What is the units digit of positive integer p?

Question

(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.

Kurtosis · Answer

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

Answer: A

msk0657 · Answer

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..

KarishmaB · Answer

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

mikeyg51 · Answer

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

MvArrow · Answer

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

Bunuel · Answer

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.

MvArrow · Answer

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

Thank you very much for the correction :-D

ydmuley · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the units digit of positive integer p?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards