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22 Mar 2025, 00:50
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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27 Mar 2025, 00:17
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OE
Replace a, b, c, and d with easy-to-use numbers that satisfy the condition a < b < c < d: for example, a = 1, b = 3, c = 6, d = 10. (See the guidelines to learn why 1, 2, 3, 4 is not a good choice.) Evaluate the two quantities: ab = (1)(3) = 3, and cd = (6)(10) = 60.
So in this case, Quantity B is greater.
Does that mean that B is the correct answer? Not necessarily. Quantity B is greater this time, but will it be greater every single time, no matter what?
What it does mean is that neither A nor C could possibly be the correct answer: Quantity A can’t be greater every single time, no matter what because it isn’t greater this time; and the quantities aren’t equal every single time, no matter what because they aren’t equal this time.
So in the few seconds that it took you to plug in 1, 3, 6, and 10 for a, b, c, and d, you were able to eliminate two of the four choices. You now know that the correct answer is either B or D, and if you could do nothing else, you would now guess with a 50 percent chance of being correct.
But, of course, you will do something else. You will try some other numbers. But which numbers? Since the first numbers you chose were positive, try some negative numbers this time.
Let a = –5, b = –3, c = –2, and d = –1.
Evaluate: ab = (–5)(–3) = 15 and cd = (–2)(–1) = 2.
So in this case, Quantity A is greater.
Quantity B is not greater all the time. B is not the correct answer.
The correct answer is D: It is impossible to determine which quantity is greater.
Answer: D
Replace a, b, c, and d with easy-to-use numbers that satisfy the condition a < b < c < d: for example, a = 1, b = 3, c = 6, d = 10. (See the guidelines to learn why 1, 2, 3, 4 is not a good choice.) Evaluate the two quantities: ab = (1)(3) = 3, and cd = (6)(10) = 60.
So in this case, Quantity B is greater.
Does that mean that B is the correct answer? Not necessarily. Quantity B is greater this time, but will it be greater every single time, no matter what?
What it does mean is that neither A nor C could possibly be the correct answer: Quantity A can’t be greater every single time, no matter what because it isn’t greater this time; and the quantities aren’t equal every single time, no matter what because they aren’t equal this time.
So in the few seconds that it took you to plug in 1, 3, 6, and 10 for a, b, c, and d, you were able to eliminate two of the four choices. You now know that the correct answer is either B or D, and if you could do nothing else, you would now guess with a 50 percent chance of being correct.
But, of course, you will do something else. You will try some other numbers. But which numbers? Since the first numbers you chose were positive, try some negative numbers this time.
Let a = –5, b = –3, c = –2, and d = –1.
Evaluate: ab = (–5)(–3) = 15 and cd = (–2)(–1) = 2.
So in this case, Quantity A is greater.
Quantity B is not greater all the time. B is not the correct answer.
The correct answer is D: It is impossible to determine which quantity is greater.
Answer: D
