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If -4 < x < 7 and -6 < y < 3, which of the following specifies all the

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

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dc123 wrote:
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.
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If -4 < x < 7 and -6 < y < 3, which of the following [#permalink]

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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

Last edited by Bunuel on 26 Oct 2012, 04:14, edited 1 time in total.
Renamed the topic, edited the question and the answer choices.

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Re: inequalities-solvingproblems [#permalink]

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librian383 wrote:
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.
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Re: If -4 < x < 7 and -6 < y < 3, which of the following [#permalink]

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librian383 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


The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-4)*(-6)=24.

Therefore -42 < xy < 24.

Answer: B.

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IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]

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New post 28 Oct 2014, 17:06
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

OA
[Reveal] Spoiler:
B


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?

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IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]

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angelfire213 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

OA
[Reveal] Spoiler:
B


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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IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]

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Conventional method:

Draw the number line as below:

Attachment:
pro.png
pro.png [ 3.42 KiB | Viewed 9423 times ]

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

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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

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

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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.
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Re: If -4 < x <7 and -6 < y < 3, [#permalink]

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HarveyKlaus wrote:
Can anybody help me workout this problem?

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


Thank you.


This is a question that tests your observation of the following facts:

- x - = +
- x + = -
+ x - = -
+ x + = +

Thus, you need to now multiply the extreme values of x (-4,7) with extreme values of y (-6, 3) to get :

-4 x -6 = 24
-4 x 3= -12
7 x - 6= -42
7 x 3 = 21

Thus you see the minimum value = -42 and the maximum value = 24 . All other combinations of xy will give you values within these 2 values.

Hence the range of xy: -42 < xy < 24

B is the correct answer.

Hope this helps.

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

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New post 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

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

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New post 17 Aug 2016, 07:43
If -4 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?

Initially consider all posssible values of xy, we can decide the ranges later
xy=24, -12, -42, 21
now pick the extremes
-42<xy<21

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

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-4<x<7 : -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 : with boundary values
-6<y<3 : - 6, -5, -4, -3, -2, -1, 0, 1, 2, 3 : with boundary values

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

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

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New post 13 Mar 2017, 00:29
Minimum value of xy is -6*7=-42
Maximum value of xy is -6*-4=24
answer is B

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

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pike 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


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

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New post 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?

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Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the   [#permalink] 21 Aug 2017, 03:10
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