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What is the least positive integer h for which 120h is equal to the cu
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15 Dec 2021, 02:49
15 Dec 2021, 02:49
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Question Stats:
62% (01:23) correct
37% (02:00) wrong based on 8 sessions
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What is the least positive integer h for which 120h is equal to the cube of an integer?
(A) 120
(B) 180
(C) 225
(D) 240
(E) 300
(A) 120
(B) 180
(C) 225
(D) 240
(E) 300
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
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Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: What is the least positive integer h for which 120h is equal to the cu
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15 Dec 2021, 06:44
15 Dec 2021, 06:44
1
We need to find the value of h which will make 120h a perfect cube
Let's start factorizing 120h. We get
120h = \(2^3 * 3 * 5 * h\)
So, for 120h to be a perfect cube
h should be equal to \(3^2 * 5^2\)
Making 120h = \(2^3 * 3 * 5 * 3^2 * 5^2\) = \(2^3 * 3^3 * 5^3\)
=> h = 9*25 = 225
So, Answer will be C
Hope it helps!
Let's start factorizing 120h. We get
120h = \(2^3 * 3 * 5 * h\)
So, for 120h to be a perfect cube
h should be equal to \(3^2 * 5^2\)
Making 120h = \(2^3 * 3 * 5 * 3^2 * 5^2\) = \(2^3 * 3^3 * 5^3\)
=> h = 9*25 = 225
So, Answer will be C
Hope it helps!
gmatclubot
Re: What is the least positive integer h for which 120h is equal to the cu [#permalink]
15 Dec 2021, 06:44
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