Compound Fractions - GRE Quantitative Reasoning
Card 0 of 7
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?
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:
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:
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Which of the following is equal to 
of the reciprocal of 
percent?
Which of the following is equal to
The first step will be to find the reciprocal of 
percent. Note that as a percent, this should be converted to a decimal form: 
.
The reciprocal of a number is given by 
divided by that number, so the reciprocal of 
is given as:
Therefore:
The first step will be to find the reciprocal of
The reciprocal of a number is given by
Therefore:
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Simplify the following:
Simplify the following:
Looking at this equation, note that since all terms in the numerator and denominator contain a 
, it is possible to rewrite it as follows:
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:
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:
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percent of 
is 
.
percent of 
is 
.
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
To make the comparison, the values of 
and 
must be determined.
We are told that 
percent of 
is 
, so its value can be determined as follows:
With 
known, it is possible to find 
, since 
percent of 
is 
:
The two quantities are equal.
To make the comparison, the values of
We are told that
With
The two quantities are equal.
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can be rewritten as 
times what?
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 
spaces, so:
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
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is a repeating decimal. What digit is in the 
place?
Examination of the value 
reveals that after the sequence 
, the decimal repeats, and that the sequence has a length of eight values.
A longer answer would be to write the sequence out and count down the digits until the 
value was found. However, this is a time-consuming process and one that is prone to error.
Rather, notice how since the numbers repeat, it's possible to skip most of the counting:
digit: 
digit: 
And so on. Since 
is the closest multiple to 
, we can subtract the two to find the digit that matches the 
digit.
So the 
digit is 
.
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
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Simplify: 
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 
in the denominator:
So, the final answer is:
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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