Directions: Each GMAT Data Sufficiency proble...
Directions: Each GMAT Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.
For integers w, x, y, and z, is wxyz = -1?
(1) wx / yz = -1
(2) w = -1/x and y = 1/z
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked,and additional data are needed.
Directions: Each GMAT Data Sufficiency problem consists of a question ...
The correct response is (B). We can plug in these values for “w” and “y” in the original equation:
(-1/x)(x)(1/z)(z) = -1. The x’s and z’s cancel out so that we get: (-1)(1) = -1. The answer will always be “Yes” no matter what the actual values are for w, x, y, and z. This is sufficient.
If you chose (A), remember this is a Y/N question. The stem does not tell us any information about what numbers w, x, y, and z are. This is a great question to pick numbers! As long as we can choose two sets of numbers: one that gives us an outcomes of “Yes” and the other that gives an outcome of “No,” we know the statement is insufficient.
Let’s choose w = 1, x = 1, y = 1, and z = -1. These numbers satisfy the condition in Statement (1) and allow us the answer the question “Yes.” However, if we chose w = 2, x = 2, y = 2, and z = -2, we would answer the question “No.” Therefore, this Statement must be insufficient.
If you chose (C), you may not have realized that we could substitute the value in Statement (2) to simplify wxyz = -1. By doing this, we realize that for ALL integers, b and d will cancel out leaving us with (-1)(1) = -1, which is always true.
If you chose (D), you correctly saw that substitution allows Statement (2) to be sufficient, but Statement (1) is not sufficient. Depending on what integers we select for the variables we can make their product equal or not equal to -1.
If you chose (E), you missed that Statement (2) is sufficient once we substitute it into the original equation. Sometimes statements will be unexpectedly sufficient in this way on the GMAT, even though we don’t know the actual values for the variables!
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