Data Interpretation Discussion

**Common Information**

Six friends — Anand, Bimal, Praveen, Kiran, Yashwanth and Rohan — availed a new SMS offer, according to which there will be no charges for the SMSs sent or received within the group. The following pie charts pertain to the details regarding the number of SMSs sent by these persons within the group during the month of October.

The first pie chart gives the break-up of total number of SMSs received by Anand from his five friends in October according to the friend from whom he received the SMSs and the second pie chart gives the break-up of the total SMSs sent by these five persons within the group (i.e., excluding Anand) in the same month according to the person sending the SMSs.

Assume that SMSs sent are received instantly and also the number of SMSs sent by each person is always an integer. For all the following questions, consider only the SMSs sent by the persons within the group in the month of October.

Q. |
What is the least possible value of $N$? |

✖ A. |
3,000 |

✖ B. |
3,750 |

✔ C. |
3,800 |

✖ D. |
4,000 |

**Solution:**

Option(**C**) is correct

Messages received from Bimal:

$= \dfrac{10}{100}× 3000$

$= 300$

Similarly messages received from Praveen, Kiran, Yashwanth and Rohan are 750, 600, 450 and 900 respectively.

The total messages sent by each person must not be less than the messages received by Anand from that person.

For Bimal: 15% of $N ≥ 300$

$⇒ N ≥ 2000$

For Praveen: 20% of $N ≥ 750$

$⇒ N ≥ 3750$

For Kiran: 16% of $N ≥ 600$

$⇒ N ≥ 3750$

For Yashwanth: 25% of $N ≥ 450$

$= N ≥ 1800$

For Rohan: 24% of $N ≥ 900$

$⇒ N ≥ 3750$

The value of $N$, that satisfies all the above cases is $N ≥ 3750$

But if total messages are 3750. than the messages sent by Kiran and Rohan are not integers.

Hence, the least possible value is **3800** (For which. all the values are integers).