Question

Q15-F is the smallest natural number,
which whenmultiplied by 7 gives a
number made of 4's only. Sumof the
digits of F is G. The last digit of G 92 is *
O​

Answer 1

Step-by-step explanation:

Here we must use a logical and trial and error method to solve this kind of Questions

So, we must do backward multiplication

Now,

In the 7's table the smallest number to be multiplied by 7 and get a 4 in the ones place is 2

2 × 7 = 14

Here 4 comes in the products ones place and 1 is carried over

so, ones place = 2

Next is a bit confusing, so stay focused

Now let the next digit be x

then 7x + 1 should be equal to 4 or 14 or 24 or so on....

because here 7 is being multiplied and we had a carry over of 1 before

So let put x = 1 we get

7(1) + 1 = 7 + 1 = 8 is not equal to 4

Similarly putting x = 2 we get

7(2) + 1 = 14 + 1 = 15 is not equal to 4

So, if we continue doing trial and error we get

x = 9

7(9) + 1 = 63 + 1 = 64

Thus 4 is the products tens place digit and 6 is carry over

So, the numbers tens digit is 9

Till now we got the number to be multiplied as (.......92)

next we say, the next digits is y

same process here except the carry over changes

7y + 6 = 4 or 14 or 24 or so on....

Thus, after trial and error we get

y = 4

7(4) + 6 = 28 + 6 = 34

Thus 4 is the products Hundreds place digit and 3 is carry over

Thus, Hundreds place of the number to be multiplied is 4

Thus, our number now is (......492)

Next, the digit be z

so, 7z + 3 = 4 or 14 or 24 or so on....

Thus, after trial and error we get

z = 3

7(3) + 3 = 21 + 3 = 24

Thus 4 is the products Thousands place digit and 2 is carry over

Thus, our number now is (......3492)

Next digit be w

so, 7w + 2 = 4 or 14 or 24 or so on....

Thus, after trial and error we get

w = 6

7(6) + 2 = 42 + 2 = 44

Thus 4 is the products Lakhs and Hundreds place digit and we can stop now because we got 44 as an ending

Thus, our number now is (63492)

Now let's just check

63492 × 7 = 4,44,444

So, F = 63492

Now G is the sum of these number

so,

G = 6 + 3 + 4 + 9 + 2 = 24

Note:-

If your Question is,

What is the last digit of G × 92

Then it is 24 × 92 = 2208

Ones place = 8

OR

Easy way is to just multiply 4 × 2 = 8

Because ones place never changes digits by adding

If your Question is,

What is the last digit of G + 92

then, 24 + 92 = 116

Ones place = 6

OR

just add 4 and 2 = 6

Remember this doesn't work for division and subtraction (The easy way)

Hope it helped and you understood it........All the best