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

It is currently 14 Oct 2019, 06:24

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

6^4− 4^4 = ?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58311
6^4− 4^4 = ?  [#permalink]

Show Tags

New post 05 Oct 2016, 03:13
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:23) correct 14% (01:36) wrong based on 225 sessions

HideShow timer Statistics

Most Helpful Expert Reply
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3990
Location: Canada
Re: 6^4− 4^4 = ?  [#permalink]

Show Tags

New post 05 Oct 2016, 06:37
5
Top Contributor
2
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040


Since the answer choices are quite spread apart, we can approximate.

NOTE: This technique relies on a nice trick that can come in handy in many cases. So, I urge that you learn it (it only takes 1 minute to learn). The technique is squaring numbers that end in 5 quickly in your head. You'll find the video at the bottom of this post.

6⁴ - 4⁴ = (6²)² - (4²)²
= (36)² - (16)²
≈ (35)² - (15)²
≈ 1225 - 225
≈ 1000

The only close answer choice is .....

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 578
Re: 6^4− 4^4 = ?  [#permalink]

Show Tags

New post 05 Oct 2016, 04:04
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040



We can write the above in terms of

(a+b) (a-b)

6^4−4^4= (6^2)2 - (4^2)2 = (6^2−4^2)*(6^2+4^2) =
(36−16)*(36+16) => 20*52 = 1040

IMO option E.
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1685
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge CAT Tests
6^4− 4^4 = ?  [#permalink]

Show Tags

New post 05 Oct 2016, 04:10
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040



\(6^4 - 4^4\)

= \((6^2)^2 - (4^2)^2\)

= \((6^2 + 4^2) (6^2 - 4^2)\)

= \((36+16) (6+4) (6-4)\)

= \((52) * (10) * (2)\)

= 1040 \((E)\)

\(OR\)

\(6^4 - 4^4\)

\(= (2 * 3)^4 - (2 * 2)^4\)

\(= 2^4 * 3^4 - 2^4 * 2^4\)

\(= 2^4 (3^4-2^4)\)

\(= 16 * (81-16)\)

\(= 16 * 65\)

\(= 1040 (E)\)

\(OR\)

\((6*6*6*6) - (4*4*4*4)\)

\(= 1296 - 216\)

\(= 1040\) \((E)\)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Senior Manager
Senior Manager
User avatar
G
Joined: 31 May 2017
Posts: 335
GMAT ToolKit User Reviews Badge
Re: 6^4− 4^4 = ?  [#permalink]

Show Tags

New post 03 Mar 2018, 12:52
6^4 -4^4

The options given makes this question easier to calculate.
The unit digits of 6^6 and 4^6 both ends in 6, so the difference between them end in 0. The only logical answer choice that ends in 0 is 1040.

Ans: E
_________________
GMAT Club Bot
Re: 6^4− 4^4 = ?   [#permalink] 03 Mar 2018, 12:52
Display posts from previous: Sort by

6^4− 4^4 = ?

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne