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

Question

(A) (-k)^2
(B) (-1)k
(C) 1 - k
(D) k + 1
(E) k - 1

PS05093

BrentGMATPrepNow · Accepted Answer

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

seed · Answer

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.

Answer: (E).

Hero8888 · Answer

Be aware if it is not mentioned that variable is integer it can be fraction/integer/irrational number
If you substitute -1/2 with all options, only E will give you negative number. Answer (E)

CrackverbalGMAT · Answer

In a must be true question on GMAT ,try to prove the answer choices false.

Eliminate answer choice A as squares are non negative

Eliminate answer choice B as a negative number multiplied with a negative number is negative

Option c can be eliminated as 1- k with k being negative will generate a non negative value

In option d, for k = -1/2, k + 1 = -1/2 + 1 = 1/2 (Eliminate)

(option e)

D.S
GMAT SME

ArnauG · Answer

If k is negative, we can determine the signs of the given expressions:

A) (-k)^2: When we square a negative number, it becomes positive. So, (-k)^2 is positive.

B) (-1)k: When we multiply a negative number (-1) by a negative number (k), the result is positive. So, (-1)k is positive.

C) 1 - k: Here, we subtract a negative number (k) from a positive number (1). When subtracting a negative number, it is equivalent to adding its positive value. So, 1 - k is positive.

D) k + 1: When we add a negative number (k) and a positive number (1), the result depends on the magnitudes. If the magnitude of k is greater than 1, the sum will be negative. However, if the magnitude of k is less than 1, the sum will be positive. Therefore, k + 1 can be positive or negative, depending on the value of k.

E) k - 1: Here, we subtract a positive number (1) from a negative number (k). When subtracting a positive number, it is equivalent to subtracting its positive value. So, k - 1 is negative.

Based on the analysis, the expression that must be negative when k is negative is E) k - 1.

DanTheGMATMan · Answer

Just work through top to bottom. Doesn't make a difference:

https://www.youtube.com/watch?v=du82tlwBVHE

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

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GMAT Problem Solving (PS) Questions

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

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