At the local grocery store, apples normally cost 40 cents each. During a recent sale, the price was reduced to 3 apples for a dollar. How much money would be saved by purchasing 30 apples at the sale price?

$1
$1.50
$2
$2.50
$3

Solution

30 apples at 40 cents apiece cost $12.Buying 30 apples at 3 per dollar would cost $10.Therefore, the sale price is $2 less than the normal price.

If bc ≠ 0, and 3b + 2c = 18, then which of the following is NOT a possible value of c?

5(³⁄₅)
6
8(²⁄₅)
9
12

Solution

This problem offers a good opportunity to plug in the answers—for simplicity’s sake, start with the integers. If c = 6, choice (B), then 3b + 2(6) = 18, so 3b + 12 = 18, 3b = 6, and b = 2.The only other requirement given is that bc ≠ 0, so 6 is, in fact, a possible value of c. If c = 9, as in choice (D), then 3b + 2(9) = 18, so 3b + 18 = 18, 3b = 0, and b = 0. A value of 0 for b would violate the given requirement, so 9 is NOT a possible value of c.

x, y, and z are consecutive even integers.

Quantity A	Quantity B
xy	yz

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given

Solution

Try Plugging In; one set of values that could work is x = −2, y = 0, and z = 2. In this case, both Quantity A and Quantity B have a value of 0.Eliminate choices (A) and (B). However, another set of values that could work is x = −6, y = −4, and z = −2. With this set of values, Quantity A has a value of 24 and Quantity B has a value of 8.Eliminate choice (C).You are left with choice (D) for the answer.

|1 – 5| = |5 – m|

Quantity A	Quantity B
m	4

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given

Solution

Solve for m. If |1 – 5| = |5 – m|, then |– 4| = |5 – m|, or 4 = |5 – m|. When you see absolute values, remember to consider both positive and negative solutions: 5 − m = 4 or 5 − m = −4, so m can equal 1 or 9, leaving you with choice (D) for the answer.

$\frac{5\times 5}{5+5}+\frac{5\times 5}{5+5}=$

1
⁵⁄₄
2
⁵⁄₂
5

Solution

Find the value of each fraction by multiplying the numbers in the numerator and adding the numbers in the denominator.The value of each fraction is $\frac{25}{10}=\frac{5}{2}$. Add the two fractions: $\frac{5}{2}+\frac{5}{2}=\frac{10}{2}=5$.

3 and 5 are factors of x.

Quantity A	Quantity B
The remainder when x is divided by 10	6

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

Solution

Plug in a value that meets the given requirements; try x = 15.The remainder when 15 is divided by 10 is 5; Quantity B is greater, so eliminate choices (A) and (C). Any acceptable value of x gives the same outcome, so select choice (B).

Katherine drank 25 percent of her bottle of soda on the way to work, and drank another 3 ounces when she got there. The bottle now contains 60 percent of what it contained originally. How many ounces of soda did Katherine’s bottle originally hold?

Solution

You have numbers in the answers and a missing variable in the question, so plug in the answers as shown below.You’d normally start with choice (C), but 10 isn’t divisible by 4, so move onto a different number. If you recognize that choice (D) is too small, so you can eliminate choices (A), (B), and (C) as well, and the answer must be choice (E). If not, try it:Take away 5 ounces, or 25%, and then another three, and you’re left with 12 ounces, which is 60% of 20.

Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Mark’s oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?

Solution

Use PITA here. If you start with choice (C), George has 20 oranges, which means Mark has 40 and Tony has 110. If we add 15 to George, he’d have 35, and Mark would get 5, so he’d have 45.These values aren’t equal—in fact, the difference between them is too large, so that’s a clue that we should try using smaller numbers. If you try choice (B), Mark now has 30,Tony has 80, and after Tony gives 15 to George and 5 to Mark, George has 30 and Mark has 35.The difference is smaller, so we know we are going in the right direction.The answer must be choice (A). If you try choice (A), George has 10, Mark has 20, and Tony has 50 to start. After the exchange, George and Mark both have 25, which is half of 50.

Wendy, Yvonne, and Elizabeth are baking cookies for a bake sale. Wendy can bake all of the cookies in 10 hours, Yvonne can bake half of the cookies in 3 hours, and Elizabeth can bake a third of the cookies in 5 hours. If Wendy and Elizabeth bake for 2 hours, how long will it take Yvonne to finish baking the rest of the cookies?

Solution

Plug in for the number of cookies.Choose a number that’s divisible by all the numbers in the question, such as 30.That means that Wendy’s rate is 3 cookies per hour. Now, be careful with Yvonne and Elizabeth’s rates.Yvonne can bake 15 cookies in 3 hours, or 5 per hour.Elizabeth can bake 10 cookies in 5 hours, or 2 per hour. If Wendy and Elizabeth bake together, they can make a total of 5 cookies in one hour. If they bake for 2 hours, they’ll bake 10 cookies. For Yvonne to finish the baking on her own, she’ll need to bake the 20 remaining cookies. At a rate of 5 cookies per hour, it will take her 4 hours to finish the job, so choice (E) is the answer

Nelson bowled 4 games and scored an average of 120 points. What score could he receive on his fifth game if he wants to have an overall average that is a multiple of 7, his favorite number?
Indicate all possible values.

A.80
B.110
C.155
D.185

Solution

A and D

First, use an Average Pie. Multiply 4 by 120 and you have a total of 480 points for the first 4 games. Now, use PITA to figure out which answers will work to give you an average that is divisible by 7. Start with choice (A), because on click-all-that-apply questions, there’s no reason to start in the middle if many answers might work. 480 + 80 = 560. 560 ÷ 5 = 112.That is divisible by 7. How about choice (B)? 480 + 110 = 590. 590 ÷ 5 = 118. Is that divisible by 7? No.Keep working until you’ve checked each answer. Choices (A) and (D) are the only ones that work

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