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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If -4 < x < 7 and -6 < y < 3, which of the following specifies all the
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17 Dec 2022, 10:44
17 Dec 2022, 10:44
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Question Stats:
35% (00:52) correct
64% (01:24) wrong based on 14 sessions
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If -4 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
A. -42 < xy < 21
B. -42 < xy < 24
C. -28 < xy < 18
D. -24 < xy < 21
E. -24 < xy < 24
A. -42 < xy < 21
B. -42 < xy < 24
C. -28 < xy < 18
D. -24 < xy < 21
E. -24 < xy < 24
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the
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19 Dec 2022, 09:28
19 Dec 2022, 09:28
Expert Reply
Minimum value of xy will be negative with highest absolute value. If x is very close to 7 and y is very close to -6, xy will be very close to -42. This is the maximum absolute value of xy with a negative sign. So it is the minimum value of xy.
Maximum value of xy will be positive with highest absolute value. When you multiply two positive numbers, you get a positive and when you multiply two negative numbers you get a positive number. The maximum absolute value will be obtained when x is very close to -4 and y is very close to -6. So xy will be very close to 24.
Answer B.
Else, take a straightforward approach. Just try all four extremity combinations:
-4<x<7
-6<y<3
If x is very close to 7 and y is very close to 3, xy will be very close to 21.
If x is very close to 7 and y is very close to -6, xy will be very close to -42.
If x is very close to -4 and y is very close to -6, xy will be very close to 24.
If x is very close to -4 and y is very close to 3, xy will be very close to -12.
The smallest value is -42 and the greatest value is 24.
Answer: B
Maximum value of xy will be positive with highest absolute value. When you multiply two positive numbers, you get a positive and when you multiply two negative numbers you get a positive number. The maximum absolute value will be obtained when x is very close to -4 and y is very close to -6. So xy will be very close to 24.
Answer B.
Else, take a straightforward approach. Just try all four extremity combinations:
-4<x<7
-6<y<3
If x is very close to 7 and y is very close to 3, xy will be very close to 21.
If x is very close to 7 and y is very close to -6, xy will be very close to -42.
If x is very close to -4 and y is very close to -6, xy will be very close to 24.
If x is very close to -4 and y is very close to 3, xy will be very close to -12.
The smallest value is -42 and the greatest value is 24.
Answer: B
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the
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02 Jan 2023, 13:10
02 Jan 2023, 13:10
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GeminiHeat wrote:
If -4 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
A. -42 < xy < 21
B. -42 < xy < 24
C. -28 < xy < 18
D. -24 < xy < 21
E. -24 < xy < 24
A. -42 < xy < 21
B. -42 < xy < 24
C. -28 < xy < 18
D. -24 < xy < 21
E. -24 < xy < 24
Let's examine the EXTREME VALUES Of x and y and see what happens.
If we want to MINIMIZE the value of xy, we need to examine what happens when 1 EXTREME value is positive and 1 EXTREME value is negative.
case a: x = -4 and y = 3, in which case xy = -12
case b: x = 7 and y = -6, in which case xy = -42
Great, so xy is MINIMIZED when x = 7 and y = -6
Of course, we're told that x < 7 and y > -6, but that's fine. Basically, this means that xy > -42
At this point, we know that the correct answer must be either A or B.
Next, if we want to MAXIMIZE the value of xy, we need to examine what happens when both EXTREME values are positive or both are negative.
case c: x = -4 and y = -6, in which case xy = 24
case d: x = 7 and y = 3, in which case xy = 21
Great, so xy is MAXIMIZED when x = -4 and y = -6
Of course, we're told that x > -4 and y > -6, but that's fine. Basically, this means that xy < 24
So, as you can see, -42 < xy < 24
Answer: B
Cheers,
Brent
