Hi there,

Good question. "The total amount" must mean a dollar amount here -- and we can conclude that it must because we must be able to compare it to "15% of the sum of the regular prices of the three items," which itself will be a dollar amount.

Make sense?

IMO B

IMO C.
OA please?

If I set a: most expensive item and b, c: other two items

Total amount of the 3 discounts: 0.2a + 0.1(b+c)

Translating the question stem, we can say the following:

0.2a + 0.1(b+c) > 0.15(a+b+c)?

This simplifies to 0.05a > 0.05(b+c), or a > b + c?

Statement 1) The regular price of the most expensive item, a, was $50 and the next most expensive item was $20. $50 > $20 plus something less than or equal to $20. Therefore, a > b+c. Sufficient.

Statement 2) The regular price of the least expensive item was $15. This doesn't tell us anything about whether the most expensive item is greater than the sum of the other two items. It could be a=$20, b=$18, c=$15, and a < b+c, or a=$100,000, b=$15, c=$15 and a > b+c. Insufficient.

IMO A

IMO A

Let x = Regular Price of Most Expensive
y = Regular Price of middle Expensive
z = Regular Price of Least Expensive

=> x > y > z .. (a)

Total Discount = 0.2x + 0.1y + 0.1z
Now we need to find: 0.2x + 0.1y + 0.1z > 0.15(x+y+z) => 0.05x > 0.05(y+z) => x > y +z ..(b)

(i) x = 50 and y = 20
=> 50 > 20 + z .. from eqn. (b)
Now when y=20; and z<y => 0<z<20 .. from eqn. (a)
=> 50 > 20 + z is true as z<20
Hence Sufficient

(ii) z = 15
Not Sufficient

The correct answer is A

Q. Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item of 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.

This is a weighted average question. Very little math is needed.

The discount on the most expensive item is 20%.
The discount on the 2 least expensive items is 10%.
If the cost of the most expensive item is equal to the total cost of the 2 least expensive items, then the total discount will be the average of the 2 percentages: (20+10)/2 = 15%.
Thus, for the total discount to be greater than 15%, more weight needs to be given to the most expensive item. In other words, the cost of the most expensive item will need to be greater than the total cost of the 2 least expensive items.

Question rephrased:

Was the price of the most expensive item greater than the sum of the prices of the other 2 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 combined prices of the other 2 items cannot be greater than 20+20 = 40.
Thus, the $50 price of the most expensive item is greater than the sum of the prices of the other 2 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 other 2 items.
Insufficient.

The correct answer is A.

a three items are $50,$20 and $1-20 (range)

discount (1) = 10+2+0.1 = 12.1 > 15%(50+20+1)
discount (20)= 10+2+2 = 14 > 15%(50+20+20)=13.5

hence sufficient.

b no clue of the other two items. Not sufficient.

A it is.