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13 Jul 2021, 04:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:19) correct
22%
(01:33)
wrong
based on 423
sessions
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Not Attempted Yet
If x/23 is a positive integer with a factor of 6, which of the following statements must be true?
I. x > 23
II. x has at least 3 prime factors
III. x is odd
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
I. x > 23
II. x has at least 3 prime factors
III. x is odd
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
13 Jul 2021, 04:43
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\(x = 23*6K\) {k is a positive integer }
\(x= 2*3*23*k\)
I. x > 23
True always
II. x has at least 3 prime factors
No of factors will be = > 2*2*2=8 i.e always greater than or equal to 8
III. x is odd
If k is even x will be even
Not true always
(D) is the correct answer IMO
\(x= 2*3*23*k\)
I. x > 23
True always
II. x has at least 3 prime factors
No of factors will be = > 2*2*2=8 i.e always greater than or equal to 8
III. x is odd
If k is even x will be even
Not true always
(D) is the correct answer IMO
13 Jul 2021, 05:09
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sumitkrocks
Your solution is perfect except at this one point, where you've answered something different from what they've asked. It's true that x must have at least 8 positive divisors in total, but they ask specifically about the prime factors of x. We know here that x has at least the three prime factors 2, 3 and 23, but we can't be sure it has any others. Still, II is true for sure.
