I encountered a question while preparing for GRE and am stuck.
In an examination paper of 5 Questions, 5 percent of the candidates answered all of them and 5 percent none. Of the rest, 25% answered only one question, 20% only 4. If 24.5% of the entire candidates answered only two questions and 200 answered only 3 questions, how many candidates appeared in examination?
Please help me in solving this.
They are being nasty, trying to fool you.
"Of the rest" means of the $90\%$ that remain after the two $5\%$ chunks are removed. So the percentage who got $1$ is $25\%$ of the $90\%$, which is $22.5\%$. Similarly, the percentage that got $4$ is $18$.
But (trying to fool you again, assuming you did not get misled already) the $24.5\%$ refers to the whole group.
Thus all the questions except $3$ account for $5+5+22.5+18+24.5$ percent of the students. This sum is $75\%$.
That leaves $25\%$ who got $3$. But there are $200$ of these, so the total is $800$.