in 1995 division a of company x had 4850 customers

[sharmin.karim]

in 1995 Division A of Company X had 4850 customers. If there were 86 service errors in Division A that year, what was the service-error rate, in number of service errors per 100 customers, for Division B of Company X in 1995?

1. In 1995 the overall service-error rate for Divisions A and B combined was 1.5 service errors per 100 customers.

2. In 1995, Division B had 9350 customers, none of which were customers of Division A.

[agha79]

Can you please post the OA:

I got "A" for the answer

[Ben Ku]

Ultimately we need to get (Errors by B) / (Customers of B). this is our rephrased quantity.

I think it's clear that statement (2) is insufficient to answer the question, so let's focus on statement (1).

Statement (2): The overall service-error rate = 100* total service errors / number of customers
= 100 * (errors by A + errors by B) / (customers of A + customers of B)

Let's fill in the info we have:
1.5 = 100 * (86 + errors by B) / (4850 + additional customers of B)
7275 + 1.5 * (additional customers) = 8600 + 100 (errors by B)
1.5 * (additional customers of B) = 1325 + 100 (errors by B)

There's no way to get (errors by B)/(customers of B).

Statements (1) + (2) Together:
With the final equation above:
1.5 * (additional customers of B) = 1325 + 100 (errors by B)
1.5 * (9350) = 1325 + 100 (errors by B)

Now this is much more managable. We can find number of errors by B, the fraction of errors per customer, and service-error rate. The answer is (A). [Editor: The answer is (C), both statements together are sufficient.]

[prithvi.chowdhury]

Ben -

Did you mean the answer is "C", and not "A"?

Ultimately we need to get (Errors by B) / (Customers of B). this is our rephrased quantity.

I think it's clear that statement (2) is insufficient to answer the question, so let's focus on statement (1).

Statement (2): The overall service-error rate = 100* total service errors / number of customers
= 100 * (errors by A + errors by B) / (customers of A + customers of B)

Let's fill in the info we have:
1.5 = 100 * (86 + errors by B) / (4850 + additional customers of B)
7275 + 1.5 * (additional customers) = 8600 + 100 (errors by B)
1.5 * (additional customers of B) = 1325 + 100 (errors by B)

There's no way to get (errors by B)/(customers of B).

Statements (1) + (2) Together:
With the final equation above:
1.5 * (additional customers of B) = 1325 + 100 (errors by B)
1.5 * (9350) = 1325 + 100 (errors by B)

Now this is much more managable. We can find number of errors by B, the fraction of errors per customer, and service-error rate. The answer is (A).

[esledge]

Ben -

Did you mean the answer is "C", and not "A"?

Yes, thanks for clarifying. Ben meant (C), you need both statements together. (I'll try to edit that message above for clarity.)

[jerly_vivek]

I wanted to know why the following approach is wrong; it would give the answeer as A.

Overall rate = rate at A + rate at B
we can caluclate rate at A since we know the total number of errors as well as the total number of customers. Also, statement I gives overall rate. so , rate at B can be caluclated.

[RonPurewal]

I wanted to know why the following approach is wrong; it would give the answeer as A.

Overall rate = rate at A + rate at B
we can caluclate rate at A since we know the total number of errors as well as the total number of customers. Also, statement I gives overall rate. so , rate at B can be caluclated.

no, you can't add these rates.

you can add work rates if you have two or more people/machines performing tasks together; that's probably what you're thinking about. but trying to add these rates together doesn't make sense.

analogy: let's say that families in Northern Esteria have babies at a rate of 2.6 children per woman, and families in Southern Esteria have babies at a rate of 3.4 children per woman.
clearly, you can't add these to say that the whole of Esteria is having 6.0 children per woman.

same here.

[kundan_scorpio]

I have a question..
from Statement 2.. we know that it is explicitly mentioned that B has certain no of customers who don't belong to A..
This gives an impression as if there could be certain customers who can belong to A as well as B.

In that case answer should be E instead of C..

Please clarify..whether we can assume this way or not.

[RonPurewal]

I have a question..
from Statement 2.. we know that it is explicitly mentioned that B has certain no of customers who don't belong to A..
This gives an impression as if there could be certain customers who can belong to A as well as B.

In that case answer should be E instead of C..

Please clarify..whether we can assume this way or not.

hmm?

statement 2 says:
In 1995, Division B had 9350 customers, none of whom were customers of Division A.
that is telling you, in no uncertain terms, that NONE of division b's customers were also customers of division a.
zero overlap.

you are right that this might not be true if you only have statement 1, but statement 1 is already insufficient -- if you add an extra measure of uncertainty, then it's "even more insufficient". so there's no problem there.

when you take the two statements together, you still know everything that is in either of the two individual statements -- so, since statement 2 says that the two divisions have no customers in common, we still know that they have no customers in common.
you can't "forget" this fact when you take the two statements together.

[supratim7]

As far as GMAT quant is concerned, would following upshot be OK?

1. "Division A of Company X had 400 customers and Division B had 500 customers" implies...
(A) Division A & B together had 900 customers
(B) Division A & B together had ≤ 900 customers

(B) Correct.
Here the stem doesn't explicitly say that there is no overlap between Div A's & B's customers and it is logically possible to have a overlap between Div A's & B's customers.

2. "Company X had 400 male workers and 500 female workers." implies...
(A) Company X had 900 workers in total.
(B) Company X had ≤ 900 workers in total.

(A) Correct.
Here it is logically impossible to have a overlap between male and female workers (hopefully).

3. "Division A of Company X had 400 customers and Division B had 500 customers, none of which were customers of Division A." implies...
(A) Division A had only 400 customers and Division B had only 500 customers.
(B) Division A had 400 customers, Division B had 500 customers, AND there could have been some additional customers who were customers of both Division A & B.

(A) Correct.
Division A of Company X had 400 customers = Division A had TOTAL 400 customers
Division B of Company X had 500 customers = Division B had TOTAL 500 customers
So, no additional customers could have been there who were customers of both Division A & B

Takeaways..

Always assume set overlap if it is not explicitly stated otherwise and if it is logically possible.


Always consider the given number of elements in a set as the TOTAL number of elements in that particular set.

Many thanks | Supratim

[tim]

Those sound like appropriate GMAT takeaways. Nice job!