GMAT Math : Arithmetic
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #1 : Ratio & Proportions
Eleanor has a a scale model of the Voyager I probe. What is the radius of the dish in the model?
I) The length of the antennae on the model is 
II) The radius of the dish on the actual probe is 
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Either statement is sufficient to answer the question.
Both statements are needed to answer the question.
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Both statements are needed to answer the question.
The secret to this problem is to set up a proportion.
We are given the ratio of one part of the model from Statement I, and asked to find the length of another part.
We need both I) and II) to set up the following proportion.
So both statements are needed.
Example Question #5 : Ratio & Proportions
In a car dealership there are 
- There are
SUVs.
- There are
sport cars.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statement 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Each statement alone is sufficient.
We can combine the given ratios into one ratio by using the least common mulitiple of 8 and 6, which is 24.
In order to arrive to 24, we need to multiply the first ratio by 3 and the second ratio by 4. We can then arrive to a single ratio of
Using our ratio, we have an equation:
Statement 1:
then 
so Statement 1 is sufficient to answer the question
Statement 2:
then 
so Statement 2 is also sufficient to answer the question
Example Question #281 : Arithmetic
What percent of students in a school are freshmen with glasses?
(1) Of the freshmen in the school, 10% wear glasses.
(2) Of the non-freshmen in the school, 20% wear glasses.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
EACH statement ALONE is sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
To answer this question, it is necessary to know the total number of students in the school and the number of freshmen with glasses.
(1) This indicates that 10% of the freshmen have glasses; neither the total number of freshmen nor the total number of students in the school is provided 
(2) Provides the percent of non-freshmen who wear glasses (irrelevant to the question at hand). It does not provide the total number of students in the school or the number of freshmen with glasses 
From (1) and (2), the percent of non-freshmen with glasses is known and the percent of the freshmen with glasses is known, but not the percent of the school who are freshmen with glasses.
For example:
If there are 100 freshmen, including 10 freshmen with glasses, and 100 non-freshmen, including 20 non-freshmen with glasses, then 
If there are 300 freshmen, including 30 freshmen with glasses and 100 non-freshmen, including 20 non-freshmen with glasses, then 
Both statements together are not sufficient.
Example Question #282 : Arithmetic
In 2013 there are 300 employees at Company ABC. If the number of employees at Company ABC increased by 200% from 1993 to 2013, by what percent did the number of employees at Company ABC increase from 2003 to 2013?
(1) In 2003 there were 160 employees at Company ABC.
(2) From 1993 to 2003 the number of employees increased by 60% at Company ABC.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
D. EACH statement ALONE is sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
D. EACH statement ALONE is sufficient.
For statement (1), since we know the numbers of employees in 2003 and 2013, we can directly calculate the percentage change: 
For statement (2), since we know the percentage change from 1993 to 2013 and the percentage change from 1993 to 2003, we can set the percentage change from 2003 to 2013 to be 
Solve 
Example Question #283 : Arithmetic
Data sufficiency question- do not actually solve the question
How many male students are in a class?
1. There are 42 students in the class.
2. 55 percent of the students are female.
Statements 1 and 2 together are not sufficient, and additional data is neeeded to answer the question
Each statement alone is sufficient
Both statements taken together are sufficienct to answer the question, but neither statement alone is sufficient
Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question
Statement 2 alone is sufficient, but statement 1 along is not sufficient to answer the question
Both statements taken together are sufficienct to answer the question, but neither statement alone is sufficient
In order to calculate the number of males in the class, you need to know the total number of students and the number of females (which can be calculated using the percentage).
Example Question #3 : Percents
Data sufficiency question- do not actually solve the question
There are 20 cats in an animal shelter. How many black, female cats are in the shelter?
1. 14 of the cats are male
2. 25 percent of the cats are black
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
Statement 2 alone is sufficient, but statement 1 is not sufficient to answer the question
Each statement alone is sufficient to answer the question
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
Statement 1 alone is sufficient, but statement 2 is not sufficient to answer the question
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
The information provided will allow you to calculate the number of females and the number of black cats, but there is not enough information to quantify the number of black, female cats
Example Question #3 : Percents
A certain pet store sells cats and dogs. The number of dogs is 250% greater than the number of cats. How many cats are in the store?
1. There are 40 dogs in the store.
2. There are 56 cats and dogs in the store.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
EACH statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statement 1: sufficient
Statement 2: sufficient
Example Question #284 : Arithmetic
Mrs. Smith purchased groceries whose price, before tax, was $147.64. What was the tax rate on those groceries (nearest hundredth of a percent)?
1) The tax she paid was $9.23.
2) The total amount she paid was $156.87
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient to answer the question.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
To determine the tax rate, you need to know the purchase price, which is given, and the amount of tax paid. The amount of tax is given in Statement 1. Statement 2 alone, however, also allows you to find the amount of tax; just subtract:
Either way, you can now find the tax rate:
Example Question #285 : Arithmetic
Jared, a jewelry salesman, makes a 10% commission on the selling price of all the jewelry he sells. Last month, he earned $4,000 in commission. What is the total selling price of the jewelry he sold this month?
1. His sales this month were 25% more than his sales last month.
2. He earned $5,000 in commission this month.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
EACH statement ALONE is sufficient to answer the question asked.
Each statement has enough information to calculate the answer.
Using statement 1, we know that he sold 25% more than last month. Given in the question, last month he earned $4,000. If $4,000 is 10% of the total price of his jewelry sold last month, we do some math (below) to find he sold $40,000 worth of jewelry. Let 
Increasing that by 25% we see that
NOTE: when multiplying the percents, make sure you use the decimal values.
Using statement 2, we know that we can just calculate the total selling price of the jewelry he sold this month based on the commission percentage. So, if we let 
or
Therefore we see we can use either statement individually to find what we are looking for.
Example Question #6 : Percents
A distributor ordered 3,250 chairs. 2,315 chairs were delivered. What percentage of the chairs have not yet been delivered?
First let's find the number of chairs not delivered:
Therefore the fraction of chairs not delivered is 
Divide the numerator by the denominator to convert this fraction into a decimal:
Multiply by 100 to turn this decimal into a percentage:
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