^x)^2 +(2^{-x})^2 + 2(2^x)(2^{-x}) =y^2\)
\(2^x.2^x +2^{-x}.2^{-x} + 2 =y^2\)
\(4^x + 4^{−x} + 2 =y^2\)
\(23 + 2 =y^2\)
\(y^2=25 ; y=+5,-5\) (\(-5\) rejected as minimum value of \(2^x + 2^{-x}\) is \(2\) at \(x =0\))
using A.M≥ G.M
\(\frac{2^x + 2^{-x}}{2}≥\sqrt{{2^x * 2^{-x}}}\)
\(2^x + 2^{-x}≥2\)
So Statement 2 alone is sufficient
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1286
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 02:29
1
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)



statement two. detailed WRONG approach :grin: where did i go wrong guys ? can anyone comment please ? :-)

\(4^x + 4^{−x} = 23\)

\(2^{2x} + 2^{2 *(−x)} = 23\) equate bases

\(2x+(-2x) = 23\) now what ? :?

gmatbusters can you explain this for me please :-)
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1205
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 03:09
1
Your Query :
\(4^x + 4^{−x} = 23\)

\(2^{2x} + 2^{2 *(−x)} = 23\) equate bases

\(2x+(-2x) = 23\) now what ? :?- YOUR APPROACH IS INVALID, Even I am confused, what u did here :dazed

Response:

if a^b = a^c
then by equating base , we can say b = c
, ONLY IF
a is not equal to 0, 1, -1

for example: 1^4= 1^98, but 4 is not equal to 98.

dave13 wrote:
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)



statement two. detailed WRONG approach :grin: where did i go wrong guys ? can anyone comment please ? :-)

\(4^x + 4^{−x} = 23\)

\(2^{2x} + 2^{2 *(−x)} = 23\) equate bases

\(2x+(-2x) = 23\) now what ? :?

gmatbusters can you explain this for me please :-)

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1205
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 03:21
1
dave13

See the approach
Attachment:
WhatsApp Image 2018-08-12 at 16.48.05.jpeg
WhatsApp Image 2018-08-12 at 16.48.05.jpeg [ 75.32 KiB | Viewed 2698 times ]


Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1286
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 04:09
gmatbusters wrote:
dave13

See the approach
Attachment:
The attachment WhatsApp Image 2018-08-12 at 16.48.05.jpeg is no longer available


Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)


gmatbusters many thanks for explanation i have some tech questions :) can you please explain how you got values marked in green :-)
Attachments

WhatsApp%20Image%202018-08-12%20at%2016.48.05.jpeg_LI.jpg
WhatsApp%20Image%202018-08-12%20at%2016.48.05.jpeg_LI.jpg [ 454.13 KiB | Viewed 2655 times ]

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1205
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 04:34
1
dave13, I used it to complete the square formula.

See this, Here I have found the Square of the Expression in the Question stem,
you will find it easier.
Attachment:
WhatsApp Image 2018-08-12 at 18.00.58.jpeg
WhatsApp Image 2018-08-12 at 18.00.58.jpeg [ 87.79 KiB | Viewed 2640 times ]


dave13 wrote:
gmatbusters wrote:
dave13

See the approach
Attachment:
The attachment WhatsApp Image 2018-08-12 at 16.48.05.jpeg is no longer available


Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)


gmatbusters many thanks for explanation i have some tech questions :) can you please explain how you got values marked in green :-)

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior Manager
Senior Manager
User avatar
D
Joined: 22 Feb 2018
Posts: 419
CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 05:25
1
dave13 wrote:
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)



statement two. detailed WRONG approach :grin: where did i go wrong guys ? can anyone comment please ? :-)

\(4^x + 4^{−x} = 23\)

\(2^{2x} + 2^{-2x} = 23\) equate bases

\(2x+(-2x) = 23\) now what ? :?

gmatbusters can you explain this for me please :-)


dave13
\(2^{2x} + 2^{-2x} = 23\)

\(2^x*2^x +2^{-x}*2^{-x}= 23\)

\((2^x)^2+(2^{-x})^2=23\) .....(1)

Now Using \(a^2 +b^2 +2ab =(a+b)^2\)
\(a^2 +b^2 =(a+b)^2 - 2ab\)

here \(a = 2^x ; b =2^{-x}\)

\((2^x)^2+(2^{-x})^2 =(2^x + 2^{-x})^2 - 2*2^x*2^{-x} =(2^x + 2^{-x})^2 - 2*2^{x-x}=(2^x + 2^{-x})^2 - 2*2^0=(2^x + 2^{-x})^2 - 2\)

\((2^x)^2+(2^{-x})^2=(2^x + 2^{-x})^2 - 2\).........(2)

Substituting value of \((2^x)^2+(2^{-x})^2\) from (2) into (1) , we get

\((2^x + 2^{-x})^2 - 2=23\)

\((2^x + 2^{-x})^2=25\)

I hope it is clear now
_________________

Good, good Let the kudos flow through you

VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1286
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 06:54
Princ wrote:
dave13 wrote:
Bunuel wrote:
What is the value of 2^x + 2^(-x) ?

(1) x < 0
(2) 4^x + 4^(−x) = 23


NEW question from GMAT® Quantitative Review 2019


(DS05989)



statement two. detailed WRONG approach :grin: where did i go wrong guys ? can anyone comment please ? :-)

\(4^x + 4^{−x} = 23\)

\(2^{2x} + 2^{-2x} = 23\) equate bases

\(2x+(-2x) = 23\) now what ? :?

gmatbusters can you explain this for me please :-)


dave13
\(2^{2x} + 2^{-2x} = 23\)

\(2^x*2^x +2^{-x}*2^{-x}= 23\)

\((2^x)^2+(2^{-x})^2=23\) .....(1)

Now Using \(a^2 +b^2 +2ab =(a+b)^2\)
\(a^2 +b^2 =(a+b)^2 - 2ab\)

here \(a = 2^x ; b =2^{-x}\)

\((2^x)^2+(2^{-x})^2 =(2^x + 2^{-x})^2 - 2*2^x*2^{-x} =(2^x + 2^{-x})^2 - 2*2^{x-x}=(2^x + 2^{-x})^2 - 2*2^0=(2^x + 2^{-x})^2 - 2\)

\((2^x)^2+(2^{-x})^2=(2^x + 2^{-x})^2 - 2\).........(2)

Substituting value of \((2^x)^2+(2^{-x})^2\) from (2) into (1) , we get

\((2^x + 2^{-x})^2 - 2=23\)

\((2^x + 2^{-x})^2=25\)

I hope it is clear now


Princ many thanks for taking to to explain. i have one question: for instance this formula \(a^2 +b^2 +2ab =(a+b)^2\) i know, but this formula \(a^2 +b^2 =(a+b)^2 - 2ab\) i didnt know :)

can you please explain what is the relationship between these two formulas :-) \(a^2 +b^2 +2ab =(a+b)^2\) , \(a^2 +b^2 =(a+b)^2 - 2ab\) are these two different formulas ? :?

thank you:)
Senior Manager
Senior Manager
User avatar
D
Joined: 22 Feb 2018
Posts: 419
CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 12 Aug 2018, 07:04
1
Quote:
Princ many thanks for taking to to explain. i have one question: for instance this formula \(a^2 +b^2 +2ab =(a+b)^2\) i know, but this formula \(a^2 +b^2 =(a+b)^2 - 2ab\) i didnt know :)

can you please explain what is the relationship between these two formulas :-) \(a^2 +b^2 +2ab =(a+b)^2\) , \(a^2 +b^2 =(a+b)^2 - 2ab\) are these two different formulas ? :?

thank you:)


dave13

These are the same formula
as you know that
\(a^2+b^2+2ab = (a+b)^2\)

Substracting \(2ab\) from both sides,we get

\(a^2+b^2+2ab-2ab = (a+b)^2-2ab\)
\(a^2+b^2= (a+b)^2-2ab\)
_________________

Good, good Let the kudos flow through you

Manager
Manager
avatar
B
Joined: 29 Jul 2018
Posts: 107
Concentration: Finance, Statistics
GMAT ToolKit User CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 16 Oct 2018, 00:10
gmatbusters why 5 why not +- 5?
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1205
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23  [#permalink]

Show Tags

New post 16 Oct 2018, 00:20
Hi
If a is positive, than \(a^x\) can never be negative.
(Min value would tend to 0, when X is negative infinity.)
Hence\(2^x\) is always positive.
I hope it resolves your query. Feel free to tag me again.

manjot123 wrote:
gmatbusters why 5 why not +- 5?

_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

GMAT Club Bot
Re: What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23   [#permalink] 16 Oct 2018, 00:20
Display posts from previous: Sort by

What is the value of 2^x + 2^(-x) ? (1) x < 0 (2) 4^x + 4^(−x) = 23

  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®.