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SA1196
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What is the last digit in the base eight representation of a number? Updated on: 09 Mar 2022, 01:26
Originally posted by SA1196 on 08 Mar 2022, 23:33.
Last edited by Bunuel on 09 Mar 2022, 01:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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What is the last digit in the base eight representation of a number?

(1) The number divided by 8 yields a remainder of 5.
(2) The number divided by 16 yields a remainder of 13.

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What is the last digit in the base eight representation of a number? 08 Mar 2022, 23:34
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Solution Provided on Varsity Tutors website:
To find the last digit in the base N representation of a number, divide the number by N; the remainder is that digit. If we know the number divided by 8 has remainder 5, we know its last base-eight digit is 5. If we know the number divided by 16 is 13, then we still know that the digit is 5, since the reminder when divided by 8 would be 13−8=5. Therefore, each statement is sufficient on its own. (D) is correct

Hi Experts Bunuel KarishmaB chetan2u egmat

Found this DS question on Varsity Tutors website, I am not satisfied with the solution provided - maybe there is something I am missing here such as "base representation of a number".
I think the solution should be (E), as there are multiple values that can be there in the units digit and still have remainder 5 when divided by 8 and 13 when divided by 16.
Could you please help me out here. Thanks
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What is the last digit in the base eight representation of a number? 09 Mar 2022, 08:39
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SA1196
Solution Provided on Varsity Tutors website:
To find the last digit in the base N representation of a number, divide the number by N; the remainder is that digit. If we know the number divided by 8 has remainder 5, we know its last base-eight digit is 5. If we know the number divided by 16 is 13, then we still know that the digit is 5, since the reminder when divided by 8 would be 13−8=5. Therefore, each statement is sufficient on its own. (D) is correct

Hi Experts Bunuel KarishmaB chetan2u egmat

Found this DS question on Varsity Tutors website, I am not satisfied with the solution provided - maybe there is something I am missing here such as "base representation of a number".
I think the solution should be (E), as there are multiple values that can be there in the units digit and still have remainder 5 when divided by 8 and 13 when divided by 16.
Could you please help me out here. Thanks
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Base 8 means we use digit 0-7. What we use in normal is 0-9 digits.

So what the way 10 behaves in normal base-10 number system, 8 will behave accordingly.

Thus statement 1 gives 5 as the answer.

Now 16 that is 2*8 will behave like 2*10.
So if 13 is the remainder when divided by 20, 13-10 will be the remainder when it is divided by 10.
Similarly 13-8 or 5 is the answer.

Don’t worry. GMAT deals with only base-10 system and this is clearly out of scope.
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What is the last digit in the base eight representation of a number? 10 Mar 2022, 08:07
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SA1196
Solution Provided on Varsity Tutors website:
To find the last digit in the base N representation of a number, divide the number by N; the remainder is that digit. If we know the number divided by 8 has remainder 5, we know its last base-eight digit is 5. If we know the number divided by 16 is 13, then we still know that the digit is 5, since the reminder when divided by 8 would be 13−8=5. Therefore, each statement is sufficient on its own. (D) is correct

Hi Experts Bunuel KarishmaB chetan2u egmat

Found this DS question on Varsity Tutors website, I am not satisfied with the solution provided - maybe there is something I am missing here such as "base representation of a number".
I think the solution should be (E), as there are multiple values that can be there in the units digit and still have remainder 5 when divided by 8 and 13 when divided by 16.
Could you please help me out here. Thanks
Show more


How do we convert a number into base 8? We divide by 8 till the remainder is less than 8. Finally, we write all the remainders from last to first.

This is a screenshot of what google shows:
Attachment:
Screenshot 2022-03-10 at 20.31.24.png

So 1032 is 2010 is base 8.
What is the units digit in base 8? That is the remainder we get when we divide the original number by 8 for the first time. So if we know that when a number is divided by 8, the remainder is 5, we know that the units digit of base 8 representation will be 5.

Alternatively, think what base 8 representation is. Say we have a number abc in base 8.

abc = 64*a + 8*b + c = 8(8a + b) + c

So in our decimal system, abc is equal to 8(8a + b) + c. When we divide our decimal representation by 8, the remainder we will get will be c which is the units digit.

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