Bunuel wrote:
docabuzar wrote:
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. Was the total discount of these three items 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
Let the regular prices be a, b, and c, so that a > b > c.
Basically the questions: is \(0.2a+0.1b+0.1c>0.15(a+b+c)\)? --> is \(a>b+c\)?
(1) The regular price of the most expensive item was $50 and the regular price of the next most expensive item was $20 --> \(a=50\), \(b=20\), \(c\leq{20}\) (as the second most expensive item was $20 then the least expansive item, the third one, must be less than or equal to 20). So the question becomes: is \(50>20+c\) --> is \(c<30\)? As we got that \(c\leq{20}\), hence the above is always true. Sufficient.
(2) The regular price of the least expensive item was $15. Clearly insufficient.
Answer: A.
Hi Bunuel. First of all, thanks for the tremendous help that you have been providing to us all.
Coming back to the question, I don't think the answer is A ( it should be C ). Algebraically, what you have said is right. However, if we take specific numerical values, the answer ranges from "Yes" ( for c= 20 ) to "No" ( for c = 10 ). Also, inequality provides us with a range of values. For some, the answer is ">15%" and for some that sanwer is "<15%".
Kindly explain.
If a = 50, b = 20 and c = 20, then \(0.2a+0.1b+0.1c=14\) and \(0.15(a+b+c)=13.5\)
Both sets (as well as all other possible sets for the first statement) give an YES answer.