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30 Jan 2011, 21:39
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C
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Difficulty:
25%
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Question Stats:
77% (01:23) correct
23%
(01:30)
wrong
based on 658
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Is the integer n a multiple of 15 ?
(1) n is a multiple of 20
(2) n + 6 is a multiple of 3
(1) n is a multiple of 20
(2) n + 6 is a multiple of 3
30 Jan 2011, 22:13
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Is the integer n a multiple of 15 ?
1) n is a multiple of 20
2) n + 6 is a multiple of 3
Please explain how to derive the answer to this question. Thanks
1) n is a multiple of 20
2) n + 6 is a multiple of 3
Please explain how to derive the answer to this question. Thanks
Start with statement 1. It is not sufficient because for a number to be a multiple for 15, it should be divisible by both 3 and 5. Clearly, 20 does not have 3 as a factor. Hence, statement 1 is not sufficient.
Statement 2 says that n+6 is a multiple of three. If you break it down, it is basically saying that n is a multiple of 3. But that we don't know whether n is a multiple of 5 or not. Hence, this is not sufficient.
If you combine both 1 and 2, you can conclude that n has both 5 (from statement 1)and 3 (from statement 2) as factors. Hence, C is the answer.
General Discussion
31 Jan 2011, 02:38
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Q: Is n a multiple of 15?
This can be solved by prime factors.
Question can be rephrased as; are at least both 3 and 5 prime factors of n
3 and 5 are factors of 15. If n also contains at least both 3 and 5 as factors, it must be divided by 15.
1. n is a multiple of 20.
Prime factors of 20 are 2*2*5
This tells us that n is definitely a multiple of 5. But, there is no 3 among its factors. We must have at least both 3 and 5 as factors for n to be a definite multiple of 15.
We also can't definitely tell that n is not a multiple of 15.
e.g.
n=40- Multiple of 20. NOT a Multiple of 15.
n=60- Multiple of 20. Also a multiple of 15.
So, the prime factors 2*2*5 tell us that n is NOT definitely a multiple of 15. It may or may not be a multiple of 15. NOT SUFFICIENT.
2. (n+6) is a multiple of 3.
6 is a muliple of 3, so n must also be a multiple of 3.
if (a+b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
if (a-b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
conversely also true,
if "a" is a multiple of x and "b" is a multiple of x,
then (a+b) must be a multiple of x
also; (a-b) must be a mutiple of x
So, we know n is definitely a multiple of 3. i.e. 3 is a factor of n. But, n is not necessarily a multiple of 15.
For "n" to be a multiple of 15, it must have at least both 3 and 5 as factors.
e.g.
6- multiple of 3. Not a multiple of 15.
30- multiple of 3. Also a multiple of 15.
NOT SUFFICIENT.
Using both statements;
We know 5 and 3 are both factors of n. Thus, n must be a multiple of 15.
SUFFICIENT.
Ans: C
This can be solved by prime factors.
Question can be rephrased as; are at least both 3 and 5 prime factors of n
3 and 5 are factors of 15. If n also contains at least both 3 and 5 as factors, it must be divided by 15.
1. n is a multiple of 20.
Prime factors of 20 are 2*2*5
This tells us that n is definitely a multiple of 5. But, there is no 3 among its factors. We must have at least both 3 and 5 as factors for n to be a definite multiple of 15.
We also can't definitely tell that n is not a multiple of 15.
e.g.
n=40- Multiple of 20. NOT a Multiple of 15.
n=60- Multiple of 20. Also a multiple of 15.
So, the prime factors 2*2*5 tell us that n is NOT definitely a multiple of 15. It may or may not be a multiple of 15. NOT SUFFICIENT.
2. (n+6) is a multiple of 3.
6 is a muliple of 3, so n must also be a multiple of 3.
if (a+b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
if (a-b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
conversely also true,
if "a" is a multiple of x and "b" is a multiple of x,
then (a+b) must be a multiple of x
also; (a-b) must be a mutiple of x
So, we know n is definitely a multiple of 3. i.e. 3 is a factor of n. But, n is not necessarily a multiple of 15.
For "n" to be a multiple of 15, it must have at least both 3 and 5 as factors.
e.g.
6- multiple of 3. Not a multiple of 15.
30- multiple of 3. Also a multiple of 15.
NOT SUFFICIENT.
Using both statements;
We know 5 and 3 are both factors of n. Thus, n must be a multiple of 15.
SUFFICIENT.
Ans: C
