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

 It is currently 26 Jun 2019, 04:14

### 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

# 5(2^4)(3^32) =

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4488

### Show Tags

16 Jan 2015, 11:33
4
8
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:50) correct 35% (02:24) wrong based on 158 sessions

### HideShow timer Statistics

$$5(2^4)(3^{32})$$ =
(A) $$5(6^{36})$$
(B) $$(10^4)(3^{32})$$
(C) $$(3^{34}) + (3^{32})$$
(D) $$(3^{35}) - (3^{33})$$
(E) $$(3^{36}) - (3^{32})$$

For a set of challenging GMAT problems on exponents and roots, as well as the OE for this problem, see:
http://magoosh.com/gmat/2014/challengin ... and-roots/

Mike

_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 01 Jan 2015
Posts: 55

### Show Tags

16 Jan 2015, 11:58
E.
Ques - 5 X (2^4=16) X 3^32 = 80 X 3^32
E = 3^32 x (3^4 - 1) = 80 x 3^32
Retired Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 234
Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)

### Show Tags

16 Jan 2015, 13:11
1
IMO its E
firstly in now way we could use or modify 3^32
secondly a trick of using negative remainder.
so i used 2^4 with 5.. though after spending 1 min on it that its 80 and hence divisible by 3^4 as negative remainder of -1
so its 81-1... which is needed to be used
now here i got confused between D AND E
i did eliminated D simply because of its odd powers which didn't gave much sense to me as its a 2mins time constraint.
so hence i arrived at E
81 is 3^4 so no use of odd powers else result would be negative elsewise.

this is my first time i solved a question and gave a bit explanation too.

kudos will entice me to work hard...
Retired Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 234
Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)

### Show Tags

17 Jan 2015, 10:09
Hello!
Another way out

5(2^4)(s^32)= 80(81^8)
as 3^4 is 81

80 can be written as 81-1
(81-1)(81^8)
(81^9)-81^8
3^36-3^32

Hence E
this is the simplest i could figured out

kindly share that binomial eq in imp for gmat?
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

### Show Tags

19 Jan 2015, 01:38
2
1
Answer = (E) $$(3^{36}) - (3^{32})$$

$$5 * 2^4 * 3^{32}$$

$$= 80 * 3^{32}$$

$$= (81 - 1) * 3^{32}$$

$$= 3^{36} - 3^{32}$$
_________________
Kindly press "+1 Kudos" to appreciate
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 410
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)

### Show Tags

01 Mar 2015, 04:36
Yep I also did it similarly.

Starting with the question stem:
5 * 2^4 * 3^32
5 * 2^1 * 2^3 * 3^32
10 * 2^3 * 3^32
80 * 3^32

Then moving on to the answer choices, A and B are relatively easy to eliminate. Plus, the fact that we see additions and subtractions should alert as to the possibility of taking a common factor and creating a multiplication as an effect.

I started witd D which resulted in 3^33 * 8. Close, but not what I was looking for. So I moved to E, which results in:
3^36 - 3^32
3^32 (3^4 - 1)
3^32 (81 - 1)
3^32 * 80, which is what we are looking for. So, ANS E
Intern
Joined: 22 Dec 2014
Posts: 34

### Show Tags

12 Jul 2015, 11:19
1
$$5 * 2^4 * 3^{32}$$

$$= 10*8 * 3^{32}$$

$$= (3^2 + 1)*(3^2-1) * 3^{32}$$

$$= (3^4 - 1) * 3^{32}$$

$$= 3^{36} - 3^{32}$$[/quote]

VP
Joined: 09 Mar 2018
Posts: 1003
Location: India

### Show Tags

12 Jan 2019, 07:51
1
mikemcgarry wrote:
$$5(2^4)(3^{32})$$ =
(A) $$5(6^{36})$$
(B) $$(10^4)(3^{32})$$
(C) $$(3^{34}) + (3^{32})$$
(D) $$(3^{35}) - (3^{33})$$
(E) $$(3^{36}) - (3^{32})$$

Quite an intriguing one.

$$5(2^4)(3^{32})$$ = 80 * $$(3^{32})$$

Now just browsing over the options you can get the value as E.
(A) $$5(6^{36})$$------------------------------------> 5* 2^{36} *3^36
(B) $$(10^4)(3^{32})$$-----------------------------> wont give 80
(C) $$(3^{34}) + (3^{32})$$-----------------------> wont give 80
(D) $$(3^{35}) - (3^{33})$$------------------------> wont give 80
(E) $$(3^{36}) - (3^{32})$$------------------------> took $$3^{32}$$ common, giving $$3^4$$- 1 =80

_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: 5(2^4)(3^32) =   [#permalink] 12 Jan 2019, 07:51
Display posts from previous: Sort by