|k| = 32 means that K = 32 or k = -32. |k+1|=31 means that k+1=31 -> k=30 or -k-1=31 -> k=-32. The two equations are simultaneously satisfied when k = -32. Thus, since 32 > -32, the answer is B.

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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I am a bit confused.

For |k+1| = 31 doesn't this mean:
k can equal 30 or k can equal -32?

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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The Question is structured incorrectly, there is no indication that the question is asking to solve for k, both equations are given independently. To correctly frame the question it should read as |K|=31 & |K+1|=31.... with linking & sign, without an & sign clearing the set of values K could be the answer should be "D", because K can be {31,32,-32}.

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.

Note that two equations given:
1) |k| = 32
From this you can say, either k = +32 or k = -32

2) |k+1| = 31
From this, you can say, either k = 30 or k = - 32

Note that k = -32 is unanimously extracted from both of the equations given,

Thus, k = -32

So, Choice B correct.
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