Q90 in OG 11th Edition

[rb90]

How many of the 60 cars sold last month by a certain dealer had neither power windows nor stereo?
(1) Of the 60 cars sold,20 had a stereo but not pwer windows
(2) Of the 60 cars sold,30 had both power windows and a stereo

Answer is E (statement 1 and 2 are both not suffieicent and additonal information is required).

But i didnt understand the explanation in the book.Need some help people.

Thanks.

[sanju09]

How many of the 60 cars sold last month by a certain dealer had neither power windows nor stereo?
(1) Of the 60 cars sold,20 had a stereo but not pwer windows
(2) Of the 60 cars sold,30 had both power windows and a stereo

Answer is E (statement 1 and 2 are both not suffieicent and additonal information is required).

But i didnt understand the explanation in the book.Need some help people.

Thanks.

In Set language, it translates to n (U) = 60, n (P or S)' = 60 - n (P or S) =?

(1) n (S - P) = 20; insufficient

(2) n (S & P) = 30; insufficient

Taken together, since n (P or S) = n (P) + n (S) - n (P & S), and we don't have values n (P) or n(S) known, [spoiler]still insufficient

E[/spoiler]

[pradeepkaushal9518]

60 car sold last month

how many of 60 cars sold had neither power windows nor stereo?

1. 20 sold had a stereo but no power windows

can we find from this cars sold with no power windows nor stereo no not SUFF A/D OUT

LEFT BCE

2.30 had both power windows and a stereo

can this help to find cars without power windows and stereo no not SUFF B out left C and E

combine both 20 with stereo no power window and 30 both stereo and power windows can can we know neither power window nor stereo with this not suff so C out left E

ans E

[Stuart@KaplanGMAT]

How many of the 60 cars sold last month by a certain dealer had neither power windows nor stereo?
(1) Of the 60 cars sold,20 had a stereo but not pwer windows
(2) Of the 60 cars sold,30 had both power windows and a stereo

Answer is E (statement 1 and 2 are both not suffieicent and additonal information is required).

But i didnt understand the explanation in the book.Need some help people.

Thanks.

Here's the simple 2-set formula:

Total # of items = (total # in group 1) + (total # in group 2) + (# in neither group) - (# in both groups)

or, more simply:

Total # = G1 + G2 - neither + both

Applying that to your question:

We know that total = 60; we want "neither".

So:

60 = stereo + power windows - both + neither

We're missing 3 variables, so we need a lot of info to solve!

(1) 20 were "stereo only"... nothing about both or power windows... insufficient.

(2) 30 were "both"... nothing about the single groups.. insufficient.

Together: we still don't know how many were "power only", so we can't solve. Insufficient, choose E.

* * *

(As an aside, there's another version of the formula we can use that's more applicable to this question:

Total # = (# in group 1 only) + (# in group 2 only) + (# in both) + (# in neither).

We use this version of the formula when we're given info such as "x people are only in group 1"; we use the other version of the formula when we're given info such as "x people are in group 1", i.e. they could also be in other groups.)