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693 and n have the same prime factors and n is a multiple of

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by Max@Math Revolution » Thu Jun 28, 2018 2:21 am
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[GMAT math practice question]

693 and n have the same prime factors and n is a multiple of 693 that is greater than 693. What is the smallest possible value of n/693?

A. 2
B. 3
C. 5
D. 7
E. 11
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by Max@Math Revolution » Sun Jul 01, 2018 4:57 pm
=>

Since 693 = 3^2*7*11, the smallest integer multiple of 693 that is greater than 693 with prime factors 3, 7 and 11 only is n = 693*3.
Thus, n / 693 = ( 693 * 3 ) / 693 = 3.

Therefore, the answer is B.
Answer : B
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by Jeff@TargetTestPrep » Mon Jul 02, 2018 8:45 am

693 and n have the same prime factors and n is a multiple of 693 that is greater than 693. What is the smallest possible value of n/693?

A. 2
B. 3
C. 5
D. 7
E. 11
Let us express 693 as a product of prime powers: 693 = 9 x 77 = 3^2 x 7 x 11. The prime factors of 693 are 3, 7 and 11. Since n has the same prime factors as 693, n also has prime factors of 3, 7, 11. Since n is a multiple of 693 that is greater than 693, the smallest value that n can be is 3 x 693 and thus the smallest possible value of n/693 is (3 x 693)/693 = 3.

Answer: B

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