How many committees of 5 members can be chosen from a group of 8 people?
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Solution
This is the number of combinations of 8 items taken 5 at a time (because the order does not matter).This number is equal to
k > j > 0
| Quantity A | Quantity B |
| The time it takes to read k words at j words per minute | The time it takes to read (k + 10) words at (j + 10) words per minute |
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Solution
Plug in numbers and use the rate formula—amount = rate × time—to check the quantities. If j = 1 and k = 2, then Quantity A is 2 minutes and Quantity B is \(\frac{20}{11}\) minutes. Quantity A is greater, so eliminate choices (B) and (C). Any acceptable set of values gives the same outcome; select choice (A).
A hat contains 18 raffle tickets, numbered 1 through 18. If two raffle tickets are chosen at random from the hat, what is the probability that both tickets are even numbers?
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Solution
Think of this problem as if you’re pulling out an even ticket and then another even ticket. So, for the first ticket there are 9 possible evens out of 18 total, so the probability that the first ticket is even is \(\frac{9}{18}\). Now you have one fewer even ticket in the hat. So there are 8 evens out of 17 total tickets for the second ticket, thus, the probability is \(\frac{9}{17}\).You want an even AND an even, so multiply:\(\frac{9}{17}\).The answer is choice (B).
For which of the following values of x is the mode of 2x, x + 5, 3x − 2, 5x − 7, and 4x equal to 4 ?
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Solution
Remember that mode means the number that appears “most often.” Plug In the Answers. For choice (C), if x = 4, then the numbers become: 8, 9, 10, 13, 16. For a list of numbers to have a mode, there has to be at least two of one of the numbers. So this list has no mode; eliminate choice (C). For choice (A), if x = 2, then the numbers become: 4, 7, 4, 3, 8.Because 4 appears twice, 4 is the mode —the answer is choice (A).
| Quantity A | Quantity B |
| The average (arithmetic mean) of 4 numbers, each less than 6 and greater than 5 | The median of 6 numbers, each less than 5 and greater than 4 |
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Solution
Although you can’t find an exact value for either quantity, you can find a possible range for each. In Quantity A, if all 4 numbers are between 5 and 6, then their average is, too. Similarly, in Quantity B, if all 6 numbers are between 4 and 5, then so is their median. Any number between 5 and 6 is greater than any number between 4 and 5, so Quantity A is greater.
Liz owns 2 green t-shirts, 4 blue t-shirts, and 5 red t-shirts
| Quantity A | Quantity B |
| The probability that Liz randomly selects a blue t-shirt | 2⁄5 |
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Solution
To calculate the probability, divide the part by the whole:\(\frac{blue\: shirts}{total\: shirts}=\frac{4}{11}\).Choice (B) is correct because \(\frac{blue\: shirts}{total\: shirts}=\frac{4}{11}\)(which is simply 2⁄5 multiplied by 2).
Susan travels by car at an average speed of 50 miles per hour for 4 hours and then at an average speed of 20 miles per hour for 2 hours. What is her average speed, in miles per hour, for the entire 6-hour trip?
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Solution
Use the given averages to figure out Susan’s total distance: 4 hours at an average speed of 50 miles per hour is a total of 200 miles, and 2 hours at an average speed of 20 miles per hour is a total of 40 miles. Susan goes a total of 240 miles in 6 hours, thus, her average speed is \(\frac{240miles}{6hours}\), or 40 miles per hour.The answer is choice (D).
2, 3, 5, 7
| Quantity A | Quantity B |
| The average (arithmetic mean) of the numbers above | The median of the numbers above |
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Solution
The mean is found by dividing the sum of the elements by the number of elements. In this case: 2 + 3 + 5 + 7 = 17, and 17 ÷ 4 = 4.25, the mean.The median is the middle number, or, if the list contains an even number of elements, the average of the middle two elements (when they are arranged in increasing order). In this case, the average of 3 and 5 is 4. Quantity A is greater than Quantity B.
| Quantity A | Quantity B |
| The average (arithmetic mean) of 14, 22, and 48 | The average (arithmetic mean) of 12, 22, and 50 |
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Solution
The average is the sum divided by the number of items.Both ask for the average of three numbers.The sum of the three numbers in both quantities is 84, so their averages must be equal.
In terms of y, what is the average (arithmetic mean) of 4y and 22 ?
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Solution
To find the average, add up the values and divide by 2: \(\frac{4y+22}{2}=\frac{2(2y+11)}{2}=2y+11\).You can also Plug In on this one. If y = 3, then \(\frac{4y+22}{2}=\frac{2(2y+11)}{2}=2y+11\) = 17, your target number. Only choice (D) hits the target.