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If 1≥ y ≥0 and z ≤ -2 , then which of the following...

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If 1≥ y ≥0 and z ≤ -2 , then which of the following...

by AAPL » Tue Jan 30, 2018 7:04 am
$$If\ 1\ge y\ge0\ and\ z\le-2$$
Then which of the following cannot be the value of y-z?

A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5

The OA is E.

I don't have clear this PS question but I think that I can solve it of the following way,

I can take the smallest value of y and the greatest value of z, then

y=0 and z=-2, y - z = 0 - (-2) = 2, this is the samllest value that can result of y - z, right? That's mean that 1.5 cannot be the value of y - z. I'm not sure. I appreciate if any expert explain it for me. Thank you so much.
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by DavidG@VeritasPrep » Tue Jan 30, 2018 8:52 am
AAPL wrote:$$If\ 1\ge y\ge0\ and\ z\le-2$$
Then which of the following cannot be the value of y-z?

A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5

The OA is E.

I don't have clear this PS question but I think that I can solve it of the following way,

I can take the smallest value of y and the greatest value of z, then

y=0 and z=-2, y - z = 0 - (-2) = 2, this is the samllest value that can result of y - z, right? That's mean that 1.5 cannot be the value of y - z. I'm not sure. I appreciate if any expert explain it for me. Thank you so much.
Sure, you can think of it that way. Algebraically, you can think of it like this. We know y is non-negative, or y >=0. If we multiply the second inequality by (-1), the inequality sign will flip, giving us -z >= 2.

Now add them:

y >= 0
-z >=2
_______
y -z >= 2.

So clearly, y-z could not be any value less than 2.
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by Brent@GMATPrepNow » Tue Jan 30, 2018 9:20 am
AAPL wrote:$$If\ 1\ge y\ge0\ and\ z\le-2$$
Then which of the following cannot be the value of y-z?

A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
My approach would have been the same as David's.

That said, here's another approach:

The question asks "Then which of the following cannot be the value of y-z? "
So, if we can find answer choice that CAN BE a value of y-z, we can ELIMINATE it.

A. 3. If y = 1 and z = -2, then y-z = 3. ELIMINATE A

B. 2.75. If y = 0.75 and z = -2, then y-z = 2.75. ELIMINATE B

C. 2.5. If y = 0.5 and z = -2, then y-z = 2.5. ELIMINATE C

D. 2 . If y = 0 and z = -2, then y-z = 2. ELIMINATE D

E. 1.5 Must be the correct answer

Answer: E

Cheers,
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by Scott@TargetTestPrep » Fri Feb 02, 2018 12:11 pm
AAPL wrote:$$If\ 1\ge y\ge0\ and\ z\le-2$$
Then which of the following cannot be the value of y-z?

A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
Since y is a nonnegative quantity between 0 and 1, when we subtract z, which is a negative quantity less than or equal to 2, from y, we are actually adding a positive quantity that is greater than or equal to 2 to y. Thus, y - z will be at least 2 and there is no way for y - z = 1.5.

Answer: E

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