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# What is the remainder when x is divided by 3?

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What is the remainder when x is divided by 3?  [#permalink]

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16 Mar 2016, 11:53
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25% (medium)

Question Stats:

72% (01:19) correct 28% (01:23) wrong based on 140 sessions

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What is the remainder when x is divided by 3?

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

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Re: What is the remainder when x is divided by 3?  [#permalink]

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16 Mar 2016, 14:20

From statement 1, the sum of the digits is 5 i.e 3+2. This is sufficient to tell that remainder will be 2
Statement 2 is pretty clear that the remainder will be 2

Hope I have chosen the right answer.
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Re: What is the remainder when x is divided by 3?  [#permalink]

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16 Mar 2016, 14:20

From statement 1, the sum of the digits is 5 i.e 3+2. This is sufficient to tell that remainder will be 2
Statement 2 is pretty clear that the remainder will be 2

Hope I have chosen the right answer.
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Re: What is the remainder when x is divided by 3?  [#permalink]

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16 Mar 2016, 18:33
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the remainder when x is divided by 3?

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

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation for 2) 1 equation, which is likely to make D the answer.
In case of 1), the remainder derived by dividing some number by 3 is as same as the remainder derived by dividing sum of all digits by 3. In 5=3*1+2, the remainder is 2, which is unique and sufficient.
For 2), in x=9p+2=3(3q)+2, the remainder derived by dividing with 3 is 2, which is unique and sufficient.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: What is the remainder when x is divided by 3?  [#permalink]

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17 Mar 2016, 22:52
st 1:
sum of digits is 5 ...remainder will always be 2
Sufficient

St2: remainder will always be 2

Ans: D
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Re: What is the remainder when x is divided by 3?  [#permalink]

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18 Mar 2016, 06:51
statement 1
sum of digits is 5 therefore possible combination 41,14,23,32 which yields remainder 2
statement 2
x/9 remainder 2 which means x= 11,20,29 etc
check above with 3 it gives 2 every time

therefore D
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Re: What is the remainder when x is divided by 3?  [#permalink]

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21 Mar 2016, 14:29
To get the remainder when a number is divided b 3 we need the remainder when sum of the digits divided by 3 so statement 1 i sufficient
now statement 2=> x=9n+2 => 3P+2=> remainder =2
hence D is sufficient
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Re: What is the remainder when x is divided by 3?  [#permalink]

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26 Jan 2017, 07:52
statement 1
As sum of digits is 5 remainder will always be 2.

Statement 2
also sufficient

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What is the remainder when x is divided by 3?  [#permalink]

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16 Aug 2019, 08:37

From statement 1, the sum of the digits is 5 i.e 3+2. This is sufficient to tell that remainder will be 2
Statement 2 is pretty clear that the remainder will be 2

Hope I have chosen the right answer.

stonecold wrote:
To get the remainder when a number is divided b 3 we need the remainder when sum of the digits divided by 3 so statement 1 i sufficient
now statement 2=> x=9n+2 => 3P+2=> remainder =2
hence D is sufficient

Can someone explain the parts in bold? Is this a rule?
What is the remainder when x is divided by 3?   [#permalink] 16 Aug 2019, 08:37
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