Basic Numeracy/Quantitative Aptitude

Detailed Solution

93. The correct answer is 12
(4i - 8)/5 = i - 4
=> 4i - 8 = 5i - 20
=> 5i - 4i = 20 - 8
=> i = 12

94. The correct answer is (5(x^2)(y^2)(z))(x + 20yz)
Find the GCF of your like terms. The GCF of 5 and 100 is 5. The GCF of x^3 and x^2 is x^2. The GCF of y^2 and y^3 is y^2. The GCF of z and z^2. So, your total GCF is 5x^2y^2z. You divide each term by that and are left with x and 20yz. You write it in the form 5x^2y^2z(x + 20yz). If you distribute 5(x^2)(y^2)(z) to x and 20yz, you have your original answer, 5x^3y^2z + 100x^2y^3z^2

95. The correct answer is (2x + 5)(2x - 5)
Both terms are perfect squares. The square root of 4x^2 is 2x, and the square root of 25 is 5. You place one of each term in two sets of parentheses, and place an addition sign in the middle of one and a subtraction sign in the middle of another. The reason a problem like this is factored this way is when you use the distributive property to multiply it out, you get 4x^2 + 10x - 10x - 25. Your +10x and -10x cancel out to 0x, which means there is no need to write the 0x in the problem

96. The correct answer is 2(x + 5)(x - 5)
Looking at the original problem, you notice a common factor of two in both terms. Factor it out now, to save yourself later trouble. You now have 2(x^2 - 25). Looking at the x^2 - 25, you notice both terms are perfect squares and, using the difference of two perfect squares technique, factor it further down to (x+5)(x-5).
Your final answer would be 2(x+5)(x-5)

97. The correct answer is (5x + 9)^2.
Looking at your first and last terms, you notice they are both perfect squares. You can place their square roots in parentheses and add them together in parentheses, like (5x+9)(5x+9). When you distribute each term, you get 25x^2+45x+45x+81. Your two middle terms can be combined, so the solution to your factoring is 25x^2 + 90x + 81. When you have two identical parentheses being multiplied together, you can write it as one parentheses squared, like (5x + 9)^2

98. The correct answer is (a + 8)(a + 3)
The key to figuring out what factors of 24 to use in your parentheses lies in your middle term, 11a. You want factors of 24 that can add up to 11. Looking at the factors of 24, we see that 8 and 3 add up to 11. Write your answer as (a + 8)(a + 3). Note that it doesn't matter what order the parentheses are in. Distributing this problem, you get a^2 + 8a + 3a + 24, which can further be simplified to a^2 + 11a + 24

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