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A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Quantity B is equal to 3/2 that is greater than 1. Quantity A is 1 minus a number greater than 0, so it must be less than 1. Thus, quantity B is greater.

Are you sure there are no typos in the text of the question? I mean the answer must be B if the quantities are the ones reported. If t is between 0 and 1, it must be positive. Then, if we subtract 1 from both quantities we get a comparison between -t and 1/2. Now, -t is -(something positive) so it is negative, while 1/2 is positive. Answer is still B

Written in this way we can sum t, subtract 1/2 and divide by 2 on both sides in order to get a comparison between 1/4 and t. Then, given that t is between 0 and 1 it may be greater than 1/4 (e.g. if equal to 1/2) but also smaller (if equal to 1/6). Answer D

A great way to approach this question is by subtracting one quantity from another. That way, you can compare the value 0 to an expression, and it'll be easier to see which quantity is greater. So let's start by subtracting Quantity A from both quantities. That would give us:

Now we can plug in the extreme values for t. Since t can go all the way down to just above 0, Quantity B in this case could go all the way down to just above -1/2. This is less than Quantity A, so we can eliminate B and C as the correct answers. Next, since t can go all the way up to just below 1, Quantity B in this case could go all the way up to just below 3/2. Since this is greater than Quantity A, we can eliminate A as the correct answer. Thus, the only answer remaining is D.
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We can solve this question using matching operations

Given: Quantity A: 1 - t Quantity B: 1/2 + t

Add t to both quantities to get: Quantity A: 1 Quantity B: 1/2 + 2t

Subtract 1/2 from both quantities to get: Quantity A: 1/2 Quantity B: 2t

Divide both quantities by 2 to get: Quantity A: 1/4 Quantity B: t

We're told that 0 < t < 1

So, for example, t COULD equal 1/4, in which case the quantities are EQUAL t COULD also equal 1/2, in which case the Quantity B is greater t COULD also equal 1/10, in which case the Quantity A is greater

Answer: D

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