Test - 9 - SAT MCQ

Call the room shared by Melvin, Carey, and Dan room X, and the other room Y. Because Mike and Melvin won't live together, Mike must be in room Y. Now, if Dave and Dan live together, Peter will live with them, but you can't fit two more people into room X, so Dave and Dan must live apart, which puts Dave in room Y also. Similarly, because Enoch will live with Chris or Carey, Chris can't be in room X either, which puts Chris, Dave, and Mike in room Y.

Take each statement one at a time. Choice (A) is true. The mode appears most often, which means the set has to have two, three, or four 90s. Choice (B) requires you to remember this formula: Total = Number × Mean. In this case, the five numbers must add up to 5 × 80 = 400. Because you know the set has at least two 90s, which add up to 180, the other three numbers must add up to 220. But because the numbers are all positive, you wouldn't have enough room for the last two numbers if 240 were in the set, which makes Choice (B) true. Choice (C) is false because making a list whose average is 80 without including any 80s in the list is easy. Try it yourself and see.

You could, of course, stop there (and you probably should, to save time, on the real test). But I want you to give you your money's worth, so I continue through the rest of the answer choices. Choice (D) is definitely true; you used this fact already when you checked Choice (A). In Choice (E), the median of an odd number of numbers is the middle number. So if the median were greater than 90, then three of the five numbers would have to be greater than 90. But you already know from Choice (A) that the set must include at least two 90s. You can't have a list with two 90s and three numbers greater than 90 and still have the average be 80. Thus, the median can't be greater than 90.

Ah, yes, an SAT classic. Every time a wheel rotates, it covers the equivalent of one circumference of distance. The circumference equals 2πr, but you have to be careful about units. The wheel has a radius of 18 inches, but your answer needs to be in feet. The circumference is 2 × 18 × π inches = 36π inches = 3π feet = about 9.4248 feet. Therefore, 50 revolutions covers 50 × 9.4248 = 471 feet.

By adding the two expressions, you discover that 4a + 4b = 20, so a + b = 5. You can also solve for the variables to get a = -2 and b = 7, which gives you the same answer.

Possible numbers for g are numbers like 3, 6, 12, 15, 21, and so on. If you try multiplying these numbers by 7 and then dividing by 9, you discover that the remainder is always 3 or 6. Because 3 isn't one of your choices, 6 is the right answer.

Because b + c = x, b = x - c. So you can substitute (x - c) for b in the first equation, and write a(x - c) = n. Because of the parentheses, you have to use the distributive law to get ax - ac = n, which is Choice (C).

All the numbers have three digits. Only Choices (A), (D), and (E) have a units (ones) digit that equals the sum of the other two digits. And, using a calculator, you can see that the square roots of 156 and 516 are decimals, while the square root of 729 is 27, which makes it your answer.

First off, you must realize that the set contains 21 numbers, not 20. Remember that to find the size of a list of numbers, you subtract the first and last numbers and then add one. (Count them if you don't believe me.) Now, the even numbers are 20, 22, . . . up to 40, which makes five numbers in the 20s, five in the 30s, and 40, which makes 11 numbers out of 21.

The easiest way to solve this problem is to make a table, dividing by 2 every 20 years:

The final answer, 1.5625, is the same as 25/16.

As is the case with several math questions on the SAT, the best strategy here is to plug the answer choices into the equation given in the question. Lucky for you, the first answer, Choice (A), works in the equation, so you can stop right there. If you'd rather do algebra to solve this problem, though, start by distributing the 2, to get 2x + 8 = 6. Subtracting 8 from both sides gives you 2x = -2, and x = -1.

The area of the pizza is πr2. The radius is 6, because the diameter is 12, and the area is 36π. Dividing by eight slices gives you 4.5π.

As is often the case on the SAT, the trial-and-error method works great here. If you don't want to use trial and error, you can call the original side of the square x, making the rectangle's sides x + 3 and x - 2. Because the area is 50, you write (x + 3)(x - 2) = 50. Use the FOIL method to get x² - 2x + 3x - 6 = 50, or x² + x - 56 = 0. (Remember, to solve a quadratic equation, you must make one side equal zero.) You can factor this equation into (x + 8)(x - 7) = 0. This equation is true when x equals either -8 or 7, but it doesn't make sense for a square to have a side of -8. Therefore, 7 is your answer.

Don't fall into the trap of thinking that 1 is prime. Two numbers, 1 and 0, are called -"special." Thus, 2 isn't a tweener because 2 - 1 = 1 and 1 isn't prime. The number 8 isn't a tweener, because 8 + 1 = 9 and 9 isn't prime, either. (It's 3 × 3.) But 30 is a tweener because 30 - 1 = 29, which is prime, and 30 + 1 = 31, which is also prime. After you've found the answer, you can move on to the next question; there's no need to check the last two options, which are wrong.

Five pounds of peanuts times $5.50 is $27.50, and two pounds of cashews times $12.50 is $25.00, so the total cost is $52.50 for seven pounds. $52.50 divided by 7 is $7.50.

Don't fall for the old "less than" trick. "Twelve less than something" is the thing minus 12 — not the other way around. So you want an expression that says "x squared is 5 times x minus 12," and (A) is the winner.