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# If p and q are both positive integers, then is p divisible by 9?

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Re: If p and q are both positive integers, then is p divisible by 9? [#permalink]
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selim wrote:
If p and q are both positive integers, then is p divisible by 9?

1) p/10 + q/10 is an integer.

2) p/9 + q/10 is an integer.

The property, when any positive integer is divided by 9, is the division leaves a non-terminating decimal except for multiple of 9, i.e.:-

Positive
Integer

1 Divided by 9 = 0.111111111
2 Divided by 9 = 0.222222222
3 Divided by 9 = 0.333333333
4 Divided by 9 = 0.444444444
5 Divided by 9 = 0.555555556
6 Divided by 9 = 0.666666667
7 Divided by 9 = 0.777777778
8 Divided by 9 = 0.888888889
9 Divided by 9 = 1
10 Divided by 9 = 1.111111111
11 Divided by 9 = 1.222222222
12 Divided by 9 = 1.333333333
13 Divided by 9 = 1.444444444
14 Divided by 9 = 1.555555556
15 Divided by 9 = 1.666666667
16 Divided by 9 = 1.777777778
17 Divided by 9 = 1.888888889
18 Divided by 9 = 2
19 Divided by 9 = 2.111111111

Since it is mentioned that both p and q are integers the only possibility is "p" is a multiple of 9 since "q" is also a positive integer.

Correct Ans B - Sufficient!! Straight and simple!!
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Re: If p and q are both positive integers, then is p divisible by 9? [#permalink]
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Re: If p and q are both positive integers, then is p divisible by 9? [#permalink]
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