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When the positive integer x is divided by 9

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by ddm » Mon Aug 25, 2008 3:21 pm
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?


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by VP_Jim » Mon Aug 25, 2008 3:36 pm
Try plugging in a number for X.

Let's say X=14 (we have to pick a number that, when it is divided by 9, the remainder is 5). Now we have have to figure out what the remainder is when 14*3=42 is divided by 9. 42/9 leaves a remainder of 6.
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by Ian Stewart » Mon Aug 25, 2008 4:21 pm
If you are going to choose a value for x here- not a bad approach for this question- I'd merely add that the smaller the value you choose for x, the faster the work. In this question, you could let x = 5 (when you divide 5 by 9, the quotient is zero and the remainder is 5). Then 3x = 15, and the remainder is 6.
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by minkathebest » Sun May 12, 2013 4:44 pm
I am trying to figure out why this approach is incorrect:

If x=14 for this question:
x/9 , remainder = 4
3x/9, if I simplify FIRST, I get x/3 and then plugin, 14/3, remainder is 2 and TWO is not an answer choice.

What am I doing wrong here?
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by GMATGuruNY » Sun May 12, 2013 5:34 pm
minkathebest wrote:I am trying to figure out why this approach is incorrect:

If x=14 for this question:
x/9 , remainder = 4
3x/9, if I simplify FIRST, I get x/3 and then plugin, 14/3, remainder is 2 and TWO is not an answer choice.

What am I doing wrong here?
You determined the remainder when x is divided by 3:
R=2.
The question stem asks for the remainder when 3x is divided by 9.
Since the two values being divided (3x and 9) are 3 times as great as the values that you used (x and 3), the remainder also will be 3 times as great:
3*2 = 6.
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