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# M26-05

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Math Expert
Joined: 02 Sep 2009
Posts: 50583

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16 Sep 2014, 00:24
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:06) correct 42% (01:23) wrong based on 195 sessions

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If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50583

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16 Sep 2014, 00:24
1
4
Official Solution:

If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

Must know for the GMAT: Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Back to the original question:

As $$-2^5=-32$$ then $$x$$ must be a little bit less than -2 hence $$x=\sqrt[5]{-37} \approx -2.1 \lt -2$$. Thus $$x^3 \approx (-2.1)^3 \approx -8.something \lt -8$$, so option D must be true.

As for the other options:

A. $$\sqrt{-x}=\sqrt{-(-2.1)}=\sqrt{2.1} \lt 2$$, $$\sqrt{-x} \gt 2$$ is not true.

B. $$x \approx -2.1 \lt -2$$, thus $$x \gt -2$$ is also not true.

C. $$x^2 \approx (-2.1)^2=4.something \gt 4$$, thus $$x^2 \lt 4$$ is also not true.

_________________
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Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)

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09 Aug 2015, 01:27
01 Minutes approach:

X5 = -37

Hence X must be less than -2

So X3 < -8

D it is.
Manager
Joined: 12 Aug 2015
Posts: 118
Location: India
Concentration: General Management, Strategy
GMAT 1: 690 Q50 V32
GPA: 3.38

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06 Jul 2016, 05:11
Bunuel,

Why option E is incorrect:

x=-2.1 (Suppose) in this case x^4>32.

Bunuel wrote:
Official Solution:

If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

Must know for the GMAT: Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Back to the original question:

As $$-2^5=-32$$ then $$x$$ must be a little bit less than -2 hence $$x=\sqrt[5]{-37} \approx -2.1 \lt -2$$. Thus $$x^3 \approx (-2.1)^3 \approx -8.something \lt -8$$, so option D must be true.

As for the other options:

A. $$\sqrt{-x}=\sqrt{-(-2.1)}=\sqrt{2.1} \lt 2$$, $$\sqrt{-x} \gt 2$$ is not true.

B. $$x \approx -2.1 \lt -2$$, thus $$x \gt -2$$ is also not true.

C. $$x^2 \approx (-2.1)^2=4.something \gt 4$$, thus $$x^2 \lt 4$$ is also not true.

Math Expert
Joined: 02 Sep 2009
Posts: 50583

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06 Jul 2016, 06:25
1988achilles wrote:
Bunuel,

Why option E is incorrect:

x=-2.1 (Suppose) in this case x^4>32.

Bunuel wrote:
Official Solution:

If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

Must know for the GMAT: Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Back to the original question:

As $$-2^5=-32$$ then $$x$$ must be a little bit less than -2 hence $$x=\sqrt[5]{-37} \approx -2.1 \lt -2$$. Thus $$x^3 \approx (-2.1)^3 \approx -8.something \lt -8$$, so option D must be true.

As for the other options:

A. $$\sqrt{-x}=\sqrt{-(-2.1)}=\sqrt{2.1} \lt 2$$, $$\sqrt{-x} \gt 2$$ is not true.

B. $$x \approx -2.1 \lt -2$$, thus $$x \gt -2$$ is also not true.

C. $$x^2 \approx (-2.1)^2=4.something \gt 4$$, thus $$x^2 \lt 4$$ is also not true.

2^4 = 16, not 32. So, E is not correct.,
_________________
Manager
Joined: 12 Aug 2015
Posts: 118
Location: India
Concentration: General Management, Strategy
GMAT 1: 690 Q50 V32
GPA: 3.38

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06 Jul 2016, 16:32
Bunuel,

Thanks. Didnt look at the options carefully. Silly mistake from my side..

Cheers!

Bunuel wrote:
1988achilles wrote:
Bunuel,

Why option E is incorrect:

x=-2.1 (Suppose) in this case x^4>32.

Bunuel wrote:
Official Solution:

If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

Must know for the GMAT: Even roots from negative number is undefined on the GMAT (as GMAT is dealing only with Real Numbers): $$\sqrt[{even}]{negative}=undefined$$, for example $$\sqrt{-25}=undefined$$.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Back to the original question:

As $$-2^5=-32$$ then $$x$$ must be a little bit less than -2 hence $$x=\sqrt[5]{-37} \approx -2.1 \lt -2$$. Thus $$x^3 \approx (-2.1)^3 \approx -8.something \lt -8$$, so option D must be true.

As for the other options:

A. $$\sqrt{-x}=\sqrt{-(-2.1)}=\sqrt{2.1} \lt 2$$, $$\sqrt{-x} \gt 2$$ is not true.

B. $$x \approx -2.1 \lt -2$$, thus $$x \gt -2$$ is also not true.

C. $$x^2 \approx (-2.1)^2=4.something \gt 4$$, thus $$x^2 \lt 4$$ is also not true.

2^4 = 16, not 32. So, E is not correct.,
Manager
Joined: 12 Dec 2015
Posts: 133

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24 Jul 2018, 06:57
1
If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

$$x=\sqrt[5]{-37}$$
=> $$x^5 = -37$$
=> $$(-x)^5 =37 \gt 32 = 2^5$$
=> $$-x \gt 2$$
=> $$x^3 \lt -8$$
Manager
Joined: 25 Jul 2017
Posts: 96

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24 Jul 2018, 19:58
Bunuel wrote:
If $$x=\sqrt[5]{-37}$$ then which of the following must be true?

A. $$\sqrt{-x} \gt 2$$
B. $$x \gt -2$$
C. $$x^2 \lt 4$$
D. $$x^3 \lt -8$$
E. $$x^4 \gt 32$$

This question can easily be solved by simplification and guesstimate.
Given, x = (-37)^1/5
=> x^5= -37

Two things from here are certain:
1. x is negative &
2. x is just less than -2 (since -2^5 = 32 & hence x ~ -2.1)

Since, x=~ -2.1, therefore x^3 =~ -9 i.e. x^3 < -8 (i.e. -9< -8)

Only option D is right. Rest all can be simply eliminated.
M26-05 &nbs [#permalink] 24 Jul 2018, 19:58
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# M26-05

Moderators: chetan2u, Bunuel

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