If a, b, c are prime numbers, x is an even number, y is an odd number. Which of the following are never true?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

a + x = b

b + y = c

ab = c

a + b = c

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We are given that a, b, c are prime numbers, x is an even number and y is an odd number.
Therefore, to solve the question we will check one by one if the statements are true or not.
Taking statement I,
a + x = b,
Now using the given information, we can write
Sum of a prime number and an even number is equal to a prime number.
Now let’s consider an example
Take
Prime number, a = 17,
Even number, x = 2
Now taking their sum we get
a + x = 17 + 2
a + x = 19
And we know 19 is a prime number.
Hence, we can say that-
Sum of a prime number and an even number is equal to a prime number.
Therefore, a + x = b is true for some values of a, x, b.
Hence the statement (1) is true for some values of a, x, b.
Now taking Statement II,
b + y = c
Now using the given information, we can write that -
Sum of a prime number and an odd number is equal to a prime number.
Now let’s consider an example
Take
Prime number, b = 2
Odd number, y = 3
Now taking their sum we get
b + y = 2 + 3
b + y = 5
And we know 5 is a prime number.
Hence, we can say that -
Sum of a prime number and an odd number is equal to a prime number.
Therefore, b + y = c is true for some values of b, y, c.
Hence the statement (2) is true for some values of b, y, c.
Now taking statement 3,
ab = c
Now using the given information, we can write that -
Product of two prime numbers is equal to a prime number.
Now, by the definition of prime numbers we know that-
A prime number is a number which is divisible by one or itself.
Now, directly from the definition of prime numbers we can see that the product of two numbers will not be the only divisible by one and itself only.
So, we can say that a product of two prime numbers can never be a prime number.
Hence statement (3) can never be true.
Now taking statement 4,
a + b = c
We can also write it as
Sum of two prime numbers is equal to a prime number.
Now let’s take an example
Prime number, a = 2
Prime number, b = 3
Now taking their sum we get-
a + b = 2 + 3
a + b = 5
Now, 5 is a prime number.
Hence, a + b = c is true for some values of a, b, c
From the above conclusion we can write that only statement (3) can never be true.

Watch 3-min video & get full concept clarity