# CAT 2000 | Question: 108

2,185 views

Convert the number $1982$ from base $10$ to base $12.$ The result is

1. $1182$
2. $1912$
3. $1192$
4. $1292$

1192
3.1192

To convert an integer to base b, divide it by b. The remainder is the ones place.

convert 1982 to base 12 ,first 1982 divide by 12 that gives quotient –  165 and remainder-  2 So the number ends in a 2

again previous quotient  divide by base 12 , 165 divide by 12 that gives quotient –  13 and remainder-  9 So the number ends in a 92

again previous quotient  divide by base 12 , 13 divide by 12 that gives quotient –  1 and remainder-  1 So the number ends in a 192

Finally, 1 is less than 12 so its representation is just 1,

so result is 1192

To convert $(1982)_{10}$ to base -12:

$(1982)_{10}\rightarrow (1192)_{12}$

Option (C) is correct.

## Related questions

506
views
506 views
There is a vertical stack of books marked $1, 2,$ and $3$ on Table-A, with $1$ at the bottom and $3$ on top. These are to be placed vertically on Table-B with $1$ at the ...
656
views
656 views
Let $\text{N} = 55^3 + 17^3 – 72^3.\; \text{N}$ is divisible byboth $7$ and $13$both $3$ and $13$both $17$ and $7$both $3$ and $17$
22.0k
views
21,964 views
Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either $635$ or $674,$ the number is odd, and the nu...
384
views
The integers $34041$ and $32506$ when divided by a three-digit integer $n\text{’}$ leave the same remainder. What is $n\text{’}?$$289$$367$$453$$307$
Let $\text{N} = 1421 \times 1423 \times 1425.$ What is the remainder when $\text{N}$ is divided by $12?$$0$$9$$3$$6$