Which of the following options correctly describes the relationship be

Question

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

generis · Answer

vinhthi - Yes. Because the problem is about the behavior of fractions between 0 and -1, it doesn't matter what value you use, as long as it is -1 < x < 0 That decimal is not easy to work with. So I used -\frac{1}{2} . (If you like decimals better, you could use -.2, or some other number that is easy to multiply. I find fractions easier with exponential values in this range; I don't have to track on zeros.) a = -\frac{1}{2} b = a^2 = -(\frac{1}{2})^2 =\frac{1}{4} c = a^3 = -(\frac{1}{2})^3 = -\frac{1}{8} d = a^4 = -(\frac{1}{2})^4 = \frac{1}{16} a < c < d < b Answer B

Bunuel · Answer

Similar question from OG: https://gmatclub.com/forum/if-r-0-345-s ... 32067.html

generis · Answer

Reply posts for this similar and good question contain a mine of information. I had forgotten about it. Thanks,  Bunuel

ScottTargetTestPrep · Answer

We see that the value of a is negative. Therefore, when it is raised to an odd power, it’s negative, and when it is raised to an even power, it’s positive. Therefore, we see that b and d are positive, and a and c are negative.

Since a is between -1 and 0, when it is raised to an odd power, the larger the exponent, the larger the value. Thus, we have a < a^3 or a < c.

On the other hand, when a is raised to an even power, the larger the exponent, the smaller the value. Thus, we have a^4 < a^2 or d < b.

Thus, the order of the quantities is: a < a^3 < a^4 < a^2, or a < c < d < b.

Answer: B

saswata4s · Answer

For convenience, consider a = −0.283 ≈ -.3

Hence,
a = −0.283 = ≈ -0.3
b = a^2 = 0.09
c = a^3 = -0.027
d = a^4 = 0.0081

So we can say, a<c<d<b

Ans: B

jaisonsunny77 · Answer

Given that

a = −0.283
b = a^2
c = a^3
d = a^4

"even" powers of a negative number are always positive; ''odd'' powers of a negative number will result in another negative number.

So, we can  eliminate (A), (D), and (E)  based on this understanding alone.

To find the correct answer between the two remaining choices, we need to determine the relation between the values of variables ''a'' and ''c''

As the odd power of a negative integer (belonging to the -1<(the number)<0 range) increases, the value gets closer to zero and therefore is considered greater than the original number itself.

For eg: (-0.1)^3 = -0.001
Since -0.001 is closer to 0 than -0.1, the greater odd power of such a negative number will result in a number that is greater than the original number itself. We can use the same understanding to establish that the variable ''c'' has a greater value than ''a''

Therefore, option   (B) is the right answer.

bumpbot · Answer

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Which of the following options correctly describes the relationship be

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