32=|k|

31=|k+1|

Quantity A	Quantity B
k	32

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.
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Given that, |k| = 32
So, either k = +32 or k = -32

BUT,

Also given that:
|k+1| = 31
So, k cannot be 32, because otherwise, |k+1| would become 33, which is not the case.

Thus, k = -32

So, Choice B correct.
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Answer: B
32 = |k|
k = -32 or k = +32
31 = |k +1| if k = 32 then |k+1| equals 33 and if k = -32 |k+1| equals 31.
So K is -32.
B is bigger than A.

I think this question shouldn't be considered as hard!
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Whenever you see a number inside ||, you are looking for the number's absolute value which is basically the number's positive value. For example, in X = |-1|, x would be 1 since we want the absolute value of -1 which is 1. in Y = |6-10|, y would be 4 because 6-10 is -4 and the absolute value of -4 is 4.

For this question 32 =|k|, k could be either 32 or -32. for 31 to be equal |k+1|, k has to be -32 because -32+1 is -31 and the absolute value of -31 is 31. Remember, you can have a negative number inside || (ex |-10|. but once you pull out the number, THE NUMBER WILL ALWAYS BE POSITIVE.

Hope it helps.