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

 It is currently 10 Dec 2018, 01:17

# Dec 10th is GMAT Club's BDAY :-)

Free GMAT Club Tests & Quizzes for 24 hrs to celebrate together!

### 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

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
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51057
If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

01 Sep 2015, 21:24
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:30) correct 26% (01:28) wrong based on 201 sessions

### HideShow timer Statistics

If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

_________________
Manager
Joined: 29 Jul 2015
Posts: 158
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

02 Sep 2015, 08:04
2
Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

$$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$
or $$4^{2x} + 4^{2x} + 4^{2x} + 4^{2x} = 4^{24}$$
or $$4(4^{2x}) = 4^{24}$$
or $$4^{2x+1} = 4^{24}$$

or $$2x+1 = 24$$
or $$2x = 23$$
or $$x = 11.5$$

Current Student
Joined: 09 Aug 2015
Posts: 84
GMAT 1: 770 Q51 V44
GPA: 2.3
If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

04 Sep 2015, 05:46
1
Make all the bases common, in this case you can choose 2 or 4.

I chose 2.

Then the equation becomes
$$2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}$$
Factor out $$2^{4x}$$ from left side, which becomes
$$2^{4x}(1+1+1+1) = 2^{48}$$
$$2^{4x}(4) = 2^{48}$$

Since 4 is just $$2^{2}$$and we can always add exponents of the same base in a product, left side can be rewritten as
$$2^{4x + 2}$$

So now $$4x + 2 = 48$$
$$4x = 46.$$

At this point you dont have to continue, see that the closest answers are 11.5 and 8. $$4*8$$ is clearly less than 46 => Answer must be E
Director
Joined: 21 May 2013
Posts: 653
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

04 Sep 2015, 07:07
1
Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

Now, 4^2x can be written as 2^2(2x)=2^4x
Therefore, (4)2^4x=2^48
2^4x+2=2^48
4x+2=48
4x=46
x=11.5
Intern
Joined: 12 Nov 2013
Posts: 40
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

05 Sep 2015, 09:41
1

Converting to common base of 2, we get 2^4x + 2^4x + 2^4x + 2^4x = 2^48

> Take 2^4x common: 2^4x (1+1+1+1) = 2^48

>2^4x (4) = 2^48

> 2^4x +2 = 2^48

> 4x + 2 = 48

> 4x = 46

> x = 11.5
_________________

Kindly support by giving Kudos, if my post helped you!

Math Expert
Joined: 02 Sep 2009
Posts: 51057
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

07 Sep 2015, 02:55
Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Here, you can note that you do a few things quite well with exponential terms:

Break their bases down to primes to get common bases. Multiply them.

So when you see a problem like this, you should recognize your strengths with exponents and look to rearrange the algebra to take advantage of them. Breaking the 4 terms down to prime factors (2), you get:

$$(2^2)^{2x} + 2^{4x} + (2^2)^{2x} + 2^{4x} = (2^2)^{24}$$

Then you can get back to multiplication to eliminate the parentheses:

$$2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}$$

Again, look for chances to do what you do well – and you know that if you can multiply the terms on the left instead of adding them, you’re then multiplying exponential terms with a common base…that’s your strength. In this problem, you may recognize quickly that you have four of the same term, and can express it as:

$$4(2^{4x}) = 2^{48}$$

Were the problem slightly more difficult, or you didn’t make that recognition, you might need to factor out the common exponential term so that you can multiply it that way:

$$2^{4x}(1+1+1+1)=2^{48}$$

$$2^{4x}(4) = 2^{48}$$

Either way, you end up with the same multiplication, which is what’s most important – now you’re doing what you do well.

$$4(2^{4x}) = 2^{48}$$

One more step is to, again, break down different bases into primes so that you can again multiply exponents. 4 = 2^2, so you have:

$$2^2(2^{4x}) = 2^{48}$$

And because you’re pretty quick when multiplying exponents of the same base, you should recognize that that can be expressed as:

$$2^{4x+2} = 2^{48}$$

Now that the bases are the same and the terms are set equal, you can note that:

$$4x+2 = 48$$

$$4x = 46$$

$$x = 11.5$$, and the answer is E.
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4271
Location: India
GPA: 3.5
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

28 Feb 2017, 07:58
Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

$$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$

Or, $$2^{4x} + 2^{4x} + 2^{4x} + 2^{4x} = 2^{48}$$

Or, $$2^{4x} ( 1 + 1 + 1 + 1 ) = 2^{48}$$

Or, $$2^{4x} *2^2 = 2^{48}$$

Or, $$2^{4x} = 2^{46}$$

Or, $$4x = 48$$

Or, $$x = 11.5$$

Thus, answer must be (E) 11.50
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4261
Location: United States (CA)
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

02 Mar 2017, 16:39
Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Let’s simplify the given equation:

4^2x + 2^4x + 4^2x + 2^4x = 4^24

2^4x + 2^4x + 2^4x + 2^4x = 2^48

2^4x(1 + 1 + 1 + 1) = 2^48

2^4x(4) = 2^48

2^4x(2^2) = 2^48

2^(4x + 2) = 2^48

4x + 2 = 48

4x = 46

x = 46/4 = 23/2 = 11.5

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 11 Aug 2016
Posts: 70
Location: India
Concentration: General Management, Finance
Schools: ISB '19, Rotman '19, IIM
GMAT Date: 02-04-2017
GPA: 3.6
WE: General Management (Other)
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

03 Mar 2017, 00:42
First Solution post on GMAT Club
Exited
Simplify and get
2^4x(2^2) = 2^48
Simplify this and get
4x+2 = 48
Simplify this and get 11.5

Bunuel wrote:
If $$4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^{24}$$, what is the value of x?

(A) 3
(B) 5
(C) 6
(D) 8.5
(E) 11.5

Kudos for a correct solution.

_________________

If you have any queries, you can always whatsapp on my number +91945412028
Ayush

Non-Human User
Joined: 09 Sep 2013
Posts: 9088
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x?  [#permalink]

### Show Tags

03 Sep 2018, 09:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If 4^{2x} + 2^{4x} + 4^{2x} + 2^{4x} = 4^24, what is the value of x? &nbs [#permalink] 03 Sep 2018, 09:13
Display posts from previous: Sort by