McGraw-Hill Education GRE 2019

Exercise Answers Discrete Quantitative Questions D Simplify the equation by dividing both sides by 2: x^2 + 10x = −24. Since yo ...

Quantitative Comparison Questions D Since the exponent on the variable is even, x = √ 16 = 4 or x = −√ 16 = −4. The relationshi ...

A company estimates the number of potential customers, P, in a day by using the following formula: P =^8 zc 43 , where c = the n ...

Going from Output to Input In the preceding example, you were given the formula for the function and its input, and you were ask ...

Let’s do another symbolism question with two symbols: If the operation # is defined for all numbers, a and b, by a # b = √ab, th ...

Example 2: The sequence a 1 , a 2 , a 3 ,... , an,... is such that an = an−1 − an−2 2 for all n > 2. If a 3 = 12 and a 4 = 5, ...

Exercise: Formulas, Functions, and Sequences Discrete Quantitative Questions For this question, write your answer in the box. I ...

For all numbers, x, the function f is defined by f(x) = ax 33 , where a is a constant. If f(3) = 45, then a = A 3 B 5 C 15 D 30 ...

In a certain sequence, each term is 7 greater than the term before it. If the third term of the sequence is 39, what is the 13t ...

The sequence a 1 , a 2 , a 3 ,... , an,... is such that an = an−1 + 7, for all n > 1. QUANTITY A QUANTITY B a 3 a 1 + 15 A B ...

A Solution: a 4 = 3a 3 + 2a 2. Thus: 35 = 3(7) + 2a 2 14 = 2a 2 7 = a 2 B To determine the 13th term, you will have to add 7 a ...

Inequalities Versus Equations The fundamental difference between equations and inequalities is the following: Whereas an equatio ...

SOLUTION: Combine like terms: −x + 2y > y − 2x + 2x + 2x x + 2y > y ↓ − y − y x + y > 0 The correct answer is C. Multip ...

For example, if you are told that xy > 1, you may be tempted to multiply both sides by y and arrive at x > y. However, thi ...

Maximization and Minimization with Inequalities Another common type of inequality question will give you two inequalities and as ...

Step 1: Isolate the absolute value: 9 + |x + 4| = 28 −9 −9 |x + 4| = 19 Step 2: Create two equations. In one equation, the expre ...

Step 3: Combine the inequalities: x < 4 and x > −10 ↓ −10 < x < 4 Test Positives and Negatives When answering a “mus ...

Exercise: Inequalities and Absolute Value Discrete Quantitative Questions If −x + y > y + 2x, which of the following must be ...

If a, b, and c are positive integers, a > b > c, and a + b + c < 27, what is the maximum value for a? A 23 B 24 C 25 D ...

For how many integers, a, is it true that 2 < |a| < 9? A 4 B 5 C 6 D 10 E 12 Quantitative Comparison Questions Each of t ...