GRE Math : Arithmetic
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Example Questions
Example Question #1 : Fractions
To solve this problem, realize that a decimal may be placed at the very end of this integer:
Now, count how many spaces the decimal will need to move to the left to reach:
It must move a total of 
Example Question #2 : Fractions
Simplify:
To solve this problem, begin with simplifying the numerator. This can be done by first finding a common denominator. For
a common denominator would be 
or
Which combines into:
But recall that this is just the numerator, and there is still a 
So, the final answer is:
Example Question #1 : How To Find The Decimal Equivalent Of A Fraction
0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
4 > √17
–|–6| = 6
1/2 < 1/8
0.3 < 1/3
0.3 < 1/3
The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.
1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.
√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.
Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.
Example Question #1 : Fractions
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
10 < n < 15
Quantity A Quantity B
7/13 4/n
The answer cannot be determined from the information given.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
Quantity A is greater.
To determine which quantity is greater, we must first determine the range of potential values for Quantity B. Let's call this quantity m. This is most efficiently done by dividing 4 by the highest and lowest possible values for n.
4/10 = 0.4
4/15 = 0.267
So the possible values for m are 0.267 < m < 0.4
Now let's find the value for 7/13, to make comparison easier.
7/13 = 0.538
Given this, no matter what the value of n is, 7/13 will still be a higher proportion, so Quantity B is greater.
Example Question #2 : Fractions
Quantity A:
Quantity B:
The relationship cannot be determined from the given information.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
Quantity B is greater.
The GRE test now has a built-in calculator. Simply convert the fractions to decimals and compare:
Quantity A = 0.333 +0.43 + 0.2 = 0.963
Quantity B = 0.1429 + 0.5 + 0.3333 = 0.976
Thus, Quantity B is larger.
Example Question #2 : How To Find The Decimal Equivalent Of A Fraction
How much less is 
Example Question #1 : How To Find The Decimal Equivalent Of A Fraction
The ogre under the bridge eats 
1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.
1/4 * 1/5 = 1/20 = 5%
Example Question #3 : How To Find The Decimal Equivalent Of A Fraction
Which of the following numbers is between 1/5 and 1/6?
0.25
0.19
0.13
0.16
0.22
0.19
Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.
Example Question #2 : Decimals
Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
2/7
8/9
3/5
1/10
9/15
2/7
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
Example Question #11 : Fractions
Choose the answer which best expresses the following fraction as a decimal (if necessary, round to the nearest hundredth):
To solve this problem, simply divide the numerator by the denomenator. We see that when we try to divide these two numbers that 9 does not go into 2 therefore we need to add a decimal place and a zero to 2. Now we have 2.0 divided by 9 from here we can see that .2 times 9 gives us 1.8 which is close to 2. Now we subtract 1.8 from 2 and are left with .2. We repeat this process.
You are left with 
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