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

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).

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)

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
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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

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.