DS Prob from GMAT Prep

[nishant1309]

Henry purchased 3 items during a sale. He received 20% discount off regular price of the most expensive item and a 10% discount off regular price off each of the other 2 items. Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

1. Regular price for most expensive item: $50 & regular price of the next expensive item: $ 20.

2. Regular price for least expensive item: $ 15.

[Night reader]

let us call the most exp. item A, the other two items B and C. We need to find if (0.8A+0.1B+0.1C)/(A+B+C)>0.85
st(1) A=50 and B=C=20 --> (40+18+18)/90<0.85 hence we can answer No on this question, Sufficient;
st(2) we have only C or B=15 BUT A can be anything, hence Not Sufficient

answer A

Henry purchased 3 items during a sale. He received 20% discount off regular price of the most expensive item and a 10% discount off regular price off each of the other 2 items. Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

1. Regular price for most expensive item: $50 & regular price of the next expensive item: $ 20.

2. Regular price for least expensive item: $ 15.

[nishant1309]

let us call the most exp. item A, the other two items B and C. We need to find if (0.8A+0.1B+0.1C)/(A+B+C)>0.85
st(1) A=50 and B=C=20 --> (40+18+18)/90<0.85 hence we can answer No on this question, Sufficient;
st(2) we have only C or B=15 BUT A can be anything, hence Not Sufficient

answer A

Henry purchased 3 items during a sale. He received 20% discount off regular price of the most expensive item and a 10% discount off regular price off each of the other 2 items. Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

1. Regular price for most expensive item: $50 & regular price of the next expensive item: $ 20.

2. Regular price for least expensive item: $ 15.

@ Night rider: To my understanding:
1. we need to check whether (0.2A+0.1B+0.1C)/(A+B+C) > 0.15.
2. St. 1 doesn't specifies regular price of least expensive item. You have assumed it to be = $ 20.

Please correct me if i got the question wrong.

[Night reader]

look I have not assumed anything -- you are given three items // correct?
one is most expensive with discount 20% // correct?
and the other two less expensive with discount 10% // correct?
in st(1) the most expensive item is priced at $50 and the next expensive is priced at $20// correct?
from st(1) you can deduce that the next after next OR just one which is not most expensive could be at MOST $20 //correct?

hence you take A=50, B=C=20 // correct?

if you answer on every query "correct?" yes, please have your doubt resolved.

let us call the most exp. item A, the other two items B and C. We need to find if (0.8A+0.1B+0.1C)/(A+B+C)>0.85
st(1) A=50 and B=C=20 --> (40+18+18)/90<0.85 hence we can answer No on this question, Sufficient;
st(2) we have only C or B=15 BUT A can be anything, hence Not Sufficient

answer A

Henry purchased 3 items during a sale. He received 20% discount off regular price of the most expensive item and a 10% discount off regular price off each of the other 2 items. Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

1. Regular price for most expensive item: $50 & regular price of the next expensive item: $ 20.

2. Regular price for least expensive item: $ 15.

@ Night rider: To my understanding:
1. we need to check whether (0.2A+0.1B+0.1C)/(A+B+C) > 0.15.
2. St. 1 doesn't specifies regular price of least expensive item. You have assumed it to be = $ 20.

Please correct me if i got the question wrong.

[GMATGuruNY]

Henry purchase 3 items during a sale. He received a 20 percent discount off the regular price of the most
expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total
amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive
item was $20
(2) The regular price of the least expensive item was $15.

This is a weighted average question.
How can we combine a 20% discount with a 10% discount to yield a combined discount that is more than 15%?
If the price discounted at 20% equals the sum of the prices discounted at 10%, the resulting discount will be exactly 15%.
Thus, to yield a discount that is more than 15%, the price discounted at 20% must be greater than the sum of the prices discounted at 10%.

Rephrased, the question is asking:

Is the regular price of the most expensive item greater than the sum of the regular prices of the two cheaper items?

Statement 1: The regular price of the most expensive item was $50, and the regular price of the next most expensive
item was $20.
The sum of the prices of the 2 cheaper items cannot be greater than 20+20 = 40.
Thus, the $50 price of the most expensive item must be greater than the sum of the prices of the 2 cheaper items.
Sufficient.

Statement 2: The regular price of the least expensive item was $15.
No way to determine whether the price of the most expensive item is greater than the sum of the prices of the 2 cheaper items.
Insufficient.

The correct answer is A.

[gig92]

Henry purchased 3 items during a sale. He received 20% discount off regular price of the most expensive item and a 10% discount off regular price off each of the other 2 items. Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

1. Regular price for most expensive item: $50 & regular price of the next expensive item: $ 20.

2. Regular price for least expensive item: $ 15.

One more :

Stmnt 2: Regular price for least expensive item: $ 15

It doesn't give any idea about prices of other two items.It could be $1000 each or $2000 and $1000
So not Sufficient

Stmnt1:

We know from the discount of 20% on $50 = $10 and the discount of 10% on $20 = $2
So to answer: Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?
We can imagine that third item is of min value of $1 and max of $20 (cause the third item can have the same price as the second one). Now 10% discount of $1 to $20 will go to a max of $2. (ONE can easily imagine that the third item can also be of $20 as there are no restrictions on the price).

The question is: Was the total amount of discount greater than 15% of the sum of the regular prices of all the 3 items?

AND from the information in Stmnt 1, one can always find a unique answer.
Hence [spoiler]A[/spoiler]


NB: This is more of a "all in the head" approach!! Mitch has explained it better with the whole concept. However, sometimes one might not have the bells ringing to see that! So a faster idea in the head may tell you that Stmnt 1 gives enough information to anwser the question.