[/quote]Cheers123 wrote:
[/list][/list]
450y=n^3
450=2*3^2*5^2; therefore y= 2^2*3*5;
out of I,II,III only I holds true..!!
GMAT Prep - Number Properties
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manpsingh87
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450y=n^3
450=2*3^2*5^2; therefore y= 2^2*3*5;
out of I,II,III only I holds true..!!
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GMATGuruNY
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450y is the cube of an integer.If n and y are positive integers and 450y = n³, which of the following must be an integer?
I. y/(3 x 2² x 5)
II. y/(3² x 2 x 5)
III. y/(3 x 2 x 5²)
a. None
b. I only
c. II only
d. III only
e. I, II, and III
When we prime-factorize the cube of an integer, we get 3 (or a multiple of 3) of every prime factor:
8 is the cube of an integer because 8 = 2³ = 2*2*2.
27 is the cube of an integer because 27 = 3³ = 3*3*3.
Thus, when we prime-factorize 450y, we need to get at least 3 of every prime factor:
450y = 2 * 3² * 5² * y
Since 450 provides only one 2, two 3's, and two 5's, y must provide the missing prime factors. We need y to provide two more 2's, one more 3, and one more 5.
Thus, the smallest possible value is y = 2² * 3 * 5.
Onto the answer choices:
I. y/(3 x 2² x 5)
(2² * 3 * 5)/(3 x 2² x 5) = 1. The smallest possible value of y yields an integer.
Eliminate every answer choice that does not include I.
Eliminate A, C and D.
II. y/(3² x 2 x 5)
(2² * 3 * 5)/(3² x 2² x 5) = 1/3. Not an integer.
Eliminate every remaining answer choice that includes II.
Eliminate E.
The correct answer is B.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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