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If a b > a + b, where a and b are integers, which of the

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If a b > a + b, where a and b are integers, which of the [#permalink] New post 30 Jan 2011, 21:18
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If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A I only
B II only
C I and II
D I and III
E II and III

though the OA is revealed, but I am not conviced with the answer
Please help
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Re: AB positive or negitive [#permalink] New post 30 Jan 2011, 21:28
girishkakkar wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A I only
B II only
C I and II
D I and III
E II and III

though the OA is revealed, but I am not conviced with the answer
Please help


Simplify the inequality:
a – b > a + b
b<0

We know for certain that II is true.

We don't have info about the value of a. Hence, I cannot be derived.

For III ab can be positive or negative depending on the value of a. Since we don't know about a, III cannot be inferred.

Hence, B is the answer
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Re: AB positive or negitive [#permalink] New post 31 Jan 2011, 00:07
well agreed.....however, if we multiply both side of the equation by "a", we get to know that III is also true.....which follows that I is also true?
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Re: AB positive or negitive [#permalink] New post 31 Jan 2011, 01:17
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Unless you know whether a is positive or not you cannot determine how the inequality will look like after you multiply it by a. You cannot still prove III to be true.

Lets consider the two cases here:
Suppose a is positive (3, say)
3-b>3+b
Multiply the inequality by 3
9-3b>9+3b
6b<0
b<0

hence, ab<0


Now, suppose a=-3
plug in the values:

-3-b>-3+b
Multiply by a(-3)
9+3b<9-3b
6b<0
b<0

hence, ab > 0

Thus the sign of ab will vary depending on the sign of a. Hope this clears up the confusion
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Re: AB positive or negitive [#permalink] New post 02 Feb 2011, 05:02
Q: If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

Through inequality; I just derived that b is -ve
a – b > a + b
-b > b --> subtracting 'a' from both sides
-2b > 0 --> subtracting 'b' from both sides
-b > 0 --> dividing both sides by 2
b < 0 --> multiplying -ve sign on both sides

The rest two; I ruled out using numbers

Let b, as we know is -ve, to be equal to -1

Case I
a=+ve, say 100
a - b = 100 – (-1) = 101
a + b = 100 + (-1) = 99

a-b > a+b

Case II
a=-ve, say -100
a - b = -100 – (-1) = -100 + 1 = -99
a + b = -100 + (-1) = -100 - 1 = -101

So, a - b > a + b

Thus, a - b > a + b is true for both +ve and -ve 'a'

We just proved that a-b>a+b is true for both +ve and -ve values of a.

We can't conclusively say that a < 0. Statement I is ruled out.

for a=+ve; ab = +ve * -ve = -ve
and
for a=+ve; ab = -ve * -ve = +ve

So, we can't conclusively say ab < 0. Statement III is ruled out.

Ans: B
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Re: AB positive or negitive [#permalink] New post 02 Feb 2011, 05:33
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girishkakkar wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A I only
B II only
C I and II
D I and III
E II and III


You don't need number plugging at all.

Given: \(a-b>a+b\) --> \(a\) cancels out (which means that from given info we can say nothing about it: it can be positive, negative or zero, so it can be ANY number) --> \(2b<0\) --> \(b<0\).

As we know nothing about \(a\) and know that \(b<0\), so only II must be true.

Answer: B.
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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 15 Oct 2014, 15:22
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If a – b > a + b, where a and b are integers, which of the following m [#permalink] New post 23 Aug 2015, 08:53
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If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only
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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 23 Aug 2015, 09:09
Expert's post
shasadou wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only


Merging topics.

Please refer to the discussion above.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 24 Aug 2015, 08:46
Bunuel wrote:
shasadou wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only


Merging topics.

Please refer to the discussion above.


can we not sqaure both sides of a – b > a + b ?
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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 24 Aug 2015, 08:55
Expert's post
anupamadw wrote:
Bunuel wrote:
shasadou wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only


Merging topics.

Please refer to the discussion above.


can we not sqaure both sides of a – b > a + b ?


1. No. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality). Check for more here: inequalities-tips-and-hints-175001.html

2. Why do you want to square?
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 24 Aug 2015, 08:56
anupamadw wrote:
Bunuel wrote:
shasadou wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only


Merging topics.

Please refer to the discussion above.


can we not sqaure both sides of a – b > a + b ?


You are only complicating the simple expression given by squaring it.

Also, as a general rule of inequalities, squaring variables in the inequalities is not a good idea until you know for sure the sign of a-b as multiplication by a negative number reverses the inequality.
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Re: If a b > a + b, where a and b are integers, which of the [#permalink] New post 24 Aug 2015, 09:01
girishkakkar wrote:
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A I only
B II only
C I and II
D I and III
E II and III

though the OA is revealed, but I am not conviced with the answer
Please help


Sorry I got my mistake
-3>-5
but 9< 25

actually after squaring we get 0>4ab , and thought III is also true :(
Re: If a b > a + b, where a and b are integers, which of the   [#permalink] 24 Aug 2015, 09:01
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