If m is an odd integer, which of the following expresses the number of even integers between m and 2m inclusive?
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Solution
Variables in the question and the answer choices tell you this is a Plug In question.Try something simple like m = 3.Between 3 and 6 inclusive there are two even integers. 2 is your target number. Now check the answer choices. Anywhere you see an m, plug in 3 and you’re looking to get 2 as an answer. Only choice (C) works.
If a and b are positive and \(\frac{ab}{x}=\sqrt{a}\) then \(\frac{x}{\sqrt{b}}\)=
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Solution
You have variables in the question and in the answer, so clearly you’re Plugging In. Since you have an a on both sides of the equal sign, start there with something nice and happy, such as a = 4.You know you’re going to have to square b, so plug in a perfect quare such as b = 9.This makes x = 18.Your target number, therefore, is 6. Only choice (B) works.
| Quantity A | Quantity B |
| \(\frac{a+b+c}{5}\) | \(\frac{1}{5ab}+\frac{c}{5}\) |
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Solution
The minute you see variables, make your set up. Start with some basic numbers such as 2, 3, and 5. Quantity A is 2 and Quantity B is \(1\frac{1}{30}\).Eliminate choices (B) and (C). How could you make Quantity B larger? Negative numbers might help by making Quantity A smaller and Quantity B larger.Try −2, −3, and something much larger like −20. Now Quantity A is 3 and Quantity B is \(4\frac{1}{30}\), so eliminate choice (A), leaving you with choice (D) for the answer.
x2 = |y|
| Quantity A | Quantity B |
| |x| | y |
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Solution
The minute you see variables, make your set-up.Try something easy first, like 2. When x = 2, then y = 4; eliminate choices (A) and (C). Generally when you square something it gets larger, but that is not always the case.You have been given no rules for what you can plug in; therefore use ZONEF and try 1 or 0 or a fraction. Any of those options will allow you to eliminate choice (B).Therefore, the answer must be choice (D).
At a crafts supply store, the price of a type of decorative string is c cents per foot. At this rate, what would be the price, in dollars, of y yards of this string?
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Solution
If the string costs c cents per foot, then it costs 3c cents per yard (because 1 yard = 3 feet). So the price of y yards of the string will be \(\frac{3cy}{100}\) cents. Dividing this by 100 (to convert from cents per dollars), the cost of the string will be dollars, choice (D). Alternatively, you can plug in values for the variables for example, let c = 100 and y = 2.Then the price of the string is 100 cents (or 1 dollar) per foot. It follows that the string is 3 dollars per yard, so the price of 2 yards would be 6 dollars. If you now Plug In c = 100 and y = 2 into the answer choices, the only one that equals 6 is choice (D).
x > 1
| Quantity A | Quantity B |
| 5x + 1 | 6x |
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Solution
The minute you see variables, make your set-up. Start with something nice and happy such as x = 2. On the left you get 26 and on the right you get 36.Cross off choices (A) and (C).The bigger x gets, the more it will exaggerate the difference. 6 to the 50th power, for example, will be way bigger than 5 to the 50th power plus 1.Can you get smaller? X still has to be greater than 1 so try x = 3⁄2. It’s a bit of a pain, but it’s worth it just to make sure. At x = 3⁄2, Quantity A = 12 and Quantity B = 14.69. Quantity B is still bigger. It’s safe to pick choice (B).
| Quantity A | Quantity B |
| x + y − 1 | x − y + 1 |
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Solution
The minute you see variables in a Quant Comp, make your set-up. Start with something simple such as x = 10 and y = 1. Quantity A equals 10 and Quantity B equals 10.Cross off choices (A) and (B).You’re adding and subtracting so try flipping the numbers to see if you can get a negative number, so x = 1 and y = 10. Now Quantity A still equals 10, but Quantity B equals −8.Your answer is choice (D).
| Quantity A | Quantity B |
| \(-\frac{x-3}{4}\) | y |
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Solution
The minute you see variables, make your set-up. In this case, plug in values that look about right for x and y.Try x = -1⁄4 and y = 3⁄4. Quantity A will be greater, so eliminate choices (B) and (C). Now vary your numbers slightly and try -1⁄8 and 7⁄8. In this case, Quantity B is greater.Eliminate choice (A) and select choice (D).
If x ≠ 0 and y = \(\frac{x+1}{x}\) – 1, what is 1⁄y ?
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Solution
The minute you see variables in the answer choices, write your answer choices down on your scratch paper and Plug In. Start with something for x such as 2. When x = 2, y will equal 1⁄2.You are asked to find 1⁄y, so your target number is 2.Check all answer choices, and you’ll find that choice (A) is the only one that works.
Rachel, David, and Kristen decide to pool their money to buy a video game system. David contributes 4 dollars more than twice what Kristen does, and Kristen contributes 3 dollars less than Rachel does. If Rachel contributes r dollars, then, in terms of r, how much does David contribute?
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Solution
Plugging In is the best approach to this question: Start with a value for r and build from there. If r = 6, then Kristen contributes 3 dollars less than r, or $3, and David contributes twice as much as Kristen plus 4 more, or 6 + 4 = $10. Now plug in 6 for r in the answer choices, and only choice (D) hits your target answer of 10: 2r − 2 = 2(6) − 2 = 12 − 2 = 10.