On a company-sponsored cruise, 2/3 of the passengers were

On a company-sponsored cruise, 2/3 of the passengers were company employees and the remaining passengers were their guests. If 3/4 of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT managers?

Since 3/4 of the company-employee passengers were managers, then 1-3/4=1/4 of the company-employee passengers were NOT managers. Therefore the number of company-employee passengers who were NOT managers is (total # of passengers)*2/3*1/4. So, we have that to answer the question we need to know how many passengers were on the cruise.

(1) There were 690 passengers on the cruise. Sufficient.

(2) There were 230 passengers who were guests of the company employees --> 230 guests represent 1-2/3=1/3 of all passengers, thus there were total of 230*3=690 passengers on the cruise. Sufficient.

Answer: D.
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Bunuel

I made a chart after this question threw me off a bit

lEmployees l Guests l Total
Manager l(3/4)(2/3X) l
Not Manager l (1/4)(2/3X)l
Total l 2/3X l 1/3 X l X

(1) 690 = X so sufficient
(2) 1/3X = 230 which gives us the total

I came close to the 2 minute mark so I determined the answer is D after constructing this chart quickly. Are the any potential setbacks in using this matrix approach?

Thank you

Hi GMAT01,

The goal on any given Quant prompt should NOT be to solve it in under 2 minutes - the goal should be to get the question correct (if possible) in an efficient way (while still making sure that you have enough time to deal with the entire Quant section). On Test Day, some Quant questions can be solved in under 30 seconds, while others will take you 3 minutes (and that's if you know what you're doing). Trying to stick to '2 minutes per question' is impractical.

The tic-tac-toe board (or Matrix Method, as some people call it) is a great way to organize information on certain questions (including this one), so it's certainly worth practicing. As you become more familiar with these types of questions, you'll be able to get to work faster, organize the information quicker, etc.

GMAT assassins aren't born, they're made,
Rich

Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of passengers, and the two characteristics are:
- company employee or not company employee
- a manager or not a manager

Okay, onto the question...
Target question: What was the number of company-employee passengers who were NOT managers?

Given: 2/3 of the passengers were company employees and the remaining passengers were guests. 3/4 of the company-employee passengers were managers.

Let's begin by setting up our diagram to show the two sets of characteristics:


Since we don't know the total number of passengers, let's let x = total number of passengers:


If "2/3 of the passengers were company employees and the remaining passengers were guests," then 1/3 are guests. This means the sum of the boxes in the left-hand column is (2/3)x and the sum of the boxes in the right-hand column is (1/3)x:


Then we're told that "3/4 of the company-employee passengers were managers"
So 3/4 of the (2/3)x passenger were managers.
3/4 of (2/3)x = (1/2)x, so (1/2)x passengers were managers:


Since the sum of the two boxes in the left-column must add to (2/3)x, we can conclude that the other box must be (1/6)x, so we can add that here.


IMPORTANT: Since none of the guests were managers, we know that the top-right box contains zero passengers as follows:


Finally, the sum of the two boxes in the right-column must add to (1/3)x, we can conclude that the other box must be (1/3)x, so we can add that here.


Okay, our goal is to determine the number of company-employee passengers who were NOT managers. In other words, we want to know the number of passengers in the bottom-left box. So, let's place a STAR in this box to remind us of this:


We're now ready to check the statements...

Statement 1: There were 690 passengers on the cruise
In other words, x = 690
From this, we can take our diagram and plug in 690 for x:


As we can see, we can determine the number of passengers in every box, which means we can definitely determine the number of company-employee passengers who were NOT managers
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There were 230 passengers who were guests of the company employees.
In other words, the boxes in the left-hand column have a sum of 230


If (1/3)x = 230, we can determine the value of x.
Once we know the value of x, we can we can definitely determine the number of company-employee passengers who were NOT managers
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =

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Can you advise how can I infer:


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There is a segregation of managers vs non managers only among the employees. Rest are all guests of employees (think kids) so there is no manager vs non manager among guests.
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I don't understand why all those explanations must be so complicated.

Here's how I solved it:
If a DS question asks for the concrete value of one element of a ratio, you will need BOTH the concrete value (of another element of the ratio) AND the relative value (of two elements of the ratio).

Following this rule, I got an answer in under 30 seconds.

Hi kamrim322,

If you can correctly answer a GMAT question in under 30 seconds, then that's great. That having been said, DS questions are interesting in that they have no 'safety net' - meaning that if you make a little mistake, then you will not realize it. You will simply convince yourself that one of the wrong answers is correct. Thankfully, the 'math' behind most DS questions isn't that complicated, so if you're certain that you know what the answer is, then it typically won't take long for you to prove that you are correct.

During your studies and practice CATs/mocks, how many times have you gotten a DS question wrong that you COULD have gotten correct if you had just done a little more work? If you can consistently hit Q51, then you should feel free to approach the Quant section however you choose. If you're consistently missing out on some easy points though, then you will have to make some changes to how you 'see' (and respond to) the Exam before you will be able to consistently score at a higher level.

GMAT assassins aren't born, they're made,
Rich

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