Question

If A, B, C, D and E are five prime numbers, sum of these five numbers = 266. It is given that
\[A < B < C < D < E\] then the value of \[{{A}^{5}}\] is
A. 243
B. 32
C. 3125
D. Can’t determined

Answer 1

Hint: To solve this question we should be known of two basic facts of numbers
First facts are all the prime numbers are odd except 2
Second fact is If we have odd numbers in even quantity then their sum will be even and if they are present in odd quantity then their sum will be odd

 Complete step-by-step answer:
We are given in question that there are total 5 prime numbers A, B, C, D and E and their sum is 266
With condition \[A < B < C < D < E\] and we have to find \[{{A}^{5}}\]
Given \[A+B+C+D+E=266\] ,
Now considering 2 conditions
1. All the prime numbers are odd except 2
2.If we have odd numbers in even quantity then their sum will be even and if they are present in odd quantity then their sum will be odd
Assume that A, B, C, D and E all are odd numbers,
But their quantity is 5
And we know that all odd numbers present in odd quantity then their sum will be odd but we got our sum as even it means out of 5 numbers there is 1 even and 4 odd number, only even prime number is 2
And we have this condition \[A < B < C < D < E\] and we know that 2 is the smallest prime number so it means value of A is 2
Now it's very easy we just have to find \[{{A}^{5}}\]
\[{{A}^{5}}={{2}^{5}}=32\]
Hence answer is 32

 So, the correct answer is “Option B”.

 Note: The concept used in this question is very important as it is asked many time in competitive exams , whenever questions is asked around prime number don’t get confused by seeing big data like in this case we are given 5 numbers A, B, C, D and E and it is not possible to find values of B, C, D and E so it is asked only for the value of A.