All of the arrangements made in a flower shop yesterday...

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

All of the arrangements made in a flower shop yesterday...

by AAPL » Wed Nov 22, 2017 3:05 pm

All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangemets made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 115

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Nov 22, 2017 3:05 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Nov 22, 2017 6:52 pm

AAPL wrote:All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangemets made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 11

Use a VENN DIAGRAM.

32 contained roses.
42 contained tulips.
41 contained lilies.

Complete the Venn diagram by working from the CENTER OUT.

5 of the arrangements made yesterday contained all three types:

16 contained roses and tulips.
18 contained lilies and tulips.
8 contained roses and lilies.
Subtracting from these figures the 5 who like all 3 types of flowers, we get:

Subtracting the values in the diagram from R=32, T=42, and L=41, we get:

Summing the values in the Venn Diagram, we get:
13+11+13+3+5+13+20 = 78.

The correct answer is C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 4:03 pm

AAPL wrote:All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangemets made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

A. 63
B. 68
C. 78
D. 83
E. 115

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

We can create the equation:

Total = total single overlaps - total double overlaps + triple overlap

Total = 32 + 42 + 41 - 16 - 18 - 8 + 5

Total = 115 - 42 + 5

Total = 78

Answer: C

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