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# What is the units digit of positive integer p?

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What is the units digit of positive integer p?  [#permalink]

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19 Feb 2016, 04:12
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80% (00:28) correct 20% (00:34) wrong based on 246 sessions

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What is the units digit of positive integer p?

(1) When p is divided by 10, the remainder is 8
(2) When p is divided by 11, the remainder is 8

Kudos for correct solution.

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Re: What is the units digit of positive integer p?  [#permalink]

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19 Feb 2016, 06:07
1
Units digit = ?
St1: p = 10k + 8 --> p = 8, 18, 28,.... --> Units digit is always 8
St1 is sufficient

St2: p = 11k + 8 --> p = 8, 19, 30,..... --> Units digit is not always the same.
St2 is insufficient

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What is the units digit of positive integer p?  [#permalink]

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30 Sep 2016, 14:42
Vyshak wrote:
Units digit = ?
St1: p = 10k + 8 --> p = 8, 18, 28,.... --> Units digit is always 8
St1 is sufficient

St2: p = 11k + 8 --> p = 8, 19, 30,..... --> Units digit is not always the same.
St2 is insufficient

Hi Vyshak

I did the same way as you did..

But for Stat1 I got doubt that suppose if Q is in fraction form i.e. 1/2 or 1/5 then we won't get 8.

10(1/2)+8 = 13 or 10(1/5)+8 = 10...

Can you please throw some light whether we can take Q in fraction form or not...under what conditions can Q be a integer if we need to consider..

Bunuel, can you share your solution too..
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Re: What is the units digit of positive integer p?  [#permalink]

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30 Sep 2016, 20:47
msk0657 wrote:
Vyshak wrote:
Units digit = ?
St1: p = 10k + 8 --> p = 8, 18, 28,.... --> Units digit is always 8
St1 is sufficient

St2: p = 11k + 8 --> p = 8, 19, 30,..... --> Units digit is not always the same.
St2 is insufficient

Hi Vyshak

I did the same way as you did..

But for Stat1 I got doubt that suppose if Q is in fraction form i.e. 1/2 or 1/5 then we won't get 8.

10(1/2)+8 = 13 or 10(1/5)+8 = 10...

Can you please throw some light whether we can take Q in fraction form or not...under what conditions can Q be a integer if we need to consider..

Bunuel, can you share your solution too..

p is given to be a positive integer.
How can quotient be a fraction? By definition, quotient and remainder are supposed to be integers.
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Re: What is the units digit of positive integer p?  [#permalink]

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30 Sep 2016, 21:11
VeritasPrepKarishma wrote:
msk0657 wrote:
Vyshak wrote:
Units digit = ?
St1: p = 10k + 8 --> p = 8, 18, 28,.... --> Units digit is always 8
St1 is sufficient

St2: p = 11k + 8 --> p = 8, 19, 30,..... --> Units digit is not always the same.
St2 is insufficient

Hi Vyshak

I did the same way as you did..

But for Stat1 I got doubt that suppose if Q is in fraction form i.e. 1/2 or 1/5 then we won't get 8.

10(1/2)+8 = 13 or 10(1/5)+8 = 10...

Can you please throw some light whether we can take Q in fraction form or not...under what conditions can Q be a integer if we need to consider..

Bunuel, can you share your solution too..

p is given to be a positive integer.
How can quotient be a fraction? By definition, quotient and remainder are supposed to be integers.

Thank you Karishma! I did your way as well...The given info prevents any fraction from being used for p..I would stay away from fraction form...I just did a few examples of long division to see my results the old fashion way lol
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Re: What is the units digit of positive integer p?  [#permalink]

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02 May 2017, 07:27
Dear experts,
I don't understand why A is the correct answer.
Is not possible that P equals 8 so 8 divided by 10 is 0 with remainder 8?

So in this case we would have P= 8 or P =108 and thus Statement 1 would be insufficient
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What is the units digit of positive integer p?  [#permalink]

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02 May 2017, 07:42
1
MvArrow wrote:
Dear experts,
I don't understand why A is the correct answer.
Is not possible that P equals 8 so 8 divided by 10 is 0 with remainder 8?

So in this case we would have P= 8 or P =108 and thus Statement 1 would be insufficient

Notice that the question does NOT ask to find the value of p. The question asks to find the units digit of p, which from (1) will always be 8.
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Re: What is the units digit of positive integer p?  [#permalink]

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02 May 2017, 09:26
Bunuel wrote:
MvArrow wrote:
Dear experts,
I don't understand why A is the correct answer.
Is not possible that P equals 8 so 8 divided by 10 is 0 with remainder 8?

So in this case we would have P= 8 or P =108 and thus Statement 1 would be insufficient

Notice that the question does NOT ask to find the value of p. The question asks to find the units digit of p, which from (1) will always be 8.

OMG thanks! I misunderstood the question and I read "the digits number" of P

Thank you very much for the correction
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Re: What is the units digit of positive integer p?  [#permalink]

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08 Jul 2017, 14:45
Bunuel wrote:
What is the units digit of positive integer p?

(1) When p is divided by 10, the remainder is 8
(2) When p is divided by 11, the remainder is 8

Kudos for correct solution.

What is the units digit of positive integer p?

(1) When p is divided by 10, the remainder is 8

When a number is divided by 10 we will and if the reminder is 8, we will always get the units digit as 8.

Examples: $$18, 28, 308, 1008$$

As we are getting getting 8 as the units digit for any number divisible by 10, this is SUFFICIENT

Hence, (1) ===== is SUFFICIENT

(2) When p is divided by 11, the remainder is 8

When we divide a number by 11 and if the number is 8 we can have multiple units digits.

Examples: 19, 30, 63, etc.

As we can see that the units digit is not consistent, we will not be able to answer the question.

Hence, (2) ===== is NOT SUFFICIENT

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Re: What is the units digit of positive integer p?  [#permalink]

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28 Aug 2018, 07:51
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