Quantitative Reasoning Answers &
Explanations
1.
The answer is C.
Explanation:
The ratio of 12 to 5 tells us that for every 12 hardcover books,
there are 5 paperback books. It also tells us that there are a
total of 12 + 5 = 17 equal parts. These 17 equal parts make up
the total of 204 books. So each of these equal parts is 204 ÷ 17
= 12 books. The paperback books consisted of 5 of these equal
parts, so there are 5 × 12, or 60 paperback books.
2. The answer is E.
Explanation:
When the product of a group of numbers is nonzero, none of the
numbers can be 0. This is because if even just one number is 0,
the product is zero. For example, 7 × 10 × 12 × 0 × 4 × 35 = 0,
because the fourth factor is a 0. Here, (v +
w)(x - y - z)(x + y +
z)z = 3, so (v + w)(x -
y - z)(x + y + z)z does
not equal 0. So each factor of this product must be nonzero. That
is:
- v + w does not equal 0
- x - y - z does not equal 0
- x + y + z does not equal 0
- z does not equal 0
The last inequality tells us that z can never equal 0.
Choice E is correct.
None of the other answer choices must be nonzero. If v
= 0, w = -3, x = 0, y = 0, and z = 1,
then (v + w)(x - y -
z)(x + y + z)z =
(-3)(-1)(1)(1) = 3, and choices A, C, and D are seen to be
incorrect, because v, x, and y can each be
0. If v = -3, w = 0, x = 0, y = 0,
and z = 1, then (v + w)(x - y
- z)(x + y + z)z = 3 and
choice B is seen to be incorrect, because w can be 0.
Only z cannot equal 0, and again, choice E is
correct.
3. The answer is B.
Explanation
A line that's perpendicular to y = -2x + 3 has a slope
that's the negative reciprocal of -2, which is 1/2. That narrows
the choices to A and B. The y-intercept of y = 2x - 3 is
-3, and that's the y-intercept in B.
4. The answer is D.
Explanation
B will have his maximum number of marbles when the others
(A and C) have their minimum number according to
the constraints. Since C has less than both A and
B, his minimum is 0.Therefore, A and B have
24 together. If A is to have more than B, and
B is to have a maximum, A will have 13 and B
will have 11.
5. The answer is D.
Explanation
Total customers per day = 15(600). (Don't multiply out any
product at first!) If six theaters shut down, then nine remain
open. If we let be the average number of customers per day for
each of the nine theaters, 15(600) = 9x, because we are
told that the number of customers remains the same. So,
15(600) = 9x
9000 = 9x
x = 1000.
Other PracticeQs:
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