GMAT Quantitative Reasoning: Problem Solving Questions
The Problem-Solving part of the Quantitative section is designed to test your ability to work with numbers. A variety of questions deal with the basic principles of arithmetic, algebra, and geometry. These questions may take the form of word problems or require straight calculations. In addition, questions involving the interpretation of tables and graphs may be included. Based upon past tests, between 50 and 55 percent of the questions in a Quantitative section will be problem-solving questions.
Q. A tower casts a shadow of 6 meters at a certain time of the day. If at exactly the same time, a man stands at the top of the tower, the length of the shadow increases by 2 meters. What is the height of the man if the tower is 5 meters high?
(A) 1 meter
(B) 1.5 meters
(C) 1.66 meters
(D) 2 meters
Step 1: This is a simple proportions problem. The basic concept is that when the man stands on the top of the tower, the length of the shadow increases proportionately to total height of the tower and the man. The following figure should make it clear:
Step 2: If we assume the height of the man as x, we can express the proportional relationship mathematically as:
Cross multiplying and simplifying the equation, we get: