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.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
24 Feb 2012, 19:11
Kudos
Bookmarks
I'm taking my test in a few days and ran across a couple of things over the course of my studies that are nagging me a bit...
1) Is 0 not included in a set of the first n integers/ set of consecutive integers? eg are the first 6 integers 1-6 or 0-5? i am rethinking this because the formula for the sum of even ints n(n+1) ignores 0 but 0 is even.
2) When can you divide both sides of an equation by a variable? with inequalities i know the answer depends on whether you know the sign. However, with an equals sign in between it seems like sometimes you can but other times it breaks a quadratic... You can always factor out variable if they are on the same side, right? Example: 3w^2=6w clearly cant factor out. But in system but in system a/b=16 and a/b^2=8, you get b^2a/ba = 2. Another example: y((3x+5)/2) = y & y does not = 0. Is the trick simply knowing that the variable isnt 0? (so in the a/b example, you can becuase they have to both be non zero otherwise they'd be undefined)
3) Only undoing a square results in an absolute value scenario eg X^2 = 9 gives +/- 3, but sqr9 = 3 only is positive because you cannot squar a neg (changes if an odd root)
4) Do i need to test validity of answers to all quadratic equations (paying attention to 0 in the denominator of course) or only in quadratic inequalities?
5) if quadratic numerator has a variable on the outside x(blah blah blah) and the denominator is x, can i factor out since i know they arent 0?
For whatever reason these are the few nagging things that I never found closure on. Any help is much appreciated!
1) Is 0 not included in a set of the first n integers/ set of consecutive integers? eg are the first 6 integers 1-6 or 0-5? i am rethinking this because the formula for the sum of even ints n(n+1) ignores 0 but 0 is even.
2) When can you divide both sides of an equation by a variable? with inequalities i know the answer depends on whether you know the sign. However, with an equals sign in between it seems like sometimes you can but other times it breaks a quadratic... You can always factor out variable if they are on the same side, right? Example: 3w^2=6w clearly cant factor out. But in system but in system a/b=16 and a/b^2=8, you get b^2a/ba = 2. Another example: y((3x+5)/2) = y & y does not = 0. Is the trick simply knowing that the variable isnt 0? (so in the a/b example, you can becuase they have to both be non zero otherwise they'd be undefined)
3) Only undoing a square results in an absolute value scenario eg X^2 = 9 gives +/- 3, but sqr9 = 3 only is positive because you cannot squar a neg (changes if an odd root)
4) Do i need to test validity of answers to all quadratic equations (paying attention to 0 in the denominator of course) or only in quadratic inequalities?
5) if quadratic numerator has a variable on the outside x(blah blah blah) and the denominator is x, can i factor out since i know they arent 0?
For whatever reason these are the few nagging things that I never found closure on. Any help is much appreciated!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
25 Feb 2012, 03:39
Kudos
Bookmarks
alphastrike
0 is certainly an even integer, but is neither positive nor negative. Formulas you are referring to are:
Sum of n first positive integers: \(1+2+...+n=\frac{1+n}{2}*n\)
Sum of n first positive odd numbers: \(a_1+a_2+...+a_n=1+3+...+a_n=n^2\), where \(a_n\) is the last, \(n_{th}\) term and given by: \(a_n=2n-1\). Given \(n=5\) first positive odd integers, then their sum equals to \(1+3+5+7+9=5^2=25\).
Sum of n first positive even numbers: \(a_1+a_2+...+a_n=2+4+...+a_n\)\(=n(n+1)\), where \(a_n\) is the last, \(n_{th}\) term and given by: \(a_n=2n\). Given \(n=4\) first positive even integers, then their sum equals to \(2+4+6+8=4(4+1)=20\).
alphastrike
Never multiply or divide inequality by a variable (or by an expression with variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.
As for equations such as \(3w^2=6w\): if you reduce by \(w\) then you are assuming with no ground for it that \(w\) doesn't equal to zero and thus excluding one legitimate solution (though you can safely reduce it by 3). Correct approach would be: \(w^2=2w\) --> \(w^2-w=0\) --> \(w(w-1)=0\) --> \(w=0\) or \(w=1\);
Another example: \(\frac{a}{b}=16\) and \(\frac{a}{b^2}=8\). On the GMAT you will definitely be told that \(b\) does not equal to zero since it's in denominator but there won;t be any restrictions on \(a\). Solving: \(\frac{a}{b^2}=8\) --> \(\frac{a}{b}*\frac{1}{b}=8\) --> \(16*\frac{1}{b}=8\) --> \(b=2\) --> \(a=32\);
Next, if given that \(\frac{y(3x+5)}{2}=y\) and \(y\neq{0}\), then you can safely reduce by \(y\) and write: \(\frac{3x+5}{2}= 1\) --> \(x=-1\)
alphastrike
1. GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.
2. Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.
When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.
That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, \(\sqrt{25}=+5\) and \(-\sqrt{25}=-5\). Even roots have only non-negative value on the GMAT.
Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
3. \(\sqrt{x^2}=|x|\).
The point here is that as square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).
So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).
What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
alphastrike
I'm not sure that understand the question: if you solve quadratic equation correctly you most certainly don't need to check. As for quadratic inequalities: in most of the cases you'll get one or two ranges and again if you solved correctly there is no need of checking.
Solving and Factoring Quadratics:
https://www.purplemath.com/modules/solvquad.htm
https://www.purplemath.com/modules/factquad.htm
Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
alphastrike
Are you talking about something like \(\frac{x^2*(y+1)}{x}\)? If yes, then again on the GMAT you'll be told that \(x\neq{0}\) (since its in denominator and division by zero is not allowed) and you can reduce by \(x\) and write \(x*(y+1)\).
Hope it helps.
25 Feb 2012, 22:58
Kudos
Bookmarks
thank you sir. that cleared everything up for me. i'm good to go now!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
