Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 1308:30 AM PDT
-09:30 AM PDT
In Episode 4 of our GMAT Ninja CR series, we tackle the most intimidating CR question type: Boldface & "Legalese" questions. If you've ever stared at an answer choice that reads, "The first is a consideration introduced to counter a position that...- May 12
07:30 AM PDT
-08:30 AM PDT
Join the Live and learn more about Picking the Right Schools 
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.- May 14
08:30 AM PDT
-09:30 AM PDT
Most GMAT test-takers are intimidated by the hardest GMAT Verbal questions. In this session, Target Test Prep GMAT instructor Erika Tyler-John, a 100th percentile GMAT scorer, will show you how top scorers break down challenging Verbal questions.. - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
05 Jul 2022, 07:09
Kudos
Bookmarks
Hello,
if we add these 2 eqns--> y - 3x>= 2 and -y + 4x >2 what should be the sign of the resultant expression? x>=4 or x>4?
Is there any rule around the same? Also, please let me know the same if a similar cases arises for multiplication.
I am assuming this issue wont be a problem for subtraction or division since there we take the sign of the first term as is irrespective of = sign (please correct me if I am wrong)
Bunuel, IanStewart, KarishmaB
if we add these 2 eqns--> y - 3x>= 2 and -y + 4x >2 what should be the sign of the resultant expression? x>=4 or x>4?
Is there any rule around the same? Also, please let me know the same if a similar cases arises for multiplication.
I am assuming this issue wont be a problem for subtraction or division since there we take the sign of the first term as is irrespective of = sign (please correct me if I am wrong)
Bunuel, IanStewart, KarishmaB
05 Jul 2022, 11:58
Kudos
Bookmarks
If they were both ≥ inequalities, then you'd need to preserve the "≥", but if one of them is "≥" and the other is ">", then when you add the two inequalities, you can safely make the result ">" always. You might be able to see conceptually why this should be true; if you know
• Amy has more money than Bimal
• Carlos has at least as much money as Daaria
then Amy and Carlos combined will surely have strictly more money than Bimal and Daaria combined, so if we had these inequalities
A > B
C ≥ D
then we can be sure A+C > B+D is true. Of course, A+C ≥ B+D is also true, but that's slightly less informative. Or you can see why algebraically: if A > B and C ≥ D, then either A > B and C > D, in which case A+C > B+D just by adding the two inequalities, or A > B and C = D. But A + C > B + C is clearly true, because we're just adding the same thing on both sides of an inequality, and if C = D, we just proved A + C > B + D.
As for your other questions, I'm not quite sure what you mean. We cannot, in general, multiply inequalities at all. For example these two inequalities are true:
1 > -3
2 > -5
but if you multiply them, you won't get something true. So the 'rules' about how to multiply inequalities when one is "≥" and the other is ">" would depend on the restrictions on your numbers. If negatives could be involved, you couldn't multiply safely at all. If zero could be involved, you'd need to preserve the "≥" and if everything was positive, then it would work like the addition case above. Perhaps I've misunderstood your question though.
• Amy has more money than Bimal
• Carlos has at least as much money as Daaria
then Amy and Carlos combined will surely have strictly more money than Bimal and Daaria combined, so if we had these inequalities
A > B
C ≥ D
then we can be sure A+C > B+D is true. Of course, A+C ≥ B+D is also true, but that's slightly less informative. Or you can see why algebraically: if A > B and C ≥ D, then either A > B and C > D, in which case A+C > B+D just by adding the two inequalities, or A > B and C = D. But A + C > B + C is clearly true, because we're just adding the same thing on both sides of an inequality, and if C = D, we just proved A + C > B + D.
As for your other questions, I'm not quite sure what you mean. We cannot, in general, multiply inequalities at all. For example these two inequalities are true:
1 > -3
2 > -5
but if you multiply them, you won't get something true. So the 'rules' about how to multiply inequalities when one is "≥" and the other is ">" would depend on the restrictions on your numbers. If negatives could be involved, you couldn't multiply safely at all. If zero could be involved, you'd need to preserve the "≥" and if everything was positive, then it would work like the addition case above. Perhaps I've misunderstood your question though.
27 Jul 2022, 15:56
Kudos
Bookmarks
SDW2
If you add y - 3x ≥ 2 and -y + 4x > 2, the result will be x > 4. Notice that y - 3x can be equal to 2 or greater than 2, but -y + 4x is definitely greater than 2. If you add something that is greater than or equal to 2 to something that is strictly greater than 2, you'll obtain some number strictly greater than 4. We would only obtain x ≥ 4 if both inequalities were greater than or equal to inequalities.
For multiplication, first note that even if a > b and c > d, it is not necessarily true that ac > bd. For instance, 1 > -2 and -3 > -4, but it is not true that 1 * -3 > -2 * -4. If we assume that a, b, c, and d are all positive, then it is true (because we can first multiply each side of a > b by c to obtain ac > bc, and multiply each side of c > d by b to obtain bc > bd, and then combine the two inequalities to obtain ac > bc > bd). In this case, if we have a ≥ b and c > d, multiplying the two inequalities together will give us ac > bd. This is because a ≥ b means either a > b or a = b. If a > b, then I just showed above that ac > bd. If a = b, then multiplying each side of c > d by a (which is equal to b), we again obtain ac > bd.
