Which of the following options correctly describes

[BTGmoderatorLU]

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!

[Jake@ThePrincetonReview]

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.

[Scott@TargetTestPrep]

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

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:

a = -1/2

b = 1/4

c = -1/8

d = 1/16

Thus, a < c < d < b,

Answer: B