(8^16)+(16^13)+(4^24) = ? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 04:32

### 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 June
Open Detailed Calendar

# (8^16)+(16^13)+(4^24) = ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Apr 2012
Posts: 53
Concentration: Strategy
WE: Project Management (Consulting)
Followers: 0

Kudos [?]: 70 [0], given: 33

### Show Tags

28 Mar 2014, 20:46
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

64% (02:36) correct 36% (01:18) wrong based on 153 sessions

### HideShow timer Statistics

(8^16)+(16^13)+(4^24) = ?

A. (4)*(2^29+1)
B. (6)*(2^48)
C. (9)*(2^49)
D. (28)*(2^53)
E. 2^148
[Reveal] Spoiler: OA

_________________

--------------------------

"The will to win, the desire to succeed, the urge to reach your full potential..."

http://gmatclub.com/forum/powerscore-cr-notes-hope-that-someone-find-it-kudosofiable-174638.html#p1384561

Moderator
Joined: 02 Jul 2012
Posts: 1231
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 116

Kudos [?]: 1391 [1] , given: 116

### Show Tags

28 Mar 2014, 21:08
1
KUDOS
(8^16)+(16^13)+(4^24)

((2^3)^16)+((2^4)^13)+((2^2)^24)

(2^48)+(2^52)+(2^48)

(2^48)+((2^48)*(2^4))+(2^48)

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

(2^48)(2+2^4)

(2^48)*2*(1+2^3)

(2^49)(9)

_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Manager
Joined: 24 Apr 2012
Posts: 53
Concentration: Strategy
WE: Project Management (Consulting)
Followers: 0

Kudos [?]: 70 [0], given: 33

### Show Tags

28 Mar 2014, 21:21
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?
_________________

--------------------------

"The will to win, the desire to succeed, the urge to reach your full potential..."

http://gmatclub.com/forum/powerscore-cr-notes-hope-that-someone-find-it-kudosofiable-174638.html#p1384561

Manager
Joined: 01 Jan 2013
Posts: 67
Location: India
Followers: 0

Kudos [?]: 27 [1] , given: 131

### Show Tags

28 Mar 2014, 21:26
1
KUDOS
royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?[/quote]

(a^m)(a^n) = a^(m+n)

Eg. 2^3.2^2 = 2^5

However
a^m + a^n is not a^(m+n)
2^3 + 2^2 is not 2^5 (i.e 8 + 4 is not 32)
Intern
Joined: 03 Aug 2012
Posts: 20
Location: United States (OR)
GPA: 3.53
WE: Analyst (Entertainment and Sports)
Followers: 0

Kudos [?]: 12 [0], given: 8

### Show Tags

30 Mar 2014, 20:53
royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?

I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)

So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.

Here's how my brain works with this one,

Step 1: Recognize a common base.

(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)

Step 2: Recognize the factor and pull out of the equation.

= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)

(2^48)(18) = (2^48)(2)(9) = (2^49)(9)

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1935 [2] , given: 193

### Show Tags

31 Mar 2014, 18:11
2
KUDOS
$$8^{16} = 2^{48}$$

$$16^{13} = 2^{52}$$

$$4^{24} = 2^{48}$$

$$2^{48} + 2^{52} + 2^{48}$$

$$= 2^{49} + 2^{52}$$

$$= 2^{49} (1+8)$$

$$= 9 * 2^{49}$$

_________________

Kindly press "+1 Kudos" to appreciate

Director
Joined: 23 Jan 2013
Posts: 579
Schools: Cambridge'16
Followers: 1

Kudos [?]: 42 [0], given: 40

### Show Tags

31 Mar 2014, 20:18
royQV wrote:
Dear MacFauz

I do understand that C is the correct choice but can you please explain why e is wrong?[/quote]

You cannot just add exponents when you sum the same bases, in this case 2. If it was multiplying you could do so. Another rule which is useful here is that 2^48+2^48=2^49. Adding as much times as base (the same) and same exponent gives us the same base with +1 in exponent
Math Expert
Joined: 02 Sep 2009
Posts: 36596
Followers: 7093

Kudos [?]: 93419 [0], given: 10563

### Show Tags

01 Apr 2014, 01:12
royQV wrote:

I do understand that C is the correct choice but can you please explain why e is wrong?

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13497
Followers: 577

Kudos [?]: 163 [0], given: 0

### Show Tags

22 Aug 2015, 19:28
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.
_________________
Manager
Joined: 17 Nov 2013
Posts: 190
Followers: 0

Kudos [?]: 14 [0], given: 17

### Show Tags

24 Nov 2016, 09:35
In this question, the trick is to do the below

2^48 + 2^48 = 2^49

I did not know the above was possible before. I will remember this for future questions.
Attachments

Capture.PNG [ 338.49 KiB | Viewed 258 times ]

Re: (8^16)+(16^13)+(4^24) = ?   [#permalink] 24 Nov 2016, 09:35
Display posts from previous: Sort by