Hi All,
Here is a similarly 'themed' question:
Henry purchased 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. What was the total amount of the 3 discounts?
(1) The average (arithmetic mean) of the regular prices of the 3 items was $30.
(2) The regular price of the most expensive of the 3 items was $50.
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There are a couple of different ways to approach this question. Regardless of what method you choose, you will have to stay organized, take plenty of notes and do enough work to prove your answer. There's a great opportunity in this question to TEST VALUES and do a little arithmetic.
Here, we know that there are 3 items purchased. We know that the MOST EXPENSIVE ITEM got a 20% discount and the other 2 items got a 10% discount. We're asked for the TOTAL amount of the discounts.
Fact 1: The AVERAGE of the prices of the 3 items was $30.
If the 3 items cost: $40, $30 and $20, then the TOTAL discount = $8 + $3 + $2 = $13
If the 3 items cost: $50, $30 and $10, then the TOTAL discount = $10 + $3 + $1 = $14
Fact 1 is INSUFFICIENT
Fact 2: The most expensive item was $50
This tells us that the discount for that 1 item was (.2)($50) = $10, but we don't know the cost of the other 2 items, so we don't know what the discounts will be.
Fact 2 is INSUFFICIENT
Combining Facts though, we know...
1) The average of the 3 items is $30, so the SUM of the 3 items = $90
2) The most expensive item is $50, so the OTHER 2 items sum up to $40
So, we know that that $50 item gets the 20% discount and the other two items (that add up to $40) each get 10%. The discount MUST be $50(20%) + $40(10%) = $10 + $4 = $14.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
Henry purchase 3 items during a sale
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Last edited by [email protected] on Thu Aug 27, 2015 12:14 pm, edited 1 time in total.
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three products as X, Y , Z
To prove
.90 X + .90 Y + .80 Z > .85 ( X + Y + Z)
90 X -85 X + 90 Y -85Y > 85 Z - 80Z
5X + 5Y >5Z
X +Y . Z
X > Z -Y
Statement A
Z = 50
Y = 20
and X is somewhere less than Y i.e. < 20
X > 50 - 20
X > 30 which is clearly NO since X must be less than 20
so Statement I is sufficient.
No much Information in Statement II so INSUFFICIENT.
Answer A
To prove
.90 X + .90 Y + .80 Z > .85 ( X + Y + Z)
90 X -85 X + 90 Y -85Y > 85 Z - 80Z
5X + 5Y >5Z
X +Y . Z
X > Z -Y
Statement A
Z = 50
Y = 20
and X is somewhere less than Y i.e. < 20
X > 50 - 20
X > 30 which is clearly NO since X must be less than 20
so Statement I is sufficient.
No much Information in Statement II so INSUFFICIENT.
Answer A
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.
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 lease expensive item was $15.
==> from the original condition, the price a<b<=c(b and c can be same). Then 0.2c+0.1(a+b)>0.15(a+b+c)?, and 02c+0.1a+0.1b>0.15a+0.15b+0.15c?. Therefore, 0.05c>0.05a+0.05b? and also c>a+b?. (Like this, using variable approach method gives us 30% chance of finding the answer just by using the original condition)
In case of 1), c=50 and b=c=20, thus 50>20+20. Therefore it is sufficient
In case of 2), since we do not know much about b,c it is not sufficient.
Therefore the answer is A.
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
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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 lease expensive item was $15.
==> from the original condition, the price a<b<=c(b and c can be same). Then 0.2c+0.1(a+b)>0.15(a+b+c)?, and 02c+0.1a+0.1b>0.15a+0.15b+0.15c?. Therefore, 0.05c>0.05a+0.05b? and also c>a+b?. (Like this, using variable approach method gives us 30% chance of finding the answer just by using the original condition)
In case of 1), c=50 and b=c=20, thus 50>20+20. Therefore it is sufficient
In case of 2), since we do not know much about b,c it is not sufficient.
Therefore the answer is A.
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
l Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8