Problems based on Numbers Test 1

Question : 25 of 40

Marks: +1, -0

Consider the following statements:
1. If n is a prime number greater than 5, then

n^4 - 1

is divisible by 2,400.
2. Every square number is of the form 5n or (5n - 1) or (5n + 1), where n is a whole number.
Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Validate

Solution:

Statement 1 is true.
We take prime number n is greater than 5 is equal to 7, 11, 13 …….
If we take n = 7,

n^4-1=(7^4-1)÷2,400

=(2,400-1)÷2,400

=2,400÷2,400=1

If we take n = 11 ,

n^4-1=(11^4-1)÷2,400

=(14,641-1)÷2,400

14,640÷2,400

= 61 and so on.

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