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# Is the number of copies of a certain manuscript that n machines of

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Manager
Joined: 26 Feb 2015
Posts: 118
Is the number of copies of a certain manuscript that n machines of  [#permalink]

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24 Jun 2015, 05:26
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5% (low)

Question Stats:

83% (00:50) correct 17% (00:49) wrong based on 255 sessions

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Is the number of copies of a certain manuscript that n machines of type A can make in one hour greater than the number of copies of the manuscript that k machines of type B can make in one hour?

(1) $$n > k$$

(2) The number of copies of the manuscript that n machines of type A can make in one hour is 20
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Joined: 08 Jul 2010
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Re: Is the number of copies of a certain manuscript that n machines of  [#permalink]

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24 Jun 2015, 06:04
erikvm wrote:
Is the number of copies of a certain manuscript that n machines of type A can make in one hour greater than the number of copies of the manuscript that k machines of type B can make in one hour?

(1) $$n > k$$

(2) The number of copies of the manuscript that n machines of type A can make in one hour is 20

Let, One Machine of "Type A" types in 1 hour = a copies
and, One Machine of "Type B" types in 1 hour = b copies

Then, 'n' Machine of "Type A" type in 1 hour = a*n copies
and, 'k' Machine of "Type A" type in 1 hour = b*k copies

Question : Is a*n > b*k?

Statement 1: $$n > k$$

But the relation between 'a' and 'b' is still unknown, therefore a*n may or may not be greater than b*k for various values of these variables

Hence, NOT SUFFICIENT

Statement 2: The number of copies of the manuscript that n machines of type A can make in one hour is 20

a*n = 20

But this value can't be compared with b*k as the values of b and k are still unknown
Hence, NOT SUFFICIENT

Combining the two statements

a*n = 20 and n>k

@a=2, n=10, k=5, b=5: a*n < b*k
and
@a=2, n=10, k=5, b=3: a*n > b*k
Hence, NOT SUFFICIENT

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Re: Is the number of copies of a certain manuscript that n machines of  [#permalink]

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11 Dec 2017, 08:35
2
erikvm wrote:
Is the number of copies of a certain manuscript that n machines of type A can make in one hour greater than the number of copies of the manuscript that k machines of type B can make in one hour?

(1) $$n > k$$

(2) The number of copies of the manuscript that n machines of type A can make in one hour is 20

We need to determine whether the number of copies of a certain manuscript that n machines of type A can make in one hour is greater than the number of copies of the manuscript that k machines of type B can make in one hour.

If we let the rate of a type A machine = a and the rate of a type B machine = b, then the work done by n machines of type A in an hour is na and the work done by k machines of type B is kb. Thus, we need to determine:

na > kb ?

Statement One Alone:

n > k

Although we know that n is greater than k, without knowing the relationship between a and b, statement one is not sufficient to answer the question.

Statement Two Alone:

The number of copies of the manuscript that n machines of type A can make in one hour is 20.

Although we know that na = 20, we still do not know anything about k or b, thus statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we still do not have enough information to answer the question. We know that na = 20 and that n > k, however, we do not have any information about b.

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Re: Is the number of copies of a certain manuscript that n machines of &nbs [#permalink] 11 Dec 2017, 08:35
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