Consider the following statements: 1) √75 is a rational number. 2) There exists at least a positive integer x such that -4x/5 < -7/8. 3) (x - 2)/x < 1 for all real values of x. 4) 4.232323.... can be expressed in the form p/q where p and q are integers. Which of the above statements are correct?

CDS 2019 PYQ with Answer — Consider the following statements: 1) √75 is a rational number. 2) Th…

2019 · Q80

Consider the following statements:

1√75 is a rational number.
2There exists at least a positive integer x such that -4x/5 < -7/8.
3(x - 2)/x < 1 for all real values of x.
44.232323.... can be expressed in the form p/q where p and q are integers.

Which of the above statements are correct?

Elementary MathematicsNumber System

A1 and 2
B2 and 3
C3 and 4
D2 and 4

Explanation

1) sqrt(75) is irrational: false. 2) -4x/5 < -7/8 iff x > 35/32, e.g. x = 2: true. 3) undefined at x = 0, so not for all real x: false. 4) a recurring decimal is rational: true. Hence 2 and 4.