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02 Mar 2022, 06:30
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E
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72% (01:35) correct
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If a is a positive number, is 0.1 < a < 0.6?
(1) 6a/5 < 1/5
(2) 500a > 45
Are You Up For the Challenge: 700 Level Questions
(1) 6a/5 < 1/5
(2) 500a > 45
Are You Up For the Challenge: 700 Level Questions
02 Mar 2022, 06:48
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Bunuel
If a is a positive number, is 0.1 < a < 0.6?
(1) 6a/5 < 1/5
(2) 500a > 45
Given: a is a positive number (1) 6a/5 < 1/5
(2) 500a > 45
Target question: Is 0.1 < a < 0.6?
Statement 1: 6a/5 < 1/5
Multiply both sides of the inequality by 5 to get: 6a < 1
Divide both sides of the inequality by 6 to get: a < 1/6
Since 1/6 ≈ 0.1667, we can write: a < 0.1667
There are many values of a that satisfy statement 1. Here are two:
Case a: a = 0.15, in which case the answer to the target question is YES, a is between 0.1 and 0.6
Case b: a = 0.01, in which case the answer to the target question is NO, a is not between 0.1 and 0.6
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 500a > 45
Divide both sides of the inequality by 500 to get: a > 45/500
Simplify: a > 9/100
Convert to a decimal to get: a > 0.09
There are many values of a that satisfy statement 2. Here are two:
Case a: a = 0.15, in which case the answer to the target question is YES, a is between 0.1 and 0.6
Case b: a = 0.091, in which case the answer to the target question is NO, a is not between 0.1 and 0.6
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that a < 0.1667
Statement 2 tells us that a > 0.09
Combine the two inequalities to get: 0.09 < a < 0.1667
There are several values of a that satisfy BOTH statements. Here are two:
Case a: a = 0.15, in which case the answer to the target question is YES, a is between 0.1 and 0.6
Case b: a = 0.091, in which case the answer to the target question is NO, a is not between 0.1 and 0.6
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
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