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If x is a positive integer and 3x + 2 is divisible by 5, then which of
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Bunuel
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If x is a positive integer and 3x + 2 is divisible by 5, then which of [#permalink] New post  13 Mar 2020, 06:51
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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.
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Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
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Dillesh4096
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Re: If x is a positive integer and 3x + 2 is divisible by 5, then which of [#permalink] New post  13 Mar 2020, 07:13
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Bunuel wrote:
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 \(5\)
--> \(3x + 2 = 5p\), for any positive integer p
--> \(3x = 5p - 2\)
--> \(x = \frac{5p - 2}{3}\)
--> Possible values of x = {1, 6, 11, 16, 21, 26, . . . . .} for p = 1, 4, 7, 10, 13, 16, . . . . .

(A) x is divisible by 3. --> Not always [x = 1, 11, . . . .]
(B) 3x is divisible by 10. --> Never [3x = 3, 16, 33, . . . . . ]
(C) x − 1 is divisible by 5. --> Always [x - 1 = 0, 5, 10, 15, 20, . . . . .]
(D) x is odd. --> Not always [x = 6, 16, 26, . . . . . ]
(E) 3x is even --> Not always [x = 3, 33, 63, . . . . . ]

Option C
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yashikaaggarwal
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Re: If x is a positive integer and 3x + 2 is divisible by 5, then which of [#permalink] New post  13 Mar 2020, 07:25
Putting integers in 3x+2 with the given constraints of being divisible by 5
Gives the value of X be 1,6,11,16,21.... So on
Now analysing options one by one.
1) x=1,6,11 is not divisible by 3 (Incorrect)
2) 3x=3,18,33 is not divisible by 10 (Incorrect)
3) X-1=0,5,10,15... All are divisible by 5 (Correct)
4) X=1,6,11,16... x is not always odd (Incorrect)
5) 3x=3,18,33,... Are not always even (Incorrect)

So OA is C

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Abhishek009
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If x is a positive integer and 3x + 2 is divisible by 5, then which of [#permalink] New post  13 Mar 2020, 09:05
Bunuel wrote:
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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If x is a positive integer and 3x + 2 is divisible by 5, then which of [#permalink]
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