Critical Reasoning

At Legal Services, LLC last year, the average annual salary for attorneys was $75,000, while the average salary for paralegals was $50,000. The average annual salary for all Legal Services, LLC employees was $45,000.

If the information above is correct, which one of the following conclusions can properly be drawn on the basis of it?

There were twice as many attorneys at Legal Services, LLC as there were paralegals last year.

There were more paralegals than attorneys at Legal Services, LLC last year.

There were two attorneys and three paralegals at Legal Services, LLC last year.

There was at least one Legal Services, LLC employee who earned less than the average paralegal earned last year.

At least one paralegal made less than $50,000 last year.

OA D


Is this a type of average question that could appear on the test ? I do not know how to approach it, although I covered tens of different average problems. In other words, if i do not know how to solve this, does it mean that I did not cover this topic well in quantitative ?

Hi!

Yes, this question could very easily show up on the GMAT.

Testluv wrote:Hi!

Yes, this question could very easily show up on the GMAT.

How to approach it ? I need the total salaries for employees in each group, in order to get the number of employees. Average for attorneys = total salaries / number of attorney

So, I have one known and two unknowns ??!!!

Hi heshamelaziry,

well, we know that both lawyers and paralegals make more than the average (on average). If that is the case, then there must be at least one employee at the firm who makes less than the average who will compensate for the "pull-up" coming from the average lawyers' and average paralegals' salaries.

It might be the mail boy who makes six dollars an hour or, perhaps, there are a whole bunch of first year attorneys and first year paralegals who make very little, say 20k, while the established attorneys are making six figures (and in the end it washes out to 75k avg for attorneys and 50k avg for paralegals).

But if there wasn't at least one employee at the firm who made less than the 45 K average, then each and every paralegal would be making more than the average and each and every attorney would be making more than the average of 45 k, which is obviously absurd. Instead, the average would be somewhere between the two numbers of 75k and 50k (depending on the ration of lawyers to paralegals, and depending on the distribution within those two categories), and that would falsify information in the passage (which information the question told us to treat as correct).

And, when it comes to average problems, don't depend on the formula. Recall the formula, yes, but also use some critical reasoning. It is helpful to know the concept of balanced average.

Let's say the average of John's first 5 test scores was 80. Let's say his desired average for all six tests is 83, and he has yet to write his sixth and final test. Let's say all tests are weighted equally. What is the minimal score he must attain on the sixth test to achieve his desired average on all six tests?

Well, let's think about how far "to the left" (on the number line) of his desired average the first five tests take him. Well, to get an average of 80 on his first five tests, he could have scored 80 on all five. Then, each test pulled him away from his desired average by 3 points (83-80) for a total pull-down of 3*5=15. Therefore, to achieve his desired average of 83, he would need to compensate for all 15 of these points. In other words, he would have to score 83+ 15= 98 on his sixth and final test.

This is a lot quicker than doing it algebraically for virtually 100 percent of the test-taking population (including, especially, the higher scorers). Remember, the GMAT wants to reward students who use alternative reasoning techniques that take you to the right answer more quickly than traditional "show-your-work" approaches. When you are reviewing anything in the GMAT, always ask if there is a quicker way to arrive at the correct response.

heshamelaziry wrote: If the information above is correct, which one of the following conclusions can properly be drawn on the basis of it?

There were twice as many attorneys at Legal Services, LLC as there were paralegals last year.

There were more paralegals than attorneys at Legal Services, LLC last year.

There were two attorneys and three paralegals at Legal Services, LLC last year.

There was at least one Legal Services, LLC employee who earned less than the average paralegal earned last year.

At least one paralegal made less than $50,000 last year.

A-No evidence for this, and besides, it would seem like there were more paralegals based on the figures anyway

B-Seems like a good answer, but it's not. All we have are the averages. What if one lawyer made $1 million a year. and then 30-40 others all made $10,000, while the company just has one paralegal who made $50,000 a year? Unlikely, but all is possible in the realm of the GMAT CR unless otherwise stated! Next.

C- Totally BS.

D-This HAS to be true based on the information we know. If the average paralegal salary is $50,000, and the average salary overall is $45,000, then somebody HAD to be making less than $50,000 a year.

E-Again, we don't know this. Apply the same scenario from option B.

Hi!

I would not at all recommend a process of elimination approach here such as the one Ludacrispat26 employed. It is time-consuming, and makes it more likely that you will get lured in by a tempting wrong answer choice...and you don't get rewarded for figuring out a reason why a wrong answer is wrong...or for figuring out four reasons why four wrong answer choices are wrong! You get the point as soon as you announce correct response.

Because it is an inference question involving numbers, and a lot of information, all you need to do is make a deduction and aggressively scan the answer choices for a match to that deduction.

When I was doing this question, I immediately made the deduction and zoomed in on the answer choice that matched...didn't even read the answer choices b/c I knew (and I know all of you know) that there is only one credited response.

When reviewing GMAT problems, be sure to review ones you are able to answer correctly, and ask yourself whether there was a quicker way to answer it correctly.

Remember, there are two factors critical to your performance: accuracy AND efficiency.

Testluv wrote:Hi!

I would not at all recommend a process of elimination approach here such as the one Ludacrispat26 employed. It is time-consuming, and makes it more likely that you will get lured in by a tempting wrong answer choice...and you don't get rewarded for figuring out a reason why a wrong answer is wrong...or for figuring out four reasons why four wrong answer choices are wrong! You get the point as soon as you announce correct response.

Testluv,

I understand your concerns, and my approach would be time consuming (you are the teacher with the 800 score). But I also approached it the same way as you, and in my post wasn't trying to show a POE. I was just detailing why the other answers were wrong in case there were discrepancies. That's all.

But, again, I understand your cause for concern. However, I just wanted to show specifically (and maybe for people who can't execute the problem as quickly as others can) why the other answer choices were wrong.

Hi!

I've seen you post fine solutions, ludacrispat26. I am relieved to know you followed more of a predict and match strategy...wasn't 100% sure from your post.

Totally understand why you were concerned about explaining why other answers were wrong...I was really concerned about conveying what I thought would be the most optimal technique for this kind of question!

Hello,

I have seen a GMAT Prep Data Sufficiency question that was based on averages of two groups. The question was about weighted averages which group has more employees.

The formula given on this forum is -

Group A - has average age of 10
Group B - has average age of 20
Average age of both the groups A and B is 13

Therefore, there will be more people in group A.

Based on this logic, I can say 'B' is a valid answer.

The answer should be D.

The 2 contenders are D and E. B is out because, we cannot assume that the organization has only attorneys and paralegals. There could be other employees that we don't know of.

E is out as well, because all of the paralegal may have made exactly 50,000.

D is the best answer here.

Hi mehravikas,

That was a great strategy for that data sufficiency question. Unfortunately, you misapplied it a bit here.

The big distinction is that, here, the total average for all employees in the firm (45k) is LESS than the average of all paralegals and LESS than the average of all attorneys.

So, in order to bring the total average down to where it's supposed to be (45k), there has to be SOME (ie "at least one") employees who are making LESS than 45k. That's what must necessarily be true.

What most probably is also true (although it could be false) is that there are a number of employees who are making less than 45k.

mehravikas wrote:Hello,

I have seen a GMAT Prep Data Sufficiency question that was based on averages of two groups. The question was about weighted averages which group has more employees.

The formula given on this forum is -

Group A - has average age of 10
Group B - has average age of 20
Average age of both the groups A and B is 13

Therefore, there will be more people in group A.

Based on this logic, I can say 'B' is a valid answer.

How did you get that the average for both groups is 13, without any numbers for how many in each group. I saw a similar question in OG 12 where 2 averages for 2 groups were given and no numbers for either groups were given and asked for the total average and the answer was E. If I look for the question I will find it.

The total average will be given in the question. Otherwise it is impossible to find without exact numbers.

heshamelaziry wrote:

mehravikas wrote:Hello,

I have seen a GMAT Prep Data Sufficiency question that was based on averages of two groups. The question was about weighted averages which group has more employees.

The formula given on this forum is -

Group A - has average age of 10
Group B - has average age of 20
Average age of both the groups A and B is 13

Therefore, there will be more people in group A.

Based on this logic, I can say 'B' is a valid answer.

How did you get that the average for both groups is 13, without any numbers for how many in each group. I saw a similar question in OG 12 where 2 averages for 2 groups were given and no numbers for either groups were given and asked for the total average and the answer was E. If I look for the question I will find it.

I will Go with option D in this case.