Of 200 people surveyed, 80 percent own a cellular phone and 45 percent own a pager. If all 200 people surveyed own a cellular phone or a pager or both, what percent of those surveyed either do not own a cellular phone or do not own a pager?
1. 35%
2. 45%
3. 55%
4. 65%
5. 75%
[spoiler]OA: E[/spoiler]
200 people surveyed. Exam pack 2
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi prata,
This question is a modified version of a typical Overlapping Sets question. You can solve it with the tic-tac-toe board or the Overlapping Sets Formula:
Total = (Group 1) + (Group 2) - Both + Neither
In this prompt, we're told that ALL 200 people own at least one of the two items, so the 'Neither' group would be 0.
80% of 200 = 160 people own a cell phone
45% of 200 = 90 people own a pager
Plugging that data into the formula, we have...
200 = 160 + 90 - Both
200 = 250 - Both
Both = 50
Since 50 of the 200 people have both items, the other 200 - 50 = 150 people have just one item. As a percentage of the total, that is 150/200 = 75%
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This question is a modified version of a typical Overlapping Sets question. You can solve it with the tic-tac-toe board or the Overlapping Sets Formula:
Total = (Group 1) + (Group 2) - Both + Neither
In this prompt, we're told that ALL 200 people own at least one of the two items, so the 'Neither' group would be 0.
80% of 200 = 160 people own a cell phone
45% of 200 = 90 people own a pager
Plugging that data into the formula, we have...
200 = 160 + 90 - Both
200 = 250 - Both
Both = 50
Since 50 of the 200 people have both items, the other 200 - 50 = 150 people have just one item. As a percentage of the total, that is 150/200 = 75%
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
We know that
Cell + Pager - Both = Total
so
160 + 90 - Both = 200
and
Both = 50
That means that 150 only own one of the two. 150 = 75% of 200, since our answer is 75%.
Cell + Pager - Both = Total
so
160 + 90 - Both = 200
and
Both = 50
That means that 150 only own one of the two. 150 = 75% of 200, since our answer is 75%.