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# 2^30-2^29/2

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

Question Stats:

85% (00:23) correct 14% (00:26) wrong based on 202 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

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Founder
Joined: 18 Apr 2015
Posts: 13357
Followers: 288

Kudos [?]: 3391 [0], given: 12192

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 $$2^{29} = 2^{29}$$

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Re: 2^30 - 2^29/2 [#permalink]  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

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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Kudos [?]: 3391 [0], given: 12192

2^30-2^29/2 [#permalink]  16 May 2018, 09:09
Expert's post
 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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Manager
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Re: 2^30-2^29/2 [#permalink]  16 May 2018, 09:22
1
KUDOS
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]  16 May 2018, 23:43
1
KUDOS
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]  17 May 2018, 04:09
Expert's post
Thank you. Formatted in a better manner.

Regards
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Which is greater 2^30 - 2^29/2 or 2^28 [#permalink]  24 Jan 2019, 20:45
1
KUDOS
 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
Founder
Joined: 18 Apr 2015
Posts: 13357
Followers: 288

Kudos [?]: 3391 [1] , given: 12192

Re: Which is greater 2^30 - 2^29/2 or 2^28 [#permalink]  27 Jan 2019, 03:47
1
KUDOS
Expert's post
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.

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Re: 2^30-2^29/2 [#permalink]  19 Feb 2020, 14:38
Expert's post
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

[Reveal] Spoiler:
C

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

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