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22 May 2018, 04:28
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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:
25%
(medium)
Question Stats:
72% (01:09) correct
28%
(01:17)
wrong
based on 243
sessions
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If x is a positive integer, which of the following must be divisible by 3?
A. (x+1)(x+2)(x+4)
B. (x)(x+2)(x+3)
C. (x)(x+3)(x+6)
D. (x−1)(x)(x+1)
E. (x)(x^2)(x^3)
A. (x+1)(x+2)(x+4)
B. (x)(x+2)(x+3)
C. (x)(x+3)(x+6)
D. (x−1)(x)(x+1)
E. (x)(x^2)(x^3)
22 May 2018, 05:03
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Solution
Given:
• The number x represents a positive integer
To find:
• Out of the given options, which one must be divisible by 3
Approach and Working:
• If we consider any 3 consecutive positive integers, one of them must be a multiple of 3
- o Considering the options given, option D shows 3 consecutive integers (x – 1), x, and (x + 1)
Hence, the correct answer is option D.
Answer: D
Note: with some examples, we can negate the other options.
• If x = 3, then (x + 1) (x + 2) (x + 4) = 4 * 5 * 7 [not a multiple of 3]
• If x = 2, then (x) (x + 2) (x + 3) = 2 * 4 * 5 [not a multiple of 3]
• If x = 1, then (x) (x + 3) (x + 6) = 1 * 4 * 7 [not a multiple of 3]
• If x = 2, then \((x) (x^2) (x^3)\) = 2 * 4 * 8 [not a multiple of 3]
22 May 2018, 05:05
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Option D is 3 consecutive integers. Since x is a positive integer, the minimum value of x is 1.
Therefore option D will always be divisible by 3.
Hence D = (x−1)(x)(x+1) is the answer.
Therefore option D will always be divisible by 3.
Hence D = (x−1)(x)(x+1) is the answer.
