Question

41) On dividing an integer P by 2, we get an integer Q. On
multiplying Q by 3, we get an integer that is greater than
(-20) and less than 30. How many possible values can P
have?

​

Answer 1

SOLUTION

GIVEN

• On dividing an integer P by 2, we get an integer Q.

• On multiplying Q by 3, we get an integer that is greater than (-20) and less than 30.

TO DETERMINE

The possible values P can have

EVALUATION

Here it is given that On dividing an integer P by 2, we get an integer Q.

$\displaystyle \sf{ \therefore \: \frac{P}{2} = Q\: }$

$\displaystyle \sf{ \implies \: P = 2 Q\: }$

Again On multiplying Q by 3, we get an integer

Let the integer is R

$\implies \sf{3Q = R}$

$\displaystyle \sf{ \therefore \: R = \frac{3P}{2} \: }$

Again R is greater than (-20) and less than 30

$\displaystyle \sf{ \therefore \: - 20 < R < 30 \: }$

$\displaystyle \sf{ \implies \: - 20 < \frac{3P}{2} < 30 \: }$

$\displaystyle \sf{ \implies \: - \frac{40}{3} < P< 20 \: }$

Hence the possible integral values of P are

Hence the possible integral values of P are - 13, - 12, - 11,..., 19

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