Probability & Statistics - GRE Quantitative Reasoning
Card 0 of 472
What is the range of the numbers: 
What is the range of the numbers:
Step 1: Re-write all numbers in order from smallest to largest
.
Step 2: Subtract the largest number and smallest number
The range is 
.
Step 1: Re-write all numbers in order from smallest to largest
Step 2: Subtract the largest number and smallest number
The range is
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What is the range of the set: {
}
What is the range of the set: {
Step 1: Arrange the numbers from smallest to largest:
We get: 
Step 2: Find the range.. To find this, subtract the biggest number from the smallest number
The range is 
Step 1: Arrange the numbers from smallest to largest:
We get:
Step 2: Find the range.. To find this, subtract the biggest number from the smallest number
The range is
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A student has 14 piece of gum, 3 are spearmint, 5 are peppermint, and the rest are cinnamon. If one piece of gum is chosen at random, which of the following is NOT true.
A student has 14 piece of gum, 3 are spearmint, 5 are peppermint, and the rest are cinnamon. If one piece of gum is chosen at random, which of the following is NOT true.
The probability of picking a spearmint or a cinnamon is the addition of probability of picking a spearmint and the probability of picking a cinnamon
not 
The probability of picking a spearmint or a cinnamon is the addition of probability of picking a spearmint and the probability of picking a cinnamon
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What is the range of the set, 
?
What is the range of the set,
Step 1: Define Range of a set..
You can calculate the range by subtracting the smallest number from the largest number in the set..
Step 2: There are no numbers in this set. This set is also known as the empty set..
The range of a set that has no elements does not exist.
Step 1: Define Range of a set..
You can calculate the range by subtracting the smallest number from the largest number in the set..
Step 2: There are no numbers in this set. This set is also known as the empty set..
The range of a set that has no elements does not exist.
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If I toss a coin 3 times, how many times will I roll at least one head?
If I toss a coin 3 times, how many times will I roll at least one head?
Step 1: We need to find out how many outcomes there will be.
If we roll a coin three times, there are 
outcomes.
If we roll a coin 
times, there will be 
outcomes.
Step 2: Find all the outcomes.
The outcomes here are: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.
Step 3: In the list of outcomes, count how many times the letter H appears at least once.
The letter "H" appears in HHH, HHT, HTH, HTT, THH, THT, and TTH.
The letter "H" appears in 
of the 
outcomes.
The probability of getting at least one H in the outcomes in Step 2 is 
.
Step 1: We need to find out how many outcomes there will be.
If we roll a coin three times, there are
If we roll a coin
Step 2: Find all the outcomes.
The outcomes here are: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.
Step 3: In the list of outcomes, count how many times the letter H appears at least once.
The letter "H" appears in HHH, HHT, HTH, HTT, THH, THT, and TTH.
The letter "H" appears in
The probability of getting at least one H in the outcomes in Step 2 is
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How many different combinations can i have when flipping a coin three times?
How many different combinations can i have when flipping a coin three times?
Step 1: Let's answer a smaller problem. How many ways can I toss one coin?
There are two ways, either I get Heads or Tails.
Step 2: How about two coins?
There are four ways... They are, HH, HT, TH, and TT
Step 3: How many different combinations for three coins?
Let's List them:
HHH, HHT, HTH, THH, TTT, THT, TTH, HTT
There are 
different combinations.
Step 1: Let's answer a smaller problem. How many ways can I toss one coin?
There are two ways, either I get Heads or Tails.
Step 2: How about two coins?
There are four ways... They are, HH, HT, TH, and TT
Step 3: How many different combinations for three coins?
Let's List them:
HHH, HHT, HTH, THH, TTT, THT, TTH, HTT
There are
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Find the mean of the following set of numbers:
Find the mean of the following set of numbers:
The mean can be found in the same way as the average of a group of numbers. To find the average, use the following formula:
So, if our set consists of
We will get our mean via:
So our answer is
The mean can be found in the same way as the average of a group of numbers. To find the average, use the following formula:
So, if our set consists of
We will get our mean via:
So our answer is
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Find the mean.
Find the mean.
To find the mean, add the terms up and divide by the number of terms.
To find the mean, add the terms up and divide by the number of terms.
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John has math test scores of 
. What could be his final test score if he wants the average of his exams to be at least 
?
John has math test scores of
To find the missing value, we add the terms up and divide them by 
to have the average of 
.
Cross-multiply.
Subtract both sides by 
Since the question is asking for a test score that will generate AT LEAST average of 
, we look for an answer that is greater than 
which is 
.
To find the missing value, we add the terms up and divide them by
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Find 
if the mean of 
is 
.
Find
To find the mean, add the terms up and divide by the number of terms.
Then add the numerator.
Cross-multiply.
Subtract 
on both sides.
To find the mean, add the terms up and divide by the number of terms.
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If average of 
and 
is 
and 
is 
what is the average of 
?
If average of
If the average of 
and 
is 
, then the sum must be 
.
If we add the sum of 
we get 
or 
.
To find the average of the three terms, we divide 
and 
to get 
.
If the average of
If we add the sum of
To find the average of the three terms, we divide
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What is the average of the first ten prime numbers?
What is the average of the first ten prime numbers?
The first ten prime numbers are 
. Prime numbers have two factors: 
and the number itself. Then to find mean, we add all the numbers and divide by 
.
The first ten prime numbers are
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If the average of seven consecutive numbers is 
, what is the value of the second number in the set?
If the average of seven consecutive numbers is
There are two methods.
Method 1:
Since the average of 
consecutive number is 
, we can express this as:
Cross-multiply
Subtract 
on both sides then divide both sides by 
Since we are looking for the second term, just plug into expression 
. That means answer is 
or 
.
Method 2:
Since the average of 
consecutive number is 
, this means the median is also 
. Consecutive means one after another and with each term having the same difference, we know the mean equals the median. Since there are 
terms, the median will have 
terms left and right of it. Then, the series will go 
. The second term is 
.
There are two methods.
Method 1:
Since the average of
Method 2:
Since the average of
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The mean of four numbers is 
.
A: The sum of the four numbers.
B: 
The mean of four numbers is
A: The sum of the four numbers.
B:
To find the sum of the four numbers, just multiply four and the average. By multiplying the average and number of terms, we get the sum of the four numbers regardless of what those values could be.
Since Quantity A matches Quantity B, answer should be both are equal.
To find the sum of the four numbers, just multiply four and the average. By multiplying the average and number of terms, we get the sum of the four numbers regardless of what those values could be.
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Mean of 
is 
. 
are all positive integers. 
is between 
and 
inclusive.
A: Mean of 
.
B: Mean of 
.
Mean of
A: Mean of
B: Mean of
Let's look at a case where 
.
Let's have 
be 
and 
be 
. The sum of the three numbers have to be 
or 
.
The average of 
is 
or 
. The avergae of 
is 
or 
.
This makes Quantity B bigger, HOWEVER, what if we switched the 
and 
values.
The average of 
is still 
or 
. The avergae of 
is 
or 
.
This makes Quantity A bigger. Because we have two different scenarios, this makes the answer can't be determined based on the information above.
Let's look at a case where
Let's have
The average of
This makes Quantity B bigger, HOWEVER, what if we switched the
The average of
This makes Quantity A bigger. Because we have two different scenarios, this makes the answer can't be determined based on the information above.
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Sam has math test scores of 
. The teacher drops the lowest test score except the final and the highest test score is counted as two exams. If Sam took his final exam and felt he scored between 
inclusive, what is the lowest possible average of his exams?
Sam has math test scores of
We have four test scores of 
. We know the range of the final exam is 
so therefore the 
is counted twice. Since the final exam grade regardless if the lowest possible value can't be dropped, this means we drop the 
and include the lowest possible test score which is 
. So the mean is:
We have four test scores of
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If 
and are positive integers from 
inclusive, then:
A: The mean of 
B: The mean of 
If
A: The mean of
B: The mean of
Let's add each expression from each respective quantity
Quantity A: 
Quantity B: 
Since 
we will let 
and 
. The sum of Quantity A is 
and the sum of Quantity B is also 
. HOWEVER, if 
was 
, that means the sum mof Quantity B is 
. With the same number of terms in both quantities, the larger sum means greater mean. First scenario, we would have same mean but the next scenario we have Quantity B with a greater mean. The answer is can't be determined from the information above.
Let's add each expression from each respective quantity
Quantity A:
Quantity B:
Since
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John picks five numbers out of a set of seven and decides to find the average. The set has 
.
A: John averages the five numbers he picked from the set.
B: 
John picks five numbers out of a set of seven and decides to find the average. The set has
A: John averages the five numbers he picked from the set.
B:
To figure out which Quantity is greater, let's find the highest possible mean in Quantity A. We should pick the 
biggest numbers which are 
. The mean is 
. This is the highest possible mean and since Quantity B is 
this makes Quantity B is greater the correct answer.
To figure out which Quantity is greater, let's find the highest possible mean in Quantity A. We should pick the
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There were 
exams graded. The average of the exams were 
. If the average of 
exams were 
, what was the average of the remaining exams?
There were
With 
exams of average 
, the sum of the scores were 
.
We already know the first 
exams with average of 
. Therefore, the sum is 
.
The remaining number of exams is 
or 
.
The remaining sum is 
or 
.
We divide 
by 
to get 
.
With
We already know the first
The remaining number of exams is
The remaining sum is
We divide
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What is the mean of the scores 95, 13, 67, 89, 13, 45, and 109?
What is the mean of the scores 95, 13, 67, 89, 13, 45, and 109?
To get the average or mean, add up all the scores and then divide by the number of scores.
There are seven scores so divide that number by 7
To get the average or mean, add up all the scores and then divide by the number of scores.
There are seven scores so divide that number by 7
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