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# 2^30 - 2^29/2

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Founder
Joined: 18 Apr 2015
Posts: 8120
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Kudos [?]: 1700 [0], given: 7473

2^30 - 2^29/2 [#permalink]  07 Sep 2017, 14:44
Expert's post
00:00

Question Stats:

74% (00:14) correct 25% (00:31) wrong based on 47 sessions
 Quantity A Quantity B $$\frac{2^{30} - 2^{29}}{2}$$ $$2^{28}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 7
Page: 114
Difficulty: medium
[Reveal] Spoiler: OA

_________________
Founder
Joined: 18 Apr 2015
Posts: 8120
Followers: 157

Kudos [?]: 1700 [0], given: 7473

Re: 2^30 - 2^29/2 [#permalink]  07 Sep 2017, 14:52
Expert's post
Explanation

In quantity A we can simplify as follow

$$\frac{2^{29}(2^1 - 1)}{2}$$. From this we do have $$\frac{2^{29}}{2}$$

At this point put $$\frac{2^{29}}{2}$$ = $$2^{28}$$. Cross multiply $$2^{29} = 2^{28} * 2$$

At the end, we do have $$2^{29} = 2^{29}$$

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 2386
Followers: 77

Kudos [?]: 2353 [1] , given: 33

Re: 2^30 - 2^29/2 [#permalink]  09 Sep 2017, 05:20
1
KUDOS
Expert's post
Carcass wrote:
 Quantity A Quantity B $$\frac{2^{30} - 2^{29}}{2}$$ $$2^{28}$$

Carcass' solution is probably how I would do this, but here's another approach:

Given:
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: (2^1)(2^28)

Simplify:
Quantity A: 2^30 - 2^29
Quantity B: 2^29

Quantity A: 2^30
Quantity B: 2^29 + 2^29

ASIDE: Quantity B features the sum of two identical values, which is the same as 2 times one value. For example, k + k = 2k, and 3w + 3w = (2)(3w)
So...

Simplify Quantity B to get:
Quantity A: 2^30
Quantity B: (2)(2^29)

Simplify again to get:
Quantity A: 2^30
Quantity B: 2^30

[Reveal] Spoiler:
C

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Re: 2^30 - 2^29/2   [#permalink] 09 Sep 2017, 05:20
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