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

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Joined: 24 Sep 2016
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If n = (2^2)(3^4)(5^6). the value of which of the following products i  [#permalink]

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Updated on: 29 Dec 2016, 05:50
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Difficulty:

45% (medium)

Question Stats:

62% (01:48) correct 38% (01:41) wrong based on 102 sessions

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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???

Originally posted by gjonrexha on 29 Dec 2016, 05:46.
Last edited by Bunuel on 29 Dec 2016, 05:50, edited 1 time in total.
Renamed the topic.
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Re: If n = (2^2)(3^4)(5^6). the value of which of the following products i  [#permalink]

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29 Dec 2016, 07:52
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:
should be correct one
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If n = (2^2)(3^4)(5^6). the value of which of the following products i  [#permalink]

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29 Dec 2016, 09:03
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 i  [#permalink]

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29 Dec 2016, 09:11
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 i  [#permalink]

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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

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Re: If n = (2^2)(3^4)(5^6). the value of which of the following products i   [#permalink] 11 Apr 2019, 15:07
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