The average (arithmetic mean) of the original six prices for six coats

Question

The average (arithmetic mean) of the original six prices for six coats at a clothing store was $85. After two of the six coats were each discounted by 20%, the average price of the six coats was $76. Was the coat with the lowest original price one of the two coats that were discounted?

(1) One of the discounted coats was the one with the highest original price.

(2) Before the discount, none of the coats had a price greater than $180.

(1) One of the discounted coats was the one with the highest original price.

(2) Before the discount, none of the coats had a price greater than $180.

Are You Up For the Challenge: 700 Level Questions

JerryAtDreamScore · Answer

Breaking Down the Info:

If we discounted all coats by 20%, the average price would be 17 less. Currently, we have 9 less while discounting only two coats (1/3 of total), so we still need to discount a very high-priced coat in order for the lowest original price coat to be the other coat that was discounted.

Hence, we need a dollar discount of  9*6 = 54

Statement 1 Alone:

Although this seems to give us some hope of sufficiency, we need the actual values to see if the highest-priced coat was high enough. Insufficient.

Statement 2 Alone:

The highest-priced coat allowed was 180. By discounting it 20%, it gives us a dollar discount of 36. Then we can assume the lowest coat got discounted 18 for sufficiency. That would assume the lowest coat was priced at 18/20% = 90, which is not feasible. Then with this statement, we can see it is not possible for the lowest priced coat to be selected for discount.

Answer: B

Mariner07 · Answer

total Cost before discount - 510
total cost after discount - 456

let the non discounted ones be x,y,z 
the discounted ones -a,b

thus before discount 
x+y+z+a+b= 510 
after discount 
x+y+z+0.8 a+ 0.8 B =456
above two equations will give 
a+b = 270
and x+y+z= 240

Now statement 1 
The price of the highest is not given, so we can assume any number for 'a' and b will vary accordingly. So cannot say say for sure that b will be the lowest

taking statement 2 
We can assume the highest value to be 180 
If it is discounted later then , if we assume a is highest , b becomes 90
and x+ y+ z= 240 we can easily observe we cannot take all these three values more than 90 and satisfy the condition
thus answer is NO the lowest value is not the one discounted

Now If we consider that the highest value is not discounted then 
y+z = 60 
and a+b=270, thus again we see that the lowest value is not discounted 
Satisfactory

thus B is the answer

Annukiran · Answer

In S2- given that the max price of a coat is caped at 180, then 0.2 of it is 36.......so we are left with a discount allocation to the cheapest is $18- which is 0.2 of the cheapest.....therefore according to this the cost of the cheapest could be 90........which cannot be true, coz with 90 the cheapest and max 180 the max price average doesn't hold true........therefore S2 concludes that the cheapest is not included in the discount...........

S1 is not getting us anywhere. And since S2 answer the conundrum Option C is not possible........So correct answer is B

S1 is not getting us anywhere. And since S2 answer the conundrum Option C is not possible........So correct answer is B

The average (arithmetic mean) of the original six prices for six coats

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The average (arithmetic mean) of the original six prices for six coats

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards