GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #22 : Calculating Percents

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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.

Possible Answers:

Correct answer:

Explanation:

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

, which is

 per month.

This represents a 

maximum raise.

The closest choice is 30%.

Example Question #23 : Calculating Percents

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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  per month, and remained with it through the remainder of the year. Mrs. Barrett woked at a salary of  per month from January 1 until she was laid off on August 31; her layoff ended on December 1, and she resumed work at her former salary. The couple also received interest income of

Assuming that there was no additional income, calculate the Barretts' income tax to the nearest dollar.

Possible Answers:

Correct answer:

Explanation:

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 #24 : Calculating Percents

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The above is an annual income tax table for single persons in a given state.

Mr. Parsons earned a salary of  per month for the entire year. He also earned  per month from April 1 to November 30 from a part-time job, and  from interest. Assuming Mr. Parsons had no other income, calculate Mr. Parsons's income tax to the nearest dollar.

Possible Answers:

Correct answer:

Explanation:

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 #101 : Arithmetic

Total sales at XYZ Corporation increased by  this year. What is the amount of sales for this year if last year's sales were ?

Possible Answers:

Correct answer:

Explanation:

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 #105 : Arithmetic

 is 35% of  is 25% of . What percent of  is ?

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

Explanation:

 is 35% of ,and  is 25% of , so

 and .

To find out what percent  is of , evaluate:

Example Question #106 : Arithmetic

 is 40% of 

 is what percent of  ?

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

Explanation:

 is 40% of , so .

The question can therefore be rewritten as follows:

 is what percent of  ?

Solve by evaluating:

Example Question #21 : Calculating Percents

 is 35% of . What percent of  is ?

Possible Answers:

Correct answer:

Explanation:

 is 35% of , so 

, so

So  is , or

 

of .

Example Question #108 : Arithmetic

 is 40% of , and  is 75% of  and  are positive integers.

True or false:  is a positive integer.

Statement 1:  is a multiple of 5.

Statement 2: is a multiple of 4.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

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.

BOTH statements TOGETHER are insufficient to answer the question. 

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone.  is 40% of , or, equivalently,  is a multiple of 5, so for some integer . Consequently, 

.

 is twice an integer so  is itself an integer.

Statement 2 alone is inconclusive.

For example, if ,   is 75% of this, which is 

,

and  is 40% of 6, which is 

which is not an integer.

But if ,   is 75% of this, which is 

,

and  is 40% of 15, which is 

which is an integer.

Example Question #108 : Arithmetic

Ten students in a class of  students have a learning disability. What is the percentage of students who do not have a learning disability in the class?

Possible Answers:

Correct answer:

Explanation:

The number of students who don't have a learning disability is:

Using part over whole we get the percentage of students who don't have a learning disability as:

Example Question #109 : Arithmetic

You bought  worth of a stock two years ago. After the first year, the value of the stock decreased by an average . During the second year, the value of the stock increased by an average . What is the value of your investment today?

Possible Answers:

Correct answer:

Explanation:

The value of the stock after the first year is 90% (0.9) of the value of the stock at time 0.

The value of the stock after the second year is 125% (1.25) of the value of the stock at the end of the first year.

The value of the investment today is:

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