Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 19 08:00 AM PDT  09:00 AM PDT Beat the GMAT with a customized study plan based on your needs! Learn how to create your preparation timeline, what makes a good study plan and which tools you need to use to build the perfect plan. Register today! Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Sep 2018
Posts: 209
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
Show Tags
Updated on: 16 Feb 2019, 03:18
Question Stats:
20% (03:00) correct 80% (01:50) wrong based on 30 sessions
HideShow timer Statistics
If \(ab >0\), is \((ab) ^2<\sqrt{ab}\) (1) \(\frac{4}{a}>7b\) (2) \(a16 > 16\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Why do we fall?...So we can learn to pick ourselves up again
If you like the post, give it a KUDOS!
Originally posted by Abhi077 on 15 Feb 2019, 10:39.
Last edited by Bunuel on 16 Feb 2019, 03:18, edited 2 times in total.
Renamed the topic and edited the question.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1387

Re: If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
Show Tags
Updated on: 15 Feb 2019, 22:06
Abhi077 wrote: If \(ab >0\), is \((ab) ^2\) < \(\sqrt{ab}\)
1.\(\frac{4}{a}\) > \(7ab\) 2. \(a16 > 16\) edit: the OP fixed a typo in the original post above, so this solution is to the question I have quoted above (with the typo in it) and not to the nowedited question at the top of the page (which I solve in a separate post below) First, if we replace "ab" with "x", the question is asking: Is x^2 <√x ? and x^2 < √x is only true if 0 < x < 1, so the question is asking "Is ab < 1?" Statement 1 tells us: 4/a > 7ab Before determining if this is sufficient, notice that we know ab > 0. So the right side of this inequality is positive, which means 4/a is greater than some positive number, and therefore a itself is positive. So Statement 1 guarantees that a is positive. But that's the only information you get from Statement 2. So you don't learn anything new by combining the two statements that you don't know from Statement 1 on its own, and the OA provided cannot be correct  the answer can only be A or E, since Statement 2 alone is clearly not sufficient. Using Statement 1 alone (which we can rewrite, since a is positive, as 4 > 7a^2 b or as 4/7 > a^2 b if we want to), it's easy to see that ab < 1 is possible, using the values a = 0.1 and b = 1, say. But it's also easy enough to find values where ab > 1. We can take, say, a = 0.1 and b = 11. So we can't say if ab < 1 is true, and the answer is E unless there's a typo in the question.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Originally posted by IanStewart on 15 Feb 2019, 14:19.
Last edited by IanStewart on 15 Feb 2019, 22:06, edited 1 time in total.



Manager
Joined: 25 Sep 2018
Posts: 209
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)

If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
Show Tags
Updated on: 18 Feb 2019, 03:38
IanStewart wrote: Abhi077 wrote: If \(ab >0\), is \((ab) ^2\) < \(\sqrt{ab}\)
1.\(\frac{4}{a}\) > \(7ab\) 2. \(a16 > 16\) First, if we replace "ab" with "x", the question is asking: Is x^2 <√x ? and x^2 < √x is only true if 0 < x < 1, so the question is asking "Is ab < 1?" Statement 1 tells us: 4/a > 7ab Before determining if this is sufficient, notice that we know ab > 0. So the right side of this inequality is positive, which means 4/a is greater than some positive number, and therefore a itself is positive. So Statement 1 guarantees that a is positive. But that's the only information you get from Statement 2. So you don't learn anything new by combining the two statements that you don't know from Statement 1 on its own, and the OA provided cannot be correct  the answer can only be A or E, since Statement 2 alone is clearly not sufficient. Using Statement 1 alone (which we can rewrite, since a is positive, as 4 > 7a^2 b or as 4/7 > a^2 b if we want to), it's easy to see that ab < 1 is possible, using the values a = 0.1 and b = 1, say. But it's also easy enough to find values where ab > 1. We can take, say, a = 0.1 and b = 11. So we can't say if ab < 1 is true, and the answer is E unless there's a typo in the question. Yes there was a typo. I'm so sorry. just corrected it
_________________
Why do we fall?...So we can learn to pick ourselves up again
If you like the post, give it a KUDOS!
Originally posted by Abhi077 on 15 Feb 2019, 21:17.
Last edited by Abhi077 on 18 Feb 2019, 03:38, edited 1 time in total.



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1387

Re: If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
Show Tags
15 Feb 2019, 22:02
Abhi077 wrote: If \(ab >0\), is \((ab) ^2\) < \(\sqrt{ab}\)
1.\(\frac{4}{a}\) > \(7b\) 2. \(a16 > 16\) With the correction, it's much easier to analyze the question algebraically. As I explained above, the only way (ab)^2 < √(ab) is true is if 0 < ab < 1, so that's what we want to know: is ab < 1? Using only Statement 1, we have two cases:  if a > 0, then we can multiply both sides of the inequality by a without reversing the inequality. So we then have 4/a > 7b 4 > 7ab 4/7 > ab So in this case, it is indeed true that ab < 1.  if a < 0, then we can again multiply both sides of the inequality by a, but because we're multiplying by a negative number, we must reverse the inequality: 4/a > 7b 4 < 7ab 4/7 < ab So when a (and also b of course, since ab > 0) is negative, then the value of ab can be anything greater than 4/7, and can indeed be larger than 1. It is easy enough to confirm this just by choosing numbers: we might have, say, that a = 4 and b = 100, for example, in which case 4/a > 7b is clearly true, since 1 > 700, and in this case ab is much larger than 1. Statement 2 alone is clearly not sufficient, since it only tells us a > 0. But once we know that a > 0, that rules out the second case above in our analysis of Statement 1. So we know only the first case is possible, and that ab < 4/7, so the two statements together are sufficient, and the answer is C.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



VP
Joined: 09 Mar 2018
Posts: 1007
Location: India

Re: If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
Show Tags
15 Feb 2019, 22:18
Abhi077 wrote: If \(ab >0\), is \((ab) ^2\) < \(\sqrt{ab}\)
1.\(\frac{4}{a}\) > \(7b\) 2. \(a16 > 16\) So i would say, nice , Lets see, given is important here ab> 0 Lets manipulate \((ab)^4\) < ab take common and it becomes => (ab) {\((ab)^3\) 1 } < 0,For representation purpose only (x) (y) < 0 Now for the above to be true, it can be that x > 0 & y< 0 or x < 0 & y > 0, So from given, only bold is valid which means we have to only focus on (ab)^3 < 1 part from 1) \(\frac{4}{a}\) > \(7b\) Can be true when a=1, b=1, this makes the question as No Can be true when a=1, b=1, this makes the question as Yes From 2) a16 > 16, this can only be true when a> 0, dont know anything about B When we combine we can directly pinpoint on the condition that a > 0 and b < 0 Sufficient to answer the question C
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up.




Re: If ab >0, is (ab)^2 < (ab)^(1/2) ?
[#permalink]
15 Feb 2019, 22:18






