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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
24 Jun 2015, 02:36
2
I am going to go with E.
1>1-ab>0; If we split this into two separate equations (1-ab<1 & 1-ab>0), we get the following solutions - ab>0 & ab<1.
I says that a/b>0. Since ab>0, it means that either a,b both are positive or both are negative. In either scenario I holds true.
III says that ab<1. We already got that result be splitting and solving the inequality.
II says that a/b<1. Let's take two cases - Case 1 (a=2, b=0.2) & Case 2 (a=0.2, b=2). II holds true for Case 2 but not Case 1, and therefore cannot always be true.
If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
Updated on: 24 Jun 2015, 10:15
1
Step 1: Subtracting 1 from all, 0>-ab>-1. Step 2: Multiplying by -1, signs are reversed. Therefore we get : 0<ab<1 Therefore, we can conclude : 1. both ab have the same sign 2. ab lies between 0 to 1
Hence E !!
Originally posted by NickHalden on 24 Jun 2015, 02:38.
Last edited by NickHalden on 24 Jun 2015, 10:15, edited 1 time in total.
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
24 Jun 2015, 07:27
1
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0 I. a/b < 1 III. ab < 1
(A) I only (B) II only (C) III only (D) I and II only (E) I and III only
Solution - a. For the part 1 > 1 - ab -> Subtract -1 from both sides gives -ab < 0 -> ab > 0. Both a and b are positive or negative. b. For the part 1 - ab > 0 -> Add ab on both sides gives -> ab<1.
I. a/b > 0. This will give us both a and b are positive or negative. Meets the condition a above. Sufficient. II. a/b < 1. This is opposite of condition a above. In Sufficient. III. ab < 1. This inequality satisfy the condition b above. Sufficient.
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
24 Jun 2015, 10:09
Rearranging the 1>1-ab>0, equation we get 1>1-ab or ab>0 ---1 1-ab>0 or ab<1 -----2 A and b both has to be same sign from equation 1, so a/b will always be >0 buy in some cases it will be >2 or <1 .Hence choose 1 From equation 2 it’s clear that ab<1, hence choose 3. [This can also be solved by taking example where we have d>a>l , and cross verify ]
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
25 Jun 2015, 03:35
chetan2u wrote:
ab<1 for all values and has to be true.. a and b have to have same sign so a/b>0.. ans E
Yes. A typo error due to copy paste. But thank you! you deserve a Kudos .
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (E). _________________
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
30 Jun 2015, 08:15
1
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0 I. a/b < 1 III. ab < 1
If you first deal with the right half of the inequality, you can add ab to both sides to get ab<1. Since III is true, you can eliminate A, B, and D.
Now test I. Looking at the left side of the inequality, add ab to both sides and subtract 1 from both sides to yield ab>0. For ab to be positive, a and b must have the same signs. This will also be true if we divide a by b. Statement I is also true. (A) I only (B) II only (C) III only (D) I and II only (E) I and III only
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
30 Jun 2015, 09:46
0 < 1-ab < 1, since (1-ab) is both positive and less than 1, 0<ab<1, so III is true. For (ab) to be less than 1 and greater than 0 the fraction a/b must be greater than 0 (must be positive), so I is also true. Ans is E?
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
15 Jul 2015, 09:19
Hello Bunuel , While solving this problem , i reached up till this inequality ( 0<ab<1) . However , statement III above says that ab<1 . This covers a lot many more numbers, which wont be satisfied by the inequality provided in the stem ( e.g since ab<1 , it will also mean that ab =-3). Should this not be reason good enough to eliminate statement III (as this has provided us with values that are unable to satisfy the stem) ?
PS: If the question had asked , "which of the following might be true ?", then,yes, we could still include statement III. I am unable to understand this. Could you please help in this ? Thanks in advance.
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
15 Jul 2015, 09:27
fetchnitin wrote:
Hello Bunuel , While solving this problem , i reached up till this inequality ( 0<ab<1) . However , statement III above says that ab<1 . This covers a lot many more numbers, which wont be satisfied by the inequality provided in the stem ( e.g since ab<1 , it will also mean that ab =-3). Should this not be reason good enough to eliminate statement III (as this has provided us with values that are unable to satisfy the stem) ?
PS: If the question had asked , "which of the following might be true ?", then,yes, we could still include statement III. I am unable to understand this. Could you please help in this ? Thanks in advance.
We have that 0 < ab < 1. Now, let me asks you is ab < 1 true?
_________________
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
15 Jul 2015, 09:56
Hello, yes,this is true .ab<1 . But my confusion is that it also contains values that are outside the range of the inequality in the question stem . Is it that, while solving these type of questions all the values of the question stem should be tried and checked with the options and not the other way round ( i.e all values of the options should fit the range of stem ). If so ,then could u explain to me the logic behind this, as i am unable to visualize this .
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
15 Jul 2015, 10:00
Hello Bunuel, yes,this is true .ab<1 . But my confusion is that it also contains values that are outside the range of the inequality in the question stem . Is it that, while solving these type of questions all the values of the question stem should be tried and checked with the options and not the other way round ( i.e all values of the options should fit the range of stem ). If so ,then could u explain to me the logic behind this, as i am unable to visualize this .
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
15 Jul 2015, 10:03
fetchnitin wrote:
Hello Bunuel, yes,this is true .ab<1 . But my confusion is that it also contains values that are outside the range of the inequality in the question stem . Is it that, while solving these type of questions all the values of the question stem should be tried and checked with the options and not the other way round ( i.e all values of the options should fit the range of stem ). If so ,then could u explain to me the logic behind this, as i am unable to visualize this .
Re: If 1 > 1 - ab > 0, which of the following must be true? [#permalink]
Show Tags
24 Feb 2018, 08:25
Top Contributor
Bunuel wrote:
If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0 I. a/b < 1 III. ab < 1
(A) I only (B) II only (C) III only (D) I and II only (E) I and III only
Kudos for a correct solution.
GIVEN: 1 > 1 - ab > 0 Multiply all 3 sides by -1 to get: -1 < -1 + ab < 0 [since I multiplied by a NEGATIVE number, I had to REVERSE the inequality symbols] Add 1 to all 3 sides to get: 0 < ab < 1
First, if 0 < ab, then a and b are the SAME SIGN, which means a/b > 0 So, statement I is TRUE ELIMINATE B and C
Second, our new inequality clearly tells us that ab < 1 So, statement III is TRUE ELIMINATE A and D
So, we need not even check whether statement II is true.
Answer: E
RELATED VIDEO
_________________
Brent Hanneson – Founder of gmatprepnow.com
gmatclubot
Re: If 1 > 1 - ab > 0, which of the following must be true?
[#permalink]
24 Feb 2018, 08:25