Question

If TWO^2 = THREE where the alphabets are single-digit integers then find T +W +O
Your Answer
a) 12
b) 25
c) 18
d) 29​

Answer 1

Given :  TWO² = THREE where the alphabets are single-digit integers

To Find : T + W + O​

a)12

b)25

c)18

d)29​

Solution:

TWO² = THREE

alphabets are single-digit integers

TWO is three digit numbers

and THREE is 5 digit numbers

Hence T must be 1  

T = 1

Now trying different possible combination

TWO are different digits

Hence can be  102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 120 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 132 , 134 , 135 , 136 , 137 , 138 , 139 , 140

142² is 6 digit number

number ending with 0 are not possible as then O = 0 and E = 0

Hence only   138² = 19044 end with repeated digit

T = 1  W = 3  , O = 8

H = 9 , R = 0 , E = 4

T + W + O​ = 1 + 3 + 8 = 12

T + W + O  = 12

Simple method :

based on  given options :

TWO is three digit numbers

and THREE is 5 digit numbers

Hence T must be 1  

T = 1

now 1 + 9 + 8 = 18  is maximum possible value

so 25 and 29 are not possible

but 189² or 198² is 6 digit number hence not possible

so only possible solution in given option is 12.

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