Last visit was: 21 Jul 2024, 22:01 It is currently 21 Jul 2024, 22:01
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Current Student
Joined: 08 Jan 2009
Posts: 245
Own Kudos [?]: 449 [116]
Given Kudos: 7
GMAT 1: 770 Q50 V46
Tutor
Joined: 16 Oct 2010
Posts: 15127
Own Kudos [?]: 66769 [45]
Given Kudos: 436
Location: Pune, India
Math Expert
Joined: 02 Sep 2009
Posts: 94441
Own Kudos [?]: 642845 [14]
Given Kudos: 86716
General Discussion
Tutor
Joined: 22 Oct 2012
Status:Private GMAT Tutor
Posts: 366
Own Kudos [?]: 2447 [6]
Given Kudos: 138
Location: India
Concentration: Economics, Finance
Schools: IIMA (A)
GMAT Focus 1:
735 Q90 V85 DI85
GMAT Focus 2:
735 Q90 V85 DI85
GMAT 1: 780 Q51 V47
GRE 1: Q170 V168
3
Kudos
3
Bookmarks
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.
Director
Joined: 26 Aug 2014
Posts: 823
Own Kudos [?]: 201 [1]
Given Kudos: 98
Concentration: Marketing
GPA: 3.4
IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
1
Kudos
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

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?
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7300 [3]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
2
Kudos
1
Bookmarks
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

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

Originally posted by PareshGmat on 29 Oct 2014, 01:23.
Last edited by PareshGmat on 29 Oct 2014, 01:26, edited 2 times in total.
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7300 [4]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
IF -4 < X < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
4
Kudos
Conventional method:

Draw the number line as below:

Attachment:

pro.png [ 3.42 KiB | Viewed 45994 times ]
Retired Moderator
Joined: 16 Jun 2012
Posts: 869
Own Kudos [?]: 8617 [1]
Given Kudos: 123
Location: United States
If -4<x<7 and -6<y<3, which of the following ... [#permalink]
1
Kudos
alexa 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

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.
SVP
Joined: 20 Mar 2014
Posts: 2359
Own Kudos [?]: 3650 [4]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Re: If -4 < x <7 and -6 < y < 3, [#permalink]
4
Kudos
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

Hope this helps.
Senior Manager
Joined: 24 Nov 2015
Posts: 405
Own Kudos [?]: 125 [0]
Given Kudos: 231
Location: United States (LA)
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
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
Intern
Joined: 19 Oct 2014
Posts: 29
Own Kudos [?]: 56 [0]
Given Kudos: 41
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 600 Q48 V25
GMAT 2: 670 Q49 V31
GPA: 3.26
WE:Operations (Manufacturing)
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
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
Intern
Joined: 28 Jul 2011
Posts: 22
Own Kudos [?]: 50 [1]
Given Kudos: 5
Location: United Kingdom
WE:Corporate Finance (Energy and Utilities)
Re: If -4<x<7 and -6<y<3, which of the following specifies all the possib [#permalink]
1
Kudos
-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
Manager
Joined: 25 Jan 2016
Status:active
Posts: 90
Own Kudos [?]: 75 [0]
Given Kudos: 12
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE:Web Development (Computer Software)
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Minimum value of xy is -6*7=-42
Maximum value of xy is -6*-4=24
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6610 [4]
Given Kudos: 1646
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
4
Kudos
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

Manager
Joined: 20 Jan 2016
Posts: 146
Own Kudos [?]: 128 [2]
Given Kudos: 64
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
2
Kudos
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?
Senior SC Moderator
Joined: 22 May 2016
Posts: 5327
Own Kudos [?]: 35772 [0]
Given Kudos: 9464
If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Fedemaravilla 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 fastest and most accurate method is often just to list the possibilities for xy.

Multiply each value of x's range (low end, high end), by each value of y's range (low and high).

-4 < x < 7
-6 < y < 3

(x)(y)?

(-4)(-6) = 24
(-4)(3) = -12
(7)(-6) = -42
(7)(3) = 21

The smallest is -42
The greatest is 24

-42 < xy < 24

Whatever the case, to maximize xy (to find the greatest number, the upper end of the inequality for xy):
-- find one end value of x which, when multiplied by one end value of y, is the greatest number. Do not assume that rightmost values for x and y will produce the greatest product. That is trap Answer A here. 24 > 21

In this case, for example: the greatest product of (x*y) consists of multiplying x's and y's SMALLEST numbers (i.e., the numbers -4 and -6, which mark the low end of their respective ranges).

To minimize, to find the smallest number xy can be:
-- use one of the end numbers from x's range which, when multiplied by an end number from y's range, yields the smallest number
-- in this case, the smallest number is -42, where -42 is the "most negative" number, the one farthest to the left of zero in the number line.
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5797 [0]
Given Kudos: 238
WE:General Management (Education)
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Always check for the 4 boundary conditions.
See the procedure in the Sketch.
Attachments

WhatsApp Image 2018-03-15 at 22.04.54.jpeg [ 86.98 KiB | Viewed 34227 times ]

GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30846 [2]
Given Kudos: 799
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
1
Kudos
1
Bookmarks
Top Contributor
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

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

Cheers,
Brent
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 959
Own Kudos [?]: 5019 [0]
Given Kudos: 690
Concentration: Accounting
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Top Contributor
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

The multiplications of xy and will be
24,21,-42,-12
So, the range will be of all values
-42 < xy < 24

Non-Human User
Joined: 09 Sep 2013
Posts: 34041
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If -4 < x < 7 and -6 < y < 3, which of the following specifies all the [#permalink]
Moderator:
Math Expert
94441 posts