The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV set, which of the following represents the price of the television set after the two successive discounts?
$$A.\ P(1-0.03x+0.02x^2)$$
$$B.\ P(1-0.03x+0.0002x^2)$$
$$C.\ P(1-0.03x+0.002x^2)$$
$$D.\ P(1-2x^2)$$
$$E.\ P(1-3x+2x^2)$$
The OA is B
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The original price of a certain TV set is discounted by x
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Hi All,
We're told that the original price of a certain TV set is discounted by X percent, the reduced price is then discounted by 2X percent and P is the original price of the TV set. We're asked which of the following represents the price of the television set after the two successive discounts. This question can be solved in a couple of different ways, including by TESTing VALUES. In addition, the design of the answer choices offers a number of different logic shortcuts that we can use to avoid a lot of redundant math.
Let's TEST P = 100 and X = 10....
IF the original price of the TV is $100, then...
a 10% discount makes the reduced price = $100 - (.1)($100) = $100 - $10 = $90 and...
a 20% discount of the reduced price = $90 - (.2)($90) = $90 - $18 = $72
Looking at the first 3 answers, we can clearly see a 'decimal shift', so we're not dealing with completely unique calculations. We can quickly eliminate Answers D and E with some math and logic....
Answer D: (100)(1 - 200) = a negative
Answer E: (100)(171) = a big number
Answers A through C all have similar pieces, but a decimal shift on the last 'piece' of the calculation will determine which of the three is correct. We're looking for an answer that equals $72, so....
(100)(this number) = $72
The missing number in the parentheses MUST equal 0.72
(1 - .3) = .7
so we need to add another .02 to the value in that parentheses. Since X^2 = (10^2) = 100, that would shift the decimal '2 spots to the left', which would make Answer A and Answer C TOO BIG. That leaves the correct answer....
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that the original price of a certain TV set is discounted by X percent, the reduced price is then discounted by 2X percent and P is the original price of the TV set. We're asked which of the following represents the price of the television set after the two successive discounts. This question can be solved in a couple of different ways, including by TESTing VALUES. In addition, the design of the answer choices offers a number of different logic shortcuts that we can use to avoid a lot of redundant math.
Let's TEST P = 100 and X = 10....
IF the original price of the TV is $100, then...
a 10% discount makes the reduced price = $100 - (.1)($100) = $100 - $10 = $90 and...
a 20% discount of the reduced price = $90 - (.2)($90) = $90 - $18 = $72
Looking at the first 3 answers, we can clearly see a 'decimal shift', so we're not dealing with completely unique calculations. We can quickly eliminate Answers D and E with some math and logic....
Answer D: (100)(1 - 200) = a negative
Answer E: (100)(171) = a big number
Answers A through C all have similar pieces, but a decimal shift on the last 'piece' of the calculation will determine which of the three is correct. We're looking for an answer that equals $72, so....
(100)(this number) = $72
The missing number in the parentheses MUST equal 0.72
(1 - .3) = .7
so we need to add another .02 to the value in that parentheses. Since X^2 = (10^2) = 100, that would shift the decimal '2 spots to the left', which would make Answer A and Answer C TOO BIG. That leaves the correct answer....
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
