Given that
a = -0.283
b = a^2
c = a^3
d = a^4
Which of the following options correctly describes the relationship between the 4 numbers?
A. a < b < c < d
B. a < c < d < b
C. c < a < d < b
D. a < c < b < d
E. d < c < b < a
The OA is B.
For convenience, consider a = -0.3,
Hence,
a = -0.3
b = 0.09
c = -0.027
d = 0.0081
So, we can say a < c < d < d. Option B.
Please, can anyone explain another way to solve this PS question? Thanks!
Which of the following options correctly describes
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Sure. All you need to understand is that the number is negative and it's a fraction between 0 and 1. There are rules. Square a negative number and the result is a positive number so b and d will both be positive while a and c are negative. (Even exponents always result in positive numbers). So with b and d, the following rule applies: when you multiply a positive fraction by a positive fraction, the result is a lesser number. So since d is equal to b x b, d is less than b. Similarly, when you multiply a negative fraction by a negative fraction an odd number of times, the result is a greater number, so since c = a x a x a, c will be greater than a. Therefore, the order is a < c < d < b.
Substituting any negative fraction such as -1/2 or the previously suggested -0.3 should make it clear.
Substituting any negative fraction such as -1/2 or the previously suggested -0.3 should make it clear.
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Since a is a number between -1 and 0, we can replace -0.283 with any similar number such as = -1/2. So we have:BTGmoderatorLU wrote:Given that
a = -0.283
b = a^2
c = a^3
d = a^4
Which of the following options correctly describes the relationship between the 4 numbers?
A. a < b < c < d
B. a < c < d < b
C. c < a < d < b
D. a < c < b < d
E. d < c < b < a
a = -1/2
b = 1/4
c = -1/8
d = 1/16
Thus, a < c < d < b,
Answer: B
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