This question has the following situation: "On December 1st, Adam weighed twice as much as Bob and Bob weighed 20 pounds less than Christy. If they gained 10 pounds during the month, which of the following must be true on January 1st?"

(I.) Adam weighs twice as much as Bob.
(II.) Bob weighs 20 pounds less than Christy.
(III.) Adam weighs more than Christy.

The correct answer is B (i.e. II only). I chose C (i.e. III only) because I thought Adam is twice as heavy as Bob, who is 20 pounds less than Christy. Adam is clearly heavier than Christy since he is double the weight of Bob.

I'm beginning to suspect that this question relates to the sufficient condition issue that I faced in previous questions. Could you please guide my through the reasoning process?

(I.) Adam weighs twice as much as Bob.
(II.) Bob weighs 20 pounds less than Christy.
(III.) Adam weighs more than Christy.

Dec 1
A = 2B
B = C-20

We can put them all in terms of B:
A = 2B
B = B
C = B + 20
Now, if we add 10 to all of these:
A+10 = 2B + 10
B+10 = B + 10
C+10 = B + 30

THe problem with the 3rd statement is that we don't have a value for B... So we don't know whether 2B + 10 is greater or whether B+20 is greater... If B is 10, for example, then Adam is 30 and Christy is 40. If B is 30, then Adam weighs 70 and Christy weighs 60.
On the other hand, we DO know that B+30 is 20 more than B+10.

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