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# k is an integer

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Moderator
Joined: 18 Apr 2015
Posts: 5185
Followers: 77

Kudos [?]: 1040 [0], given: 4676

k is an integer [#permalink]  27 Nov 2017, 10:30
Expert's post
00:00

Question Stats:

62% (01:33) correct 37% (00:37) wrong based on 8 sessions
K is an integer for which

$$\frac{1}{2^{1-k}} < \frac{1}{8}$$

 Quantity A Quantity B k -2

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.
[Reveal] Spoiler: OA

_________________
Moderator
Joined: 18 Apr 2015
Posts: 5185
Followers: 77

Kudos [?]: 1040 [0], given: 4676

Re: k is an integer [#permalink]  27 Nov 2017, 11:47
Expert's post
Explanation

the most common strategy here is testing number. Picking a number and substitute to k and see what happens. This is true but is time-consuming.

The best way to attack the question is to manipulate the stem

$$2^{1-k} > 8$$

$$2^{1-k} > 2^3$$

$$1-k > 3$$

$$-k > 2$$

$$k < -2$$ which means that B is greater. Hence, B is the right answer
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GRE Instructor
Joined: 10 Apr 2015
Posts: 1244
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Kudos [?]: 1135 [1] , given: 7

Re: k is an integer [#permalink]  30 Nov 2017, 13:53
1
KUDOS
Expert's post
Carcass wrote:
K is an integer for which

$$\frac{1}{2^{1-k}} < \frac{1}{8}$$

 Quantity A Quantity B k -2

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.

Given: 1/[2^(1-k)] < 1/8

Since 2^(1-k) is POSITIVE for all values of k, we can safely take 1/[2^(1-k)] < 1/8 and multiply both sides by [2^(1-k)]
When we do this, we get: 1 < [2^(1-k)]/8
Rewrite 8 as follows: 1 < [2^(1-k)]/[2^3]
Since we have the same base, we can apply the quotient law to get: 1 < 2^(1 - k - 3)
In other words, 2^0 < 2^(1 - k - 3)
From this, we can conclude that 0 < 1 - k - 3
Simplify: 0 < -2 - k
Add k to both sides to get: k < -2

We get:
Quantity A: k (which is some number that's LESS THAN -2)
Quantity B: -2

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Re: k is an integer   [#permalink] 30 Nov 2017, 13:53
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