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M26-05

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M26-05  [#permalink]

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New post 16 Sep 2014, 00:24
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A
B
C
D
E

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. \(x^4 \gt 32\)

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Re M26-05  [#permalink]

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New post 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.


Answer: D
_________________

New to the Math Forum?
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M26-05  [#permalink]

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New post 09 Aug 2015, 01:27
01 Minutes approach:

X5 = -37

Hence X must be less than -2

So X3 < -8

D it is.
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Re: M26-05  [#permalink]

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New post 06 Jul 2016, 05:11
Bunuel,

Why option E is incorrect:

x=-2.1 (Suppose) in this case x^4>32.
SO it can right.. Please advise




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.


Answer: D
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Posts: 50583
Re: M26-05  [#permalink]

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

Why option E is incorrect:

x=-2.1 (Suppose) in this case x^4>32.
SO it can right.. Please advise




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.


Answer: D


2^4 = 16, not 32. So, E is not correct.,
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Posts: 118
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Re: M26-05  [#permalink]

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New post 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.
SO it can right.. Please advise




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.


Answer: D


2^4 = 16, not 32. So, E is not correct.,
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M26-05  [#permalink]

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New post 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. \(x^4 \gt 32\)

Answer: D
\(x=\sqrt[5]{-37}\)
=> \(x^5 = -37\)
=> \((-x)^5 =37 \gt 32 = 2^5\)
=> \(-x \gt 2\)
=> \(x^3 \lt -8\)
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M26-05  [#permalink]

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New post 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.
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M26-05 &nbs [#permalink] 24 Jul 2018, 19:58
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