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

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What is the remainder when 5-digit positive integer pqpqp is divided  [#permalink]

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02 May 2017, 16:20
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Difficulty:

55% (hard)

Question Stats:

48% (01:19) correct 52% (01:11) wrong based on 146 sessions

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

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

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Re: What is the remainder when 5-digit positive integer pqpqp is divided  [#permalink]

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02 May 2017, 18:33
ziyuen wrote:
What is the remainder when 5-digit positive integer pqpqp is divided by 3?

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

1. 2X2X2 / 3 - cannot determine the remainder - not sufficient
2. X3X3X / 3 - remainder would be 0. Since X+3+X+3+X = 3X+6 = multiple of 3. Hence sufficient
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Re: What is the remainder when 5-digit positive integer pqpqp is divided  [#permalink]

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04 Oct 2018, 19:10
hazelnut wrote:
What is the remainder when 5-digit positive integer pqpqp is divided by 3?

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

Q- Stem : pqpqp is divisible by 3 when the sum of the digts is divisible by 3. i.e. p+q+p+q+p or 3p+2q is divisible by 3.
Now (3p+2q)/3 = p+ 2q/3......... the Q is asking what is the remainder when 2q is divided by 3.

(1) p=2 ....................no info about q...... NS
(2) q=3 ...............................................Sufficient ...... Ans B
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Re: What is the remainder when 5-digit positive integer pqpqp is divided  [#permalink]

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02 Nov 2018, 15:41
The digit sum of any number divisible by 3 must be a multiple of 3.

So:

Stmt 1 p+q+p+q+p = 3(2)+2q = do not know digit sum, q can be 1,2,3, all bets are off

Stmt 2 3p+2*3 = will be a multiple of 3, 3(p+2) is the simplified form, hence b alone is sufficient
Re: What is the remainder when 5-digit positive integer pqpqp is divided   [#permalink] 02 Nov 2018, 15:41
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