Directions: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.
How many students participated in sports event?
I. Only 40% of students were qualified for certain sports events.
II. If 44 more students were qualified then percentage of students qualified for sports would have been 62%.
Let’s check each statement individually-
Statement I-
Only 40% of students were qualified for certain sports events.
It gives only information about percent of candidates is qualified in the sports event.
We cannot find the total number of students using statement I alone.
Statement II-
If 44 more students were qualified, then percentage of students qualified for sports would have been 62%.
It gives the information about qualified students.
But as we don’t know number of total students we cannot find answer for question using statement II alone.
Combining the statements, I and II-
Let the total number of students participating be X.
∴ 40% of students were qualified for certain sports events.
∴ 0.40X students got qualified for sports event. ---- (1)
If 44 more students were qualified, then percentage of students qualified for sports would have been 62%.
∴ 0.4X + 44 = 0.62X
∴ 0.62X – 0.4x = 44
∴ 0.22X = 44
∴ X = 200
∴ Both statements I & II are necessary to find required answer.