Make sure to draw the picture first. The question asks for a fraction, so plug in any numbers you want, as long as they make sense with the problem. Make the radius of the circle 4. That means that RQ and RP are both equal to 4.RS is also 4, because it is a radius as well. The problem states that a line goes through the midpoint of RS, so RT must be 2. Now you have a right triangle with leg 2 and hypotenuse 4. If you use the Pythagorean theorem to find the third side, it will be 2√3 . Thus, you have 30-60-90 triangles for RTQ and RTP.This means angle R is 120 degrees and the arc is ¹⁄₃ of the circumference.Thus, choice (B) is correct

The problem asks for the least value of x. Instead of doing the messy algebra, simply plug in the answers.The question asks for the least value, so start with the smallest value given and work your way up. Start with choice (E). If x equals 50, then the cost is 80(50) + 9,000, which is 13,000.The money made from the sale of the rings is 260(50), or 13,000.The problem says the company must not lose money (which is not the same as making money), so choice (E) is correct.

This algebra problem has numbers in the answers, so solve it by Plugging In the Answers. Start with choice (C): If Reservoir A contains 700 million gallons of water, then Reservoir B has 450 million gallons less, or 250 million gallons. When 100 million gallons are drained from Reservoir A to Reservoir B, then the reservoirs will hold 600 million and 350 million gallons of water, respectively. That’s not the relationship you’re looking for—Reservoir A should have twice the water as Reservoir B—so eliminate choice (C).Try choice (B): If Reservoir A contains 600 million gallons of water, then Reservoir B has 450 million gallons less, or 150 million gallons. When 100 million gallons are drained from Reservoir A to Reservoir B, then the reservoirs will hold, respectively, 500 million and 250 million gallons of water.That’s the relationship you’re looking for—Reservoir A has twice as much water as Reservoir B—so select choice (B).

This is another hidden Plug In problem. It asks for a fraction of an unknown total, so just make up your own number. Plug in 15 for the total. So ¹⁄₅ of 15 = 3 fiction books.Then ¹⁄₃ of 3 is 1, so there’s 1 fewer self-help than fiction, or 3 − 1 = 2 self-help books. Together, there are 3 + 2 = 5 fiction and self-help books out of 15 total books so \(\frac{5}{15}=\frac{1}{3}\).

When you see, “What is the value of x,” you know what to do.The answers (Column 1) represent the price of a bagel. If one bagel costs $1.60, then 56 bagels would cost $89.60 (Column 2). Fortunately there is a discount of $1.40 per dozen, so the total discount is $5.60 (Column 3).The actual price paid, therefore, is $84 (Column 4) or an aveage of $1.50 per bagel (Column 5).This is too much, so cross off Choices (C), (D), and (E). It’s too much by a lot, so try choice (A). It works.

A percent question with no specific values indicates a hidden Plug In question.The question mentions “the original price,” but gives no actual number, so assume that the original price of the garment was $100. After the first reduction, the sale price was $100 − (20% of $100) = $80. After the second reduction, the final price was $80 − (10% of $80) = $72.The total reduction from the original price was therefore $28, which is 28% of the original price.Choice (D) is the answer.

This is another question on which you can avoid algebra by simply Plugging In the Answers.The question asks for the value of m, so see which of the choices works in the problem. Start with choice (C), which is ³⁄₂.The problem states that mn = 9, so that means ³⁄₂n = 9. Solve for n, you get 6. Now you just have to make sure that ⁿ⁄_m = 4. It does, because \(\frac{6}{\frac{3}{2}}=6\times \frac{2}{3}\), which is 4.Thus, choice (C) is the answer.

Don’t attempt messy algebra if you can avoid it!The question wants to know the value of x, and it must be one of the answers provided. So just plug in the answers. Normally, you’d start with choice (C), but that’s a messy radical, so start with choice (B) instead. Plug in 0 for x and you get \(\sqrt{0+3}=\sqrt{0}+\sqrt{3}\).These two are equal, so choice (B) is the answer.

The question wants the total amount of tips, so try Plugging In the Answers. In choice (D), if the total earned in tips was $120, then the 4 waiters combined receive ²⁄₃ of $120, or $80.The manager receives ¹⁄₄ of $120, or $30, and the busboy receives the remaining $10.Because 4 waiters received $80, and 1 waiter received $20, 1 waiter and the busboy together receive $30.

There are two important things to notice about this problem. The first is that it contains no values whatsoever. The second is that it asks for a ratio, which is just a special type of fraction. A fraction question with missing numbers equals a hidden Plug In. Plug in a number for the radius of the smaller circle—say 2. If the radius of the smaller circle is equal to 2, then the area of the smaller circle is 4π. To find the area of the larger circle, make a right triangle. The legs of the triangle are 2 each and the diagonal is 2√2. This is equal to the radius of the larger circle, which therefore has an area of (2√2)²π, or 8π.The ratio of these two numbers is equal to 2.