Data Interpretation Discussion

**Common Information**

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

The following Pie-Chart provides information about the marks obtained by six students A, B, C, D, E and F in four different subjects P, Q, R and S. The marks obtained by each of the students in subject P is indexed to the maximum marks that can be obtained in subject P. This holds true for the other three subjects as well.

For example, if the maximum marks that can be obtained in subject P is ‘40k’, then the marks obtained in subject P by student A is 15k, by student B is 20k and so on. This holds true for the marks obtained by the students in the other three subjects as well.

The marks obtained by A in subject P is not less than that obtained by him in subject Q or subject R, but not more than that obtained by him in subject S. This holds true for the marks obtained by each of the other 5 students as well.

Q. |
How many students have definitely obtained lesser marks than $X$ in subject Q? |

✔ A. |
5 |

✖ B. |
4 |

✖ C. |
3 |

✖ D. |
2 |

**Solution:**

Option(**A**) is correct

Let the maximum marks which can be obtained in the subjects P, Q, R and S be $40p, 50q, 60r$ and $80s$ respectively.

From the given information we can conclude that:

$15p≥20q$, $20p≥10q$, $25p≥15q$, $10p ≥18q$, $25p≥32q$ and $30p≥ 12q$

$⇒ p ≥ 1.8q$ -------- (i)

$15p≥8r$, $20p≥16r$, $25p≥20r$, $10p≥24r$, $25p≥10r$ and $30p≥20r$

$⇒ p≥2.4r$ -------- (ii)

$15p≤25s$, $20p≤15s$, $25p≤20s$, $10p≤30s$, $25p≤10s$ and $30p≤35s$

$⇒ p≤ 0.4s$ -------- (iii)

Given that $X = 20p - 10q$.

For the minimum value of $X, p$ should be the minimum and the minimum value of $p$ is $1.8q$ {from (i)}.

⇒ The minimum value of $X$ is:

$⇒20(1.8q) - 10q = 26q$

So, the students A, B, C, D and F (i.e. **5 students**) have definitely obtained lesser marks than $X$ in subject Q.