What is the remainder when the two-digit, positive integer x is divide

Question

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 
(2) The remainder when x is divided by 9 is 5

Bunuel · Accepted Answer

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 --> x can be 14, 41, 23, 32, or 50. Each of this numbers gives the remainder of 2 when divided by 3. Sufficient.

(2) The remainder when x is divided by 9 is 5 -->  x = 9q + 5 = 9q + 3 + 2 =3(3q+1)+2  --> the remainder when x is divided by 3 is 2. Sufficient.

Answer: D.

zerosleep · Answer

A no is divisile by 3 if the sum of the digits is divisible by 3. The remainder any no with 3 can be found by just dividing the sum of digits(of that no) with 3. If it is zero, the no is divisible by 3, otherwise the remainder obtained is same as what we would have got if we divide the no by 3. 
1) sum of digits of x is 5. Hence, the remainder obtained by dividing x by 3 is same as remainder obtained by dividing 5 by 3, i.e. 2. 
2) x = 9k + 5. => 3*3k + 3 + 2 = 3(3k + 1)+ 2. Now if we divide this by3, the remainder will be 2.

Hence, each statement is sufficient. Ans- D

sahilchaudhary · Answer

1. Possible choices - 14,41,23,32,50. All give remainder 2 when divided by 3. So, sufficient.
2. Take for example 14 or any other no. which gives remainder 5 when divided by 9, it will always give remainder 2 when divided by 3. So, sufficient.

So, the correct answer is D.

jlgdr · Answer

What is the logic in statement 1? How come all numbers that add to 5 give remainder 2? Bunuel, I look forward to your response

PS. Actually, now that I think about it is because they are 2 more than multiples of 3? I guess thats the reason

Cheers
J

Bunuel · Answer

Yes, the first statement gives the numbers which are 2 more than multiples of 3.

Rookie124 · Answer

Kuddos chacha (awesome explanation)

Icecream87 · Answer

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 :   rule of divisibility by 3 = sum of the digits must be divisible by 3, since 5 is two more than 3, the remainder is 2  
(2) The remainder when x is divided by 9 is 5 :   Since 9 is a multiple of 3, and leaves a remainder of 5 then we just know that 3 will enter one more time in 5 and leave a remainder of 2

arvind910619 · Answer

Imo D
From statement 1
We will get remainder 2 from every number upon division by 3
From statement 2
Again we have remainder​ of 2 
Sent from my ONE E1003 using  GMAT Club Forum mobile app

salaxzar · Answer

No is divisile by 3 => sum of the digits is divisible by 3. 
1) sum of digits of x is 5. Hence, the remainder obtained by dividing x by 3 is same as remainder obtained by dividing 5 by 3, i.e. 2. 
2) x = 9k + 5. => 3*3x + 3 + 2 = 3(3x + 1)+ 2. Now if we divide this by 3, the remainder will be 2.

Hence, each statement is sufficient. Ans- D

ydmuley · Answer

What is the remainder when the two-digit, positive integer x is divided by 3?

(1) The sum of the digits of x is 5 : rule of divisibility by 3 = sum of the digits must be divisible by 3, since 5 is two more than 3, the remainder is 2
(2) The remainder when x is divided by 9 is 5 : Since 9 is a multiple of 3, and leaves a remainder of 5 then we just know that 3 will enter one more time in 5 and leave a remainder of 2

cyy12345 · Answer

Hi Bunuel,

What is the rationale behind the manipulation you performed in (2)? Why there has to be a 3q+1? Why can't we just do 3(3q) + 5? (which is wrong..). What did I miss here?

Thanks a lot!

Bunuel · Answer

It's not wrong: 3(3q) is divisible by 3 and 5 divided by 3 gives the remainder of 2. In the solution we just re-wrote 9q + 5 so that we directly got (a multiple of 3) + remainder because we separated a number which is less than the divisor (3). Recall that the remainder is always non-negative integer less than divisor  0\leq{r}<d , so  0\leq{r}<3 .

Hope it's clear.

cyy12345 · Answer

Thanks a lot, Bunuel!

crazi4ib · Answer

Hi Bunuel, I still do not understand the conversion to 9q + 3 + 2 =3(3q+1)+2. Could you kindly explain the logic of these two steps? Thanks!

MBAHOUSE · Answer

Better do plug in numbers I think.

TargetMBA007 · Answer

Bunuel  - Tag:Gmatprep

Bunuel · Answer

_________________________
Added the tag. Thank you!

bumpbot · Answer

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What is the remainder when the two-digit, positive integer x is divide

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