Is L divisible by 27?
1. L is not a multiple of 45
2. L is a multiple of 10
OA: C
Divisibility
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- eagleeye
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Hi HG10:
We are asked if L is divisible by 27.
1. L is not a multiple of 45.
27 is not a multiple of 45, however it is divisible by 27.
Also, 1 is not a multiple of 45t, but it is not divisible by 27.
Hence not sufficient.
2. L is a multiple of 10.
10 is a multiple of 10. But 10 is not divisible by 27.
270 is a multiple of 10. But 270 is divisible by 27.
Again, insufficient.
Now let's consider them together.
L is a multiple of 10, but L is not a multiple of 45.
Now multiples of 10 that are divisible by 27 are of the form: 270*m (where m is a positive integer).
But 270*m = 3*3*3*2*5*m = 3*3*5* (2*3*m) = 45 * 6m. Clearly all multiples of 10 that are divisible by 27 are also multiples of 45. Therefore, there exists no such number L which is divisible by 27. Since we have a clear NO answer, both statements together are SUFFICIENT. Hence C.
Let me know if this helps
We are asked if L is divisible by 27.
1. L is not a multiple of 45.
27 is not a multiple of 45, however it is divisible by 27.
Also, 1 is not a multiple of 45t, but it is not divisible by 27.
Hence not sufficient.
2. L is a multiple of 10.
10 is a multiple of 10. But 10 is not divisible by 27.
270 is a multiple of 10. But 270 is divisible by 27.
Again, insufficient.
Now let's consider them together.
L is a multiple of 10, but L is not a multiple of 45.
Now multiples of 10 that are divisible by 27 are of the form: 270*m (where m is a positive integer).
But 270*m = 3*3*3*2*5*m = 3*3*5* (2*3*m) = 45 * 6m. Clearly all multiples of 10 that are divisible by 27 are also multiples of 45. Therefore, there exists no such number L which is divisible by 27. Since we have a clear NO answer, both statements together are SUFFICIENT. Hence C.
Let me know if this helps
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- Anurag@Gurome
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While analyzing both of the statements together, we can simplify the logic chain as follows,HG10 wrote:Is L divisible by 27?
1. L is not a multiple of 45
2. L is a multiple of 10
- From statement 1, L is not a multiple of both 5 and 9.
From statement 2, L is a multiple of 5.
Hence, L is not a multiple of 9.
Hence, L is not a multiple of 27.
Anurag Mairal, Ph.D., MBA
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