Question

p and q are two numbers such that p x q is an integer but p - q is NOT an integer. Which of the following could be the values of p and q?​

Answer 1

SOLUTION

COMPLETE QUESTION

p and q are two numbers such that p × q is an integer but p - q is NOT an integer. Which of the following could be the values of p and q?

A) - 4 , 4

B) 4 , 4

$\displaystyle \sf{ C) \: \: \frac{1}{4} , \frac{1}{4} }$

$\displaystyle \sf{D) \: \: 4 , \frac{1}{4} }$

EVALUATION

CHECKING FOR OPTION : A

Here p = - 4 & q = 4

Then p × q

= - 4 × 4

= - 16 : which is an integer

p - q

= - 4 - 4

= - 8 : which is an integer

So this option is not correct

CHECKING FOR OPTION : B

Here p = 4 & q = 4

Then p × q

= 4 × 4

= 16 : which is an integer

p - q

= 4 - 4

= 0 : which is an integer

So this option is not correct

CHECKING FOR OPTION : C

$\displaystyle \sf{ Here \: \: p = \frac{1}{4} ,q = \frac{1}{4} }$

Then

$\displaystyle \sf{ p \times q}$

$\displaystyle \sf{ = \frac{1}{4} \times \frac{1}{4} }$

$\displaystyle \sf{ = \frac{1}{16} } \: \: : which \: is \: not \: an \: integer$

p - q

$\displaystyle \sf{ = \frac{1}{4} - \frac{1}{4} }$

$\displaystyle \sf{ = 0} \: \: : which \: is \: an \: integer$

So this option is not correct

CHECKING FOR OPTION : D

$\displaystyle \sf{ Here \: \: p = 4 ,q = \frac{1}{4} }$

Then

$\displaystyle \sf{ p \times q}$

$\displaystyle \sf{ = 4 \times \frac{1}{4} }$

= 1 : which is an integer

p - q

$\displaystyle \sf{ = 4 - \frac{1}{4} }$

$\displaystyle \sf{ = \frac{15}{4} } \: \: : which \: is \: not \: an \: integer$

So this option is correct

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{D) \: \: 4 , \frac{1}{4} }$

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Answer 2

Answer:

If we take option :D

p= 4 and q= 1/4

A.T.Q

pxq = is an integer

4x 1/4 = 1 which is an integer

p-q = not an integer

4- 1/4 = 15/4 which is not an integer

I hope you guys can understand