IMAT 2011 Q16 [House Numbers]

A street of houses is numbered starting on one side with 1,2,3,4…. At the far end the numbers continue down the other side in the opposite direction so the largest number is opposite number 1. The houses are of identical widths so each house has another directly opposite it.

If number 17 is directly opposite number 56, how many houses are there in the street?

A. 36

B. 37

C. 39

D. 72

E. 73

Simple steps to solve word problems:

  1. Underline key information

  2. Determine what they are trying to ask, and what you will need to solve it

  3. Eliminate any non-essential information

  4. Draw a picture, graph, or equation

  5. In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.

  6. Solve.

Important info: The largest number is opposite number 1. This means that we need to use the data given to find the house infront of 1.

Givens: 17 is in front of 56, they are increasing in opposite directions.

Taking this info, you can count backwards from 17 to 1, and count from 56 to your answer. You could do this in your head by doing 17-1 = 16, 16 + 56 = 72. However I would recommend writing the numbers out to be sure to not make a mistake.

\begin{array} {|r|r|}\hline 17 & 56 \\ \hline 16 & 57 \\ \hline 15 & 58 \\ \hline 14 & 59 \\ \hline 13 & 60 \\ \hline 12 & 61 \\ \hline 11 & 62 \\ \hline 10 & 63 \\ \hline 9 & 64 \\ \hline 8 & 65 \\ \hline 7 & 66 \\ \hline 6 & 67 \\ \hline 5 & 68 \\ \hline 4 & 69 \\ \hline 3 & 70 \\ \hline 2 & 71 \\ \hline 1 & 72 \\ \hline \end{array}

Therefore the answer is D. 72