Came across this on the web

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bingojohn: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Mon Aug 06, 2007 12:04 pm

by bingojohn » Fri Aug 17, 2007 12:07 pm

Anonymous wrote:In a group of 30 students, 8 are enrolled in an English class and 16 are enrolled in an Algebra class. How many students are enrolled in both an English and an Algebra class?

(1) 20 are enrolled in exactly one of these two classes.

(2) 3 are not enrolled in either of these classes.

Answer ?

Use formula:
total = first group + second group + neither group - both groups
=> 30 = 8 english + 16 algebra + neither - both

(1) gives us nothing, NS

(2) gives us the number of students enrolled in neither english nor algebra... which if plugged into the equation above, gives us 'both' as 3.

Hence Sufficient.

Source: Beat The GMAT — Data Sufficiency | Fri Aug 17, 2007 12:07 pm

ratindasgupta: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Jun 11, 2007 10:32 pm; Location: Mumbai

Re: Came across this on the web

by ratindasgupta » Sun Aug 19, 2007 3:46 am

Anonymous wrote:In a group of 30 students, 8 are enrolled in an English class and 16 are enrolled in an Algebra class. How many students are enrolled in both an English and an Algebra class?

(1) 20 are enrolled in exactly one of these two classes.

(2) 3 are not enrolled in either of these classes.

there seems to be some error in the data. cant put my finger on it. maybe i'm wrong.

And i dont think its B anyway. Coz goin by bingo's formula

30 = 8 + 16 + 3 - x. Which means x is -3.

beny: Master | Next Rank: 500 Posts; Posts: 214; Joined: Fri Jul 20, 2007 1:35 am; Thanked: 3 times

by beny » Sun Aug 19, 2007 9:27 am

Yes, there is an error in the data. Assuming that there are 30 students, and only 3 are not enrolled in either class, then 27 must be enrolled in at least 1 class.

Yet, the total number of students (8+16) is only 24.

Bharat: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Jul 22, 2007 11:43 pm; Thanked: 8 times

by Bharat » Mon Aug 27, 2007 1:57 am

Hi,
Please look at this:
Let E: student reading only English
A: Student reading only Algebra
X: student reading English & Algebra Both
E + X = 8
A + X = 16
From 1: E + A = 20

Using the above three eqns: X = 2. Hence 1 is sufficient.

Bharat: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sun Jul 22, 2007 11:43 pm; Thanked: 8 times

by Bharat » Mon Aug 27, 2007 1:58 am

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