Question

Alice wants to write down the list of prime numbers less than 100, using each of the digits 1, 2, 3, 4, and 5 exactly once and no other digits.
Which prime number must be in her list?
A.2
B.5
C.31
D.41
E.53

Answer 1

Hint: Prime number is the number that is divisible by 1 and itself. So write such a prime number that should be taken from the digits 1, 2, 3, 4, and 5 only once (the taken number should not repeat again in another prime number) and we should use maximum digits that are mentioned above.


Complete step by step solution
Given:
The digits that can be used are 1, 2, 3, 4 and 5.
We know that the 100 is a 3 digit number and the numbers less than 100 will be 2 digit number, so we can use maximum 2 digits to list the prime numbers from the given 1, 2 3, 4 and 5, not more than that because we need to list the prime number that is less than 100 only.
So the two digit prime numbers that can be formed from the mentioned digits are (and less than 100) 11, 13, 23, 31, 41, and 53. So these are the prime numbers that can be formed by using the digits.
If we remember the statement that we have to use the digits only once, then 41 and 53 will be eliminated from the numbers 11, 13, 23, 31, 41, and 53. (1 and 3 is repeated in 41 and 53) and the prime numbers that are one digit are 2 and 5 (that are in the options).
Now, the remaining prime numbers are 11, 12, 23, 31, then if we look up the options, we can find 2, 5 and 31 are in the options.
Therefore, the numbers 2, 5 and 31 are the prime numbers that must be in the list of the Alice, it means the option (c) is correct.


Note: In this solution, we have to pick the three options that are prime numbers, we may be confused while answering because not more than one option can be selected (but in this question we can select). Before listing the prime numbers, be sure whether you are satisfying the given conditions or not.