If x is a positive integer and 3x + 2 is divisible by 5, then which of

Question

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.

CareerGeek · Accepted Answer

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   
(B) 3x is divisible by 10. -->  Never   
(C) x − 1 is divisible by 5. -->  Always   
(D) x is odd. -->  Not always   
(E) 3x is even -->  Not always

Option C

yashikaaggarwal · Answer

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

Posted from my mobile device

Abhishek009 · Answer

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)

Anonymous · Answer

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

KarishmaB · Answer

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

KarishmaB · Answer

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)

GulfTube · Answer

since 2 divide by 5 leaves remainder of 2, For 3x+2 to be divisible by 5, 3x has to leave a remainder which when added to 2, becomes a multiple of 5.
Thus, 3x when divided by 5 should leave a remainder of  Multiple of 5  - 2. In other words,  3x  is 2 less than a multiple of 5.
We can now list out possible values for 3x = {3,8,13,18,23,28,33,...} and for x = {1,8/3,13/3,6,23/3,28/3,11,...}. since x is given to be positive  integer , x can only take values = {1,6,11,....}
none of these values is divisible by 10 so (B) is out.
3x as seen is not necessarily even , hence (E) is out.
as seen, x is not necessarily divisible by 3 or odd , hence (A) and (D) are out.

correct answer is (C)

vasu1104 · Answer

x> 0

3x + 2 = 5k

need to find what must be true for x.

here when we add 2 to multiple of 3, it becomes multiple of 5.
so we need to find those multiple of 3 that when added to 2 gives multiple of 5.

x=1,6,11,16

A not all the time, so not must be true.
B not at all.
C yes, x-2 must be always divisible by 5.
D not all time. 
E not all time.

choice C

If x is a positive integer and 3x + 2 is divisible by 5, then which of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x is a positive integer and 3x + 2 is divisible by 5, then which of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards