Question

A group of \[110\] People is divided into \[4\] committees. If each committee contains at least \[2\] people, which of the following statements must be true?
A. Each committee has at least \[4\] people
B. No \[4\] Committees have the same number of people
C. No committee has more than \[100\] people
D. At least \[1\] committee has more than \[25\] people
E. The largest committee has \[3\] more people than the smallest committee

Answer 1

Hint: We need to solve the word problem by performing mathematical operations. Here, a group of \[110\] people into \[4\] committees. So we need to find the solution from the given statement if each contains at least \[2\] people.

Complete step by step solution:
The Given data are converted into mathematical expression,
There are group of \[110\] people is divide into \[4\] committees
Each committee contains at least \[2\] people
To find number of people in each committee
Total number of people \[ \div \] Number of committees \[ = \dfrac{{110}}{4} = 27\] people in each committee
By checking the correct statement with respect to the given values,
Check option (D) At least \[1\] committee has more than \[25\] people
 \[25\] people \[ \times \] \[4\] committees \[ = 100\] people.
But, here we have \[110\] people and \[27\] people in a committee. So, we get
Finally, The correct answer is option (D) At least \[1\] committee has more than \[25\] people.
So, the correct answer is “Option D”.

Note: First of all, we need to convert the word problem into mathematical expression and then perform arithmetic operation to find the solution with the given data and check which options match the results..