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## Comment on

Double Matrix Method## Another method shows the

## That method is exactly the

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

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?

## You're referring to this

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

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

## Hi Jingyjess,

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

## 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

## Hi Aashay,

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

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?

## Hi Bertyy,

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?

## Not quite.

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

## The wording isn't great. I'd

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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