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# GRE Math Challenge #2- (2^30 - 2^29)/2

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Director
Joined: 16 May 2014
Posts: 597
GRE 1: 326 Q165 V161
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GRE Math Challenge #2- (2^30 - 2^29)/2 [#permalink]  29 May 2014, 01:44
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

100% (01:12) correct 0% (00:00) wrong based on 13 sessions
Attachment:

2.JPG [ 19.04 KiB | Viewed 10129 times ]

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Intern
Joined: 16 Sep 2014
Posts: 1
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Kudos [?]: 2 [2] , given: 2

Re: GRE Math Challenge #2 [#permalink]  24 Oct 2014, 18:54
2
KUDOS
Quantity A

2^30 - 2^29/2
= 2^29(2^1 - 1)/2
= 2^29(2 - 1)/2
= 2^29(1)/2
= 2^29/2^1
= 2^28

Quantity B

2^28

[Reveal] Spoiler:
(C) The two quantities are equal
GRE Instructor
Joined: 10 Apr 2015
Posts: 666
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Kudos [?]: 503 [1] , given: 3

Re: GRE Math Challenge #2 [#permalink]  18 May 2015, 14:59
1
KUDOS
Expert's post
soumya1989 wrote:
Attachment:
2.JPG

My first (favorite) approach is the same as mclchu's.

However, I do have a second approach:
Let's use the technique of performing the same operation on each quantity. By the way, we have a free video on this strategy here: http://www.greenlighttestprep.com/module/gre-quantitative-comparison?id=1097

Quantity A: (2^30 - 2^29)/2
Quantity B: 2^28

Multiply both quantities by 2 to get:
Quantity A: 2^30 - 2^29
Quantity B: (2^28)(2^1) = 2^29

Add 2^29 to both quantities to get:
Quantity A: 2^30
Quantity B: 2^29 + 2^29

NOTE: adding the same quantity to itself is the same a multiplying that quantity by 2. For example, 7 + 7 = 2(7) and 11 + 11 = 2(11)
So, 2^29 + 2^29 = 2(2^29)

So, we get:
Quantity A: 2^30
Quantity B: 2(2^29) = (2^1)(2^29) = 2^30

[Reveal] Spoiler:
C

Cheers,
Brent
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Re: GRE Math Challenge #2   [#permalink] 18 May 2015, 14:59
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