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28 Oct 2020, 02:06
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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:
5%
(low)
Question Stats:
93% (01:12) correct
7%
(01:37)
wrong
based on 61
sessions
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Not Attempted Yet
A positive integer X, divided by 7 has a remainder 2. Which of the following must be true?
I. X is odd
II. X cannot be a prime number
III. (X + 5) divided by 7 has remainder 0.
(A) I only
(B) I and II only
(C) III only
(D) I and III only
(E) I, II and III
I. X is odd
II. X cannot be a prime number
III. (X + 5) divided by 7 has remainder 0.
(A) I only
(B) I and II only
(C) III only
(D) I and III only
(E) I, II and III
28 Oct 2020, 04:17
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Sajjad1994
Taking values and solving will help
Statement I: Not True. 16 divided by 7 gives a remainder of 2. 16 is even.
Statement II: Not True. 2 divided by 7 gives a remainder of 2. 2 is prime.
Statement III: Always true True. Since the remainder is 2, adding 5 will get us to a number which is a multiple of 7.
Option C
Arun Kumar
28 Oct 2020, 06:15
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We can represent X as 7n+2. The important word here is "must" so if there exists a number for which the statement is false we can eliminate that option.
1) 2 is even. 7n will be even for all even values of n. Option 1 eliminated.
2) We can test for a few values of n=1,2,3 etc. For n=3 X=23 (Prime). Option 2 eliminated
3) X+5=7n+7 which will always be divisible by 7. Hence option 3 must be true.
Answer is C.
1) 2 is even. 7n will be even for all even values of n. Option 1 eliminated.
2) We can test for a few values of n=1,2,3 etc. For n=3 X=23 (Prime). Option 2 eliminated
3) X+5=7n+7 which will always be divisible by 7. Hence option 3 must be true.
Answer is C.
