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Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

Expert's post 00:00

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.

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

_________________
Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

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: 3907
Followers: 163

Kudos [?]: 4766  , given: 70

2
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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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_________________

Brent Hanneson – Creator of greenlighttestprep.com Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

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.
_________________ Manager Joined: 26 Jan 2018
Posts: 189
GRE 1: Q165 V156 Followers: 1

Kudos [?]: 136  , given: 3

1
KUDOS
In A, taking 2^29 common and solving would give same value as B

Hence they are both equal Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

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
Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

Expert's post
Thank you. Formatted in a better manner.

Regards
_________________ Intern Joined: 24 Jan 2019
Posts: 28
Followers: 0

Kudos [?]: 2  , given: 29

Which is greater 2^30 - 2^29/2 or 2^28 [#permalink]
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: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676  , given: 12912

Re: Which is greater 2^30 - 2^29/2 or 2^28 [#permalink]
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.

_________________
GRE Instructor Joined: 10 Apr 2015
Posts: 3907
Followers: 163

Kudos [?]: 4766 , given: 70

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
_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 19 Feb 2020
Posts: 28
Followers: 0

Kudos [?]: 1 , given: 1

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