ibex aptitude test prep

What would be the next number in the following series? 7 | 14 | 28 | 32 | 64 | 128 | ? | ? A. 257|1128 B. 208|514 C. 132|264 D. 340|686

The answer is (C). The series repeatedly increases by x2, x2, +4.

Which of the following statements is true for this formula? A. When the value of b is greater than 2, a is negative. B. When the value of b is less than 2, a is positive. C. When the value of b is less than -2, a is negative. D. When the value of b is greater than -2, a is negative.

The correct answer is (C). If a = ½ b + 1, then a = 0 when b = -2. Then, a > 0 when b > -2 and a < 0 when b < -2. Only answer (C) supports this conclusion.

What would be the next number in the following series? 3 | 3 | 3 | 6 | 3 | 9 | 3 | ? A. 3 B. 27 C. 12 D. 6

The correct answer is (C).There are two ways to look at this series: (1) There are two inner series. each following a different rule:Odd terms- remain constant: 3. Even terms- increase by 3: 3+3=6, 6+3=9, 9+3=12.

What is the value of X? 5x - 2x - x = 11 - 2 + 15 A. 4 B. 6 C. 8 D. 12

The correct answer is (D). 5x - 2x - x = 11 - 2 + 15 Combine like terms 3x - x = 9 + 15 Combine like term s2x = 24 Divide each side by 2. x = 12 (* Multiplication and division precede addition and subtraction).

Which expression is equivalent to the expression (𝑥 + 5)(𝑥 − 5)? A. 𝑥2 + 2𝑥 - 25 B. 𝑥2 − 𝑥 - 25 C. 𝑥2 - 5 D. 𝑥2 - 25

The correct answer is (D). In this problem, multiply the two factors. To do that, multiply each component in the first factor with each component in the second factor, and sum those products:(𝑥 + 5)(𝑥 − 5) = 𝑥2 + 5𝑥 − 5𝑥 − 25 = 𝑥2 − 25, and the correct answer is (D).

Factor the polynomial x² - 3x - 18 a) (x + 3)(x − 6) b) (x + 9)(x − 2) c) (x + 6)(x − 3) d) (x + 2)(x −9)

The correct answer is (x + 3)(x − 6). Every quadratic formula is following the same construct Ax2 + Bx + C, when the coefficients A, B, and C are real numbers. How to recognize the correct answer by looking at the answers? Each of the answers is a product of two binomials. If in both cases the coefficient of x is 1 (as in this case), then the correct answer would consist of numbers that follow two conditions: The sum of the numbers is equal to the coefficient B The product of the numbers is equal to the coefficient C Look at all four answers. Only the correct answer satisfies both of these conditions: (x - 6)(x + 3) → Sum = -6 + 3 = -3 Product = -6 * 3 = -18 The polynomial is x2 − 3x − 18. Remember - As another alternative solution path, you can always use the FOIL method and multiply each of the factors suggested in the answers. One of them ought to yield the correct polynomial.

Consider the following formula: A = (B - 2)(C + 5) If A = 6 and B = 0, what is the value of C? a)-0.5 b)4 c)0.5 d)-8

The correct answer is -8. In order to solve this problem correctly, you need to remember the order of operations (PEMDAS): Parentheses Exponents Multiplication/Division Addition/Subtraction In order to find a solution, you need to isolate C. First step - placing the values of A and B: A = (B - 2)(C + 5), Remember A = 6; B = 0 6 = (0 - 2)(C + 5) 6 = -2(C + 5) Second step - removing the parentheses: 6 = -2(C + 5) -2 is a factor of both C and 56 = -2*C - 2*5 6 = -2C - 10 Third step - isolating C and finding the solution: 6 = -2C - 10 Add 10 to both sides 6 + 10 = -2C Simplify the right side 16 = -2C -8 = C

What is the next number in the following series of numbers? 7 10 15 22 31 a)39 b)41 c)42 d)40

The correct answer is 42. Explanation: Look at the differences between the numbers: 7 10 15 22 31 +3. +5 +7. +9 +2 +2 +2 The difference between each term is greater by two in every step. Therefore, the difference between the last displayed number of the series and the next number should be 9 + 2 = 11 Therefore, the next number of the series is 31 + 11 = 42 For learning purposes, calculate the values of the differences of the series if you had continued the series: +3 +5 +7 +9 +11 +13 +15 Therefore, the next numbers of the series would be: 42 + 13 = 55 55 + 15 = 70

Evaluate the expression: For x = 11, x2 - 15x + 56 = ? a)12 b)11 c)-56 d)15

The correct answer is A. (12). x2 - 15x + 56 =Substitute value of 'x' in the equation 112 - 15*11 + 56 =According to PEMDAS, solve exponents first PEMDAS = 121 - 165 + 56 The order of addition and subtraction can be changed if and only if each number maintains its arithmetic sign = 121 + 56 - 165Add terms = 177 - 165 Subtract terms = 12

Evaluate the value of the unknown variable: Y = 27 Z = Y/9 X = Y x Z X =__?__ a) 81 b) 61 c) 91 d) 71

The correct answer is A. (81). Z = Y/9 Find the value of "Z" by putting the value of "Y" in this equation, from the question Z = 27/9 Solve the fraction by dividing the numerator by the denominator Z = 3 X = Y x Z Now take the main equation involving all three variables and substitute the value of 'Y' from the question and 'Z' from above X = 27 x 3Multiply both the terms X = 81