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If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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23 Jun 2015, 22:42
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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24 Jun 2015, 01:36
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I am going to go with E. 1>1ab>0; If we split this into two separate equations (1ab<1 & 1ab>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. Which means that only I and III are always true.



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If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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24 Jun 2015, 01:38
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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 !!
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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24 Jun 2015, 06:27
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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.Thanks Kudos Please.
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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24 Jun 2015, 09:09
Rearranging the 1>1ab>0, equation we get 1>1ab or ab>0 1 1ab>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 ]
Hence answer is E Thanks,



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If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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25 Jun 2015, 01:59
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. 1 > 1  ab > 0 has two parts 1 > 1  ab and 1  ab > 0 i.e. ab > 0 and 1 > ab i.e. 0 < ab < 1I. a/b > 0 will always be true as a and b must have same sign for ab to be between 0 and 1 II. a/b < 1 will not always be true @a=1/3 and b=1/2 III. ab < 1 will always be true as inferred from the given range of ab Answer: Option
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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25 Jun 2015, 02:22
GMATinsight wrote: 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. 1 > 1  ab > 0 has two parts 1 > 1  ab and 1  ab > 0 i.e. ab > 0 and 1 > ab i.e. 0 < ab < 1I. a/b > 0 will always be true as a and b must have same sign for ab to be between 0 and 1 II. a/b < 1 will not always be true @a=1/3 and b=1/2 III. ab < 1 will not always be true as inferred from the given range of abAnswer: Option ab<1 for all values and has to be true.. a and b have to have same sign so a/b>0.. ans E
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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25 Jun 2015, 02:35
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 .
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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26 Jun 2015, 06:53
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. 1 > 1  ab > 0 Hence 0 > ab > 1 Hence 0< ab < 1 Hence ab is positive and ab is less than 1 if ab is positive, then a and b both are of same sign and a/b is positive. Hence statement 1 and statement 3 are correct. Hence option E is correct.



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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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27 Jun 2015, 09:25
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E 1<1ab<0 or 0<ab<1 I. a/b > 0  true as ab>0 then a/b>0 I. a/b < 1  could be III. ab < 1  true



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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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27 Jun 2015, 09:46
answer is E.. ab has to be positive, greater than 0 but less than 1



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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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29 Jun 2015, 05:22
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. MANHATTAN GMAT OFFICIAL SOLUTION: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).
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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30 Jun 2015, 07:15
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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



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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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30 Jun 2015, 08:46
0 < 1ab < 1, since (1ab) 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?
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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15 Jul 2015, 08:19
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.



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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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15 Jul 2015, 08:27
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?
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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15 Jul 2015, 08:56
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 .
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Re: If 1 > 1  ab > 0, which of the following must be true? [#permalink]
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15 Jul 2015, 09:00
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 .
Thanks



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