What is the remainder when 5-digit positive integer pqpqp is

[hazelnut01]

What is the remainder when 5-digit positive integer pqpqp is divided by 3?

(1) p=2
(2) q=3

Source : Math Revolution

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Hi ziyuenlau,

This DS question is built around a Number Property rule called "the rule of 3."

For a number to be divisible by 3 (meaning that the remainder would be 0), the sum of the digits of that number must total a number that is also divisible by 3.

For example, 18 is divisible by 3, since 1+8=9 and 9 is divisible by 3.
In that same way, 25 is NOT divisible by 3, since 2+5=7, and 7 is NOT divisible by 3.

We're told that we have a five-digit integer PQPQP. We're asked for the remainder when it is divided by 3.

1) P=2

With this Fact, we don't know the value of Q...

IF...
Q=0, then the number is 20202. 20202/3 = 6734 remainder 0
Q=1, then the number is 21212. 21212/3 = 7070 remainder 2
Fact 1 is INSUFFICIENT

2) Q=3

With this Fact, we don't know the value of P. However, we know that the digit "P" shows up 3 times, so the sum of the digits would be...

P3P3P --> 3P + 6

Regardless of the value of P, the sum of the digits would be a multiple of 3. Thus, P3P3P would always have a remainder of 0.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Jay@ManhattanReview]

What is the remainder when 5-digit positive integer pqpqp is divided by 3?

(1) p=2
(2) q=3

Source : Math Revolution

Statement 1: p = 2

This number is 2q2q2

For a number to be completely divisible by '3', the sum of its digits must be divisible by '3,' else we get a remainder.

Sum of digits = 2+q+2+q+ = 6 + 2q

We see that '6' is divisible by '3', and the remainder of '2q' divisible by '3' would depend on the value of 'q'. You may try any value for q from 0,1,2,...9. The remainders are not the same for the chosen digits. Insufficient.

Statement 2: q = 3

This number is p3p3p

Sum of digits = p+3+p+3+p = 6 + 3p = 3(2 + p).

Since 3(2 + p) is a factor of '3,' it is completely divisible by '3,' leaving a remainder '0.' The value of q does not affect the remainder. Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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