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

Question

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.

GMATGuruNY · Answer

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Scott@TargetTestPrep · Answer

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.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

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

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER