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

Question

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?

I. 54
II. 84
III. 216

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

I. 54
II. 84
III. 216

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

nick1816 · Answer

Total number of two different types of ice cream combinations possible are 7C2(=21), 8C2(=28) or 9C2(=36).
Total number of two different types of sauces combinations possible are 3C2(=3) or 4C2(=6)

There are total 6 Combinations possible of number of different Deluxe Sundaes that Eva can order
1. 21*3=63
2.  28*3=84 
3. 36*3= 108
4. 21*6=126
5. 28*6=168
6.  36*6=216

IMO D

GmatPrime · Answer

Let's find the range:

Minimum possibilities= 7C2 * 3C2 = 63
Maximum possibilities = 9C2 * 4C2 = 216

Eva can order any number of combinations from 63 to 216

Option D

ScottTargetTestPrep · Answer

For ice cream flavors, we choose 2 out of 7, 2 out of 8, or 2 out of 9, so we have 7C2 = (7 x 6)/2 = 21, 8C2 = (8 x 7)/2 = 28, or 9C2 = (9 x 8)/2 = 36.

For the sauces, we choose 2 out of 3 or 2 out of 4, so we have 
 3C2 = (3 x 2)/2 = 3 or 4C2 = (4 x 3)/2 = 6

Thus, the total number of Deluxe Sundaes on any particular day could be 21 x 3 = 63, 21 x 6 = 126, 28 x 3 = 84, 28 x 6 = 168, 36 x 3 = 108 or 36 x 6 = 216. Roman numerals II and III are correct.

Answer: D

CrackverbalGMAT · Answer

This is a fairly simple question on the concept of combinations. But since the given data involves ranges, it has been framed as a ‘could be’ type of question.
The best approach is to find the lower and upper limits and see which of the statements fit in.

Two flavours of ice cream can be selected from 7 flavours in  7_C_2  ways; two different sauces can be selected from 3 sauces in  3_C_2  ways. Selecting both can be done in  7_C_2 * 3_C_2  ways. This works out to 63, which is the lower bound for the number of Deluxe Sundaes.

For the upper bound, we select 2 flavours from 9 and 2 sauces from 4. This will naturally give us a higher number of combinations. The number of combinations will be  9_C_2  *  4_C_2 , which comes to 216.

54 is not between 63 and 216. So, statement I cannot be the number of Deluxe sundaes that she can order. So, options containing statement I – A and E – can be eliminated. Since 84 and 216 are both possible values, the correct answer option is D.

In ‘Could be’ questions with a range given in the data, identify the lower and the upper limits of the required answer, eliminate the impossibilities and whatever remains has to be the answer.

Hope this helps!

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

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