Question

If 1+4 = 5
2+5 = 12
3+ 6 = 21
Then 8+5 = ? What I answered 45 & 34 but my brother is saying I am wrong why?

Answer 1

Correct Question

If 1+4 = 5

2+5 = 12

3+ 6 = 21

Then 5+8= ?

Answer

5 + 8 = 45

$\rule{200}2$

Method 1.

First one is simple i.e. 1 + 4 = 5. Nothing can be added, subtracted, squared, divided etc.

Now, let's cone to the second one i.e.

2 + 5 = 12

But 2 + 5 = 7. Now, subtract 7 from 12 (12 - 7 = 5). On subtracting we get 5.

So, 2 + 5 + (5) = 12

Also, 3 + 6 = 21

But 3 + 6 = 9. Again, subtract 9 from 21, we get 12.

So, 3 + 6 + (12) = 21

If we notice carefully the above are like that:

→ 1 + 4 = 5

→ 2 + 5 + (5) = 12

→ 3 + 6 + (12) = 21

What we get after addition, we are adding that number in the second one and so on.

Therefore,

→ 1 + 4 = 5

→ 2 + 5 + (5) = 12

→ 3 + 6 + (12) = 21

[ 4 + 7 + 21 = 32 ]

→ 5 + 8 + (32) = 45

Method 2.

→ 1 + 4 = 5

= (1×4) + 1 = 5

→ 2 + 5 = 12

= (2×5) + 2 = 10 + 2 = 12

→ 3 + 6 = 21

= (3×6) + 3 = 18 + 3 = 21

First, one multiply with four and one is added. Then, two multiply with five and two is added.

What we multiply first is added again.

Similarly, three multiplied with six and then three is added.

If we continue that then other number will be like;

4 + 7 = 25

= (4×7) + 4 = 21 + 4 = 25

Now,

→ 5 + 8 = 45

= (5×8) + 5 = 40 + 5 = 45

Answer 2

1+4 = (1×4)+1 = 5

2+5 = (2×5)+2 = 12

3+6= (3×6)+3 = 21

similarly , 5+8 = (5×8) + 5 = 45

or common difference is 7

5+7=12+7= 21+7= 28+7 = 35

Thus answer could be both 45 and 35

both patterns are correct

if your brother is refusing 45 then ask about 35

34 cannot be the answer as

1+4= 5

2+5+5 = 12

3+6+12= 21

4+7+21 = 32

5+8+32 = 45

Thus answer could be 35 or 45 but never 34