A prime number is squared and then added to a different prime number. The number thus obtained is:
I. An even number
II. An odd number
III. A positive number

I only

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II only

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III only

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I and III only

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I, II, and III

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Solution

The correct option is E I, II, and III
Only even prime number is $2$ . All other prime numbers are odd.
Case I:
One of the two prime number is $2$ . Then the sum of an odd and even number is always odd. Thus the number will be an odd number.
Case II:
None of the prime numbers is $2$ . Then the sum of two odd numbers is even. Hence the number will be even.
Thus I, II and III, all the cases are possible.

Suggest Corrections

Similar questions

State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

(b) The sum of two odd numbers and one even number is even.

(d) If an even number is divided by 2, the quotient is always odd.

(e) All prime numbers are odd.

(f) Prime numbers do not have any factors.

(g) Sum of two prime numbers is always even.

(h) 2 is the only even prime number.

(i) All even numbers are composite numbers.

(j) The product of two even numbers is always even.

p_{1}^{2} - p_{2}^{2}

State true (T) of false (F):

$(i)$ The sum of primes cannot be a prime.

$(i i)$ The product of primes cannot be a prime.

$(i i i)$ An even number is composite.

$(i v)$ Two consecutive numbers cannot be both primes.

$(v)$ Odd numbers cannot be composite.

$(v i)$ Odd numbers cannot be written as sum of primes.

$(v i i)$ A number and its successor are always co-primes.

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