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Updated on: 21 Aug 2019, 13:20
Originally posted by freedom128 on 24 Jul 2019, 19:12.
Last edited by freedom128 on 21 Aug 2019, 13:20, edited 5 times in total.
Last edited by freedom128 on 21 Aug 2019, 13:20, edited 5 times in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (02:49) correct
56%
(02:10)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, is n a multiple of 121?
(1) 44 is the greatest common divisor of 220 and n
(2) 968 is the least common multiple of 121 and n
(1) 44 is the greatest common divisor of 220 and n
(2) 968 is the least common multiple of 121 and n
26 Jul 2019, 18:45
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Hi TheNightKing,
This explanation may enlighten you.
Known: n is a positive integer.
Is n a multiple of 121? --> basically, the question is whether n has double factor of 11.
(1) 44 is the greatest common divisor (GCD) of 220 and n
From this statement, we understand that \(44(=11*2^2)\) is a factor of n. However, we can only deduce that n has single, double, or even more factor(s) of 11. Examples:
1) 44 is the GCD of 220 and n= 44 --> is n a multiple of 121? NO, n has only single factor of 11.
2) 44 is the GCD of 260 and n= 44*11 = 484 --> is n a multiple of 121? YES, n has double factors of 11.
NOT SUFFICIENT
(2) 968 is the least common multiple (LCM) of 121 and n
Since \(968=8*121=8*11^2\) and 121 has double factor of 11, then n could have zero, single factor, or even double factor of 11. Example:
1) 968 is the LCM of 121 and n= 8 --> n isn't a multiple of 121, since n has zero factor of 11.
2) 968 is the LCM of 121 and n= 8*11 = 88 --> n isn't a multiple of 121, since n has only single factor of 11.
3) 968 is the LCM of 121 and n= 8*11*11 = 968 --> n is a multiple of 121, since n has double factor of 11.
NOT SUFFICIENT
Combining (1) and (2)
From both statements, we can only deduce that n has either single or double factor(s) of 11:
Case #1. n has only single factor of 11 and thus, isn't a multiple of 121.
\(n= 8*11 = 88\) --> 44 is the GCD of 220 and 88 (OK) --> 968 is the LCM of 121 and 88 (OK)
Case #2. n has double factor of 11 and thus, is a multiple of 121.
\(n= 8*11*11 = 968\) --> 44 is the GCD of 220 and 968 (OK) --> 968 is the LCM of 121 and 968 (OK)
NOT SUFFICIENT
Answer is (E)
This explanation may enlighten you.
Known: n is a positive integer.
Is n a multiple of 121? --> basically, the question is whether n has double factor of 11.
(1) 44 is the greatest common divisor (GCD) of 220 and n
From this statement, we understand that \(44(=11*2^2)\) is a factor of n. However, we can only deduce that n has single, double, or even more factor(s) of 11. Examples:
1) 44 is the GCD of 220 and n= 44 --> is n a multiple of 121? NO, n has only single factor of 11.
2) 44 is the GCD of 260 and n= 44*11 = 484 --> is n a multiple of 121? YES, n has double factors of 11.
NOT SUFFICIENT
(2) 968 is the least common multiple (LCM) of 121 and n
Since \(968=8*121=8*11^2\) and 121 has double factor of 11, then n could have zero, single factor, or even double factor of 11. Example:
1) 968 is the LCM of 121 and n= 8 --> n isn't a multiple of 121, since n has zero factor of 11.
2) 968 is the LCM of 121 and n= 8*11 = 88 --> n isn't a multiple of 121, since n has only single factor of 11.
3) 968 is the LCM of 121 and n= 8*11*11 = 968 --> n is a multiple of 121, since n has double factor of 11.
NOT SUFFICIENT
Combining (1) and (2)
From both statements, we can only deduce that n has either single or double factor(s) of 11:
Case #1. n has only single factor of 11 and thus, isn't a multiple of 121.
\(n= 8*11 = 88\) --> 44 is the GCD of 220 and 88 (OK) --> 968 is the LCM of 121 and 88 (OK)
Case #2. n has double factor of 11 and thus, is a multiple of 121.
\(n= 8*11*11 = 968\) --> 44 is the GCD of 220 and 968 (OK) --> 968 is the LCM of 121 and 968 (OK)
NOT SUFFICIENT
Answer is (E)
General Discussion
26 Jul 2019, 11:56
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chondro48
If n is a positive integer, is n a multiple of 121?
(1) 44 is the greatest common divisor of 220 and n
(2) 968 is the least common multiple of 121 and n
+1 kudo if you think it is good question.
(1) 44 is the greatest common divisor of 220 and n
(2) 968 is the least common multiple of 121 and n
+1 kudo if you think it is good question.
Anybody can help on the solution?
I marked D. Each is sufficient
