unit.Some of the most challenging formula problems on the GRE are those that involve unspecified amounts. Typically, these questions focus on the increase or decrease in the value of a certain formula, given a change in the value of the variables. Just as with other GRE problems with unspecified amounts, solve these problems by picking numbers.
If the length of the side of a cube decreases by two-thirds its original value, by what percent will the volume of the cube decrease?
First consider the formula involved here. The volume of a cube is defined by the formula V = s3, where s represents the length of a side. Then pick a number for the length of the side of the cube.
Say the cube has a side of 3 units. Note that this is a “smart” number to pick because it is divisible by 3 (the denominator of two-thirds).
Then its volume equals s3 = 3 × 3 × 3 = 27.
If the cube’s side decreases by two-thirds, its new length is
unit.
Its new volume equals s3 = 1 × 1 × 1 = 1.
You determine percent decrease as follows:
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When Tom moved to a new home, his distance to work decreased by
the original distance and the constant rate at which he travels to work increased by
the original rate. By what percent has the time it takes Tom to travel to work decreased?