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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.
(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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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
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
09 Mar 2022, 08:39
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SA1196
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.
