Question

Find the missing number.
6 : 35 :: 11: ?
(a) 120
(b) 121
(c) 115
(d) 122

Answer 1

Hint: Here, we need to find the missing number. We will use the operations of addition, subtraction, multiplication, and division to form a relation between 6 and 35. Then, we will apply this relation to the number 11 to get the value of the missing number.

Complete step-by-step answer:
We need to use logical reasoning to find the missing number.
We will use the basic mathematical operation to form a relation between 6 and 35.
We can observe that 35 is the difference of 36 and 1.
Thus, we can write
\[35 = 36 - 1\]
Now, we know that 36 is the square of 6.
Thus, we get
\[35 = {6^2} - 1\]
We can observe that the number 35 is one less than the square of 6.
This is the relation.
We will apply this relation to the number 11 to get the value of the missing number.
The square of 11 is 121.
Thus, we get
\[{11^2} = 121\]
Subtracting 1 from both sides of the equation, we get
\[{11^2} - 1 = 120\]
Therefore, we get the missing number as 120.
Thus, the correct option is option (a).

Note: Since this is a question of logical reasoning, more than one answer is possible. We have shown the answer which gives us a value of the missing number from the chosen options.
We will also check two other relations between 6 and 35, which result in different values of the missing number.
(i) We know that 35 is the product of 7 and 5. We can write this as \[35 = 7 \times 5\].
Rewriting the equation, we get
\[35 = \left( {6 + 1} \right) \times 5\]
Thus, we have found a relation between 6 and 35.
Applying the same relation to 11, we get
\[\left( {11 + 1} \right) \times 5 = 12 \times 5 = 60\]
Thus, using this relation, we get the value of the missing number as 60.
Therefore, we can see that by forming different relations, we can get different values of the missing number.