Data Analysis - GRE Quantitative Reasoning
Card 0 of 1128
What is the probability of drawing 2 hearts from a standard deck of cards without replacement?
What is the probability of drawing 2 hearts from a standard deck of cards without replacement?
There are 52 cards in a standard deck, 13 of which are hearts
13/52 X 12/51 =
1/4 X 12/51 =
12/ 204 = 3/51 = 1/17
There are 52 cards in a standard deck, 13 of which are hearts
13/52 X 12/51 =
1/4 X 12/51 =
12/ 204 = 3/51 = 1/17
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Salisbury is at an ice cream shop that is somewhat limited in selection, but with a quality that makes up for it. There are ten flavors of ice cream and four kinds of toppings. If Salisbury orders the two-pair special, which is two random unique ice cream scoops and two random toppings, what is the probability of him getting vanilla and chocolate with almonds and sprinkles?
Salisbury is at an ice cream shop that is somewhat limited in selection, but with a quality that makes up for it. There are ten flavors of ice cream and four kinds of toppings. If Salisbury orders the two-pair special, which is two random unique ice cream scoops and two random toppings, what is the probability of him getting vanilla and chocolate with almonds and sprinkles?
In this problem, the order of selection for ice cream and toppings does not matter, so it's dealing with combinations.
The number of possible combinations for 
selections out of 
items is:
So the number of possible ice cream choices in this problem is:
And the chance of choosing a chocolate+vanilla selection is 
.
For the toppings, the number of combinations is:
With the almond sprinkle combination having a 
chance of being chosen.
The chance of BOTH of these selections being made is then the product of the two probalities:
In this problem, the order of selection for ice cream and toppings does not matter, so it's dealing with combinations.
The number of possible combinations for
So the number of possible ice cream choices in this problem is:
And the chance of choosing a chocolate+vanilla selection is
For the toppings, the number of combinations is:
With the almond sprinkle combination having a
The chance of BOTH of these selections being made is then the product of the two probalities:
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What is the median in the following set of numbers?
16, 19, 16, 7, 2, 20, 9, 5
What is the median in the following set of numbers?
16, 19, 16, 7, 2, 20, 9, 5
16, 19, 16, 7, 2, 20, 9, 5
Order the numbers from smallest to largest.
2,5,7,9,16,16,19,20
The median is the number in the middle.
In this case, there is a 9 and 16 in the middle.
When that happens, take the average of the two numbers.
16, 19, 16, 7, 2, 20, 9, 5
Order the numbers from smallest to largest.
2,5,7,9,16,16,19,20
The median is the number in the middle.
In this case, there is a 9 and 16 in the middle.
When that happens, take the average of the two numbers.
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Quantity A:
The sum of the median and mode of Set G
Quantity B:
The range of Set G
Quantity A:
The sum of the median and mode of Set G
Quantity B:
The range of Set G
The median is the middle value in a set of numbers, and the mode is the number that occurs.
In Column A, the median is 6 and the mode is 6, so the sum of the median and the mode of Set G is 12.
The range is the difference between the highest and lowest numbers of the set.
In Column B, the range is 12 – 2 = 10.
Column A is greater than Column B.
The median is the middle value in a set of numbers, and the mode is the number that occurs.
In Column A, the median is 6 and the mode is 6, so the sum of the median and the mode of Set G is 12.
The range is the difference between the highest and lowest numbers of the set.
In Column B, the range is 12 – 2 = 10.
Column A is greater than Column B.
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What is the probability of drawing 2 hearts from a standard deck of cards without replacement?
What is the probability of drawing 2 hearts from a standard deck of cards without replacement?
There are 52 cards in a standard deck, 13 of which are hearts
13/52 X 12/51 =
1/4 X 12/51 =
12/ 204 = 3/51 = 1/17
There are 52 cards in a standard deck, 13 of which are hearts
13/52 X 12/51 =
1/4 X 12/51 =
12/ 204 = 3/51 = 1/17
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Salisbury is at an ice cream shop that is somewhat limited in selection, but with a quality that makes up for it. There are ten flavors of ice cream and four kinds of toppings. If Salisbury orders the two-pair special, which is two random unique ice cream scoops and two random toppings, what is the probability of him getting vanilla and chocolate with almonds and sprinkles?
Salisbury is at an ice cream shop that is somewhat limited in selection, but with a quality that makes up for it. There are ten flavors of ice cream and four kinds of toppings. If Salisbury orders the two-pair special, which is two random unique ice cream scoops and two random toppings, what is the probability of him getting vanilla and chocolate with almonds and sprinkles?
In this problem, the order of selection for ice cream and toppings does not matter, so it's dealing with combinations.
The number of possible combinations for selections out of items is:
So the number of possible ice cream choices in this problem is:
And the chance of choosing a chocolate+vanilla selection is .
For the toppings, the number of combinations is:
With the almond sprinkle combination having a chance of being chosen.
The chance of BOTH of these selections being made is then the product of the two probalities:
In this problem, the order of selection for ice cream and toppings does not matter, so it's dealing with combinations.
The number of possible combinations for
So the number of possible ice cream choices in this problem is:
And the chance of choosing a chocolate+vanilla selection is
For the toppings, the number of combinations is:
With the almond sprinkle combination having a
The chance of BOTH of these selections being made is then the product of the two probalities:
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What is the median in the following set of numbers?
16, 19, 16, 7, 2, 20, 9, 5
What is the median in the following set of numbers?
16, 19, 16, 7, 2, 20, 9, 5
16, 19, 16, 7, 2, 20, 9, 5
Order the numbers from smallest to largest.
2,5,7,9,16,16,19,20
The median is the number in the middle.
In this case, there is a 9 and 16 in the middle.
When that happens, take the average of the two numbers.
16, 19, 16, 7, 2, 20, 9, 5
Order the numbers from smallest to largest.
2,5,7,9,16,16,19,20
The median is the number in the middle.
In this case, there is a 9 and 16 in the middle.
When that happens, take the average of the two numbers.
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Quantity A:
The sum of the median and mode of Set G
Quantity B:
The range of Set G
Quantity A:
The sum of the median and mode of Set G
Quantity B:
The range of Set G
The median is the middle value in a set of numbers, and the mode is the number that occurs.
In Column A, the median is 6 and the mode is 6, so the sum of the median and the mode of Set G is 12.
The range is the difference between the highest and lowest numbers of the set.
In Column B, the range is 12 – 2 = 10.
Column A is greater than Column B.
The median is the middle value in a set of numbers, and the mode is the number that occurs.
In Column A, the median is 6 and the mode is 6, so the sum of the median and the mode of Set G is 12.
The range is the difference between the highest and lowest numbers of the set.
In Column B, the range is 12 – 2 = 10.
Column A is greater than Column B.
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Column A
The mean of the sample of numbers 2, 5, and 10.
Column B
The mean of the sample of numbers 1, 5, and 15.
Column A
The mean of the sample of numbers 2, 5, and 10.
Column B
The mean of the sample of numbers 1, 5, and 15.
The arithmetic mean is the average of the sum of a set of numbers divided by the total number of numbers in the set. This is not to be confused with median or mode.
In Column A, the mean of 5.66 is obtained when the sum (17) is divided by the number of values in the set (3).
In Column B, the mean of 7 is obtained when 21 is divided by 3. Because 7 is greater than 5.66, Column B is greater. The answer is Column B.
The arithmetic mean is the average of the sum of a set of numbers divided by the total number of numbers in the set. This is not to be confused with median or mode.
In Column A, the mean of 5.66 is obtained when the sum (17) is divided by the number of values in the set (3).
In Column B, the mean of 7 is obtained when 21 is divided by 3. Because 7 is greater than 5.66, Column B is greater. The answer is Column B.
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Column A: The median of the set
Column B: The mean of the set
Column A: The median of the set
Column B: The mean of the set
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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Bill runs for 30 minutes at 8 mph and then runs for 15 minutes at 13mph. What was his average speed during his entire run?
Bill runs for 30 minutes at 8 mph and then runs for 15 minutes at 13mph. What was his average speed during his entire run?
Rate = distance/time.
Find the distance for each individual segment of the run (4 miles and 3.25miles). Then add total distance and divide by total time to get the average rate, while making sure the units are compatible (miles per hour not miles per minute), which means the total 45 minute run time needs to be converted to 0.75 of an hour; therefore (4miles + 3.25 miles/0.75 hour) is the final answer.
Rate = distance/time.
Find the distance for each individual segment of the run (4 miles and 3.25miles). Then add total distance and divide by total time to get the average rate, while making sure the units are compatible (miles per hour not miles per minute), which means the total 45 minute run time needs to be converted to 0.75 of an hour; therefore (4miles + 3.25 miles/0.75 hour) is the final answer.
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Sample Set A has 25 data points with an arithmetic mean of 50.
Sample Set B has 75 data points with an arithmetic mean of 100.
Quantity A: The arithmetic mean of the 100 data points encompassing A and B
Quantity B: 80
Sample Set A has 25 data points with an arithmetic mean of 50.
Sample Set B has 75 data points with an arithmetic mean of 100.
Quantity A: The arithmetic mean of the 100 data points encompassing A and B
Quantity B: 80
Note that:
The arithmetic mean of the 100 data points encompassing A and B =
(total data of Sample Set A + total data of Sample Set B)/100
We have Mean of Sample Set A = 50, or:
(total of Sample Set A) / 25 = 50
And we have Mean of Sample Set B = 100, or:
(total of Sample Set B) / 75 = 100
We get denominators of 100 by dividing both of the equations:
Divide \[(total of Sample Set A) / 25 = 50\] by 4:
(total of Sample Set A) / 100 = 50/4 = 25/2
Multiply \[(total of Sample Set B)/75 = 100\] by 3/4:
(total of Sample Set B)/100 = 75
Now add the two equations together:
(total data of Sample Set A + total data of Sample Set B)/100
= 75 + 25/2 > 80
Note that:
The arithmetic mean of the 100 data points encompassing A and B =
(total data of Sample Set A + total data of Sample Set B)/100
We have Mean of Sample Set A = 50, or:
(total of Sample Set A) / 25 = 50
And we have Mean of Sample Set B = 100, or:
(total of Sample Set B) / 75 = 100
We get denominators of 100 by dividing both of the equations:
Divide \[(total of Sample Set A) / 25 = 50\] by 4:
(total of Sample Set A) / 100 = 50/4 = 25/2
Multiply \[(total of Sample Set B)/75 = 100\] by 3/4:
(total of Sample Set B)/100 = 75
Now add the two equations together:
(total data of Sample Set A + total data of Sample Set B)/100
= 75 + 25/2 > 80
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The average (arithmetic mean) of x, y and z is 15. If w is 10, then what is the average of w, x, y and z?
The average (arithmetic mean) of x, y and z is 15. If w is 10, then what is the average of w, x, y and z?
We can calculate the arithmetic mean by adding up the numbers in a set, and dividing that total by the count of numbers in the set.
Thus, we know that (x + y + z) / 3 = 15. (Multiply both sides by 3.)
x + y + z = 45
We add w = 10 to that, and divide by the new count, 4.
55 / 4 = 13.75
We can calculate the arithmetic mean by adding up the numbers in a set, and dividing that total by the count of numbers in the set.
Thus, we know that (x + y + z) / 3 = 15. (Multiply both sides by 3.)
x + y + z = 45
We add w = 10 to that, and divide by the new count, 4.
55 / 4 = 13.75
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The combined height of John and Sandy is 130 inches. Sandy, John, and Allen together have a combined height of 215 inches. Sandy and Allen have combined height of 137 inches. How tall is John?
The combined height of John and Sandy is 130 inches. Sandy, John, and Allen together have a combined height of 215 inches. Sandy and Allen have combined height of 137 inches. How tall is John?
Translate the question into a series of equations:
J + S = 130; J + S + A = 215; S + A = 137
Although there are several ways of approaching this, let us choose the path that is most direct. Given that J, S, A are all involved in the second equation, we can isolate J if we eliminate S and A - which can be done by using the data we have in the third equation. Since S + A = 137, we can rewrite J + S + A = 215 as:
J + 137 = 215.
Now, we only need to solve for J:
J = 215 - 137
J = 78 inches.
Translate the question into a series of equations:
J + S = 130; J + S + A = 215; S + A = 137
Although there are several ways of approaching this, let us choose the path that is most direct. Given that J, S, A are all involved in the second equation, we can isolate J if we eliminate S and A - which can be done by using the data we have in the third equation. Since S + A = 137, we can rewrite J + S + A = 215 as:
J + 137 = 215.
Now, we only need to solve for J:
J = 215 - 137
J = 78 inches.
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On a given exam, four students have an average score of 81 points. If another student takes the exam, what must he or she score in order to increase the overall average to at least 83 points?
On a given exam, four students have an average score of 81 points. If another student takes the exam, what must he or she score in order to increase the overall average to at least 83 points?
Begin by translating the current state of affairs into an equation. We know that for four students, the average is ascertained by taking the sum of the scores (s) and dividing that by four:
s / 4 = 81; s = 324
Now, when we add the additional student, that person's score (x) will be added to the value for s. The average of this new group will be divided among five students. We must solve for the case in which the average is 83 points (thus giving us the case for the minimum score x necessary.) This yields the following equation:
(324 + x) / 5 = 83
Solve for x:
324 + x = 415; x = 91
The minimum score necessary is 91 points.
Begin by translating the current state of affairs into an equation. We know that for four students, the average is ascertained by taking the sum of the scores (s) and dividing that by four:
s / 4 = 81; s = 324
Now, when we add the additional student, that person's score (x) will be added to the value for s. The average of this new group will be divided among five students. We must solve for the case in which the average is 83 points (thus giving us the case for the minimum score x necessary.) This yields the following equation:
(324 + x) / 5 = 83
Solve for x:
324 + x = 415; x = 91
The minimum score necessary is 91 points.
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Find the arithmetic mean of the following series of numbers:
1, 2, 2, 3, 4, 5, 11, 12
Find the arithmetic mean of the following series of numbers:
1, 2, 2, 3, 4, 5, 11, 12
To find the arithmetic mean of a series of numbers, add up all of the numbers and divide by the number of numbers in the series. Adding all the numbers gives us 40 and there are 8 numbers in the series. 40/8 = 5
To find the arithmetic mean of a series of numbers, add up all of the numbers and divide by the number of numbers in the series. Adding all the numbers gives us 40 and there are 8 numbers in the series. 40/8 = 5
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Consider the given set of numbers 70, 81, 91, 83, 88, and 55.
A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original?
Consider the given set of numbers 70, 81, 91, 83, 88, and 55.
A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original?
Reorder the set: 55, 70, 81, 83, 88, 91
Since the set is even, we find the median by taking the average of the middle two values: (81 + 83)/2 = 82
The average of the first set = (55 + 70 + 81 + 83 + 88 + 91)/6 = 468/6 = 78
The new value to be added is 82 * 1.12 = 91.84
This means the new mean is 559.84/7 = 79.9771
The increase in mean value is 79.9771 – 78 = 1.9771
This is (1.9771/78) 100, or 2.535% larger than the original mean.
Reorder the set: 55, 70, 81, 83, 88, 91
Since the set is even, we find the median by taking the average of the middle two values: (81 + 83)/2 = 82
The average of the first set = (55 + 70 + 81 + 83 + 88 + 91)/6 = 468/6 = 78
The new value to be added is 82 * 1.12 = 91.84
This means the new mean is 559.84/7 = 79.9771
The increase in mean value is 79.9771 – 78 = 1.9771
This is (1.9771/78) 100, or 2.535% larger than the original mean.
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A group of ten candy bars has an average cost of \$0.89 per candy bar. How many bars must be bought at the cost of \$0.72 a piece to bring the average down to \$0.80?
A group of ten candy bars has an average cost of \$0.89 per candy bar. How many bars must be bought at the cost of \$0.72 a piece to bring the average down to \$0.80?
We know to begin with that for x candy bards:
x / 10 = 0.89; x = 8.90
We are trying to ascertain how many bars (y) must be added to this to amount to have an average of 0.80. This is represented:
(8.9 + 0.72y) / (10 + y) = 0.8
8.9 + 0.72y = 0.8 (10 + y)
8.9 + 0.72y = 8 + 0.8y
8.9 – 8 = 0.8y - 0.72y
0.9 = 0.08y
y = 0.9 / 0.08 = 11.25
However, since we cannot have a partial amount of candy bars, we will have to buy 12.
We know to begin with that for x candy bards:
x / 10 = 0.89; x = 8.90
We are trying to ascertain how many bars (y) must be added to this to amount to have an average of 0.80. This is represented:
(8.9 + 0.72y) / (10 + y) = 0.8
8.9 + 0.72y = 0.8 (10 + y)
8.9 + 0.72y = 8 + 0.8y
8.9 – 8 = 0.8y - 0.72y
0.9 = 0.08y
y = 0.9 / 0.08 = 11.25
However, since we cannot have a partial amount of candy bars, we will have to buy 12.
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In a given translation project, three translators each took sections of a book to translate. The first translator took 15000 words, which he translated at a rate of 500 words per 20 minutes. The second translator took 200000 words, which he translated at a rate of 1250 words per half hour. The third took 10000 words, which he translated at a rate of 250 words per 15 minutes. In terms of words per hour, what was the overall average translation rate for this project?
In a given translation project, three translators each took sections of a book to translate. The first translator took 15000 words, which he translated at a rate of 500 words per 20 minutes. The second translator took 200000 words, which he translated at a rate of 1250 words per half hour. The third took 10000 words, which he translated at a rate of 250 words per 15 minutes. In terms of words per hour, what was the overall average translation rate for this project?
To find the answer, we need to know the total words and the total number of hours involved.
The first is easy: 15000 + 200000 + 10000 = 225000 words
To ascertain the number of hours, we have to look at each translator separately. Although there are several ways to do this, let's consider it this way:
Translator 1 can translate at 500 words per 20 minutes OR 1500 words per hour.
Translator 2 can translate at 1250 words per half hour OR 2500 words per hour.
Translator 3 can translate at 250 words per 15 minutes OR 1000 words per hour.
Therefore, we know each translator took the following amount of time:
Translator 1: 15000 / 1500 = 10 hours
Translator 2: 200000 / 2500 = 80 hours
Translator 3: 10000 / 1000 = 10 hours
The total number of hours was therefore 10 + 80 + 10 = 100 hours.
The average rate was 225000 words/100 hours, or 2250 words per hour.
To find the answer, we need to know the total words and the total number of hours involved.
The first is easy: 15000 + 200000 + 10000 = 225000 words
To ascertain the number of hours, we have to look at each translator separately. Although there are several ways to do this, let's consider it this way:
Translator 1 can translate at 500 words per 20 minutes OR 1500 words per hour.
Translator 2 can translate at 1250 words per half hour OR 2500 words per hour.
Translator 3 can translate at 250 words per 15 minutes OR 1000 words per hour.
Therefore, we know each translator took the following amount of time:
Translator 1: 15000 / 1500 = 10 hours
Translator 2: 200000 / 2500 = 80 hours
Translator 3: 10000 / 1000 = 10 hours
The total number of hours was therefore 10 + 80 + 10 = 100 hours.
The average rate was 225000 words/100 hours, or 2250 words per hour.
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A certain function takes the value 1 with probability 1/2, 2 with probability 1/3, and 3 with probability 1/6. What is the mean value of the function?
A certain function takes the value 1 with probability 1/2, 2 with probability 1/3, and 3 with probability 1/6. What is the mean value of the function?
To find the mean or expected value, we multiply each value by its corresponding probability and add them up. So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.
To find the mean or expected value, we multiply each value by its corresponding probability and add them up. So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.
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