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# If r is between –1 and 0, then which of the following is true?

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If r is between –1 and 0, then which of the following is true? [#permalink]

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01 Oct 2017, 23:36
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If r is between –1 and 0, then which of the following is true?

A. $$r^5 < r^6 < r^7$$

B. $$r^5 < 0 < r^7$$

C. $$r^7 < r^6 < r^5$$

D. $$r^7 < r^5 < r^6$$

E. $$r^3 < r^7 < r^6$$
[Reveal] Spoiler: OA

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If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 01:26
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The best way is to choose a number and look at the various options.
If r = -$$\frac{1}{2} r^5 = -\frac{1}{32} = - 0.03125, r^3 = -\frac{1}{8} = -0.125$$ and $$r^7 = -\frac{1}{128} = -0.007$$
However, r^even is always positive

Options A,B and C are eliminated because, we have a even power
in between two odd powers and the positive term will always be the biggest.
$$r^7$$ is greater than $$r^5$$, so Option D cannot be the answer.

Therefore, $$r^3 < r^7 < r^6$$(Option E) is the answer option that is always true!
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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 08:02
The best way is to choose a number and look at the various options.
If r = -12,r5=−132=−0.03125,r3=−18=−0.12512,r5=−132=−0.03125,r3=−18=−0.125 and r7=−1128=−0.007r7=−1128=−0.007
However, r^even is always positive

Options A,B and C are eliminated because, we have a even power
in between two odd powers and the positive term will always be the biggest.
r7r7 is greater than r5r5, so Option D cannot be the answer.

Therefore, r3<r7<r6r3<r7<r6(Option E) is the answer option that is always true!
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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 09:29
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. $$r^5 < r^6 < r^7$$

B. $$r^5 < 0 < r^7$$

C. $$r^7 < r^6 < r^5$$

D. $$r^7 < r^5 < r^6$$

E. $$r^3 < r^7 < r^6$$

Solving the problem conceptually

we know that $$r$$ is negative, hence $$r$$ will be greatest when power is even. So choice A, B & C are out

Again as $$r$$ is negative and greater than $$-1$$ i.e a negative proper fraction, higher powers of $$r$$ will be greater than the lower powers, So option D is out.

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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 10:22
Others have also solved it perfectly. Some of you might have picked D.

You would have figured out $$r^6$$>0, hence it would be highest. The other 2 would be negative. This rules out A,B,C

Now $$|r^7|< |r^5|$$, but since both of these terms are negative, $$r^7> r^5$$
Hence D is wrong.

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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 11:56
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. $$r^5 < r^6 < r^7$$

B. $$r^5 < 0 < r^7$$

C. $$r^7 < r^6 < r^5$$

D. $$r^7 < r^5 < r^6$$

E. $$r^3 < r^7 < r^6$$

Even power of r will always be greater than odd powers and 0, as even power will result in positive number and odd power will result in -ve number.
Odd power of r will always be less than even power and 0 .

A. Wrong
B. Wrong
C. Wrong

Now between D and E.. we know r^3 <r^5 <r^7 ...

So, r^3 < r^7 <r^6 ..

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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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02 Oct 2017, 21:29
Since we know r has to be -ve number, options A, B and C cannot be right. Three of them have a odd number on r, followed by either 0 or an even digit on r.
D or E must be correct.
For D: r^7 < r^5 cannot be right.
E has to be the answer.
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Re: If r is between –1 and 0, then which of the following is true? [#permalink]

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04 Oct 2017, 15:37
Bunuel wrote:
If r is between –1 and 0, then which of the following is true?

A. $$r^5 < r^6 < r^7$$

B. $$r^5 < 0 < r^7$$

C. $$r^7 < r^6 < r^5$$

D. $$r^7 < r^5 < r^6$$

E. $$r^3 < r^7 < r^6$$

We know that when a negative number is raised to an odd power, the result is negative, and when a negative number is raised to an even power, the result is positive. Furthermore, if the number is between -1 and 0, raising it to a larger odd power will increase its value since the result will be closer to zero (despite still being negative). Thus, we see that:

r^3 < r^7 < r^6

Notice that r^7 will be larger than r^3, and r^6 will be larger than the prior two because it’s positive.

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Re: If r is between –1 and 0, then which of the following is true?   [#permalink] 04 Oct 2017, 15:37
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