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Re M2605
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16 Sep 2014, 00:24
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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Re: M2605
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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.



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Re: M2605
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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. 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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Re: M2605
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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. 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Aug 2015
Posts: 118
Location: India
Concentration: General Management, Strategy
Schools: Kellogg 1YR '18, LBS '19, Insead Sept '17, Oxford"18, Judge"18, HKUST '19, ISB '18, IIMA , IIMB, IIMC , NTU '18, XLRI GM"18, IIMA PGPX"18
GPA: 3.38

Re: M2605
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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. 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.,



Manager
Joined: 12 Dec 2015
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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. \(x^4 \gt 32\)
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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Joined: 25 Jul 2017
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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.










