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Which of the following quantities is the largest?
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Updated on: 27 Dec 2013, 04:27
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Which of the following quantities is the largest? (A) \(\sqrt{2}\) (B) \(\sqrt[3]{3}\) (C) \(\sqrt[4]{4}\) (D) \(\sqrt[5]{5}\) (E) \(\sqrt[6]{6}\)
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Originally posted by mrinal2100 on 14 Jun 2011, 09:22.
Last edited by Bunuel on 27 Dec 2013, 04:27, edited 2 times in total.
Renamed the topic, edited the question added the answer choices and OA.




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14 Jun 2011, 19:08
mrinal2100 wrote: sorry guys for the wron quote but the choices were a)2(pow)(1/2) b)3(pow)(1/3) c)4(pow)(1/4) d)5(pow)(1/5) e)6(pow)(1/6)
its not 6*(sqroot of 6) So I am assuming that the choices are: \(2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 4^{\frac{1}{4}}, 5^{\frac{1}{5}}, 6^{\frac{1}{6}}\) Since fractional powers are a pain, let me multiply all the powers by 60 (LCM) to make them manageable. \(2^{30}, 3^{20}, 4^{15} ( = 2^{30}), 5^{12}, 6^{10}\) Bases and powers, both are different. To compare, we need to make one of them the same. \(2^{30} = 8^{10}\) \(3^{20} = 9^{10}\) \(6^{10}\) Obviously, out of these three, \(9^{10}\) is greatest. Now we just need to compare \(3^{20}\) with \(5^{12}\) \(3^{20} = 243^{4}\) \(5^{12} = 125^{4}\) \(3^{20} ( = 3^{\frac{1}{3}})\) is the greatest.
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Re: Which of the following quantities is the largest?
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27 Dec 2013, 04:20
mrinal2100 wrote: Which of the following quantities is the largest?
(A) \(\sqrt{2}\)
(B) \(\sqrt[3]{3}\)
(C) \(\sqrt[4]{5}\)
(D) \(\sqrt[5]{5}\)
(E) \(\sqrt[6]{6}\) The question shows another answer choice for C, but I second your approach Karishma Now, let's assume the question as is 2^30, 3^20 and 5^15 In this case, I assume it would be a matter of setting all exponents to GCF and compare the bases So we would end up with 64^5, 81^5, 64^5 Clearly now B is the winner here Kudos rain! Cheers! J



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Re: Which of the following quantities is the largest?
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27 Dec 2013, 04:48



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Re: Which of the following quantities is the largest?
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30 Dec 2013, 23:26
jlgdr wrote: Now, let's assume the question as is 2^30, 3^20 and 5^15 In this case, I assume it would be a matter of setting all exponents to GCF and compare the bases So we would end up with 64^5, 81^5, 64^5 Clearly now B is the winner here Kudos rain! Cheers! J 2^30, 3^20 and 5^15 Yes, you can get the common power of 5 64^5, 81^5 and 125^5 So 5^15 is greatest here.
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Re: Which of the following quantities is the largest?
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22 Oct 2015, 11:56
VeritasPrepKarishma wrote: mrinal2100 wrote: sorry guys for the wron quote but the choices were a)2(pow)(1/2) b)3(pow)(1/3) c)4(pow)(1/4) d)5(pow)(1/5) e)6(pow)(1/6)
its not 6*(sqroot of 6) So I am assuming that the choices are: \(2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 4^{\frac{1}{4}}, 5^{\frac{1}{5}}, 6^{\frac{1}{6}}\) Since fractional powers are a pain, let me multiply all the powers by 60 (LCM) to make them manageable. \(2^{30}, 3^{20}, 4^{15} ( = 2^{30}), 5^{12}, 6^{10}\) Bases and powers, both are different. To compare, we need to make one of them the same. \(2^{30} = 8^{10}\) \(3^{20} = 9^{10}\) \(6^{10}\) Obviously, out of these three, \(9^{10}\) is greatest. Now we just need to compare \(3^{20}\) with \(5^{12}\) \(3^{20} = 243^{4}\) \(5^{12} = 125^{4}\) \(3^{20} ( = 3^{\frac{1}{3}})\) is the greatest. I Karishma  it's very clear and simple until the end. To compare 3^20 with 5^12, it seems that we need to know what 3^16 and 5^8 are. Isn't 3^16 a uncommon number to memorize? Or is this expected for the gmat / there is an easier way to compare? Thanks so much!
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Re: Which of the following quantities is the largest?
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22 Oct 2015, 12:08
happyface101 wrote: VeritasPrepKarishma wrote: mrinal2100 wrote: sorry guys for the wron quote but the choices were a)2(pow)(1/2) b)3(pow)(1/3) c)4(pow)(1/4) d)5(pow)(1/5) e)6(pow)(1/6)
its not 6*(sqroot of 6) So I am assuming that the choices are: \(2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 4^{\frac{1}{4}}, 5^{\frac{1}{5}}, 6^{\frac{1}{6}}\) Since fractional powers are a pain, let me multiply all the powers by 60 (LCM) to make them manageable. \(2^{30}, 3^{20}, 4^{15} ( = 2^{30}), 5^{12}, 6^{10}\) Bases and powers, both are different. To compare, we need to make one of them the same. \(2^{30} = 8^{10}\) \(3^{20} = 9^{10}\) \(6^{10}\) Obviously, out of these three, \(9^{10}\) is greatest. Now we just need to compare \(3^{20}\) with \(5^{12}\) \(3^{20} = 243^{4}\) \(5^{12} = 125^{4}\) \(3^{20} ( = 3^{\frac{1}{3}})\) is the greatest. I Karishma  it's very clear and simple until the end. To compare 3^20 with 5^12, it seems that we need to know what 3^16 and 5^8 are. Isn't 3^16 a uncommon number to memorize? Or is this expected for the gmat / there is an easier way to compare? Thanks so much! It is not \(3^{16}\) that you need to remember. When you end up comparing \(3^{20}\) and \(5^{12}\), try to raise the 2 numbers to the same power. In this case the common GCD of 20 and 12 is 4. Thus \(3^{20}=(3^5)^4\) and \(5^{12} = (5^3)^4\) Giving you the 2 values as \(243^4\) and \(125^4\). So now can easily see that the 2 numbers are raised to the same power but with a differnet base giving you \(3^{20} > 5^{12}\)



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Re: Which of the following quantities is the largest?
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19 Feb 2018, 14:33
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Re: Which of the following quantities is the largest? &nbs
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