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If x and n are positive integers, what is the least common multiple of
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03 Nov 2018, 10:11
Question Stats:
60% (01:35) correct 40% (01:39) wrong based on 52 sessions
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If x and n are positive integers, what is the least common multiple of 96 and x? 1) x = \(2^n * 3^2 *5\) 2) n < 5 Weekly Quant Quiz #7 Question No 6
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Re: If x and n are positive integers, what is the least common multiple of
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03 Nov 2018, 10:30
Prime factor of 96 = \(2^5*3^1\)
From statement 1:
x = \(2^n3^25^1\) LCM of 96 and x will be \(2^n3^25^1\). LCM is dependent on n. Hence insufficient.
From statement 2:
only n is given no info about x. Insufficient.
Combining both n<5. Then LCM will be \(2^53^25^1\)
C is the answer.



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Re: If x and n are positive integers, what is the least common multiple of
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03 Nov 2018, 10:37
If x and n are positive integers, what is the least common multiple of 96 and x? 1) x = 2n∗32∗52n∗32∗5 2) n < 5
Lcm of 96 and x. Prime factorisation of 96: 2^5*3^1
Now. Statement 1: Lcm can be calculated by taking the highest prime facotrs of both the integers. Now since the value of n is unknown there can be 2 cases:
N less than or equal tp 5: LCM= 5*9*2^5 N more than 5:: Lcm = 5*9*2^n
hence since 2 values, NS
Statement 2: clearly NS.
Combine : CLearly sufficient.
Hence, ANS C



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Re: If x and n are positive integers, what is the least common multiple of
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03 Nov 2018, 10:38
If x and n are positive integers, what is the least common multiple of 96 and x?
Option A: x= (2^n) * (3^2)*5
96= 2*2*2*2*2*3= (2^5)*3
LCM of 96 and x is not sure because if n < 5, it will be 2^5*3^2*5. and if n>5 it will be (2^n)*3^2*5
so option A is not sufficient
Option B: n< 5 wow this definitely leads to the answer
so B is sufficient



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Re: If x and n are positive integers, what is the least common multiple of
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03 Nov 2018, 10:48
e_) both are not sufficiet as 96=2power 5 x3 and for LCM we need to get n it can be 1,2,3,4 so we cant find the real lcm



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Re: If x and n are positive integers, what is the least common multiple of
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04 Nov 2018, 02:17
We need to find LCM of 96 and x or \(2^5 * 3 , x\)
Statement 1 : \(x = 2^n * 3^2 * 5\)
LCM = \(2^n * 3^2* 5\) or \(2^5* 3^2 * 5\)
Since we don't know whether n <= 5 , we cannot find the lcm
Statement 2 : n < 5 It gives us nothing to go on
Together : No we know n < 5 ; LCM = \(2^5* 3^2 * 5\)
Ans C




Re: If x and n are positive integers, what is the least common multiple of
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04 Nov 2018, 02:17






