**Question 1**

If 11 + 21 = 3, 34 + 45 = 32 and 42 + 53 = 23 then 64 + 75 = ?

a)59 b)43 c)69 d)53

**Answer :**a)59

Solution :

Let AB be the first number of the addition and CD be the second one. By closely observing, we can conclude that questions are in the general form AB + CD = (A x B) + (C x D).

i.e.,11 + 21 = 1 x 1 + 2 x 1 = 1 + 2 = 3

34 + 45 = 3 x 4 + 4 x 5 = 12 + 20 = 32

42 + 53 = 4 x 2 + 5 x 3 = 8 + 15 = 23.

Therefore, the result for 64 + 75 = 6 x 4 + 7 x 5 =24 + 35 = 59.

**Question 2**

If 15 + 22 = 32, 19 + 35 = 62 and 23 + 49 = 101 then 34 + 52 = ?

a)91 b)101 c)172 d)72

**Answer :**c)172

Solution:

By observing the question we can generalize the equations to, AB + CD = (AB x C) + D

Then,

15 + 22 = (15 x 2)+ 2 = 30 + 2 = 32

19 + 35 = (19 x 3)+ 5 = 57 + 5 = 62

23 + 49 = (23 x 4)+ 9 = 92 + 9 = 101

Similarly,34 + 52 = (34 x 5)+ 2 = 170 + 2 = 172

Hence 172 is the required answer.

**Question 3**

If 3 + 5 = 19, 5 + 9 = 61 and 9 + 12 = 117 then 13 + 14 = ?

a)128 b)152 c)124 d)183

**Answer :**d)183

Solution:

The above question seems to be in the general form A + B = (A x B)+(A - B)

^{2}

3 + 5 = (3 x 5)+(3 - 5)

^{2}= 15 + 4 = 19

5 + 9 = (5 x 9)+(5 - 9)

^{2}= 45 + 16 = 61

9 + 12 = (9 x 12)+(9 - 12)

^{2}= 108 + 9 = 117

Similarly, 13 + 14 = (13 x 14)+(13 - 14)

^{2}= 182 + 1 = 183.

Hence the answer is 183.

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