Data Sufficiency

Vincen wrote: ↑

Tue Aug 17, 2021 6:38 am

If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was $65, what was the cost of the cardigan sweater?

(1) The average cost per sweater for the 3 pullover sweaters was $55.
(2) The most expensive of the 3 pullover sweaters cost $30 more than the least expensive.

Answer: A

Source: Official Guide

Given: The average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was $65
Let P = the combined price of ALL 3 pullover sweaters
Let C = the price of 1 cardigan sweater
Aside: It would be nice to let P = the price of ONE pullover, which would mean 3P = the price of THREE pullovers. However, we don't know whether all pullovers have the same price

The average price of all 4 sweaters is $65
So, we can write: (P + C)/4 = 65
Multiply both sides of the equation by 4 to get: P + C = 260

Target question: What is the value of C (the cost of the cardigan sweater)?

Statement 1: The average cost per sweater for the 3 pullover sweaters was $55.
Since P = the combined price of ALL 3 pullover sweaters, we can write: P/3 = 55
Multiply both sides of the equation by 3 to get: P = 165
He already know that: P + C = 260
Replace P to get: 165 + C = 260
Solve, to get: C = 95
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The most expensive of the 3 pullover sweaters cost $30 more than the least expensive.
There are several scenarios that satisfy statement 2 (and the given information). Here are two:
Case a: The prices of the three pullovers are $10, $20 and $40, which means P = $10 + $20 + $40 = $70. Since we also know that P + C = 260, we get: 70 + C = 260, in which case the answer to the target question is C = 190
Case b: The prices of the three pullovers are $30, $40 and $60, which means P = $30 + $40 + $60 = $130. Since we also know that P + C = 260, we get: 130 + C = 260, in which case the answer to the target question is C = 130
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent