## If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was $65, what was the ##### This topic has expert replies Legendary Member Posts: 2656 Joined: 07 Sep 2017 Thanked: 6 times Followed by:4 members ### If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was$65, what was the

by Vincen » Tue Aug 17, 2021 6:38 am

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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 ### GMAT/MBA Expert GMAT Instructor Posts: 15793 Joined: 08 Dec 2008 Location: Vancouver, BC Thanked: 5254 times Followed by:1267 members GMAT Score:770 ### Re: If the average (arithmetic mean) cost per sweater for 3 pullover sweaters and 1 cardigan sweater was$65, what was t

by [email protected] » Wed Aug 18, 2021 6:40 am

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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