At the start of a museum digitization project, an archivist estimated

Question

At the start of a museum digitization project, an archivist estimated both the number of records to be cataloged and the number of workdays the project would take. Based on those estimates, she computed a planned average (arithmetic mean) number of records per workday. After the project was finished, did the planned average (arithmetic mean) differ from the actual average (arithmetic mean) number of records cataloged per workday by no more than 4 records per workday?

(1) The estimated number of records was 40 more than the actual number of records cataloged.
(2) The estimated number of workdays was 5 more than the actual number of workdays used.

Bunuel · Accepted Answer

GMAT Club Official Solution:

At the start of a museum digitization project, an archivist estimated both the number of records to be cataloged and the number of workdays the project would take. Based on those estimates, she computed a planned average (arithmetic mean) number of records per workday. After the project was finished, did the planned average (arithmetic mean) differ from the actual average (arithmetic mean) number of records cataloged per workday by no more than 4 records per workday?

Let A be the actual number of records cataloged, and let D be the actual number of workdays used. The actual average was A/D.

The question asks whether the planned average differed from the actual average by no more than 4 records per workday.

(1) The estimated number of records was 40 more than the actual number of records cataloged.

So the estimated number of records was A + 40.

But we do not know the estimated number of workdays, so we cannot determine the planned average.

Not sufficient.

(2) The estimated number of workdays was 5 more than the actual number of workdays used.

So the estimated number of workdays was D + 5.

But we do not know the estimated number of records, so we cannot determine the planned average.

Not sufficient.

(1)+(2) Together, the planned average was:

(A + 40)/(D + 5)

The actual average was:

A/D

We need to know whether these two averages differ by no more than 4. But this is not fixed.

For example, if A = 40 and D = 5, then:

Actual average = 40/5 = 8

Planned average = (40 + 40)/(5 + 5) = 80/10 = 8

The difference is 0, so the answer is YES.

But if A = 200 and D = 5, then:

Actual average = 200/5 = 40

Planned average = (200 + 40)/(5 + 5) = 240/10 = 24

The difference is 16, so the answer is NO.

Both cases satisfy both statements, but they give different answers.

Not sufficient.

Answer: E.

ankushsambare · Answer

Let:
 
 Actual records = R 
 Actual workdays = D  
Then:
 
 Estimated records = R + 40 
 Estimated workdays = D + 5  
Actual average:
R/D
Planned average:
(R + 40)/(D + 5)
We need to know whether the two averages differ by no more than 4.

Statement (1) alone:
Estimated records were 40 more than actual.
We still do not know the number of workdays.
 Not sufficient.

Statement (2) alone:
Estimated workdays were 5 more than actual.
We still do not know the number of records.
 Not sufficient.

Statements (1) and (2) together:
Test values.
Example 1:
R = 40, D = 5
Actual average = 40/5 = 8
Planned average = 80/10 = 8
Difference = 0
Answer to the question: YES

Example 2:
R = 100, D = 1
Actual average = 100
Planned average = 140/6 ≈ 23.3
Difference is greater than 4
Answer to the question: NO

Since we can get both YES and NO, the statements together are not sufficient.
 Answer: E

rajdeep212003 · Answer

What I did here was take:

estimated records = x 
estimated workdays = y

So:

planned average = x/y

From the statements:

actual records = x - 40 
actual workdays = y - 5

Therefore:

actual average = (x - 40)/(y - 5)

Now the question is asking whether the two averages differ by no more than 4.

But even after combining both statements, the result still depends on the values of x and y.

Different values of x and y will give different differences between the averages.

So we still cannot determine a definite YES or NO answer.

For example, with one set of values the difference can be small, and with another set it can become much larger.

That means even together, the statements are not sufficient.

So the correct answer should be:

(E)

I found it easier to test the structure algebraically here instead of plugging random numbers immediately.

If anyone found a cleaner shortcut, feel free to tag me.

— Rajdeep

SS990 · Answer

Given: Average days  Ae  to catalogue estimated number of records  Ne  in estimated   Number of Workdays  We

To find: if Actuals average days take  Aa  to catalogue the actual number of records  Na  in the actual number of workdays taken to complete  Wa

Ap = Aa (+/-) 4 where A=N/W

(1) Ne=Na+40 we know nothing about W or A so not sufficient to know about A

(2) We= Wa+ 5 we know nothing of N or A fo this is insufficient

Together we have 4 variabls but 2 equations which are not in ratio format, hence together these are insufficient.

Hence E is the answer

BongBideshini · Answer

(1) 
Estimated records = R
Actual records = r
R=40+r
No information about workdays
 Insufficient

(2) 
Estimated workdays = D
Actual workdays = d
D = d + 5
No information about records
 Insufficient

(1)+(2) combined 
Case 1:
r = 100, d = 5
Planned = 140/10 = 14
Actual = 100/5 = 20
Difference = 6 => NO

Case 2:
r = 360, d = 15
Planned = 400/20 = 20
Actual = 360/15 = 24
Difference = 4 => YES

Answer: E

At the start of a museum digitization project, an archivist estimated

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