If n is a positive integer, is 361 a factor of n? 1) 76 is the greate

Question

If n is a positive integer, is 361 a factor of n?

(1) 76 is the greatest common divisor of 380 and n
(2) 5,776 is the least common multiple of 304 and n

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TarunKumar1234 · Answer

If n is a positive integer, is 361 a factor of n?

361 = 19^2

(1) 76 is the greatest common divisor of 380 and n

GCD = 76 = 2^2*19
380 = 2^2*5*19

For n = 2^2*19 = 76, GCD = 76. 361 is not a factor of n.

For n = 2^2*19^2 = 361*4 = 1444, GCD = 76. 361 is a factor of n

Not Sufficient

(2) 5,776 is the least common multiple of 304 and n

LCM = 5776 = 2^4*19^2
304 = 2^4*19

For n = 19^2 = 361, LCM = 5776. 361 is a factor of n

For n = 19^2*2 = 722, LCM = 5776. 361 is a factor of n.

Sufficient

Option B

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GCMEMBER · Answer

If n is a positive integer, is 361 a factor of n?

361 = 19^2

(1) 76 is the greatest common divisor of 380 and n

GCD = 76 = 2^2*19
380 = 2^2*5*19

For n = 2^2*19 = 76, GCD = 76. 361 is not a factor of n.

For n = 2^2*19^2 = 361*4 = 1444, GCD = 76. 361 is a factor of n

Not Sufficient

(2) 5,776 is the least common multiple of 304 and n

LCM = 5776 = 2^4*19^2
304 = 2^4*19

For n = 19^2 = 361, LCM = 5776. 361 is a factor of n

For n = 19^2*2 = 722, LCM = 5776. 361 is a factor of n.

Sufficient

Option B

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ranjan1 · Answer

If n is a positive integer, is 361 a factor of n?

(1) 76 is the greatest common divisor of 380 and n
(2) 5,776 is the least common multiple of 304 and n

Solution:-

361/n = Integer? where n --> Positive integer.
361 = 19^2.

(1) 76 is the greatest common divisor of 380 and n

76= 2^2*19, 380 = 2^2*19*5. Hence, n must be 2^2*19*y, where y could be any positive integer. Without value of y, we can't confirm that n would be divisible by 19^2. Insufficient.

(2) 5,776 is the least common multiple of 304 and n

L.C.M(n,304) = 5776 = 19^2* 2^4, while if we factorize 304, we get 19*2^4. Therefore, to make the L.C.M as 19^2*2^4, n must be 19^2*p. Sufficient.

IMO B

If n is a positive integer, is 361 a factor of n? 1) 76 is the greate

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GMAT Data Sufficiency (DS) Questions

If n is a positive integer, is 361 a factor of n? 1) 76 is the greate

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