Bunuel wrote:
Is 11x/23 < 7x/13 ?
(1) x is an integer.
(2) x > 0
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:Question Type: Yes/No. This type asks whether 11x/23 is less than 7x/13.
Given information from the question stem: You can think of the question stem as asking whether 11x/23 is less than 7x/13. 11/23 is slightly less than 1/2 and 7/13 is slightly more than 1/2. Since both numbers are multiplied by the same variable, x, it would appear that the answer will be “yes” 11x/23 is less than 7x/13, at least if x is a positive integer. However, if x is a negative number or a fraction it may not be the case.
Statement 1: “x is an integer.” With this information you know that x is not a fraction. However, x could still be negative. If x is negative then 7x/13 will be
“more negative” (further to the left on the number line) and therefore a smaller number than 11x/23 . This would give the answer of “no.” You can also get a “yes” from Statement 1 if x is a positive integer. For this reason Statement 1 is not sufficient. Eliminate choices A and D.
Statement 2: “x is positive.” This eliminates the possibility of x being negative (and also eliminates the possibility of x being 0, which would also have given a “no” answer to the question). However, Statement 2 does allow for x to be a noninteger—a fraction or decimal. Does it matter if x is a non-integer? It does not. Even if x is 1/2, 7x/13 will still be a larger number than 11x/23 . The number property at work in this question is “positive/negative” and the fact that x cannot be negative and cannot be zero is enough to ensure that the answer to the question is always yes” 11x/23 is smaller than 7x/13. This statement is sufficient and
the answer is B.
The important takeaways from this question: When a problem deals with the combination of inequalities and variables and/or when a statement specifically defines a variable as positive (>0) or negative (<0), be certain to check positive/negative number properties as part of your analysis.
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