Aptitude - Numbers - Discussion

When any two numbers are divided, they are related as Divisor*Quotient + Remainder = Dividend

Now we know the divisor, and the remainder

Let's assume quotient as 1
then in our case 56*1 + 29 = 85 is the number which gives remainder as 29 when divided by 6

Dividend this same number by 8 gives us the remainder as 5.

Alternative,

Let the dividend be 56*Q + 29, where Q is the quotient

Now dividing this same number by 8, there are two things
1. Since 56 is divisible by 8 therefore 56*Q will give us 0 remainder
2. Dividing 29 by 8 will give us remainder 5

In short the only way to to attempt the question is divided the number by previous divisor and the remainder individually and add the result.

If You get any questions like this you can frame like this:

Dividend(D) = divisor(d) * Quotient(Q) + Remainder(R).
D = 56 * Q + 29.

So, [56 * Q + 29 ]/8 [ Since, in the question its given if the same number is divided by 8 what would be the remainder].

56 * Q comes under the multiple of 8 so it will give a remainder as 0, so now only thing left is 29/8, which will clear results our answer or we can say the remainder i.e 29/8 = 5. So, 5 is the remainder.

Let the number be x and quotient be y.

According to the rule: Dividend=Divisor*Quotient+Remainder. (eq....1).

In 1st case divisor is 56, number is x, quotient is y and remainder is 29.

Keeping values in eq....(1).

x = 56*y+29.

Now lets break this in multiples of 8 to get the remainder by 8.

x = (8*7q)+(8*3)+5.

c = 8(7q+3)+((5)).

Hence 5 is the answer.

Read carefully and then understand.

Let us consider that the number divisible by 56 and leaves a remainder 29 be x+29. When the same number is divided by 8 definitely the x is divisible by 8 since it is divisible 56 and 56 is divisible 8 now we should take care about 29. When 29 is divided by 8 it leaves the remainder 5.

So the answer is 5.

Let the number x and the quotient is why. Then the actual number will be

X=56y+29.

Now we have to find out the remainder when x or 56y+29 is divided by 8.

We can easily visualize that 56y is completely divisible by 8. Hence we only have to work out on 29 and one can easily find out the remainder when 29 is divided by 8. It will be 5.

Let the number is x.

x/56 gives reminder 29.

So,
x = (56 * Quotient) + 29.

Notice that remainder is the last number after "+" sign-->(29 here).

Then,

x = (8 * 7 * Quotient) + [(8 * 3) + 5].

So When expressed as multiples of 8 we get the last number after "+" sign-->(5 here).

So 5 is reminder.

If any no. X divisible by another no Y then any no. divisible by X , will also divisible by Y and all factors of Y.

Here, X be any no divisible by 56 and 56 is divisible by 8 and 8 is factor of 56. that why we use,

Number = (k*56+29).
Number = (k*56+24+5).
Number = 8* (k*7+3) +5.

So divided number by 8, We get reminder 5.

This is the simplest way of all.

Since a number is divisible by 56 and gives remainder as 29.

Let the least possible number that satisfies the above condition,

So the number is = (56+29) ;

Number = 85;

(if you want just check it, 85%56 = 29).

So the same number 85%8 = 5 (as stated in the question).

As simple as that.

Take the simplest possible case.

Since 56 leaves a remainder of 29, let us assume that the quotient is '1', since even with the quotient as '1' the conditions are still satisfied.

Therefore, dividend = divisor x quotient+remainder;.

Hence, dividend = 56 x 1+29 = 85;.

When 85 is divided by 8 the remainder left over is 8.

We know that 56 is completely divided by 8, means what ever number divided by 56, 8 can also divide it without remaining any remainder.

We know the remainder which we got during dividing with 56 is 29 ..
Lets see how much more we can solve it by dividing 8.

8)29(3
24
-----
5

We get remainder as 5 .

Thank you.