gmat word problems
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- 1. id what value the question is asking for (desired value)
- 2. id unknown values and label them with variables
- 3. id relationships and translate them into equations
- 4. use the equation to solve for the desired value
additive relationships - subj. algebraic translation
- adding terms with the same units does not change the units
- the units of every term are the same
multiplicative relationships - subj. algebraic translation
- treat units like numerators and denominators
- units that are multiplied together DO change
common relationships - subj. algebraic translation
- total cost ($) = unit price ($/unit) x quantity purchased (units)
- profit ($) = revenue ($) - cost ($)
- total earnings ($) = wage rate ($/hour) x hours worked (hours)
- miles = miles per hour x hours
- miles = miles per gallons x gallons
ex. If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates? (54, 55, 56, 57, 58)
If Kelly received 1/3 more votes than Mike, she received 4/3 the number of votes. So what times 4/3 will equal an integer? only multiple of 3 will cancel out the 3 in the denominator. the number of votes Mike received is a multiple of 3, then the number of votes Kelly received must be a multiple of 4. Taken together, the total number of votes cast must then be a multiple of 7. (answer is 56)
DS ex. A store sells erasers for $0.23 each and pencils for $0.11 each. How many erasers and pencils did Jessica buy from the store?
(1) Jessica bought 5 erasers
(2) Jessica spent $1.70 on erasers and pencils
- Statement 1 by itself is not sufficient
- On the surface, statement 2 should not be enough.
- If J bought 1 eraser, 170 - 23 = 147 cents on pencils (but 147 isn't divisible by 11)
- ... If J bought 5 erasers and 5 pencils: 5(23) + 5(11) = 170
- thus, statement 2 is sufficient by itself
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