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Venn Diagram Problem

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Venn Diagram Problem

by gander123 » Wed Jan 02, 2013 8:29 am
I shouldnt have complained about OG explanations. I miss them ;)

Maybe you can help me out on this one:

"Of the 25 cars sold at a certain dealership yesterday, some had automatic transmission and some had antilock brakes. How many of the cars had automatic transmission but not antilock brakes?

(1) All of the cars that had antilock brakes also had automatic transmission.

(2) 2 of the cars had neither automatic transmission, nor antilock brakes."

Correct answer: E

What I set up:

Ct: number of cars with only automatic transmission
Cl: number of cars with only antilock brakes
C: Total number of cars sold
x: number of cars with both antilock brakes and automatic transmission
w: number of cars with neither automatic transmission nor antilock brakes

Thus, C= Ct + Cl + x + w = 25 => Determine the value of Ct: number of cars with only automatic transmission


For statement (1) I desperately tried to convert the satement into an equation..without success. How do you rate the statement insufficient ?

For statement (2) Rather easy. Given w, you cannot determine the value of Ct without knowing Cl or x.Thus statement (2) insufficient.

Lacking the argument for (1) I cannot say that both together are still insufficient, can you?

Cheers,

Tobi
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Source: — Data Sufficiency |
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by sana.noor » Wed Jan 02, 2013 11:05 am
A very easy Question..the answer is E..i wish i could make a chart here for better understanding
the question tells that 25 cars sold and we want to know the number of the cars that had automatic transmission but not antilock brakes?
From statement 1) all those cars that had antilock brakes also has automatic transmission....Insufficient we are not given with any clue/numbers
From statement 2) 2 of the cars had neither automatic transmission, nor antilock brakes....again insufficient no information is given

Together for two statements we an write a formula
A for antilock brakes
B for Automatic transmission
N for neither

A + B - 2(number of cars that has both A+B)+ neither = total number of cars

A + B - 2(A+B) + 2 = 25
A + B -2AB = 25-2
A + B -2AB =23
you cannot solve this equation further because to solve this equation you need to know the value of one variable A or B. neither of the two statements give any hint about A or B. So E is the answer
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by GMATGuruNY » Wed Jan 02, 2013 12:41 pm
gander123 wrote:
"Of the 25 cars sold at a certain dealership yesterday, some had automatic transmission and some had antilock brakes. How many of the cars had automatic transmission but not antilock brakes?

(1) All of the cars that had antilock brakes also had automatic transmission.

(2) 2 of the cars had neither automatic transmission, nor antilock brakes."
The following cases satisfy both statements:

Case 1: 2 cars have neither, 1 car has both antilock breaks and automatic transmission, 22 cars have only automatic transmission.

Case 2: 2 cars have neither, 22 cars have both antilock breaks and automatic transmission, 1 car has only automatic transmission.

Since the number of cars that have only automatic transmission can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by ceilidh.erickson » Sat Jan 05, 2013 8:17 am
To sana.noor's point, here is what it would look like if you set up a chart to organize the information:

Image

You can see that without knowing what x is, we can't get a value for the number of cars with transmission but no brakes.[/img]
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