enigma123
Are the integers z and f to the right of 0 on the number line?
(1) The product of z and f is positive.
(2) The sum of z and f is positive.
Target question: Are the integers z and f to the right of 0 on the number line?This is a good candidate for
rephrasing the target question. If z and f to the right of 0 on the number line, then that means
z and f are both POSITIVELet's now REPHRASE the target question....
REPHRASED target question: Are integers z and f both POSITIVE?Aside: the video below has tips on rephrasing the target question Statement 1: The product of z and f is positive. There are two possible scenarios that satisfy statement 1:
Case a: z and f are both positive. In this case, the answer to the REPHRASED target question is
YES, z and f are both POSITIVE Case b: z and f are both negative. In this case, the answer to the REPHRASED target question is
NO, z and f are not both POSITIVE Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The sum of z and f is positive.There are infinitely-many values of z and f that satisfy statement 2. Here are two:
Case a: z = 1 and f = 1. In this case, the answer to the REPHRASED target question is
YES, z and f are both POSITIVE Case b: z = -1 and f = 2. In this case, the answer to the REPHRASED target question is
NO, z and f are not both POSITIVE Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined From statement 1, we concluded that EITHER z and f are both positive OR z and f are both negative
If z and f are both positive, then the
sum of z and f will be POSITIVEIf z and f are both negative, then the
sum of z and f will be NEGATIVEStatement 2 tells us that The sum of z and f is positive.
AHA!
This means it must be the case that z and f are both positive
So, the answer to the REPHRASED target question is
YES, z and f are both POSITIVE Since we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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