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If n = (2^2)(3^4)(5^6), the value of which of the following products

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gjonrexha
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If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   Updated on: 20 Dec 2021, 01:52
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If \(n = (2^2)(3^4)(5^6)\), the value of which of the following products is greater than \(\sqrt{n}\)?

I. \((2)(3^3)(5^2)\)
II. \(2(3)(5^4)\)
III. \((2^2)(3^2)(5^3)\)

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

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I understand the question and whats its asking but can someone explain the concept/shortcut of answering these types of questions???
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Official Answer
E

Originally posted by gjonrexha on 29 Dec 2016, 05:46.
Last edited by Bunuel on 20 Dec 2021, 01:52, edited 2 times in total.
Edited the question.
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Alexey1989x
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   29 Dec 2016, 07:52
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1. 2*(3^3)*(5^2) < 2*(3^2)*(5^3) since 5>3.
2. 2*3*(5^4) > 2*(3^2)*(5^3) since 5>3
3. (2^2)*(3^2)*(5^3) > 2*(3^2)*(5^3) left side has one more power of 2
Quote:
Answer E
should be correct one
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   29 Dec 2016, 09:03
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gjonrexha wrote:
If n = (2^2)(3^4)(5^6). the value of which of the following products is greater than sqrt of n?

I. (2)(3^3)(5^2)
II. 2(3)(5^4)
III. (2^2)(3^2)(5^3)

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

I understand the question and whats its asking but can someone explain the concept/shortcut of answering these types of questions???

My approach below:

Our choices must be greater than \(2*3^2*5^3\)
I. \((2)(3^3)(5^2)\) --> We lost 5, but gained just 3.
II. \(2(3)(5^4)\)--> We lost 3, but gained 5.
III. \((2^2)(3^2)(5^3)\) --> We gained 2.

Only in II & III we gained overall, so E :)

Hope its clear.
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   29 Dec 2016, 09:11
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gjonrexha wrote:
If n = (2^2)(3^4)(5^6). the value of which of the following products is greater than sqrt of n?

I. (2)(3^3)(5^2)
II. 2(3)(5^4)
III. (2^2)(3^2)(5^3)

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

I understand the question and whats its asking but can someone explain the concept/shortcut of answering these types of questions???


\(\sqrt{n} = \sqrt{(2^2)(3^4)(5^6)}\) =

Or, \(\sqrt{n} = 2*3^2*5^3\) = \(2250\)

I. \((2)(3^3)(5^2) = 1350\) < \(\sqrt{n}\)

II. \(2(3)(5^4) = 3750\) > \(\sqrt{n}\)

III. \((2^2)(3^2)(5^3) = 4500\) > \(\sqrt{n}\)

Hence, the correct answer will be (E) both II and III.
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   11 Apr 2019, 15:07
gjonrexha wrote:
If n = (2^2)(3^4)(5^6). the value of which of the following products is greater than sqrt of n?

I. (2)(3^3)(5^2)
II. 2(3)(5^4)
III. (2^2)(3^2)(5^3)

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III

I understand the question and whats its asking but can someone explain the concept/shortcut of answering these types of questions???


Under 1 min Solution:



On GMAT, factorize instead of multiply whenever possible.

1) Calculate sqrt (n) => (2)(3^2)(5^3)
2) Use this template: sqrt (n) / Given statement
If numerator >= denominator, then no.
If numerator < denominator, then yes.

For stmt 1: 5/3 => No
For stmt 2: 3/5 => Yes
For stmt 3: 2/4 => Yes

ANSWER: E
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink] New post   07 Mar 2023, 10:15
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Re: If n = (2^2)(3^4)(5^6), the value of which of the following products [#permalink]
07 Mar 2023, 10:15
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