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

 It is currently 20 Oct 2019, 12:47

### 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

# If A = 2B, is A^4 > B^4?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58434
If A = 2B, is A^4 > B^4?  [#permalink]

### Show Tags

23 Jun 2016, 02:12
1
6
00:00

Difficulty:

75% (hard)

Question Stats:

47% (02:20) correct 53% (02:33) wrong based on 93 sessions

### HideShow timer Statistics

If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

_________________
Director
Joined: 04 Jun 2016
Posts: 556
GMAT 1: 750 Q49 V43
Re: If A = 2B, is A^4 > B^4?  [#permalink]

### Show Tags

23 Jun 2016, 02:43
If A = 2B, is A^4 > B^4?
A and B both can be positive or both can be negative. (Question stem )
(1) A^2 = 4B^2.
YES , If A=2B, squaring will give A^2=4B^2 (since it a square function, it will take care of any negative sign)

(2) 2A + B <A/2+B
2A<A/2
A/2>2A
A>4A => A is negative; so B is also negative.
A has a bigger magnitude than B
so A^4>B^4 (rasing a negative number to a even power will yield a positive number and since A is greater in magnitude its value after ^4 will be more than B)
YES

OPTION D is the answer

Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 228
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Re: If A = 2B, is A^4 > B^4?  [#permalink]

### Show Tags

23 Jun 2016, 04:12
LogicGuru1 wrote:
If A = 2B, is A^4 > B^4?
A and B both can be positive or both can be negative. (Question stem )
(1) A^2 = 4B^2.
YES , If A=2B, squaring will give A^2=4B^2 (since it a square function, it will take care of any negative sign)

(2) 2A + B <A/2+B
2A<A/2
A/2>2A
A>4A => A is negative; so B is also negative.
A has a bigger magnitude than B
so A^4>B^4 (rasing a negative number to a even power will yield a positive number and since A is greater in magnitude its value after ^4 will be more than B)
YES

OPTION D is the answer

Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

I think the answer is B. The reason is condition 1 fails for B = 0
_________________
Aiming for a 3 digit number with 7 as hundredths Digit
Math Expert
Joined: 02 Aug 2009
Posts: 7991
Re: If A = 2B, is A^4 > B^4?  [#permalink]

### Show Tags

17 Jul 2017, 09:41
4
Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

Hi..
$$A=2B.......A^4=16B^4$$...
is $$A^4 > B^4$$?
if A=B=0 ans is NO, otherwise YES

lets see the statements

(1) $$A^2 = 4B^2$$.
Nothing New .. already given from A=2B
insuff

(2) 2A + B < A/2 + B
$$\frac{3A}{2}<0$$..
so A is NOT equal to 0
suff

B
_________________
Intern
Joined: 15 Sep 2017
Posts: 23
GMAT 1: 750 Q50 V42
GPA: 3.5
Re: If A = 2B, is A^4 > B^4?  [#permalink]

### Show Tags

24 Feb 2018, 15:11
1
A = 2B, then the question is if 16B^4 > B^4?
B^4 is always positive and if B^4 ≠ 0, we can affirm that 16B^4 > B^4. But as B could be equal to Zero, we need to evaluate the statements

Statement 1:
A^2 = 4B^2
Well, the question stem gave the information that A = 2B so A^2 is 4B^2. We know that from the question stem and this statement doesn't help at all.

Statement 2:
2A + B < A/2 + B (rule out the Bs)
2A < A/2
2A - A/2 < 0
3A/2 < 0

So A is a negative number and ≠ than 0.
Statement 2 is sufficient to answer the question and affirm that 16B^4 > B^4!
_________________
"Revenge is a dish best served cold"
Re: If A = 2B, is A^4 > B^4?   [#permalink] 24 Feb 2018, 15:11
Display posts from previous: Sort by

# If A = 2B, is A^4 > B^4?

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

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