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06 Apr 2022, 08:30
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B
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Difficulty:
95%
(hard)
Question Stats:
33% (03:11) correct
67%
(02:51)
wrong
based on 169
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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.
Are You Up For the Challenge: 700 Level Questions
(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
08 Apr 2022, 08:52
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Bunuel
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
08 Apr 2022, 13:50
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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
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
