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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
What is the units digit of positive integer p?  [#permalink]

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Question Stats: 81% (00:56) correct 19% (01:05) wrong based on 186 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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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: What is the units digit of positive integer p?  [#permalink]

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1
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

Retired Moderator G
Joined: 26 Nov 2012
Posts: 569
What is the units digit of positive integer p?  [#permalink]

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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..
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: What is the units digit of positive integer p?  [#permalink]

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

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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
Current Student B
Joined: 06 Sep 2016
Posts: 125
Location: Italy
Schools: EDHEC (A$) GMAT 1: 650 Q43 V37 GPA: 3.2 WE: General Management (Human Resources) Re: What is the units digit of positive integer p? [#permalink] Show Tags Dear experts, I don't understand why A is the correct answer. Is not possible that P equals 8 so 8 divided by 10 is 0 with remainder 8? So in this case we would have P= 8 or P =108 and thus Statement 1 would be insufficient Math Expert V Joined: 02 Sep 2009 Posts: 58453 What is the units digit of positive integer p? [#permalink] Show Tags 1 MvArrow wrote: Dear experts, I don't understand why A is the correct answer. Is not possible that P equals 8 so 8 divided by 10 is 0 with remainder 8? So in this case we would have P= 8 or P =108 and thus Statement 1 would be insufficient Notice that the question does NOT ask to find the value of p. The question asks to find the units digit of p, which from (1) will always be 8. _________________ Current Student B Joined: 06 Sep 2016 Posts: 125 Location: Italy Schools: EDHEC (A$)
GMAT 1: 650 Q43 V37 GPA: 3.2
WE: General Management (Human Resources)
Re: What is the units digit of positive integer p?  [#permalink]

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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   Retired Moderator P
Joined: 19 Mar 2014
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Location: India
Concentration: Finance, Entrepreneurship
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Re: What is the units digit of positive integer p?  [#permalink]

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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

Hence, Answer is A
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_________________ Re: What is the units digit of positive integer p?   [#permalink] 22 Sep 2019, 20:08
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