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22 Mar 2022, 01:30
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D
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Difficulty:
75%
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Question Stats:
52% (01:48) correct
48%
(01:43)
wrong
based on 222
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If x is a positive two-digit integer, is x divisible by 17 ?
(1) x is divisible by 7.
(2) x has exactly 3 unique prime factors.
Are You Up For the Challenge: 700 Level Questions
(1) x is divisible by 7.
(2) x has exactly 3 unique prime factors.
Are You Up For the Challenge: 700 Level Questions
22 Mar 2022, 07:01
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Bunuel
Given: x is a positive two-digit integer
Target question: Is x divisible by 17 ?
STRATEGY: Whenever there's a limited number of cases that satisfy a target question, it's useful to list all possible cases.
For this question, there are only five positive two-digit integers that are divisible by 17. They are: 17, 34, 51, 68, 85
This means we can rephrase the target question as follows...
REPHRASED target question: Does x equal 17, 34, 51, 68 or 85?
Aside: the video below has tips on rephrasing the target question
Statement 1: x is divisible by 7.
When we test 17, 34, 51, 68 and 85, we see that NONE of them are divisible by 7.
So, the answer to the REPHRASED target question is NO, x does not equal 17, 34, 51, 68 or 85
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x has exactly 3 unique prime factors.
Let's check all values in the set {17, 34, 51, 68, 85}
17 is prime. So, it has exactly 1 prime factor.
34 = (2)(17). So, 34 has exactly 2 unique prime factors (2 & 17)
51 = (3)(17). So, 51 has exactly 2 unique prime factors (3 & 17)
68 = (2)(2)(17). So, 68 has exactly 2 unique prime factors (2 & 17)
85 = (5)(17). So, 85 has exactly 2 unique prime factors (5 & 17)
So, the answer to the REPHRASED target question is NO, x does not equal 17, 34, 51, 68 or 85
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
VIDEO ON REPHRASING THE TARGET QUESTION:
General Discussion
22 Mar 2022, 19:28
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If x is a positive two-digit integer, is x divisible by 17 ?
To be divided by 17, x must be 17, 34, 51, 68 and 85. (We need to take two digit integers only)
Stat1: x is divisible by 7.
None of 17, 34, 51, 68 and 85 is divisible by 7. Sufficient
Stat2: x has exactly 3 unique prime factors.
None of 17, 34, 51, 68 and 85 has 3 unique prime factors, they have only two unique prime factors. Sufficient
So, I think D.
To be divided by 17, x must be 17, 34, 51, 68 and 85. (We need to take two digit integers only)
Stat1: x is divisible by 7.
None of 17, 34, 51, 68 and 85 is divisible by 7. Sufficient
Stat2: x has exactly 3 unique prime factors.
None of 17, 34, 51, 68 and 85 has 3 unique prime factors, they have only two unique prime factors. Sufficient
So, I think D.
