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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 5x + 11y < 0 and 4x + 10y < 0, then....
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27 Oct 2021, 05:51
27 Oct 2021, 05:51
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Question Stats:
48% (01:20) correct
51% (01:04) wrong based on 41 sessions
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5x + 11y < 0
4x + 10y < 0
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
4x + 10y < 0
Quantity A |
Quantity B |
x + y |
0 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 5x + 11y < 0 and 4x + 10y < 0, then....
[#permalink]
28 Oct 2021, 05:36
28 Oct 2021, 05:36
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GreenlightTestPrep wrote:
5x + 11y < 0
4x + 10y < 0
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
4x + 10y < 0
Quantity A |
Quantity B |
x + y |
0 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
I created this question to highlight an important property of inequalities.
If two inequalities are such that their inequality symbols are facing the same direction, then we can ADD those inequalities, but we can't subtract those inequalities
In other words, we can't subtract the bottom inequality from the top inequality to get the very convenient inequality x + y < 0
There are several values of x and y that satisfy BOTH given inequalities. Here are two such cases:
Case a: x = -1 and y = -1. In this case, x + y = (-1) + (-1) = -2, which means Quantity B is greater than Quantity A
Case b: x = 5 and y = -3. In this case, x + y = 5 + (-3) = 2, which means Quantity A is greater than Quantity B
Answer: D
General Discussion
Re: If 5x + 11y < 0 and 4x + 10y < 0, then....
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19 Jul 2024, 02:33
19 Jul 2024, 02:33
1
We can also explain this in another way
We cannot subtract because when we do so the <,> changes which makes it difficult to subtract.
But since the Question above has same < we may try and add resulting in not a meaningful equation.
Hence D should be the answer.
We cannot subtract because when we do so the <,> changes which makes it difficult to subtract.
But since the Question above has same < we may try and add resulting in not a meaningful equation.
Hence D should be the answer.
