Test - 10 - SAT MCQ

Lyle's cost is 2 packages × 10 pounds × $3.99 = $79.80. Gretchen's cost is 20 pounds × $3.49 = $69.80, and the difference between them is $79.80 - $69.80 = $10.

The tricky part here is the phrase "subtracted from." "Two subtracted from five," for example, means 5 - 2, not 2 - 5. Take care not to write (-8) - 10 for this problem. Instead, do 10 - (-8) = 10 + 8 = 18.

A bunch of phrases signal subtraction — "subtracted from," "less than," and "fewer than" are the most common — and they all require you to switch the order of the quantities being subtracted.

Rick's score was 9 (because it's 4 + 5). For Jacob to have the same score, three times his lowest roll must also be 9, so his lowest roll must be 3. So he could roll a 3 and a 3, a 3 and a 4, a 3 and a 5, or a 3 and a 6. Ah, but be careful. To roll a 3 and a 4, for example, he could roll 3 then 4 or 4 then 3. Jacob can really roll 7 possible combinations: (3, 3); (3, 4); (4, 3); (3, 5); (5, 3); (3, 6); or (6, 3). So 7 is the numerator (the top half of the fraction). Now what? You have to find the denominator (the bottom half of the fraction), which counts the total number of possibilities. Using the counting principle, you multiply the number of possibilities for each action. In this case, there are 6 possibilities for each die, so there are 6 × 6 = 36 total possibilities, and your answer is 7/36.

The answer choices have only v and w in them, so you need to start this problem by turning everything into those letters. You already know that x = vw, so y = wx = w(vw) = vw². To continue, you need to remember two things: First, the ws both have an "invisible 1" as their exponents, and second, you need to add exponents when you multiply powers of the same bases. Because z = xy, z = (vw)(vw²) = v²w³. You're looking for yz, which your work tells you equals (vw²)(v²w³) = v³w⁵.

This is a classic ratio problem, made more complicated by the presence of both feet and inches. You could convert everything to inches, but because I like fractions (a sad but true statement about my life), I'm going to change 1 foot 3 inches to 11/4 feet. So the ratio says that . Notice that the top numbers stand for the shadows, while the bottom ones stand for the heights of the objects in question. Doing that crazy cross-multiplication thing gives you (11/4)(x) = (5)(7) or 11/4x = 35. Now don't be scared: You have to divide both sides by 11/4, or 5/4. To divide 35 by 5/4, multiply by the reciprocal, or 4/5: 35 × 4/5 = 140/5 = 28.

The first step in answering this problem is drawing the line in question:

After you draw the line, don't jump the gun and start calculating the slope. Doing so is a waste of time because the question doesn't ask for the slope. All you have to do is look at the graph to determine that the slope is positive and then mark Choice (A).

To figure out what kind of slope a line has, imagine an ant walking on the line from left to right. If it's going uphill, the slope is positive. If it's going downhill, the slope is negative. The ant isn't going up or down when the line is horizontal (flat), so a horizontal line has a slope of zero. And, finally, the ant could be going up or down on a vertical line, so a vertical line has no slope.

When f(x) = 0, the graph has a height of 0; in other words, it crosses the x-axis. As you can see from the graph, it crosses the x-axis in three places. Notice that you don't actually need to know where it crosses the x-axis. You just need to count the number of times it does so.

Start with the last fact given in the question, that the three-digit number ABC is divisible by 5. Every number that's divisible by 5 ends in either 0 or 5, so C must be one of those numbers. The first and second facts make it impossible for C to be zero, because, if C were zero, A and B would be equal to each other, which is illegal. Therefore, C must be 5. Because B = A + C, and A must be at least 1, B must be at least 6.

LM is a diameter, which means it divides the circle into two 180° arcs. Because N is an inscribed angle (it's on the edge of the circle), its measure is half of the lower 180° arc, or 90°. Yep, it's a right triangle! Because you know the lengths of two sides of the triangle, you can find the third. Remember that 26 is the hypotenuse, so your equation should be x2 + 242 = 262, which gives you x2 + 576 = 676, x2 = 100, and x = 10. Now for the real problem — finding the area of the shaded portion of the circle, which equals the area of the circle minus the area of the triangle. The circle's diameter is 26, so its radius is 13, and the area of a circle = πr2 = π(13)2 = 169π. The triangle's area is 1/2 × base × height, but you need to be careful. Twenty-six isn't the base because you don't have a height to go with it. Instead, you need to use the two legs of the right triangle as the base and height. (It may help to rotate the book if you have trouble visualizing this concept.) So the triangle's area is 1/2(10)(24) = 120, and the answer is 169π - 120.

Don't waste your time trying to draw graphs to solve this problem. If the graph of an equation passes through a point, then the coordinates of the point are a solution to the equation. So you need to plug in -1 for x and 4 for y in each of the equations given in the answer choices. Solve the equations. In the equation in Choice (C), the key is that -(-1) = 1, so the equation becomes 1 + 3 = 4, which is a correct equation.

Make sure you don't mix up the numbers. For example, if you carelessly put -1 in for y and 4 in for x in the equation y = x - 5 in Choice (A), you'd end up choosing Choice (A) as the correct answer — and you'd be wrong!

 You could write an algebra equation for this problem, but reasoning it out works fine, too. The fraction of the tables that Nandan had to set up changed from 1/3 to 1/2. In math, change is always a cue to subtract, and 1/2 - 1/3 = 1/6. (Solve this without a calculator just for the practice.) So Nandan had to set up 1/6 more tables than he expected — 4 tables, according to the problem. If 4 is 1/6 of the total, then the total number of tables is 4 × 6 = 24.

You know there are 24 hours in a day, so to find the number of hours in a week, calculate 24 hours × 7 days = 168 hours. Now you have 168w hours. Add 24d for the leftover days. Another approach: In w weeks and d days, there are 7w + d total days. Multiplying by 24 hours in a day gives you 24(7w + d), and distributing gives you 168w + 24d.

From 10:45 p.m. to midnight is 1 hour 15 minutes, and from midnight to 2 a.m. is another 2 hours. Thus, the train was moving for 3 hours 15 minutes minus the 30 minutes (1/2 hour) it was stopped, for a total of 2 hours 45 minutes. Two hours × 80 miles per hour is 160 miles. Because 45 minutes is 3/4 of an hour, you need to add another 3/4 × 80 = 60 miles, giving you 220 miles.

All the answer choices involve multiplication, and the only way to get an odd number as the answer to a multiplication problem is to multiply two odd numbers. Thus, you can throw out Choices (A) and (E) right away because you multiply by e in both of them. Choices (C) and (D) are also no good: If o is odd, o - 1 and o + 1 are both even. These calculations leave you with Choice (B). As always, check to make sure that your answer really does work. An odd plus or minus an even is always odd, so both o - e and o + e are odd, and the product must also be odd.

The easiest approach to this problem is to start at the end: Katie used her $10 coupon and paid $35, so the price was $45 without the coupon. Because this price was 50% off the original price, it originally cost twice as much, or $90.