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If x is a positive integer, is the remainder 0 when (3x +

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If x is a positive integer, is the remainder 0 when (3x + [#permalink] New post 04 Jan 2005, 09:21
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A
B
C
D
E

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If x is a positive integer, is the remainder 0 when (3x + 1)/10?

(1) x = 3n + 2, where n is a positive integer.

(2) x > 4
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 [#permalink] New post 04 Jan 2005, 10:27
The only way for (3x + 1)/10 to have a remainder of 0 would be if 3x has a units digit of 9, so that when you add 1 to it you get a mulitple of 10. So x=3, 13, 23, etc would do it.

Statement 2 is obviously not sufficient by itself, as x would work for 13, but not for say 10 for example.

Statement 1 gives a way to determine x. If you try n=1 it doesn't work and you have x>4. So you know that statement 2 doesn't add any value and your answer must be A or E. Now you have to try and see if there is a case where it would work. If you can find a case where it does work using statement 1 then your answer is E, if you can't find a case where it works then your answer is A, as statement 1 would tell you that (3x+1)/10 does not have a remainder of 0.

In order for it to work you need x to have a units digit of 3. So 3n+2 must have a units digit of 3. Because you are adding 2 you need 3n to have a units digit of 1. This occurs when x=7 because 7*3=21.

So x=3(7)+2=21+2=23.

3x+1=3*23+1=69+1=70

70/10 has a remainder of 0

So the answer must be E.
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 [#permalink] New post 04 Jan 2005, 10:32
I think both Statement are insufficient. (e)

from the statment1 we get that

(3(3n+2)+1) = 9n+7 now this equation will always given a non zero remainder when divided by 10, except for when n=7 then it is zero.

statement 2 can be expressed as above, so therefor both taken together give no definite answer.

Therefore answer is E, if somehow statment 2 narrowed the scope of numbers to say 7, then i would pick C.
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 [#permalink] New post 05 Jan 2005, 03:05
In just picking numbers for n, we see that statement 1 is not enough (n=6 and n=7 for instance)

Second statement does not discriminate anything so my answer is also E
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 [#permalink] New post 05 Jan 2005, 11:00
Toddmartin's answer is excellent and helpful. :good

I simply plug in numbers and give trial and error and get E as my answer.
  [#permalink] 05 Jan 2005, 11:00
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If x is a positive integer, is the remainder 0 when (3x +

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