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Logic Level 3

Above shows a long division. What is the sum of values of all the missing digits?

The answer is 61.

1 solution

A Former Brilliant Member
Feb 1, 2016

$\LARGE{ \begin{array}{rllll} \phantom{0}\ \boxed{\color{#3D99F6}{3}} \ \boxed{\color{#3D99F6}{3}} \ \boxed{\color{#3D99F6}{2}} && \\[-4pt] \boxed{\color{#3D99F6}{1}} \ \boxed{\color{#3D99F6}{9}} \ \enclose{longdiv}{\boxed{\color{#3D99F6}{6}} \ \boxed{\color{#3D99F6}{3}} \ \boxed{\color{#3D99F6}{0}}\ \boxed{\color{#3D99F6}{8}} }&& \\[-4pt] \underline{\boxed5 \ \boxed{\color{#3D99F6}{7}} \ \phantom0 \ \phantom0 \ \phantom0} && \\[-4pt] \boxed{6} \ \boxed{\color{#3D99F6}{0}} \ \phantom0 \ && \\[-3pt] \underline{\boxed{\color{#3D99F6}{5}} \ \boxed{7} \ \phantom0 \ } && \\[-3pt] \boxed{\color{#3D99F6}{3}} \ \boxed{8} && \\[-2pt] \boxed{\color{#3D99F6}{3}} \ \boxed{\color{#3D99F6}{8}} && \\[-2pt] \overline{ \phantom0 \ \phantom{0} \ \phantom0 \ } && \\[-2pt] \end{array} }$

Therefore, Sum of missing digits $\boxed{\color{#624F41}{61}}.$

How to solve this??Steps please..

Sagar Shah - 5 years, 4 months ago

●Think of a number like this when it is multiplyed by anything gives last digit as 7 and 8 and is two digit no. .
U will here find divisor as $\boxed{19}$ .
●Now in last two boxes since Remider is 0, this fills last two boxes as $\boxed{3's , 8}$ .
●Now 2nd box from top...no. will be $\boxed{57=(19×3)}$ ....because tens digit given is five.
●Now u got quotient multiply this with divisor to get divident..
Now we find dividend as $\boxed{6308}$ .
●From last, 4th box $\boxed{60-57=3}$ ....here 0 can be any no. upto 6 but it will be 0 because from 6308(dividend).

$\rightarrow$ You got that now?

A Former Brilliant Member - 5 years, 4 months ago

My approach is different from yours:
In the middle there is:
6_
7
The one on the left of 7 is either 5 or 6
If it is 6 then divisor $=67$ , then it is impossible to make a 5 in the hundred place
So it is 57
Then divisor is $19$ or $57$
To make a _8 in the digit place, the divisor has to be $19$ .

展豪張 - 5 years, 3 months ago

@展豪張 – Good! :)

A Former Brilliant Member - 5 years, 3 months ago

Does that make you mad?

The answer is 61.

1 solution

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