Data Sufficiency

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 a automatic transmission but not antilock brakes?
(1) all of the cars that had antilock brakes also had an automatic transmission
(2) 2 of the cars had neither automatic transmission nor antilock brakes

Which of company x and company y earned the greater gross profit last year?

(1) last year the expenses of company x were 5/6 of the expenses of company y
(2) lat year the revenues of company x were $6 million less than the rev of company y

Ist Problem: -
Ist Problem: -
1. It says "all of the cars that had antilock brakes also had an automatic transmission " that means there is no car that had either of two. So the answer is 0. Hence A.
2. It says "2 of the cars had neither automatic transmission nor antilock brakes" - Not sufficient by itself.
A.

2nd Problem: -
1. By only expenses we can't tell the profit - so this is insufficient. (Rules out A & D).
2. By only Revenues we can't tell the profit - so this is insufficient. (Rules out B).
We're left with C & E.

Combining both:-

Suppose Revenue(x) = 1
Suppose Revenue(Y) = 7

Suppose expenses of Y = 2
therefore,expenses of X = 2*5/6 = 1.66.
Clearly Profits of Y > Profits of X.

Suppose Revenue(x) = 94
Suppose Revenue(Y) = 100

Suppose expenses of Y = 60
therefore,expenses of X = 60*5/6 = 50.
So, Profits of Y = 40
So, Profits of X = 44
Clearly Profits of X > Profits of Y.

So answer is E.

For Question 1, I think the answer is E.

(1)If we picture a Venn diagram, statement (1) tells us that the circle representing AntiLock Brakes is within the circle representing Automatic Transmission, but not that they are necessarily the same size (i.e. Venn Diagram could look like a bullseye with one circle inside the other). In other words, all cars with AntiLock Brakes have Automatic Transmission, but this does not imply that all cars with Automatic Transmission have AntiLock Brakes. Essentially this leaves us with 3 categories: Cars with neither ALB or AT, Cars with both ALB and AT, and Cars with AT but not ALB. We are interested in the last group. NOT SUFFICIENT

(2)From this we know that there are 2 cars on the outside of the circles in our Venn Diagram, so 23 have ALB, AT, or BOTH, but we know nothing more. NOT SUFFICIENT.

(1)&(2) Statement (1) gave us 3 categories and Statement (2) tells us the value of 1 of them, but we still have 2 groups (Cars with BOTH and Cars with AT but not ALB) that make up the remaining 23 cars. No way to tell how much of the 23 goes to either group. NOT SUFFICIENT.

1 - E

2 - E

jc114 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 a automatic transmission but not antilock brakes?
(1) all of the cars that had antilock brakes also had an automatic transmission
(2) 2 of the cars had neither automatic transmission nor antilock brakes

Which of company x and company y earned the greater gross profit last year?

(1) last year the expenses of company x were 5/6 of the expenses of company y
(2) lat year the revenues of company x were $6 million less than the rev of company y

For what it is worth, I had this very same question in my real GMAT exam.

Ans should be

(1) E
(2) E

mendiratta wrote:Ist Problem: -
Ist Problem: -
1. It says "all of the cars that had antilock brakes also had an automatic transmission " that means there is no car that had either of two. So the answer is 0. Hence A.

"All A are B" does NOT necessarily mean that "All B are A".

For example, "All the animals that have 4 legs also have 2 eyes" does not mean that "all the animals that have 2 eyes also have 4 legs".

So, statement (1) tells us that every car in the antilock group is also in the autamatic group, but NOT vice-versa. As a result, we have too many variables to solve, even with statement (2).

If we had written the original overlapping sets formula:

True # = (# with characteristic 1) + (# with characteristic 2) + (# with neither) - (# with both)

25 = antilock + automatic + neither - both

And the question is: "what is automatic - both?"

(1) lets us know that antilock = both, but no real numbers: insufficient.

(2) 25 = antilock + automatic + 2 - both

23 - antilock = automatic - both

Still one too many variables: insufficient.

Together:

knowing that antilock = both, we can substitute:

23 - both = automatic - both
23 = automatic.

However, the question isn't asking us to solve for the total # with automatic transmissions, it's asking us how many cars have ONLY automatic transmissions, i.e. "auto - both".

With the info we have, both could be any number from 1-23, so there's no way to solve: choose (e).

Hi can you please post the source of these questions.

They are good.. would want to see other problems there too..

Thanks in advance

I tried tackling the first problem using the MGMAT Double Matrix method but I got the wrong answer. Stuart, can you please clarify my error?

I have the below Matrix from the question stem?
Automatic Non-Automatic Total
Antilock Z=?
Non-AL
Total 25


Statement 1 gives:
___________| Automatic | Non-Automatic | Total
Antilock ____| __ X ____ | ____ Z=? ___ | X+Z
Non-AL ____| __ 0 ____ | ____ ? _____ | ?
Total ______| __ X ____ | ____ Y ______ | 25

We know nothing about variables X and Y so we cannot find Z for which the question is asking. Statement 1 is eliminated.

Statement 2 gives:
___________| Automatic | Non-Automatic | Total
Antilock ____| __ X ____ | ____ Z=? ___ | X+Z
Non-AL ____| __ ? ____ | ____ 2 _____ | ?+2
Total ______| __ X+?___ | ____ Y=2+Z __ | 25

We know nothing about variables X and Y so we cannot find Z for which the question is asking. Statement 2 is eliminated.

Statement 1 and 2 gives:
___________| Automatic | Non-Automatic | Total
Antilock ____| __ X ____ | ____ Z=? ___ | X+Z=23
Non-AL ____| __ 0 ____ | ____ 2 _____ | 2
Total ______| __ X ____ | ____ Y=2+Z __ | 25

The following equations can be made:
X+Z=23
Y-Z=2
X+Y=25

We have three equations and three variables. So the system of equations should be solvable to obtain Z. So I assumed the answer to be C. But the answer is E. Where did I go wrong?

jc114 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 a automatic transmission but not antilock brakes?
(1) all of the cars that had antilock brakes also had an automatic transmission
(2) 2 of the cars had neither automatic transmission nor antilock brakes

You know from (2) that 23 cars had either an automatic trans. or anti lock breaks, but by itself is insufficient

From (1), we know that all of the cars with antilock brakes also have an automatic transmissions. This by itself doesn't tell us is how many of the cars had only automatic transmissions. so this by itself is insufficient.

(1) and (2) combined doesn't tell us anything else either. When a question says some, some can mean all of the cars, or just 1 of the cars. so (1) might be saying that all 23 cars have both, but it might also be saying that only 10 cars have both. Because we are still unsure, answer is E imo.

jc114 wrote:Which of company x and company y earned the greater gross profit last year?

(1) last year the expenses of company x were 5/6 of the expenses of company y
(2) lat year the revenues of company x were $6 million less than the rev of company y

Another E I think, but I'll work this out.

Looking briefly at both (1) and (2), you are not actually given what the revenue or the expenses of the company are, so while you may be able to come up with equations like 5/6(x exp.)=(y exp) or X rev - 6mil = y rev, we are still in the dark. The expense of y could have been 600,000,000 and it's revenue could have bee 500,000,000. This would mean that X's expenses would have been 500,000,000. However, the revenue of X would have been 494,000,000. meaning company X lost 6million, but company y lost 100,000,000. .

Hope this all helps

Yes, your logic using a venn diagram-like approach certainly makes sense.

But why did my system of equations lead me to a false answer?

you actually only have two equations hidden in 3 I believe. Let's subsitute.

X+Z=23
Y-Z=2
X+Y=25

Y-Z=2
Z=Y-2

X+Z=23
X + (Y-2)=23
X + Y = 25

Doh! Thanks talkativetree! I am glad that you are quite talkative, lol