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3 DS problems

Expert replies
by Veronica » Thu Sep 23, 2010 12:44 am
Of the cans of peaches inspected yesterday at a certain plant, 1.5% failed to pass inspection. Of the cans that failed inspection, 5/6 were incorrectly labeled and the rest were dented. If all of the cans that were incorrectly labeled or dented failed inspection, how many of the cans of peaches inspected yesterday at the plant were dented?
1. 450 of the cans of peaches inspected yesterday at the plant failed to pass inspection
2. 29,550 of the cans of peaches inspected yesterday at the plant passed inspection

The annual rent collected by a corporation from a certain building was x% more in 1998 than 1997 and y% less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
1. x>y
2. xy/100<x-y

If n is an integer and 100<n<200, what is the value of n?
1. n/36 is an odd integer
2. n/45 is an even integer

Please help, thank you!
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Source: — Data Sufficiency |

by kmittal82 » Thu Sep 23, 2010 1:09 am
Ans 1:

Let total cans = x
Failed to pass inspection = 0.015x
Passed inspection = 0.985x

Incorrectly labelled = (5/6)x0.015x
Dented = (1/6)x0.015x

Stmt 1) 0.015x = 450. This gives us x, enough to give us number of dented cans

Stmt 2) 0.0985x = 29550. This gives us x, enough to give us the number of dented cans

Hence (D), i.e. either statement is sufficient
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by kmittal82 » Thu Sep 23, 2010 1:20 am
Ans 2

Let rent in '97 = 100
Rent in '98 = 100 + x
Rent in '99 = 100 + x - (y/100)(100+x) = 100 + x -y - (xy/100)

The question stem is now asking:

Is 100 + x -y -(xy/100) > 100
Reduce it further

Is x - y > xy/100

Stmt 1)
If x and y are integers, then the above statement will be true, however, if x and y are decimals, then its false. Not sufficient

Stmt 2)
Directly gives you xy/100 < x - y, enough to answer the question.

Should be (B)
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by kmittal82 » Thu Sep 23, 2010 2:27 am
Ans 3:

Stmt 1)

n/36 is odd
36 x 3 = 108
36 x 5 = 180

Both satisfy the question criteria, hence not sufficient

Stmt 2)

n/45 is even

45 x 4 = 180

This is the only number that satisfies the criteria, hence sufficient

Answer: (B)
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