Data Sufficiency

AAPL wrote: ↑

Mon Sep 27, 2021 8:24 am

Manhattan Prep

Ivan operates an ice cream stand in the summer, selling exclusively chocolate, vanilla and strawberry cones. On a recent afternoon, the ratio of chocolate to vanilla to strawberry cones sold by Ivan was 6:3:2. How many cones did Ivan sell on that afternoon?

1) Ivan sold 24 vanilla cones
2) Ivan sold twice as many chocolate cones as vanilla cones

OA A

Given: On a recent afternoon, the ratio of chocolate to vanilla to strawberry cones sold by Ivan was 6 : 3 : 2.
ASIDE: This information tells us that there are infinitely many possibilities with regards to the number of cones sold.
For example, it COULD be the case that Ivan sold 6 chocolate, 3 vanilla, and 2 strawberry cones
Or it COULD be the case that Ivan sold 12 chocolate, 6 vanilla, and 4 strawberry cones
Or it COULD be the case that Ivan sold 18 chocolate, 9 vanilla, and 6 strawberry cones
Or it COULD be the case that Ivan sold 24 chocolate, 12 vanilla, and 8 strawberry cones
etc...
Notice that we can keep creating equivalent ratios by multiplying each part of the original ratio (6 : 3 : 2) by the same value.

Target question: How many cones did Ivan sell on that afternoon?

Statement 1: Ivan sold 24 vanilla cones.
The original ratio, 6 : 3 : 2, the 3 represents the number of vanilla cones sold.
So if we multiply each part of the ratio by 8 we get the equivalent ratio 48 : 24 : 16
So the total number of cones sold = 48 + 24 + 16 = 98
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Ivan sold twice as many chocolate cones as vanilla cones
Since the ratio of chocolate to vanilla to strawberry cones sold is 6 : 3 : 2, we can see that the number of chocolate cones sold will always be twice the number of vanilla cones sold (since 6 is TWICE the value of 3)
Consider these two possible cases:
Case a: Ivan sold 6 chocolate, 3 vanilla, and 2 strawberry cones. In this case, the answer to the target question is Ivan sold 11 cones
Case b: Ivan sold 12 chocolate, 6 vanilla, and 4 strawberry cones. In this case, the answer to the target question is Ivan sold 22 cones
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent