Data Interpretation Discussion

**Common Information**

Answer the questions on the basis of the information given below.

The $2006$ batch of a premier B- school in India fared poorly in the three courses namely Statistics, Economics and Business Maths in their first semester examinations.

The batch was divided into four sections $A$, $B$, $C$ and $D$ and every student in the batch wrote the examination on each of the three mentioned courses.

The following bar graph provides information about the number of students who failed in each of the courses in the four sections.

It also provides information about the total number of students and the number of students who failed in two courses in each of the four sections. No student failed in all the three courses.

Q. |
Across all the four sections at most how many students passed in both Statistics and Business Maths? |

✖ A. |
121 |

✖ B. |
136 |

✖ C. |
153 |

✔ D. |
197 |

✖ E. |
217 |

**Solution:**

Option(**D**) is correct

No. of students who passed in Statistics and BM is Equivalent to no of students who failed only in Economics & the no of students who passed in all the three subjects.

In Section A:

Out of the 49 students who failed in two courses, let us assume that 49 students failed in BM & Statistics.

Maximum possible no. of students who failed only on Economics is 45.

In Section B:

Similarly in section B maximum possible no of students who failed only in Economics is 23.

In Section C:

Out of the 43 students who failed in two courses, let us assume that 28 students failed in BM & Statistics.

This means that $43 - 28 = 15$ students failed in Economics and one of the other course.

Maximum possible no. of students who failed only on Economics is:

$61-15 = 46$

In Section D:

Following the same logic as given for section $C$, at most:

$[24 - (21 - 19)] =22$

So across all the four sections the no of students who passed in statistics & BM:

$= (45 + 23 + 46 + 22) + 61$

$=197$

**Paresh**

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on what basis are these assumptions made. I did not understand.Please explain in simpler words.