The best strategy to answer such question is checking by option and rejecting the wrong ones by finding values outside the ramge that options represent
e.g.
-4<x<7 and -6<y<3
Option 1) -42<xy<21
For Minimum value of "xy" the sign of the product of xy must be negative with maximum absolute value
Minimum (xy) = Minimum of [(-4)*3 or 7*(-6)] = -42
Maximum (xy) = Maximum of [7*3 or (-4)*(-6)] = 24
But the option suggests that maximum of xy can't exceed 21 therefore option 1 is WRONG Option Therefore REJECTED
Option 2) -42<xy<24
For Minimum value of "xy" the sign of the product of xy must be negative with maximum absolute value
Minimum (xy) = Minimum of [(-4)*3 or 7*(-6)] = -42
Maximum (xy) = Maximum of [7*3 or (-4)*(-6)] = 24
The option suggests that maximum of xy can't exceed 24 and Minimum can't be lower than -42 which matches with our finding therefore option 2 is CORRECT Option Therefore [spoiler]ANSWER OPTION B[/spoiler]
How to approach these kind
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GMATinsight
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Let's examine the EXTREME VALUES Of x and y and see what happens.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
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
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GMATinsight
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With our working while checking option 1, We realized that
Minimum value of xy must be greater than -42 [Which rejected Option 3, 4, and 5 Immediately]
and
Maximum value of xy must be Lesser than 24 [Which rejects option 1]
So we end up getting [spoiler]option 2[/spoiler] as correct option
Minimum value of xy must be greater than -42 [Which rejected Option 3, 4, and 5 Immediately]
and
Maximum value of xy must be Lesser than 24 [Which rejects option 1]
So we end up getting [spoiler]option 2[/spoiler] as correct option
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GMATGuruNY
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Perform the given operation -- xy -- with EVERY COMBINATION OF ENDPOINTS.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
(-4)(-6) = 24.
(-4)(3) = -12.
(7)(-6) = -42.
(7)(3) = 21.
The smallest resulting product is -42, while the greatest resulting product is 24.
Thus:
-42 < xy < 24.
The correct answer is B.
Here's another:
Perform the given operation (y-x) with EVERY COMBINATION OF ENDPOINTS.If -4 < x < 7 and -6 < y < 3, what is the range of y - x?
-6 - (-4) = -2.
-6 - 7 = -13.
3 - (-4) = 1.
3 - 7 = -4.
The smallest resulting difference is -13, while the greatest resulting difference is 1.
Thus:
-13 < y-x < 1.
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Hi phanikpk,
This question is built around "Number Properties" - the "little rules" around which all math is built.
We're dealing with the following Number Properties in this question:
(Positive) x (Positive) = Positive
(Negative) x (Negative) = Positive
(Positive) x (Negative) = Negative
We're also dealing with the idea of minimums and maximums, so we have to think about the smallest and biggest possibilities given the restrictions in the question.
The big "quirk" in this question is that you actually have to multiply to the two most extreme NEGATIVE possibilities to find the largest POSITIVE product. More than anything else, this question is testing your thoroughness and attention to detail, since the math is just basic multiplication.
GMAT assassins aren't born, they're made,
Rich
This question is built around "Number Properties" - the "little rules" around which all math is built.
We're dealing with the following Number Properties in this question:
(Positive) x (Positive) = Positive
(Negative) x (Negative) = Positive
(Positive) x (Negative) = Negative
We're also dealing with the idea of minimums and maximums, so we have to think about the smallest and biggest possibilities given the restrictions in the question.
The big "quirk" in this question is that you actually have to multiply to the two most extreme NEGATIVE possibilities to find the largest POSITIVE product. More than anything else, this question is testing your thoroughness and attention to detail, since the math is just basic multiplication.
GMAT assassins aren't born, they're made,
Rich
