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If -4<x<7 and -6<y<3, which of the following specifies all the possible values to xy?

-42<xy<21 -42<xy<24 -28<xy<18 -24<xy<21 -24<xy<24

Answer says its B....I dont get it....Help plz

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 straight forward 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.

Smallest value is -42 and greatest value is 24.
_________________

if -4<x<7 and -6 < y< 3, which of the following specifies the all possible values of xy? 1.-42<xy<21 2.-42<xy<28 3.-28<xy<18 4.-24<xy<21 5.-24<xy<24

I think the answer should be -42<xy<24, which is not one of the options.

To find the range of xy, we need to find the minimum this number can be. Since from the ranges given for both x and y cover both positive and negative numbers, the range of xy would also range from negative number to positive number.

To find the minimum, we have to find the maximum negative number possible => one of the x and y is positive and the other is negative and the magnitude of the product is maximum. This can be achieved when x~7 (x cannot be equal to 7 but can be as close as possible) and y~-6. This combination gives xy~-42

To find the maximum, we have to find a positive number =>either both x and y are negative OR both x and y are positive => we compare the products (-4*-6) and (7*3) =>maximum of these is 24.
_________________

So I got this wrong on the exam because I was pressed for time and was multiplying the 2 extreme positive and negative numbers and not finding my answer. Also I since it say x and y were LESS than, I looked at XY with the idea that x was -3 to 6 inclusive and Y was -5 to 2 inclusive.

Anyway, when I reviewed, I drew out the number line on each and could clearly see the right answer. My question is "is there a faster way to do this than diagramming it all out or is that generally the best/fastest approach?

So I got this wrong on the exam because I was pressed for time and was multiplying the 2 extreme positive and negative numbers and not finding my answer. Also I since it say x and y were LESS than, I looked at XY with the idea that x was -3 to 6 inclusive and Y was -5 to 2 inclusive.

Anyway, when I reviewed, I drew out the number line on each and could clearly see the right answer. My question is "is there a faster way to do this than diagramming it all out or is that generally the best/fastest approach?

Multiply all the possible combinations in such cases:

-4 * 7 = -28

-4 * -6 = 24 >>> Highest

-4 * 3 = -12

7 * -6 = -42 >>> Lowest

7 * 3 = 21

Answer = B
_________________

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Last edited by PareshGmat on 29 Oct 2014, 01:26, edited 2 times in total.

If -4<x<7 and -6<y<3, which of the following ... [#permalink]

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08 Nov 2014, 02:01

1

This post received KUDOS

alexa wrote:

Please help!!

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

Hi

This is min/max question. To find the range of xy, you need to find MAX xy and MIN xy

The easiest way is to test and see what max and min are. Max = -4*-6 = 24 Min = -6*7 = -42

Range: -42 < xy < 24

Hope it helps.
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]

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02 May 2016, 03:49

Minimum value of xy is the product in absolute terms of x and y that give a min value = 7 * (-6) = - 42 Maximum value of xy is the product in absolute terms of x and y that give a max value = (-4) * (-6) = 24 thus the range in which all possible values of xy can lie is -42< xy <24 correct option - B

what is the minimum and maximum product valud of XY we can get here Start multiplying the boundary values : -4*-6 = 24 7*3 = 21 -7 * -6 = -42 -4 * 3 = -12

out of these values take the minimum and maximum values ; -42< xy < 24

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

To determine the largest possible value of xy, we either multiply together the two smallest negative values or the two largest positive values. Since (-4)(-6) = 24 and (7)(3) = 21, and 24 > 21, we see that the largest possible product of x and y is less than 24.

To determine the smallest value of xy, we multiply the largest positive number by the smallest negative number. Thus, the product of x and y must be greater than (7)(-6) = -42. Thus:

-42 < xy < 24

Answer: B
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]

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21 Aug 2017, 03:10

possible values of x = -3, -2, -1, 0 ,1, 2, 3, 4, 5, 6 Possible values of y = -5 ,-4 ,-3 ,-2, -1, 0, 1, 2

values of xy ranges between -30 to 15

With this logic, I chose option A.

My question here is, why are we assuming xy could be 24 (-6).(-4) because it doesn't say inclusive? Why are we considering -6 and -4 as possible values of y and x respectively?