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If integer x is divisible by 3 which of the following is not divisible

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Joined: 02 Sep 2009
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If integer x is divisible by 3 which of the following is not divisible  [#permalink]

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New post 22 May 2018, 04:24
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

100% (00:49) correct 0% (00:00) wrong based on 56 sessions

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Joined: 30 May 2017
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Location: United States
Schools: HBS '21
GMAT 1: 690 Q50 V32
GRE 1: Q168 V164
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Re: If integer x is divisible by 3 which of the following is not divisible  [#permalink]

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New post 22 May 2018, 05:17
Bunuel wrote:
If integer x is divisible by 3, which of the following is not divisible by 3?

A. 6 − x
B. x + 9
C. 2x
D. 3x + 5
E. 4x − 6


Since x is a multiple of 3, any addition, multiplication or subtraction operation that is a multiple of 3 or multiple of x done to x, will ensure that the resultant answer is divisible by 3.

It is only option D that violates the condition above.

Hence option D = 3x + 5 is the answer.
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Re: If integer x is divisible by 3 which of the following is not divisible  [#permalink]

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New post 22 May 2018, 05:39

Solution



Given:
• The variable x is divisible by 3

To find:
• Which of the given options is not divisible by 3

Approach and Working:
As it is given that x is divisible by 3, we can assume x = 3k, where k is a non-zero constant
Now considering each of the options as follows:
• 6 – x = 6 – 3k = 3(2 – k)
    o Divisible by 3
• x + 9 = 3k + 9 = 3(k + 3)
    o Divisible by 3
• 2x = 2 * 3k = 6k = 3 * 2k
    o Divisible by 3
• 3x + 5 = 3 * 3k + 5 = 9k + 3 + 2 = 3(3k + 1) + 2
    o Not divisible by 3
• 4x – 6 = 4 * 3k – 6 = 12k – 6 = 3(4k – 2)
    o Divisible by 3

We can see option D is not divisible by 3

Hence, the correct answer is option D.

Answer: D
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Re: If integer x is divisible by 3 which of the following is not divisible  [#permalink]

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New post 22 May 2018, 06:05
option D

3x+5 = 3.3m +5 = 9m+5

9m+5 will leave a remainder when divided by 3 as only 9m is a multiple of 3 and not 5.
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Re: If integer x is divisible by 3 which of the following is not divisible &nbs [#permalink] 22 May 2018, 06:05
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