Question

What is the value of x for which x,x+1,x+3 are prime numbers?
a) 0
b) 1
c) 2
d) 101

Answer 1

Hint: In the above type of question when we need to find the a number from a given option we will make use of the option provided we will substitute the options one by one to check whether or not that option satisfies the given question.

Complete step by step solution:
In the above type of question we need to find the value of x which will satisfy three different equations i.e. x, x+1, x+3 and when substituted the value of x it should give us the final product as prime numbers.
Prime numbers are numbers which can only be divisible by itself or by 1 for example 3, 5, 7 and many more.
So to check whether the numbers formed from the options are prime or not we are going to use these numbers one by one.
Let us start with option a) 0. So, we get x, x+1, x+3 as 0, 1, 3. Here we know that 0 and 1 cannot be considered as prime numbers, so this cannot be correct.
Next, we move to option b) 1. So, we get x, x+1, x+3 as 1, 2, 4. Here we know that 1 cannot be considered as a prime number, 2 is a prime number and 4 is not a prime number, so this cannot be correct.
Moving to option c) 2. Here, 2 is a prime number and when 1 is added it equals 3 which is also a prime number and when 3 is added to 2 it equals 5 which is also a prime number. So, we get x, x+1, x+3 as 2, 3, 5. This satisfies the given condition and it is correct.
Last, we will check option d) 101. So, we get x, x+1, x+3 as 101, 102, 104. 101 is a prime number but when we go to our next number i.e. 102, it is an even number and so is 104. Hence it cannot become a prime number so this option is also wrong.

So, the correct answer is “Option c”.

Note: In the above type of questions when there is nothing mentioned about the numbers or the things that need to be found always make use of the option given to check by substituting it in the given equations. We can also eliminate options like 0 and 1 since we know that they are neither prime nor composite. Do not make the mistake of eliminating 2 since 2 is the only even prime number.