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12 Jan 2017, 06:58
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If 1≥ y ≥0 and z ≤ -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
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
12 Jan 2017, 07:11
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Bunuel
If 1≥ y ≥0 and z ≤ -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
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
The lesser our z, the larger the value of our expression y - z.
\((y - z)_{min} = y_{min} - z_{max} = 0 - (-2) = 2\). Hence 2 is the min value that our difference y - z can take.
Answer E.
16 Jan 2017, 18:05
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Bunuel
If 1≥ y ≥0 and z ≤ -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
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
We are given that 1 ≥ y ≥ 0 and z ≤ -2, and we need to determine which of the answer choices CANNOT be equal to y - z.
A) 3
If y = 1 and z = -2, then y - z = 1 - (-2) = 3.
B) 2.75
If y = 0.75 and z = -2, then y - z = 0.75 - (-2) = 2.75.
C) 2.5
If y = 0.5 and z = -2, then y - z = 0.5 - (-2) = 2.5.
D) 2
If y = 0 and z = -2, then y - z = 0 - (-2) = 2.
E) We see that there is no way for y - z to equal 1.5. Recall that y is a number between 0 and 1 (inclusive), and z is a number less than or equal to -2. Therefore, y minus z (i.e., y minus -2) is equivalent to y plus 2. When a number between 0 and 1 (inclusive) is added to 2, the sum will be at least 2.
Alternate Solution:
Since z ≤ -2, multiplying each side by -1 (and reversing the inequality sign), we have -z ≥ 2. Also, y ≥ 0; adding the two inequalities together, we have y - z ≥ 2. Among the choices, only 1.5 does not satisfy this inequality.
Answer: E
