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If x and y are numbers on the number line above, which of the followin
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16 Dec 2021, 03:10
16 Dec 2021, 03:10
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Note: Figure not drawn to scale
If x and y are numbers on the number line above, which of the following statements must be true?
I. |x+y| < y
II. x + y < 0
III. xy < 0
A. I only
B. III only
C. I and II
D. I and III
E. II and III
Kudos for a correct solution.
If x and y are numbers on the number line above, which of the following statements must be true?
I. |x+y| < y
II. x + y < 0
III. xy < 0
A. I only
B. III only
C. I and II
D. I and III
E. II and III
Kudos for a correct solution.
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x and y are numbers on the number line above, which of the followin
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16 Dec 2021, 04:40
16 Dec 2021, 04:40
Carcass wrote:
Note: Figure not drawn to scale
If x and y are numbers on the number line above, which of the following statements must be true?
I. |x+y| < y
II. x + y < 0
III. xy < 0
A. I only
B. III only
C. I and II
D. I and III
E. II and III
Kudos for a correct solution.
If x and y are numbers on the number line above, which of the following statements must be true?
I. |x+y| < y
II. x + y < 0
III. xy < 0
A. I only
B. III only
C. I and II
D. I and III
E. II and III
Kudos for a correct solution.
I. |x+y| < y
Statement I is not necessarily true.
For example, if x = -5 and y = 1, the inequality |x+y| < y becomes: |(-5) + 1| < 1, which simplifies to be: 4 < 1, which is not true.
This means we can eliminate answer choices A, D and D since they state that statement I is true.
II. x + y < 0
Statement II is not necessarily true.
For example, if x = -1 and y = 2, the inequality x + y < 0 becomes: (-1) + 2 < 0, which simplifies to be: 1 < 0, which is not true.
This means we can eliminate answer choice E since it states that statement II is true.
By the process of elimination, the correct answer is B
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If x and y are numbers on the number line above, which of the followin
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30 Dec 2021, 20:55
30 Dec 2021, 20:55
1
It is given to us that x is negative and y is positive but we do not know the actual values of x and y
Since it is a must be true question so let's take values of x and y to prove the option choices wrong
I. |x+y| < y Now on LHS (Left Hand Side) we have |x+y| and RHS (Right Hand Side) we have y
So, we need to get a value of |x+y| which is bigger or equal to y in order to prove this wrong
Lets take a small negative value of x and small positive value of y
x = -100, y = 10
|x+y| = |-100+10| = |-90| = 90 > 10 (Watch this video to learn the Basics of Absolute Value)
=> |x+y| < y MUST not be true always
II. x + y < 0
x = -10, y = 100
x+y = 90 > 0
=> x + y < 0 MUST not be true always
III. xy < 0
x = -10, y = 100
or x = -100, y = 10
In any case xy < 0 (Watch this video to learn the Basics of Inequalities)
As product of a negative number and a positive number < 0
=> xy < 0 is Always True
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Since it is a must be true question so let's take values of x and y to prove the option choices wrong
I. |x+y| < y Now on LHS (Left Hand Side) we have |x+y| and RHS (Right Hand Side) we have y
So, we need to get a value of |x+y| which is bigger or equal to y in order to prove this wrong
Lets take a small negative value of x and small positive value of y
x = -100, y = 10
|x+y| = |-100+10| = |-90| = 90 > 10 (Watch this video to learn the Basics of Absolute Value)
=> |x+y| < y MUST not be true always
II. x + y < 0
x = -10, y = 100
x+y = 90 > 0
=> x + y < 0 MUST not be true always
III. xy < 0
x = -10, y = 100
or x = -100, y = 10
In any case xy < 0 (Watch this video to learn the Basics of Inequalities)
As product of a negative number and a positive number < 0
=> xy < 0 is Always True
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
