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08 Jun 2020, 17:14
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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Question Stats:
59% (01:54) correct
41%
(02:18)
wrong
based on 341
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If r and s are positive integers and 150s=r^3, which of the following must be an integer?
I. \(\frac{s}{3*5*2^{3}}\)
II. \(\frac{s}{3^{2}*5*2}\)
III. \(\frac{s}{3*2^{2}*5^{2}}\)
(A) I only
(B) II only
(C) II and III only
(D) I and II only
(E) None of the above
I. \(\frac{s}{3*5*2^{3}}\)
II. \(\frac{s}{3^{2}*5*2}\)
III. \(\frac{s}{3*2^{2}*5^{2}}\)
(A) I only
(B) II only
(C) II and III only
(D) I and II only
(E) None of the above
I have this question, and I have the answer. The study guide says it is choice B. I do not understand why. Can someone please explain it to me?
Source if from the GMAT workbook by Admit Master.
Source if from the GMAT workbook by Admit Master.
KhulanE
08 Jun 2020, 18:23
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150s=2*3*5^2*s=r^3
since s and r are positive integers, r^3 must be a at least 3 power of prime numbers.
so, minimum number of s must be 2^2*3^2*5.
so that the equation has 3 powers of prime numbers. 150=2*3*5^2, s=2^2*3^2*5 -> 150s=2^3*3^3*5^3
otherwise, r will be fractions. for example: if s=2*3*5, then 150s=2^2*3^2*5^3=r^3. you can see from this r cannot be not integers.
remember s must have at least 2^2*3^2*5.
so let's check the answers.
I. s/(3∗5∗2^3)=(2^2*3^2*5)/(3*5*2^3)=3/2 fraction
II. s/(3^2∗5∗2)=(2^2*3^2*5)/(3^2∗5∗2)=2 yeah, we can divide s.
III. s/(3∗2^2∗5^2)=(2^2*3^2*5)/(3∗2^2∗5^2)=3/5 fraction
only II fulfills, so B is the answer.
hope it helps
since s and r are positive integers, r^3 must be a at least 3 power of prime numbers.
so, minimum number of s must be 2^2*3^2*5.
so that the equation has 3 powers of prime numbers. 150=2*3*5^2, s=2^2*3^2*5 -> 150s=2^3*3^3*5^3
otherwise, r will be fractions. for example: if s=2*3*5, then 150s=2^2*3^2*5^3=r^3. you can see from this r cannot be not integers.
remember s must have at least 2^2*3^2*5.
so let's check the answers.
I. s/(3∗5∗2^3)=(2^2*3^2*5)/(3*5*2^3)=3/2 fraction
II. s/(3^2∗5∗2)=(2^2*3^2*5)/(3^2∗5∗2)=2 yeah, we can divide s.
III. s/(3∗2^2∗5^2)=(2^2*3^2*5)/(3∗2^2∗5^2)=3/5 fraction
only II fulfills, so B is the answer.
hope it helps
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08 Jun 2020, 21:09
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s should minimum be of the form
\(3^2 * 2^2 *5\)
thus s be divided by
\(3^2 * 2^2 *5\)
only B satisfies the given form
rest A and B have either 3 or 5 extra.
Thus B
\(3^2 * 2^2 *5\)
thus s be divided by
\(3^2 * 2^2 *5\)
only B satisfies the given form
rest A and B have either 3 or 5 extra.
Thus B
