GMAT Math : Calculating percents
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Example Questions
Example Question #21 : Calculating Percents
A number is divided by four; the quotient is divided by three; that quotient is multiplied by five; and the decimal point in that product is moved to the left one place. What percent of the original number is that final result?
The best way to solve this is to start with the original number being 100. The result is the percent.
The result of subsequent divisions by four and three, multiplication by five, and shifting the decimal point one place left - or division by ten - is
or, equivalently,
This can be calculated as
So for any number at which we start out, the final result is 
Example Question #22 : Percents
The above is an annual income tax table for single persons in a given state.
Mr. McKenzie earned a salary of $2,270 per month until August 1, when he received a 10% raise. He also received a $2,000 bonus and $511 in interest.
Assuming that there was no additional income, calculate Mr. McKenzie's income tax to the nearest dollar.
None
Mr. McKenzie earned $2,270 per month for seven months, earning a total of
His raise on August 1 was 10%, making his new salary
He earned this over the remaining five months, earning
Add these and the bonus and interest to get
This places Mr. McKenzie in the $20-40,000 income bracket, so he will pay $50 plus 0.8% of earnings above $20,000. This will be
The correct response is $137.
Example Question #23 : Percents
The above is an annual income tax table for single persons in a given state.
Between January 1 and July 1, Mr. Smith earned $722 per month from a part time job. He earned a raise beginning on July 1, but he ended up not paying any income tax for the year. Assuming he had no other income, what percent was the highest possible raise in his salary? Choose the answer that is closest to the maximum possible raise.
Since Mr. Smith did not pay any income tax, his income was at most $10,000.
He earned $722 per month over six months for a total of
The maximum he earned over the remaining six months is
This represents a
maximum raise.
The closest choice is 30%.
Example Question #21 : Calculating Percents
The above is an annual income tax table for married couples in a given state.
Mr. Barrett began a job on March 1 that paid a salary of 
Assuming that there was no additional income, calculate the Barretts' income tax to the nearest dollar.
Mr. Barrett earned $3,872 per month for ten months for a total of
Mrs. Barrett earned $2,882 per month for nine months for a total of
These salaries and the interest add up to
This puts the Barretts in the $60-80,000 range, so their tax is $470 plis 1.7% of earnings above $60,000. This is
The correct response is $554.
Example Question #22 : Calculating Percents
The above is an annual income tax table for single persons in a given state.
Mr. Parsons earned a salary of 
Mr. Parsons earned $3,122 per month for twelve months in his main job for a total of
He earned $886 per month for eight months in a part-time job for a total
Add these, and the $817 he earned from interest:
This puts Mr. Parsons in the $40-60,000 tax bracket, so he will pay $210 plus 1.3% of what he earns above $40,000. This will be
This rounds to $280.
Example Question #26 : Percents
Total sales at XYZ Corporation increased by 
The amount of sales for this year is 125% of last year's sales. Therefore, we can calculate in the following way:
Or:
Example Question #23 : Calculating Percents
Insufficient information is given to answer the question.
To find out what percent 
Example Question #24 : Calculating Percents
Insufficient information is given to answer the question.
The question can therefore be rewritten as follows:
Solve by evaluating:
Example Question #29 : Percents
So 
of 
Example Question #30 : Percents
True or false: 
Statement 1: 
Statement 2: 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. 
Statement 2 alone is inconclusive.
For example, if 
and 
which is not an integer.
But if 
and 
which is an integer.
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