ISI2018-DCG-2

Question

If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$?

• A. $0.25$
• B. $0.50$
• C. $0.48$
• D. none of these

Answer 1

$\underline{\textbf {Answer: C}}$

$\underline{\mathbf {Explanation:}}$

For $\mathbf {p(p+1)}$ being divisible by $4$, either $\mathbf p$ or $\mathbf {(p+1)}$ should be a multiple of $4$,

One among $\mathbf p$, $\mathbf {(p+1)}$ will be even and other will definitely be odd.

$\mathbf{\underline{Eg:}}$ $(3, 4) \; \text{or}\; (4, 5)$.

So, total number divisible by $12$ till $50 = \dfrac{50}{12} = 12.25 = 12\;\text{multiples}$.

These $12$ can be either $\mathbf p$ or $\mathbf {(p+1)}$, So total = $2\times12 = 24$

So, probability of $\mathbf{p(p+1)}$ divisible by $4 = \dfrac{24}{49} = 0.48$

$\therefore \mathbf C$ is the correct option.

Comments

@priyankabedekar

Yes, you are correct.

Thanks!!

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In the answer section we have to divided 50 by 4 so that the 12.25 comes a part .

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Isn’t total pairs 50 ….(1,2),(2,3)...(50,51) → total 50 pairs. It is mentioned that P ranges from 1 to 50 . P+1 will range from 2 to 51.