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15 Aug 2019, 12:37
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (01:57) correct
39%
(01:39)
wrong
based on 23
sessions
History
Date
Time
Result
Not Attempted Yet
What is the smallest positive integer k such that 3528*√k is the cube of a positive integer?
A. 21
B. 36
C. 441
D. 225
E. 144
A. 21
B. 36
C. 441
D. 225
E. 144
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15 Aug 2019, 12:58
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fauji
3528 = 2^3 x 3^2 x 7^2
To make this part a perfect cube we need 3*7 = 21
Further to make √k part a perfect square we need additionally 21
Thus, the Answer must be 21*21 = 441 , (C)
15 Aug 2019, 12:59
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When we are asked to determine a number to make an expression be the square, cube, etc of a positive integer, we always have to factorize that expression and then find the number that make the exponents of all factors equal 2 (square), 3 (cube), etc.
Let's go ahead. I will apply the mentioned steps to find the answer:
1) Factorize the expression:
From the given expression, only the number 3528 can be factorized. The new expression would equal (2^3)*(3^2)*(7^2)*(k)^1/2
2) Find the number that makes the exponents of all factors equal 3 :
for the factor 2, we already have the cube of it in the expression, but for 3 and 7, we need additionally 3 and 7.
But since we are given the root of k, we would need the number to have the factors 3^2 and 7^2 so that in overall we can have (2^3)*(3^3)*(7^3)
So the right answer would be 3^2*7^2=441
Option C
Let's go ahead. I will apply the mentioned steps to find the answer:
1) Factorize the expression:
From the given expression, only the number 3528 can be factorized. The new expression would equal (2^3)*(3^2)*(7^2)*(k)^1/2
2) Find the number that makes the exponents of all factors equal 3 :
for the factor 2, we already have the cube of it in the expression, but for 3 and 7, we need additionally 3 and 7.
But since we are given the root of k, we would need the number to have the factors 3^2 and 7^2 so that in overall we can have (2^3)*(3^3)*(7^3)
So the right answer would be 3^2*7^2=441
Option C
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
