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Is y a prime number?
(1) y^2 has exactly 3 positive factors.
(2) y is of form 6q + 1, where q is a positive integer
(1) y^2 has exactly 3 positive factors.
(2) y is of form 6q + 1, where q is a positive integer
14 Jan 2023, 09:53
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We need to find if y is a prime number?
Theory: Prime Numbers are numbers which have only two factors, 1 and the number itself
STAT 1: y^2 has exactly 3 positive factors.
Let's take examples to prove this option both right and wrong
Ex1: y = +3 => y^2 = 9 and 9 has only three factors 1, 3, 9 => y is PRIME => TRUE
Ex2: y = -3, => y^2 = 9 and 9 has only three factors 1, 3, 9 => but y CANNOT be Prime as y is negative => FALSE
=> NOT SUFFICIENT
STAT 2: y is of form 6q + 1, where q is a positive integer
Let's take examples to prove this option both right and wrong
Ex1: q = 1 => y = 6*1 + 1 = 7 => y is PRIME => TRUE
Ex2: q = 4 => y = 6*4 + 1 = 25 => but y is NOT Prime => FALSE
=> NOT SUFFICIENT
Taking both the statements together we get
y^2 has exactly 3 positive factors and y is of form 6q + 1, where q is a positive integer
=> y is positive and y^2 has exactly 3 positive factors and y = 6q + 1
Ex: Let y is a prime number, so y will have only two factors 1 and y itself
=> y^2 will have only three factors 1, y and y^2
=> y is PRIME as only prime numbers satisfy these conditions
=> SUFFICIENT
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Prime Numbers
Theory: Prime Numbers are numbers which have only two factors, 1 and the number itself
STAT 1: y^2 has exactly 3 positive factors.
Let's take examples to prove this option both right and wrong
Ex1: y = +3 => y^2 = 9 and 9 has only three factors 1, 3, 9 => y is PRIME => TRUE
Ex2: y = -3, => y^2 = 9 and 9 has only three factors 1, 3, 9 => but y CANNOT be Prime as y is negative => FALSE
=> NOT SUFFICIENT
STAT 2: y is of form 6q + 1, where q is a positive integer
Let's take examples to prove this option both right and wrong
Ex1: q = 1 => y = 6*1 + 1 = 7 => y is PRIME => TRUE
Ex2: q = 4 => y = 6*4 + 1 = 25 => but y is NOT Prime => FALSE
=> NOT SUFFICIENT
Taking both the statements together we get
y^2 has exactly 3 positive factors and y is of form 6q + 1, where q is a positive integer
=> y is positive and y^2 has exactly 3 positive factors and y = 6q + 1
Ex: Let y is a prime number, so y will have only two factors 1 and y itself
=> y^2 will have only three factors 1, y and y^2
=> y is PRIME as only prime numbers satisfy these conditions
=> SUFFICIENT
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Prime Numbers
