If 1 1 - ab 0, which of the following must be true?

Question

If 1 > 1 - ab > 0, which of the following must be true? I. a/b > 0 II. 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

BrentGMATPrepNow · Accepted Answer

GIVEN: 1 > 1 - ab > 0 Multiply all 3 sides by -1 to get: -1 < -1 + ab < 0 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 https://www.youtube.com/watch?v=Od98BOicIq4

abhinavgaur · Answer

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. Which means that only I and III are always true.

NickHalden · Answer

Step 1: Subtracting 1 from all, 0>-ab>-1. Step 2: Multiplying by -1, signs are reversed. Therefore we get : 0

balamoon · Answer

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.

lipsi18 · Answer

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 ]

Hence answer is E
Thanks,

GMATinsight · Answer

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 < 1 I. 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 E

chetan2u · Answer

ab<1 for all values and has to be true..
a and b have to have same sign so a/b>0..
ans E

GMATinsight · Answer

Yes. A typo error due to copy paste. But thank you! you deserve a Kudos :wink:

.

vishwaprakash · Answer

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.

mika84 · Answer

E 1<1-ab<0 or 0 0 - true as ab>0 then a/b>0 I. a/b < 1 - could be III. ab < 1 - true

info123talk · Answer

answer is E.. ab has to be positive, greater than 0 but less than 1

Bunuel · Answer

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).

OptimusPrepJanielle · Answer

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.

TimeTraveller · Answer

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?

fetchnitin · Answer

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.

Bunuel · Answer

We have that 0 < ab < 1. Now, let me asks you is ab < 1 true?

fetchnitin · Answer

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 .

Thanks

fetchnitin · Answer

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

Bunuel · Answer

I think that you should practice Must or Could be true questions more: search.php?search_id=tag&tag_id=193 Hope it helps.

If 1 > 1 - ab > 0, which of the following must be true?

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