If P, Q, R, S, T, X, Y, and Z each represents one digit between 0 and

Question

If P, Q, R, S, T, X, Y, and Z each represents one digit between 0 and 9, what is the remainder when the eight-digit number PQRSTXYZ is divided by 8?
(1) The four-digit number PQRS leaves a remainder of 7 when divided by 8.
(2) The four-digit number TXYZ leaves a remainder of 3 when divided by 8.

AndrewN · Answer

I think the timer statistics tell an interesting story on this one. For those who know the divisibility test/rule for 8, as discussed in  this thread  about another question, this is about a 30-60 second question; for others, this is probably going to be a nightmare. (The real kicker is that no calculation is required.)

I hope that other thread sheds some light on this question. Happy reading, and good luck with your studies, everyone.

- Andrew

jhavyom · Answer

If P, Q, R, S, T, X, Y, and Z each represents one digit between 0 and 9, what is the remainder when the eight-digit number PQRSTXYZ is divided by 8?

A number is divisible by 8, if its last three digits are divisible by 8.
i. e. a number leaves a remainder of 0, if its last three digits are divisible by 8.

(1) The four-digit number PQRS leaves a remainder of 7 when divided by 8.
No information about the last three digits.
Not sufficient

(2) The four-digit number TXYZ leaves a remainder of 3 when divided by 8. 
Therefore, XYZ are the last three digits, which leave a remainder of 3 when divided by 8
So, PQRSTXYZ will also leave a remainder of 3 when divided by 8 irrespective of the value of PQRST.
Sufficient

Choice B is the answer.

rocky620 · Answer

A number is completely divisible by 8 when its last three digits are divisible by 8.

Its remainder will be the same as the one obtained by dividing the last three digits.

So, Option B.

bumpbot · Answer

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If P, Q, R, S, T, X, Y, and Z each represents one digit between 0 and

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