IMAT 2020 Q4 [Math Survey Project]

As part of a maths project, a class of 30 children conduct a survey amongst themselves of how
many brothers and sisters they have. They each write their name in the appropriate space on the chart below. No one in the class has a brother or sister who is also in the class.


How many of the 30 families involved in the survey have a total of 3 or more children?

A. 6
B. 7
C. 11
D. 10
E. 8

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Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

For this question, we can determine which boxes in the charts meet the parameters and then find out how many students are in each. We need to find anyone with at least 2 siblings because it means that the family has 3 total children or more (the student themself + their 2 or more siblings = 3 total children). It also makes life easier knowing that their siblings are not in the class so we can just calculate how many per box without any more complications.

Eliminating boxes of families with 3 or fewer children:

The top left box is for only children, therefore we can eliminate it from our tally. We can also eliminate the box immediately to the right (1 brother and 0 sisters) and the box below it (0 brothers and 2 sisters) because they only have 2 children in their families.

That leaves us with anyone who has at least 1 brother and sister or more, at least 2 sisters or more, and at least 2 brothers or more.

If we add up the students, we will get 11 total students. We can also do 30 (class total) - 19 (the students in the 3 boxes that do not meet requirements.

\fcolorbox{red}{grey!30}{Therefore the answer is C, $11$}

Can you write the solution i cant understand