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psm12se
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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
While solving this question, I arrived at the correct answer as b then thought the answer could be e. OA is b
Here is the approach, which led me to select the answer as e
450y must be the cube root and factoring 450 we get;
450 = 2 x 3² x 5²
so value of y can be 3 x 2² x 5
Thus I is an integer in this case.
Also y can have other values such as y = (3 x 2² x 5) x (3³ x 2³ x 5³) in which case II & III could also be true.
Please confirm the issue with this approach.
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
While solving this question, I arrived at the correct answer as b then thought the answer could be e. OA is b
Here is the approach, which led me to select the answer as e
450y must be the cube root and factoring 450 we get;
450 = 2 x 3² x 5²
so value of y can be 3 x 2² x 5
Thus I is an integer in this case.
Also y can have other values such as y = (3 x 2² x 5) x (3³ x 2³ x 5³) in which case II & III could also be true.
Please confirm the issue with this approach.
