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14 Apr 2023, 06:14
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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:
95%
(hard)
Question Stats:
36% (02:35) correct
64%
(02:47)
wrong
based on 53
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If x is a positive integer, is x a prime number?
(A) x - p = q - x = k, where p, q, and k are prime numbers.
(B) The total odd factor of 15k\(^3\) is 4, where k is a prime number.
(A) x - p = q - x = k, where p, q, and k are prime numbers.
(B) The total odd factor of 15k\(^3\) is 4, where k is a prime number.
14 Apr 2023, 09:29
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ChandlerBong
We can start with statement 2, as it is easier between the two statements.
Statement 2
(B) The total odd factor of 15k\(^3\) is 4, where k is a prime number.
15k^3 = 5 * 3 * k^3
We are given that 5*3*k^3 has four odd factors. As 5^1 and 3^1 will already have contributed four odd factors (1, 3, 5 and 15) k must be an even prime.
That is the value of k should be 2.
However, we don't know the value of x using this statement. Hence, the statement is not sufficient and we can eliminate B and D.
Statement 1
(A) x - p = q - x = k, where p, q, and k are prime numbers.
A trick to solve this question quickly is to take the value of k as 2 and evaluate whether the statement is sufficient. If we get a contradictory result using the value of k = 2, we can be sure that the combination of statements wouldn't work as well and we can directly mark E as the answer without having to evaluate the statements combined. If the statement leads to a concrete answer then the answer is A.
So, the statement can be re-phrased as
x - p = q - x = 2 ;where p, and q are prime numbers
Case 1:
x = 5 ; p = 3 and q = 7
5 - 3 = 7 - 5 = 2
In this case, x is a prime number.
Case 2:
x = 9 ; p = 7 and q = 11
9 - 7 = 11 - 9 = 2
In this case, x is a not prime number.
As we are getting contradictory answers, we can eliminate A and C directly.
Option E
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