Wednesday, September 29, 2010

Henry purchased 3 items during a sale. He received a 20 percent discount

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









From the question, Let I1 > I2, I3 where I1 is the most expensive item and I1 and I2 be the least expensive ones.

After, 20% off on I1 and 10% off on I2, I3, their prices reduce to .8I1, .9I2 and .9I3 respectively

Now converting the wording in the question to mathematical expression we need to find - >

.2I1 + .10I2 + .10I3 > .15(I1 + I2 +i3)

solving, we get I1 > I2 + I3 ( This is actually the question......we need to determine)

1) I1 =50 and I2 or I3 = 20, therefore if I2 or I3 =20 (the 2nd expensive one), the least expensive cannot be more than 20
so A answers the question...as YES

2) is insufficient as it only tells about one number.

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