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2^30-2^29/2

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2^30 - 2^29/2 [#permalink] New post 07 Sep 2017, 14:44
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Question Stats:

84% (00:23) correct 15% (00:29) wrong based on 236 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.


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

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Re: 2^30 - 2^29/2 [#permalink] New post 07 Sep 2017, 14:52
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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 \(2^{29} = 2^{29}\)

The answer is C.
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Re: 2^30 - 2^29/2 [#permalink] New post 09 Sep 2017, 05:20
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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

Add 2^29 to both quantities:
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

Answer:
[Reveal] Spoiler:
C


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2^30-2^29/2 [#permalink] New post 16 May 2018, 09:09
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Re: 2^30-2^29/2 [#permalink] New post 16 May 2018, 09:22
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In A, taking 2^29 common and solving would give same value as B

Hence they are both equal
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Re: 2^30-2^29/2 [#permalink] New post 16 May 2018, 23:43
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simplify qty A:
Take \(2^{29}\) common

\(\frac{2^{29}(2-1)}{2}\) this reduces to

\(\frac{2^{29}}{2^1}\)

when \(2^1\) goes into the numerator the expression further simplifies to:
\(2^{29} * 2^{-1} = 2^{28}\)

option C
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Last edited by Carcass on 17 May 2018, 04:09, edited 1 time in total.
Edited by Carcass
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Re: 2^30-2^29/2 [#permalink] New post 17 May 2018, 04:09
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Which is greater 2^30 - 2^29/2 or 2^28 [#permalink] New post 24 Jan 2019, 20:45
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Quantity A
Quantity B
\(\frac{2^{30} - 2^{29}}{2}\)
\(2^{28}\)


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

Last edited by Carcass on 27 Jan 2019, 03:40, edited 1 time in total.
Edited by Carcass
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Re: Which is greater 2^30 - 2^29/2 or 2^28 [#permalink] New post 27 Jan 2019, 03:47
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In the first quantity \(\frac{2^{29} * (2^1 - 1 )}{2}\)

This is the rule of a common factor.

Now, \(2^1\) is 2.

\((2-1) = 1\)

All the expression boils down to

\(\frac{2^{29}}{2}\) which is \(\frac{2^{28} * 2^1}{2}\)

Simplify the 2 we get indeed \(2^{28}\) which is equal to quantity B

The two quantities are equal.

C is the answer
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Re: 2^30-2^29/2 [#permalink] New post 19 Feb 2020, 14:38
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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, I 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

Answer:
[Reveal] Spoiler:
C


Cheers,
Brent
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Re: 2^30-2^29/2 [#permalink] New post 24 Feb 2020, 02:12
Thank you
Re: 2^30-2^29/2   [#permalink] 24 Feb 2020, 02:12
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