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26 Jan 2022, 09:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:39) correct
40%
(01:40)
wrong
based on 43
sessions
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If the digits of a three-digit positive number X are non-zero and distinct, is the sum of its digits equal to 10?
(1) The product of the digits of X is equal to 30
(2) Each digit of X is a prime number
(1) The product of the digits of X is equal to 30
(2) Each digit of X is a prime number
26 Jan 2022, 10:58
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Bunuel
Given: The digits of a three-digit positive number X are non-zero and distinct
Let X = abc, where a, b and c are the DIGITS of X.
Target question: Does a + b + c = 10
Statement 1: The product of the digits of X is equal to 30
30 = (2)(3)(5)
So, the three digits COULD be 2, 3 and 5 (e.g., X = 235), in which case the answer to the target question is YES, a + b + c = 10
However, the three digits COULD also be 1, 6 and 5 (e.g., X = 165), in which case the answer to the target question is NO, a + b + c does not equal 10
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Each digit of X is a prime number
Consider these two possible cases....
Case a: X = 235, in which case the answer to the target question is YES, a + b + c = 10
Case b: X = 237, in which case the answer to the target question is NO, a + b + c does not equal 10
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 the three digits (a, b and c) can be 2, 3 and 5 OR 1, 5 and 6
Statement 2 tells us that a, b and c are all prime numbers
Since both statements must be true, it must be the case that the three digits are 2, 3 and 5, which means the answer to the target question is YES, a + b + c = 10
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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