GRE Math : Compound Fractions
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Example Questions
Example Question #1 : Fractions
Edward rolls three dice; two are six-sided, and one is twenty-sided, with 1 through 6 represented on the six-sided dice, and 1 through 20 represented on the twenty-sided die.
What is the probability that the sum of his roll will equal 5?
The first step will be to calculate how many total different potential rolls are possible. This is given by the product of the number of possible rolls for each of the dice: 6, 6, 20:
Next it is necessary to account for the total number of rolls that will sum up to 5. Writing them out can help, such as in the format of:
Knowing that there are 6 different rolls that sum up to 5, the probability of rolling a 5 can be found by taking the number of events that satisfy this sum and dividing it by the number of total possible events:
Example Question #411 : Arithmetic
Simplify the following:
Looking at this equation, note that since all terms in the numerator and denominator contain a 
or
Now the parenthetical terms must be addressed. The problem statement and answer choices give a clue that they are some sort of multiples of 
In fact, Pascal's triangle reveals that the top and bottom are the cube and square of this term respectively:
Cancelling terms, we are left with:
Example Question #1 : Fractions
Examination of the value 
A longer answer would be to write the sequence out and count down the digits until the 
Rather, notice how since the numbers repeat, it's possible to skip most of the counting:
And so on. Since 
So the 
Example Question #2 : Fractions
Which of the following is equal to 
The first step will be to find the reciprocal of 
The reciprocal of a number is given by 
Therefore:
Example Question #1 : Fractions
Quantity A:
Quantity B:
The relationship between A and B cannot be determined.
Quantity A is greater.
The two quantities are equal.
Quantity B is greater.
The two quantities are equal.
To make the comparison, the values of 
We are told that 
With 
The two quantities are equal.
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:
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