It is currently 24 Apr 2019, 12:33
My Tests

Close

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
Your Progress

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 | x + 1 | <= 5 and | y — 1| <= 5, what is the least

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 6241
Followers: 100

Kudos [?]: 1202 [1] , given: 5749

CAT Tests
If | x + 1 | <= 5 and | y — 1| <= 5, what is the least [#permalink] New post 05 Mar 2017, 13:03
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

63% (01:00) correct 36% (02:03) wrong based on 19 sessions


If \(| x + 1 | \leq 5\) and \(|y — 1| \leq 5\), what is the least possible value of the product \(xy\) ?

Enter your value

[Reveal] Spoiler:
\(-36\)

_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
GRE Prep Club Legend
GRE Prep Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 107

Kudos [?]: 1833 [1] , given: 397

Re: If | x + 1 | <= 5 and | y — 1| <= 5, what is the least [#permalink] New post 11 Mar 2017, 21:07
1
This post received
KUDOS
Expert's post
Explanation

Find \(| x + 1 | \leq 5\):

\(-5 \leq x + 1 \leq 5\) or \(-6 \leq x \leq 4\)

Now calculate \(| y - 1 | \leq 5\):

\(-5 \leq y - 1 \leq 5\) or \(-4 \leq y \leq 6\)

To find the least possible value of the product xy, put numbers from the extremes of x and y. Keep in mind that two positive numbers and two negative numbers will result in a positive number.

Since we want the least value, we are looking for a negative number and must use one positive and one negative value to obtain it.

If x = 4 and y = –4, then xy = –16
If x = –6 and y = 6, then xy = –36

The least possible value is –36.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1675
Followers: 57

Kudos [?]: 1592 [1] , given: 8

CAT Tests
Re: If | x + 1 | <= 5 and | y — 1| <= 5, what is the least [#permalink] New post 08 Mar 2019, 11:13
1
This post received
KUDOS
Expert's post
Carcass wrote:


If \(| x + 1 | \leq 5\) and \(|y — 1| \leq 5\), what is the least possible value of the product \(xy\) ?

Enter your value

[Reveal] Spoiler:
\(-36\)


When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive


GIVEN: |x + 1| ≤ 5
From Rule #1 above, we can write: -5 ≤ x + 1 ≤ 5
Subtract 1 from all sides to get: -6 ≤ x ≤ 4
So, x can be ANY value from -6 to 4 INCLUSIVE


GIVEN: |y - 1| ≤ 5
From Rule #1 above, we can write: -5 ≤ y - 1 ≤ 5
Add 1 to all sides to get: -4 ≤ y ≤ 6
So, y can be ANY value from -4 to 6 INCLUSIVE

What is the least possible value of the product xy?
The LEAST product will be NEGATIVE
So, one value (x or y) must be POSITIVE, and the other value must be NEGATIVE
The LEAST product occurs when x = -6 and y = 6
So, the least product = (-6)(6) = -36

Answer: -36

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

Re: If | x + 1 | <= 5 and | y — 1| <= 5, what is the least   [#permalink] 08 Mar 2019, 11:13
Display posts from previous: Sort by

If | x + 1 | <= 5 and | y — 1| <= 5, what is the least

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.