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If 1≥ y ≥0 and z ≤ -2 , then which of the following cannot b
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04 Jan 2021, 10:28
04 Jan 2021, 10:28
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Question Stats:
51% (01:31) correct
48% (01:23) wrong based on 45 sessions
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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
Kudos for the right answer and explanation
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 1≥ y ≥0 and z ≤ -2 , then which of the following cannot b
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05 Jan 2021, 09:39
05 Jan 2021, 09:39
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Carcass wrote:
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
Kudos for the right answer and explanation
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
Kudos for the right answer and explanation
The question asks "Then which of the following cannot be the value of y-z? "
So, if we 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,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 1≥ y ≥0 and z ≤ -2 , then which of the following cannot b
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05 Jan 2021, 09:40
05 Jan 2021, 09:40
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Carcass wrote:
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
Kudos for the right answer and explanation
A. 3
B. 2.75
C. 2.5
D. 2
E. 1.5
Kudos for the right answer and explanation
Here is an alternative approach:
Key concept: If two inequalities have the inequality symbols facing the same direction, then we can add the quantities
For example if we have the following:
x > 5
y > 7
Then we can add the inequalities to get: x + y > 5 + 7, which simplifies to be x + y > 12
Given: 1≥ y ≥ 0
We can take this, and just focus on the part that says y ≥ 0
Also given: z ≤ -2 [notice that the inequality symbol is facing the opposite direction as in the inequality above]
Multiply both sides of the inequality by -1 to get: -z ≥ 2 [ since we multiplied both sides of the inequality by a NEGATIVE value, we had to REVERSE the direction of the inequality symbol]
At this point we have:
y ≥ 0
-z ≥ 2
Since the inequality symbols are facing the same direction, we can add the two inequalities to get: y + (-z) ≥ 0 + 2
Simplify to get: y - z ≥ 2, which means y - z CANNOT equal 1.5
Answer: E
