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 least how many students did not fail only in Statistics? |

✖ A. |
271 |

✖ B. |
279 |

✖ C. |
261 |

✖ D. |
275 |

✔ E. |
274 |

**Solution:**

Option(**E**) is correct

In order to find the answer to the question we need to maximise the number of students who failed only in Statistics.

In **Section A:**

Out of the 49 students who failed in two courses, let us assume that 45 students failed in Economics and Business Maths.

This means that $49 – 45 = 4$ students failed in Statistics and Business Maths.

So, maximum possible number of students who failed only in Statistics $= 56 – 4 = 52.$

Therefore, at least $115 – 52 = 63$ students did not fail only in Statistics.

In **Section B:**

Following the same logic as given for Section $A$, at least:

$99 – \{48 – (26 – 23)\} = 99 – 45 = 54$

students did not fail only in Statistics.

In **Section C:**

Out of the 43 students who failed in two courses, let us assume that all 43 failed in Economics and Business Maths.

Therefore a maximum of 28 students failed only in Statistics.

So, at least $139 – 28 = 111$ students did not fail only in Statistics.

In **Section D:**

Out of the 21 students who failed in two courses, let us assume that all 21 failed in Economics and Business Maths.

Therefore a maximum of 19 students failed only in Statistics.

So, at least $65 – 19 = 46$ students did not fail only in Statistics.

So across all the four sections, at least:

$=63 + 54 + 111 + 46=274$ students did not fail only in Statistics.

**Paresh**

*()
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we can assume this by the fact that there are only 45 students who failed in economics in section A which is the maximum number we can assign to the failed in both economics and business studies.

how can we assume 45 students failed in Statistics and Business Maths in section A.