SAT MATH QUESTIONS

Remember, this test is named: SAT I Reasoning Test and it tests reasoning skills more than it tests math skills.

(A) 26
(B) 22
(C) 18
(D) 14
(E) 10

CORRECT ANSWER: B

Many students will rip their hair out trying to put together different equations to solve for this. (In fact, you probably wrote down T = 2L and L = K + 4 as you were reading the question, but then started to get lost with all of the letters.) To solve this algebraically would be ridiculously complicated. Instead, understand what the question is asking, and then reason your way to the answer. The question asks us, "How old is Tom now?" You need to realize that Tom's age has to be one of the five answer choices, so let's just pick one of them and work backwards. We'll start with Choice C, 18, because it's in the middle.

Now re-read the problem assuming that Choice C is correct. If Tom is 18 and he is "twice as old as Linda", that means that Linda is 9. Now we learn that "Linda is four years younger than Karen", that means that Karen is four years older or 13. Next, we find that "Karen is one-third as old as Brian". Well, this might appear to be a bit confusing, but let's think about it logically - If Karen is one-third of Brian's age, that means that Brian is 3 times as old as she is. We might need a calculator for 13 × 3 to get to 39. Finally, "Brian will be twice as old as Tom next year". Next year Brian will be 40 (he is 39 now) and Tom will be 19 (he is 18 from the beginning of the problem). So, is 40 twice as much as 19? No, so we'll need to try another number.

The second time around this goes much quicker. Let's choose Choice B, 22. If Tom is 22, Linda is 11. If Linda is 11, then Karen is 15. If Karen is 15, then Brian is 45. Next year Brian will be 46 and Tom will be 23. Is 46 twice as much as 23? Yes - there's our answer.

(A)
(B)
(C)
(D)
(E)

CORRECT ANSWER: E

There are a lot of ways to solve this problem, but at EUREKA, we like to choose the easiest way. At EUREKA, we hate variables and we love numbers - so let's just replace the variables with numbers. Now we can't just pick any numbers for a and b, they have specific parameters that must be met.

We know that a and b are consecutive even integers and b > a > 0, so let's pick numbers that make that statement true. We'll use a = 2, b = 4. The question asks you which one of the answer choices is the "product". Since we know that a "product" is arrived at by multiplying, we can multiply 2 × 4 = 8. There - the problem is done. Our answer is 8. Now, all we have to do is plug 2 in the answer choices every time we see a, and 4 every time we see b. The only one that comes up to 8 is Choice E. We've proven our answer right!

(A)
(B)
(C)
(D)
(E)

CORRECT ANSWER: C

There are 2 ways to do this problem: The long, complicated algebraic way, and the EUREKA way! If we go about this using algebra, we can simplify the expression like this: . If that was too complex for you, then you're not going to like this next step. You'll need to factor a -1 out of the numerator to cancel out some of the terms: . Now we can cancel out the similar terms on the numerator and denominator and distribute the -1 and we're left with: .

Of course there is an easier way to do this - the EUREKA way! Do you remember from the previous question how we feel about variables? We hate them! So instead of working with x, let's put a number in its place. The problem tells us that we cannot use ±2, so let's pick 0 for x. Once we do that, the problem looks like this: . That leads us to -2 as our answer. Now, just plug that into your answer choices. The only one that comes up with -2 is Choice C. Once again we proved our answer correct. This trick works with any number we pick, so go ahead and try it again with any number you like!

(A) 3
(B) 5
(C) 5.20
(D) 6
(E) 6.93

CORRECT ANSWER: C

At EUREKA there is one shape that we love more than anything - TRIANGLES. Almost every geometry problem has something to do with triangles, so try to work with them as often as possible. If we draw a line between M and N, we've made a triangle. There's a special rule that comes into play now: A right angle can be made inside a circle by connecting two opposite points of the diameter to any other point on the circle.

We have a right triangle, but even better, a 30-60-90 triangle. There are special relationships you should have memorized for these type of triangles, but if not, don't worry, the directions have a diagram similar to this:

Since the radius of the circle is 3, we know the diameter (LN) is 6. If LN = 6, then MN = 3 and LM must be or 5.20

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