Question

Find the next number on the series by using basic mathematical operation \[496:204::329:?\]
A.90
B.110
C.115
D.135

Answer 1

Hint: This question is based on the logical reasoning. Here we will analyze the given numbers and find the pattern between each number. Then we will use the pattern and try to find the next number on the series by using basic mathematical operation.

Complete step-by-step answer:
It is given \[496:204::329:?\]
As we can see that 496 can be written as
\[496 = {8^3} - \left( {8 \times 2} \right)\]
Next we can write 204 as
\[204 = {6^3} - \left( {6 \times 2} \right)\]
Similarly 329 can be written as
\[329 = {7^3} - \left( {7 \times 2} \right)\]
We can write \[496:204::329:?\] as
\[{8^3} - \left( {8 \times 2} \right):{6^3} - \left( {6 \times 2} \right)::{7^3} - \left( {7 \times 2} \right):?\]
As (:) implies the ratio between the two terms and (::) implies equal to, on simplifying above we get,
Let the unknown term is \[x\] so we can get its values as,
According to the pattern the next number will have one term less than 6 as will follow the same pattern as,
\[x = {5^3} - \left( {5 \times 2} \right)\]
Applying the exponent on the terms, we get
\[ \Rightarrow x = 125 - 10\]
Subtracting the terms, we get
\[ \Rightarrow x = 115\]
So we will get our missing term as 115.
Hence, option (C) is correct.

Note:The (::) symbol represents the proportion we can write the = sign also between two ratios. Thus, proportion is like equality of two ratios. This double colon rule is somewhat obscure and therefore it is not used very often. Double colon is also used in C++ programming as a scope resolution operator. We can see in this question it doesn’t completely satisfy the two ratios on both sides but as the pattern is going our answer is correct.