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Bunuel
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?

(A) x is divisible by 3.
(B) 3x is divisible by 10.
(C) x − 1 is divisible by 5.
(D) x is odd.
(E) 3x is even.

Plug in the values of x and check

If \(x = 1\) ; \(\frac{3x + 2}{5} = \frac{3*1 + 2}{5}\) is divisible by 5

If \(x = 6\) ; \(\frac{3x + 2}{5} = \frac{3*6 + 2}{5}\) is divisible by 5

Now check the options...

(A) x is not always divisibly by 3
(B) 3x is not always divisible by 10.
(C) x − 1 is always divisible by 5.
(D) x is not alwaysodd.
(E) 3x is not always even

Thus, Answer must be (C)
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Bunuel
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?

(A) x is divisible by 3.
(B) 3x is divisible by 10.
(C) x − 1 is divisible by 5.
(D) x is odd.
(E) 3x is even.
Hi Bunuel and GMAT Experts! I had a different line of reasoning and would like your opinion on its effectiveness and validity.

  • Since 3x +2 is divisible by 5, it must end in 0 or 5.

  • If 3x+2 ends in 0, then the unit digit of 3x must be 8 (8+2=10).
  • If 3x+2 has unit digit 5, then the last digit of 3x must be 3 (because 3+2=5).
  • This excludes options: (A) x divisible by 3 means the unit digit is 3/9/7/1 which that for 3x unit digit is 9/7/1/3 which doesn't cover the first case. Option (D) is true for the second case but not the first, and (E) is valid for the first but not the second.
  • Option (B) : if 3x is divisible by 10 then 3x+2 cannot be divisible by 5 (cancels the given fact from the question stem).
  • Conclusion (C) x-1 must be divisible by 5.

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Bunuel
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?

(A) x is divisible by 3.
(B) 3x is divisible by 10.
(C) x − 1 is divisible by 5.
(D) x is odd.
(E) 3x is even.
Hi Bunuel and GMAT Experts! I had a different line of reasoning and would like your opinion on its effectiveness and validity.

  • Since 3x +2 is divisible by 5, it must end in 0 or 5.

  • If 3x+2 ends in 0, then the unit digit of 3x must be 8 (8+2=10).
  • If 3x+2 has unit digit 5, then the last digit of 3x must be 3 (because 3+2=5).
  • This excludes options: (A) x divisible by 3 means the unit digit is 3/9/7/1 which that for 3x unit digit is 9/7/1/3 which doesn't cover the first case. Option (D) is true for the second case but not the first, and (E) is valid for the first but not the second.
  • Option (B) : if 3x is divisible by 10 then 3x+2 cannot be divisible by 5 (cancels the given fact from the question stem).
  • Conclusion (C) x-1 must be divisible by 5.

GMATCoachBen avigutman KarishmaB ScottTargetTestPrep

This is not correct:

This excludes options: (A) x divisible by 3 means the unit digit is 3/9/7/1


If x is divisible by 3, it could have any other units digit too such as 8 in 18 or 6 or 2 in 12 etc. Only if you have exponents of 3, then the units digit will only be 3/9/7/1
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Bunuel
If x is a positive integer and 3x + 2 is divisible by 5, then which of the following must be true?

(A) x is divisible by 3.
(B) 3x is divisible by 10.
(C) x − 1 is divisible by 5.
(D) x is odd.
(E) 3x is even.

3x + 2 is divisible by 5 means that 3x - 3 is also divisible by 5 (the previous multiple of 5).
This means that 3(x-1) is divisible by 5 which means (x-1) is divisible by 5.

Answer (C)
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