Lesson: Double Matrix Method

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Euro's picture

Another method shows the matrix a 3X3 to leave room for the totals, in the 2X2 you write out the number anyway.
gmat-admin's picture

That method is exactly the same. The only difference is a small change in how we show the totals for each row and column.

For the motel ques below, the 2/3rd statement is a bit confusing. Read it as 2/3 of rented, not 2/3 of AC rooms. How can I avoid mistakes like this - the question writing is a bit vague if you ask me

One night a certain motel rented 3/4 th of its rooms, including 2/3rd of its air-conditioned rooms. If 3/5th of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?
gmat-admin's picture

You're referring to this question: http://www.beatthegmat.com/motel-t271938.html

This is an official GMAT question, and I think the wording is fine. We're told that 2/3 of the air-conditioned rooms were rented, so I'm not sure what could be changed to make it more readable.

Hi, Brent! I used the double Matrix Method for the following question. But I got different result than the answer choice. I got 34%. After compared with the explanation, I think the major confusion that I have is how to interpret "75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts". This to me means out of all interns who received fewer than 6 hours of sleep, there are 75% report feeling tired during their shifts. If I used 100 as total intern number, the grid of less than 6 hours and tired intern should be 0.75 X 80 = 60. But the answer states that there are 75 people in this grid. Could you please help me out?

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

A) 6
B) 14
C) 19
D) 20
E) 81

Answer C
gmat-admin's picture

Hi Jingyjess,

The key word here is AND: "At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep AND report feeling tired during their shifts."

If the test-makers wanted to convey your interpretation, they'd write "OF THE interns who received fewer than 6 hours of sleep, 75% report feeling tired during their shift." (Notice that's there's no AND here. Instead, we have OF THE)

Does that help?

Cheers,
Brent

Thank you for the feedback!I understand where you are coming from. I just still need take some time to digest and prepare better strategy for tricky wordings like this in the future!

Hey Brent,
Please help me with the following question posted on Beat the GMAT. I am extremely confused wrt using the double matrix method for this.

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?
(1) 16 students at the school study both French and Japanese.
(2) 10 percent of the students at the school who study Japanese also study French.

Thanks in advance,
Aashay
gmat-admin's picture

Hi Aashay,

I'm happy to help.
You'll find my solution here: http://www.beatthegmat.com/at-least-100-students-at-a-certain-high-schoo...

Cheers,
Brent

On a certain road 10 percent of the motorists exceed the posted speed limit and receive speeding tickets, but 20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?


My concern is: .1x + .2x = x, but this is not right. Why is 10% of the speeders who get a ticket 10, but those who speed and not get a ticket not 20, but .2x? I can't see why you don't add .1x of some unknown to .2x of some unknown to get a total of x?
gmat-admin's picture

Hi Bertyy,

The question tells us that "10 percent of the motorists exceed the posted speed limit and receive speeding tickets"

So, if there are 100 motorists in TOTAL, then 10 of them 10 percent of the motorists exceed the posted speed limit AND receive speeding tickets.

We're also told that "20 percent of the motorists who exceed the posted speed limit do not receive speeding tickets."

Here, we are limiting the discussion to ONLY those motorists who speed. AMONG those speeders, 20% receive a ticket. In this case, we do not know how many speeders there are. So, if we let x = the number of SPEEDERS, then 0.2x = the number of SPEEDERS who receive a ticket.

Does that help?

Here's my full solution: https://gmatclub.com/forum/on-a-certain-road-10-of-the-motorists-exceed-...

Cheers,
Brent

Thanks Brent,

Starting to get it.

So, the inclusion of "And" (everything in the Double Matrix Box) makes it an "Absolute" if you have a total number, like 100 in the problem. And everything on the periphery on the Double Matrix is "Only", so no "Absolute" and thus you can't draw from the total?
gmat-admin's picture

Not quite.

"On a certain road 10 percent of the motorists exceed the..."

Here we are talking about 10% of ALL of the motorists. We know this, because there are no words that restrict the KIND of motorists we are examining.

"20 percent of the motorists WHO EXCEED the posted speed limit do not..."

Here the words "WHO EXCEED" restrict the discussion to those who exceed the speed limit. So, we are no longer talking about all motorists; we are talking about just those motorists WHO EXCEED the speed limit.

Does that help?

Cheers,
Brent

Hi Brent,

The question below seems to be bizarrely worded, maybe not..maybe it's just me. Anyways. Here it is:

Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?
(A) 135
(B) 120
(C) 115
(D) 105
(E) 90
gmat-admin's picture

The wording isn't great. I'd definitely change the last part to read "how many applicants applied to college X or college Y BUT NOT BOTH?"

There's a nice solution (with double matrix charts) by mevicks here: http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t2...

Let me know if you need any clarification.

Cheers,
Brent

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