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13 Oct 2021, 06:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
51% (01:46) correct
49%
(02:04)
wrong
based on 192
sessions
History
Date
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Not Attempted Yet
If x is odd, is x prime?
(1) The sum of the digits of x is 5
(2) x < 300
(1) The sum of the digits of x is 5
(2) x < 300
13 Oct 2021, 07:36
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Bunuel
Given: x is odd
Target question: Is x prime?
Statement 1: The sum of the digits of x is 5
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 23. In this case, the answer to the target question is YES, x is prime
Case b: x = 221. In this case, the answer to the target question is NO, x is not prime (since 221 = 13 times 17)
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < 300
There are several values of x that satisfy statement 2.
Important: Before we try identifying values of x that satisfy statement 2, it's always a good idea to see if we can RE-USE values we found for statement 1.
In this case, the same two numbers work. That is...
Case a: x = 23. In this case, the answer to the target question is YES, x is prime
Case b: x = 221. In this case, the answer to the target question is NO, x is not prime (since 221 = 13 times 17)
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Important: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED
In other words,
Case a: x = 23. In this case, the answer to the target question is YES, x is prime
Case b: x = 221. In this case, the answer to the target question is NO, x is not prime (since 221 = 13 times 17)
Since we still can't answer the target question with certainty, the combined statements are NOt SUFFICIENT
Answer: E
Cheers,
Brent
03 Nov 2021, 06:42
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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
