Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Set A, B, C have some elements in common. If 16 elements are [#permalink]
11 Mar 2008, 11:30

1

This post was BOOKMARKED

Set A, B, C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three of the sets A, B, and C have in common?

(1) Of the 16 elements that are in both A and B, 9 elements are also in C. (2) A has 25 elements, B has 30 elements, and C has 35 elements.

A union B union C = A + B + C - A inte B - A inter C - B inter C + A inter B inter C, where inter is intersection Also A union B = A + B - A inter B Given Originally A union B = 16, A union C = 17, B Union C = 18

Statement 1: Gives us A inter B inter C = 9 So question cannot be answered alone with this statement.

Statement 2: Gives us A, B, & C. This alone cannot answer the question. However with the help of A, B & C and A union B = 16, A union C = 17, B Union C = 18, we can obtain A inte B, A inter C, and B inter C using formula mentioned in line 2 above.

Combining both statments: We have all the things needs for calculation of A union B union C.

A union B union C = A + B + C - A inte B - A inter C - B inter C + A inter B inter C, where inter is intersection Also A union B = A + B - A inter B Given Originally A union B = 16, A union C = 17, B Union C = 18

Statement 1: Gives us A inter B inter C = 9 So question cannot be answered alone with this statement.

Statement 2: Gives us A, B, & C. This alone cannot answer the question. However with the help of A, B & C and A union B = 16, A union C = 17, B Union C = 18, we can obtain A inte B, A inter C, and B inter C using formula mentioned in line 2 above.

Combining both statments: We have all the things needs for calculation of A union B union C.

Answer C.

actually OA is A. you yourself tell that from 1 we know abc.