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If 2 + 5a – b/2 = 3c, what is the value of b?
(1) a + c = 13
(2) -12c = -20a + 4
Given: 2 + 5a – b/2 = 3c Let's make things a little easier and eliminate the fraction by multiplying both sides of the equation by 2 to get: 4 + 10a - b = 6c
Target question: What is the value of b?This is a good candidate for
rephrasing the target question.
We can take our equation, 4 + 10a - b = 6c, and solve for b to get: b = 10a - 6c + 4
REPHRASED target question: What is the value of 10a - 6c + 4?Aside: the video below has tips on rephrasing the target question Statement 1: a + c = 13 If we solve the equation for a, we get: a = 13 - c
Now replace a with 13 - c in the REPHRASED target question to get:
What is the value of 10(13 - c) - 6c + 4?Since we don't know the value of c, we can’t answer the
REPHRASED target question with certainty
Statement 1 is NOT SUFFICIENT
Statement 2: -12c = -20a + 4Multiply both sides of the equation by -1, to get: 12c = 20a - 4
Divide both sides of the equation by 2, to get: 6c = 10a - 2
Subtract 6c from both sides of the equation: 0 = 10a - 6c - 2
Add 2 to both sides of the equation: 2 = 10a - 6c
Now replace 10a - 6c with 2 in the REPHRASED target question to get:
What is the value of (2) + 4?So, the answer to the target question is
6Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
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