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If k is negative, which of the following must also be negati

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by Jay@ManhattanReview » Sun May 13, 2018 8:41 pm
alanforde800Maximus wrote:If k is negative, which of the following must also be negative?


A) (-k)^2


B) (-1) k


C) 1 - k


D) k + 1


E) k - 1
We are given that k is negative, and we have to find out which of the following must also be negative.

Let's take each option one by one.

A) (-k)^2

=> [-(-|k|)]^2

=> [|k|]^2

=> A positive number.

B) (-1)k

=> (-1)*(-|k|)

=> |k|

=> A positive number.

C) 1 - k

=> 1 - (-|k|)

=> 1 + |k|

=> A positive number.

D) k + 1

=> -|k| + 1

=> A negative number + A positive number

The result can be positive or negative depending on the value of k.

If |k| > 1, the result is that k + 1 is a negative number; however, if |k| < 1, the result is that k + 1 is a positive number. This is not a must-be-true condition.

E) k - 1

=> -|k| - 1

=> A negative number. The correct answer.

The correct answer: E

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Mon May 14, 2018 7:51 am
alanforde800Maximus wrote:If k is negative, which of the following must also be negative?


A) (-k)^2


B) (-1) k


C) 1 - k


D) k + 1


E) k - 1
NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

So, beginning with E...

E) k - 1
If we think of the number line, we know that, since k is NEGATIVE, it lies to the LEFT of zero on the number line.
When we subtract 1, we move one unit (space) to the LEFT.
So, since k already lies to the left of zero on the number line, when we move one more space to the left, we will STILL BE left of zero on the number line
This means k-1 must be negative.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Mon May 14, 2018 11:11 am
A. (-k)^2 --> (+ve)^2 --> +ve.

B. (-1)k --> (-ve)*(-ve) --> +ve.

C. 1 - k --> 1 - (-ve) --> 1 + ve --> +ve.

D. k + 1 --> (-ve) + 1 --> Can be -ve or ve depending on value of k.

E. k - 1 --> (-ve) - 1 --> -ve - 1 --> always -ve.

Option E is the correct answer.

Regards!
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by [email protected] » Mon May 14, 2018 11:16 am
Hi alanforde800Maximus,

We're told that K is NEGATIVE. We're asked which of the following MUST also be NEGATIVE. This question can be solved by TESTing VALUES.

IF... K = -1

Answer A = (1)^2 = 1
Answer B = (-1)(-1) = 1
Answer C = 1 - (-1) = 2
Answer D = (-1) + 1 = 0
Answer E = (-1) - 1 = - 2

Final Answer: E

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hi

by Jeff@TargetTestPrep » Tue May 15, 2018 3:43 pm
alanforde800Maximus wrote:If k is negative, which of the following must also be negative?


A) (-k)^2


B) (-1) k


C) 1 - k


D) k + 1


E) k - 1
Since 1 less than a negative number will always be negative, k - 1, will always be negative.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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