# Data Interpretation - Table Charts - Discussion

Discussion Forum : Table Charts - Table Chart 7 (Q.No. 2)
Directions to Solve

A school has four sections A, B, C, D of Class IX students.

The results of half yearly and annual examinations are shown in the table given below.

 Result No. of Students Section A Section B Section C Section D Students failed in both Exams 28 23 17 27 Students failed in half-yearlybut passed in Annual Exams 14 12 8 13 Students passed in half-yearlybut failed in Annual Exams 6 17 9 15 Students passed in both Exams 64 55 46 76

2.
How many students are there in Class IX in the school?
336
189
335
430
Explanation:

Since the classification of the students on the basis of their results and sections form independent groups, so the total number of students in the class:

= (28 + 23 + 17 + 27 + 14 + 12 + 8 + 13 + 6 + 17 + 9 + 15 + 64 + 55 + 46 + 76)

= 430.

Discussion:
18 comments Page 2 of 2.

Shashwat Shekhar said:   1 decade ago
How do they form independent groups?

Darshana said:   10 years ago
The four group are independent so the answer is sum of all the numbers.

I think the correct answer is 336.

Total students in the class = (no of students passed in both exams + no of students failed in both exams).

Students failed in both the exams can't pass any or both of the exam.

Student failed in half yearly only can't failed in both exam also pass both the exam also pass annual.

So all the 4 groups are independent of each other.

NOW short cut to solve this question.

Just add all the tens position number only.

20+20+10+20 (first row over) +10+10+0+10 (second row over) +0+10+0+10 (third row over) +60+50+40+70 = 340.

Now see the options only one option is bigger than 340 tick it and enjoy the life.

According to me the answer would be 335.

How do they form independent groups?

Shweta shinde said:   1 decade ago
Consider 2 venn diagrams for fail and pass students.

In fail we have failed in both, failed in annual but not half,

Failed in half but not annual, so total failed students are addition of all (28+23+17+27 + 14+12+... +16+17+... ) = x.

Now in pass venn diagram we have passed in both,

And passed in 1 and failed in other is already considered so add 64+55+... To x n we get 430.

Ashish Jain said:   1 decade ago
430 is right one because there may be 4 persons e.g A, B, C and D whose result may vary.

A passed in both exams.

B failed in both exams.

C passed in half yearly and failed in annual. This is diff from B.

D failed in half yearly and passed in annual. This is diff from A.

Please correct me if I'm wrong.