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

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693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post 28 Jun 2018, 03:37
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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 \(\frac{n}{693}\)?

\(A. 2\)
\(B. 3\)
\(C. 5\)
\(D. 7\)
\(E. 11\)

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693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post Updated on: 28 Jun 2018, 06:06
MathRevolution wrote:
[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 \(\frac{n}{693}\)?

\(A. 2\)
\(B. 3\)
\(C. 5\)
\(D. 7\)
\(E. 11\)


\(693 = 3^2*7*11\)
Since n must have the same prime factors as 693 but must be greater than 693, the least possible option for \(n = 693 * 3\).
Thus, least possible value of \(\frac{n}{693} = \frac{(693*3)}{693} = 3\).


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Originally posted by GMATGuruNY on 28 Jun 2018, 03:50.
Last edited by GMATGuruNY on 28 Jun 2018, 06:06, edited 1 time in total.
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693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post 28 Jun 2018, 05:15
MathRevolution wrote:
[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 \(\frac{n}{693}\)?

\(A. 2\)
\(B. 3\)
\(C. 5\)
\(D. 7\)
\(E. 11\)


If the numbers n and 693 have the same prime factors and n is a multiple of 693,
the smallest value of \(\frac{n}{693}\) must be the smallest prime factor of 693.

693 when prime-factorized gives \(3^2*7*11\).
The minimum value of n is \(3*693\)(as n and 693 have same prime numbers)

Therefore, the smallest value of \(\frac{n}{693}\) is \(\frac{3*693}{693} = 3\)(Option B)
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693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post 28 Jun 2018, 05:28
MathRevolution wrote:
[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 \(\frac{n}{693}\)?

\(A. 2\)
\(B. 3\)
\(C. 5\)
\(D. 7\)
\(E. 11\)


\(693\) and \(n\) have the same prime factors and \(n\) is a multiple of \(693\) that is greater than \(693\)....

when will n and 693 have the same prime factors :- when n is multiple of 693 and its prime factors

so lowest value of \(\frac{n}{693}\) will come from lowest value of n and will be equal to the smallest prime number of 693, which is 3.

lets solve it also
693 is clearly a multiple of 3 and there are NO other odd prime numbers < 3.....
so n lowest value but > 693 is 693*3
therefore \(\frac{n}{693}=\frac{3*693}{693}=3\)
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: 693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post 01 Jul 2018, 18:12
=>

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, \(\frac{n}{693} = \frac{( 693 * 3 )}{693} = 3.\)

Therefore, the answer is B.
Answer : B
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Re: 693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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New post 02 Jul 2018, 09:42
MathRevolution wrote:
[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 \(\frac{n}{693}\)?

\(A. 2\)
\(B. 3\)
\(C. 5\)
\(D. 7\)
\(E. 11\)


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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Re: 693 and n have the same prime factors and n is a multiple of 693 that &nbs [#permalink] 02 Jul 2018, 09:42
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