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Depending on the day, an ice cream shop offers seven to nine

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4709
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1605 [0], given: 375

CAT Tests
Depending on the day, an ice cream shop offers seven to nine [#permalink] New post 30 Dec 2017, 14:02
Expert's post
00:00

Question Stats:

100% (04:28) correct 0% (00:00) wrong based on 1 sessions
Depending on the day, an ice cream shop offers seven to nine possible ice cream flavors and three to four possible sauces. A Deluxe Sundae consists of two different types of ice cream and two different sauces. Which of the following could be the number of different Deluxe Sundaes that Eva can order?

Indicate all possible values.

A. 36
B. 54
C. 84
D. 216
E. 432
F. 864

Drill 1
Question: 14
Page: 321


[Reveal] Spoiler: OA
C, D

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4709
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1605 [0], given: 375

CAT Tests
Re: Depending on the day, an ice cream shop offers seven to nine [#permalink] New post 08 Jan 2018, 16:20
Expert's post
Explanation

Simplify this problem by dealing with the two combinations separately.

To select 2 out of 7, 8, or 9 ice creams, calculate \(\frac{7}{2}\times\frac{6}{1}\), \(\frac{8}{2}\times\frac{7}{1}\) and \(\frac{9}{2}\times\frac{8}{1}\) to yield 21, 28, or 36 possible combinations of ice creams, respectively.

Now, so the same thing for sauces: \(\frac{3}{2}\times\frac{2}{1}\)= 3, and \(\frac{4}{2}\times\frac{3}{1}\)= 6, so you have 3 or 6 possible combinations of sauces.

The possible numbers of different Deluxe Sundaes, then, are 21 × 3 = 63; 21 × 6 = 126; 28 × 3 = 84; 28 × 6 = 168; 36 × 3 = 108; and 36 × 6 = 216.

Only choices (C) and (D) work.
_________________

Sandy
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Re: Depending on the day, an ice cream shop offers seven to nine   [#permalink] 08 Jan 2018, 16:20
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Depending on the day, an ice cream shop offers seven to nine

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