Each of the cards shown in the figure above has a number on each side. The product of the pair of numbers on each card is even. How many of these cards must have an even number on the side of the card not shown?

Note that the SAT doesn’t test properties of even and odd like this, although the old SAT (pre-2016) used to. The product of two numbers will be even if and only if one or both of the numbers being multiplied is even. Therefore, you know any card showing an odd number must have an even (more…)

A vending machine sells sodas for $2 each, storing the money inside. On Monday, the vending machine has 40 sodas in it and it contains $30. Write a function equation that gives the number of dollars the vending machine has, d, in terms of how many sodas the vending machine has, s.

d = 30 + 2(40 – s) The machine begins the day with $30 inside, so that’s the “30 +” part. Easy enough. The variable s is defined as how many sodas the machine has in it, but what we really care about is how many sodas are sold. We know the machine begins the day with (more…)

In the xy-plane what is the slope of the line that passes through the origin and makes a 42° angle with the positive x-axis? A. 0.67 B. 0.74 C. 0.90 D. 1.11

Trigonometry does the trick here. Below is that line making a 42° angle with the positive x-axis. I’ve also drawn a dotted segment to make myself a neat little right triangle. Remember that slope is rise over run—how high the line climbs divided by how far it travels right. In this case, the dotted segment (more…)

Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

You can make two equations here. First, you know the total number of marbles is 103, so: The second equation is more complicated, so let’s do it in parts. First, he gives away 15 red marbles, so he should have r – 15 left. He gives away 2/5 of his blue marbles, so he should have (more…)

Tariq and Penelope baked cookies and brownies for a school bake sale. Tariq made 30 brownies per hour, and Penelope made 48 cookies per hour. If the students worked for the same amount of time and produced 312 treats altogether, for how many hours did they work? Could you please include any tips you have on how to deal with these sort of problems? I’m usually stuck on these

This question comes from my own book, so my tips on how to deal with these can be found in the same chapter. The main key to getting it right is making sure you translate the words into math correctly. Note that although the question tells you that Tariq makes brownies and Penelope makes cookies, (more…)

If A(-3,0) and C(5,2) are the endpoints of diagonal AC of rectangle ABCD, with B on the x-axis, what is the perimeter of rectangle ABCD?

Draw this out. Start with the two points you’re given. Now remember that the shape is a rectangle, and that you’re told that point B is on the x-axis. The only way that happens is if B is at (5, 0). Point D, by the same logic, must be at (–3, 2). Now draw the rectangle (more…)

Hey! I stumbled upon this problem while practicing for the SAT. The boiling point of water at sea level is 212 degrees Fahrenheit. For every increase of 1,000 feet above sea level, the boiling point of water drops approximately 1.84 Fahrenheit. Which of the following equations gives the approximate boiling point B, in Fahrenheit, at h feet above sea level? A) B = 212 – 1.84h B) B = 212 – (0.00184)h C) B = 212h D) B = 1.84(212) – 1,000h Can you please help me? Thank you!

One way to make sure you get questions like these right is to plug in some values to see which equation makes sense. For example, you might choose to plug in 0 for h here because you know that at zero feet above sea level the boiling point should be 212° F. Choices C and D (more…)

During a storm, the atmospheric pressure in a certain location fell at a constant rate of 3.4 millibars (mb) per hour over a 24-hour time period. Which of the following is closest to the total drop in atmospheric pressure, in millimeters of mercury (mm Hg), over the course of 5 hours during the 24-hour time period? (Note: 1,013 mb = 760 mm Hg) Can you help me solve this please? Thank you ❤️

If it’s falling at a constant rate during the period, then we can conclude that it fell (3.4 mb/hr)(5 hr) = 17 mb. Now we just need to convert mb to mm Hg, using the given scale. Solve that for x and you get roughly 12.8. from Tumblr https://ift.tt/2w1cbUe

In an isosceles triangle with a height 10 and a base 10, a square is inscribed with side x along the base of the triangle as shown above. What is the area of the square?

I’ll draw this as best I can:   Look OK? Now let me draw a few more segments in blue… See what’s going on there? All of the small triangles in the figure are the same! (You can prove this with triangle similarity/congruence rules easily enough—I won’t spend the time doing so here, though.) We (more…)

The function f is defined by f(r) = (r-4)(r+1)^2 . If f(h-3) = 0, what is one possible value for h? I don’t see the correlation between the two functions. Can you please elucidate? Thank you <3

The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)

sqrt(3m^2 + 24) = 2m + 2. What is the sum of all the solutions to the equation? I know how to find the sum algebraically, but why can’t I use the -b/a formula here? Is it because there’s a radical? Thank you!

Whenever you have to square both sides to solve, you have to check for extraneous solutions. That tells you m could be 2 or –10, but because part of the solution was squaring both sides, you need to run both possible solutions through the original equation.Try 2 first: That works, now how about –10? Nope. Remember (more…)