SajjadAhmad wrote:

How many baseball cards do Keith, Pat, and Steve own in total?

(1) Keith and Pat together own half as many baseball cards as Steve does.

(2) Keith and Steve together own 109 baseball cards, and Pat and Steve together own 126 baseball cards.

We can let the number of cards Keith owns = k, the number Pat owns = p, and the number Steve owns = s. We need to determine k + p + s.

Statement One Alone:Keith and Pat together own half as many baseball cards as Steve does.

We can create the following equation:

k + p = (1/2)s

Thus k + p + s = (1/2)s + s = (3/2)s. However, since we do not know the value of s, we can’t determine the value of k + p + s. Statement one alone is not sufficient to answer the question.

Statement Two Alone:Keith and Steve together own 109 baseball cards, and Pat and Steve together own 126 baseball cards.

We can create the following two equations from statement two:

k + s = 109

and

p + s = 126

If we subtract one equation from the other, we have k - p = -17 or k = p - 17. Thus, Keith has 17 fewer baseball cards than Pat. However, since we do not know individual values of k, p, and s, we can’t determine the value of k + p + s. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:We can add the two equations from statement two to obtain the following:

k + p + 2s = 235

Since k + p = (1/2)s, we have:

(1/2)s + 2s = 235

(5/2)s = 235

s = 235 x 2/5 = 94

Since k + p = (1/2)s = 1/2 x 94 = 47, k + p + s = 47 + 94 = 141.

(Note: we could have stopped when we knew we had enough information to determine an answer).

Answer: C

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