CrushTheTest SAT Math Preparation

(A) p – 1
(B) 1 – p
(C) p
(D) –p
(E) p²

You can view "x" as "x/1" and then just turn both sides upside down to get 1/x = p. So the answer is (C).

(A) x^ab
(B) x^a+b
(C) x^a–b
(D) x^a + x^b
(E) x^a/b

Think of it this way: x² = x·x and x³ = x·x·x. So x²·x³ must be x·x·x·x·x or x⁵. In other words, when you multiply, you add the exponents. The answer is x^a+b or (B).

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(A) a⁵b⁵
(B) a/b⁵
(C) b/a⁵
(D) 1/(a⁵b⁵)
(E) 5^ab

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The negative sign in a power means "1 over." So (ab)^-5 is 1 over (ab)⁵. The answer is (D).

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(A) xy
(B) x · (y + 1)
(C) xy + 1
(D) y · (x + 1)
(E) xy – 1

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The y on the bottom cancels with a y in each term on top. The second term doesn't vanish, however. Instead, a "1" is left behind. So the answer is xy + 1 or (C).

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(A) x
(B) –x
(C) 1
(D) –1
(E) cannot be simplified

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When you switch two things you're subtracting, you get a negative sign. For example, (2-3) = -(3-2). So the answer to this problem is -1 or (D).

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(A) (x – y)²
(B) (x + y)²
(C) x/y + y/x
(D) (x + y) · (x – y)
(E) x² + xy + y²

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A difference of squares factors to (x+y)·(x-y). The answer is (D). Note that the "cross terms" +2xy and -2xy cancel.

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(A) a/x = b/y
(B) ay = bx
(C) y/b = x/a
(D) x = ay/b
(E) all of these

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With a proportion like this, you can turn both sides upside down, switch a and y, switch b and x, multiply both sides by y, and multiply both sides by b. So the answer is "all of these" or (E).

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(A) kx
(B) 100kx
(C) 100k + x
(D) k + 100x
(E) kx/100

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30 percent of x means 0.30 · x. So "k percent of x" means (k/100) · x or (E).

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(A) 1.3x
(B) x + 30
(C) x + 0.30
(D) 0.3x
(E) 130x

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The quickest way to increase by 30 percent is to multiply by 1.3; to decrease by 30 percent, you would multiply by 0.7. The answer is (A).

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(A) x
(B) x⁶
(C) x⁵
(D) x²·√x
(E) x·√x

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√(x³) = √(x²·x) = (√x²)·(√x) = x · √x or (E).

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1. if x = 1/p then 1/x = (A) p – 1 (B) 1 – p (C) p (D) –p (E) p² Show Brief Solution You can view "x" as "x/1" and then just turn both sides upside down to get 1/x = p. So the answer is (C). Show Answer Choices	2. If w = x^a and z = x^b then wz = (A) x^ab (B) x^a+b (C) x^a–b (D) x^a + x^b (E) x^a/b Show Brief Solution Think of it this way: x² = x·x and x³ = x·x·x. So x²·x³ must be x·x·x·x·x or x⁵. In other words, when you multiply, you add the exponents. The answer is x^a+b or (B). Show Answer Choices
3. The quantity (ab)^–5 = (A) a⁵b⁵ (B) a/b⁵ (C) b/a⁵ (D) 1/(a⁵b⁵) (E) 5^ab Show Brief Solution The negative sign in a power means "1 over." So (ab)^-5 is 1 over (ab)⁵. The answer is (D). Show Answer Choices	4. The quantity (xy² + y) / y = (A) xy (B) x · (y + 1) (C) xy + 1 (D) y · (x + 1) (E) xy – 1 Show Brief Solution The y on the bottom cancels with a y in each term on top. The second term doesn't vanish, however. Instead, a "1" is left behind. So the answer is xy + 1 or (C). Show Answer Choices

5. The quantity (x – 1)/(1 – x) = (A) x (B) –x (C) 1 (D) –1 (E) cannot be simplified Show Brief Solution When you switch two things you're subtracting, you get a negative sign. For example, (2-3) = -(3-2). So the answer to this problem is -1 or (D). Show Answer Choices	6. The quantity (x² – y²) = (A) (x – y)² (B) (x + y)² (C) x/y + y/x (D) (x + y) · (x – y) (E) x² + xy + y² Show Brief Solution A difference of squares factors to (x+y)·(x-y). The answer is (D). Note that the "cross terms" +2xy and -2xy cancel. Show Answer Choices
7. If a/b = x/y and x≠0 then: (A) a/x = b/y (B) ay = bx (C) y/b = x/a (D) x = ay/b (E) all of these Show Brief Solution With a proportion like this, you can turn both sides upside down, switch a and y, switch b and x, multiply both sides by y, and multiply both sides by b. So the answer is "all of these" or (E). Show Answer Choices	8. If k is a positive number then k percent of x is equal to: (A) kx (B) 100kx (C) 100k + x (D) k + 100x (E) kx/100 Show Brief Solution 30 percent of x means 0.30 · x. So "k percent of x" means (k/100) · x or (E). Show Answer Choices