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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
What is the remainder when x is divided by 3?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:19) correct 31% (01:19) wrong based on 150 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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Current Student Joined: 18 Oct 2014
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Re: What is the remainder when x is divided by 3?  [#permalink]

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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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I welcome critical analysis of my post!! That will help me reach 700+
Current Student Joined: 18 Oct 2014
Posts: 796
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: What is the remainder when x is divided by 3?  [#permalink]

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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.
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the remainder when x is divided by 3?  [#permalink]

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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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st 1:
sum of digits is 5 ...remainder will always be 2
Sufficient

St2: remainder will always be 2

Ans: D
Senior Manager  G
Joined: 04 Apr 2015
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Re: What is the remainder when x is divided by 3?  [#permalink]

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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
Current Student D
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GRE 1: Q169 V154 Re: What is the remainder when x is divided by 3?  [#permalink]

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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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statement 1
As sum of digits is 5 remainder will always be 2.

Statement 2
also sufficient

Manager  B
Joined: 02 Nov 2018
Posts: 54
What is the remainder when x is divided by 3?  [#permalink]

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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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