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24 Jun 2015, 05:26
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E
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Difficulty:
5%
(low)
Question Stats:
85% (01:14) correct
15%
(01:14)
wrong
based on 371
sessions
History
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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
(1) \(n > k\)
(2) The number of copies of the manuscript that n machines of type A can make in one hour is 20
24 Jun 2015, 06:04
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erikvm
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
Answer: option
General Discussion
11 Dec 2017, 08:35
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erikvm
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.
Answer: E
