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Algebra and Probability

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Algebra and Probability

by Tagne » Tue Mar 15, 2011 3:53 pm
1. If n and y are positive integers and 450y = n^3, which of the following must be an integer?
a. y/ 3 x 2^2 x 5
b. y/3^2 x 2x 5
c. y/3 x 2 x 5^2

2. A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
a. 3/40,000
b. 1/3,600
c. 9/2,000
d. 1/60
e. 1/15
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by Night reader » Tue Mar 15, 2011 4:28 pm
firstly, we need to perform prime factorization for 450
450 (2) 225
225 (3) 75
75 (3) 25
25 (5) 5
5 (5) 1 ---> 2* 3^2 * 5^2

next, we define that for 2* 3^2 * 5^2 to be integer to the power of 3 we are missing exactly 2^2 *3*5, hence y must be equal to y=2^2 *3*5

answer choices could be values which when y is divided by them a),b) or c) will give integer
a) (2^2 *3*5) : (3* 2^2 *5) this could be integer - Correct answer
b) (2^2 *3*5) : (3^2 * 2*5) this could not be integer - Not correct answer
c) (2^2 *3*5) : (3*2*5^2) this could not integer - Not correct answer

Tagne wrote:1. If n and y are positive integers and 450y = n^3, which of the following must be an integer?
a. y/ 3 x 2^2 x 5
b. y/3^2 x 2x 5
c. y/3 x 2 x 5^2
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by Night reader » Tue Mar 15, 2011 4:38 pm
probability of selecting sibling out of 1000 junior students is 60/1000 and the probability of selecting the same matching sibling out of 800 senior students is 1/800. The probabilities must be multiplied for selecting both --> 60/1000 * 1/800= 60/800,000 OR 3/40,000

IOM a

Tagne wrote:2. A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
a. 3/40,000
b. 1/3,600
c. 9/2,000
d. 1/60
e. 1/15
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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