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
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If k is negative, which of the following must also be negati
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alanforde800Maximus
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A
B
C
D
E
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Jay@ManhattanReview
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We are given that k is negative, and we have to find out which of the following must also be negative.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
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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Brent@GMATPrepNow
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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.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
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
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!
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Jeff@TargetTestPrep
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Since 1 less than a negative number will always be negative, k - 1, will always be negative.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
Answer: E
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