Working Backwards

Official Guide practice (find these in your Official Guide or at www.gmatclub.com)

Develop your skills solving the following Official Guide problems by deliberately using the strategy of Working Backwards, even if your habit pulls you towards the strategy of making an equation. All of the problems below can be solved without using any algebra. After reading the problem and organizing the information, pick answer B, C, or D and work backwards from there.

PS15358 A collection of 16 coins,

PS15402 Thabo owns exactly 140 books,

PS15523 Company Q plans to make

PS06601 The smaller rectangle in the figure

PS03635 If then r =

PS04734 What number is 108

PS69400.02 Last year a state senate

PS02820 The figure shown above represents a modern painting

PS36090.02 If 65 percent of a certain firm’s employees

PS16259 If Jake loses 8 pounds

PS16810 The present ratio of students

PS06570 Each year for 4 years,

PS07491 At his regular hourly rate, Don

PS08480 A border of uniform width is placed around a rectangular photograph

PS16898 If , then x could be

Reflection task

Look again at the problems above and note what clues they contain that tell you that Working Backwards is a suitable strategy for solving them. (Suggestions are at the bottom of this page.)

If solving problems using algebra is your habit, then pick out a few of the above problems and try to solve them by algebra. Compare this strategy with Working Backwards. (Note that the problems above are listed in order of difficulty.)

Go back to a practice test that you have done recently and try to find problems that can be solved by working backwards.

Clues that Working Backwards might be an efficient strategy for a certain problem:

1.      Easy-to-work with numbers, such as small positive integers. (PS15358)

2.      Steps that would be complicated to turn into algebra. (e.g. PS07491)

3.      Long wordy problems. (e.g. PS15402)

4.      Given equations that would be hard to solve (e.g. PS16898)