Harry bought 3 items and got 20% discount off regular price of most expensive item and 10% discount off regular price of the other two. Was the total amount of the 3 discounts greater than 15% of the sum of the regular prices of the 3 items?
(1) Regular price of most expensive item was $50 and regular price of next most expensive was $20
(2) Regular price of least expensive item was $15
Solution:-
Lets first look at what the question is asking:- Harry bought 3 items. Harry got a discount of 20% on the most expensive item and 10% discount on the other two.
The question is asking whether the discount Harry received is greater than 15% of the sum of the prices of all 3 items. While we can solve this question algebraically lets try and avoid algebra. We can use the concepts in weighted average to solve this question without making any calculations.
Statement 1 - The most expensive item is 50$ and the second most expensive item is 20$, therefore we can conclude that the value of the third item cannot be greater than 20$. To solve this question using the concepts of weighted average we will club the price of second and third items which cannot be greater than 40$ since the discount on the second and third items are of equal value. We know that the discount on the 50$ item is 20% and 10% on the 40$ items. The total discount on all the three items would have been equal to 15% if the price of the most expensive item and the other two items would have been equal but since the most expensive item is of a greater value (50$) and is discounted by a greater percentage of 20% the weighted average discount would be greater than 15%. Therefore statement 1 is sufficient
Statement 2 - We are only given the price of the least expensive item and therefore there is insufficient information to solve the question. Statement 2 is insufficient.
Answer - A
Tip - One can avoid algebra by simply using LOGIC to solve such questions. Algebraic equations can be time consuming and not the most efficient way to solve such questions.
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