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If a & b are non-zero integers and a × b >b, which of the following

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If a & b are non-zero integers and a × b >b, which of the following  [#permalink]

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New post 08 Mar 2019, 00:23
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Question Stats:

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If a & b are non-zero integers and a × b >b, which of the following must be true?

I. a/b>o
II. (a-b)>0
II. (a+b)>1

A. I only
B. II only
C. I&II only
D. II&III only
E. I,II& III
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If a & b are non-zero integers and a × b >b, which of the following  [#permalink]

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New post Updated on: 23 May 2019, 03:59
1
kiran120680 wrote:
If a & b are non-zero integers and a × b >b, which of the following must be true?

I. a/b>o
II. (a-b)>0
II. (a+b)>1

A. I only
B. II only
C. I&II only
D. II&III only
E. I,II& III



assign values for a and.

NOTE : a and b are non zero integers but we don't know about their sign.

a = -2
b = -4

ab = 8.

I) a/b>0. Yes . This option is correct for all integers. If we consider positive values , the result will be the same.

II) a - b>0. Not always. a=-2 and b=-4, The answer will be Positive. a=2 b=4. The answer is Negative.

III) a + b> 0. What if both a and b are negative. NOT always.

Thus, only I is correct.

The best answer is A.

Originally posted by KSBGC on 08 Mar 2019, 00:43.
Last edited by KSBGC on 23 May 2019, 03:59, edited 1 time in total.
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Re: If a & b are non-zero integers and a × b >b, which of the following  [#permalink]

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New post 22 May 2019, 05:51
KSBGC wrote:
kiran120680 wrote:
If a & b are non-zero integers and a × b >b, which of the following must be true?

I. a/b>o
II. (a-b)>0
II. (a+b)>1

A. I only
B. II only
C. I&II only
D. II&III only
E. I,II& III



assign values for a and.

NOTE : a and b are non zero integers but we don't know about their sign.

a = -2
b = -4

ab = 8.

I) a/b>0. Yes . This option is correct for all integers. If we consider positive values , the result will be the same.

II) a - b>0. Not always. a=-2 and b=-4, The answer will be negative. a=4 b=2. The answer is positive.

III) a + b> 0. What if both a and b are negative. NOT always.

Thus, only I is correct.

The best answer is A.


Hi KSBGC,
Could you please explain how the highlighted portion is correct? I think a-b>0 is always true.
TIA!
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Re: If a & b are non-zero integers and a × b >b, which of the following  [#permalink]

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New post 22 May 2019, 06:42
Let's rearrange the equation as ab-b > 0
b(a-1)>0

So either
b>0 and (a-1)>0, that is a>1
or
b<0 and (a-1)<0, that is a<1

Notice that when a<1, it is implied that a<0 since a is a non zero integer

So from the stem, a and b are either both positive or both negative

(1) will be always true

(2) If (a,b)=(4,3) true
If (a,b)=(3,4) not true

(3) If (a,b)=(4,3) true
If (a,b)=(-4,-3) not true

So, only statement 1 will always be true

Answer is (A)

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If a & b are non-zero integers and a × b >b, which of the following  [#permalink]

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New post 23 May 2019, 04:00
neha283 wrote:
KSBGC wrote:
kiran120680 wrote:
If a & b are non-zero integers and a × b >b, which of the following must be true?

I. a/b>o
II. (a-b)>0
II. (a+b)>1

A. I only
B. II only
C. I&II only
D. II&III only
E. I,II& III



assign values for a and.

NOTE : a and b are non zero integers but we don't know about their sign.

a = -2
b = -4

ab = 8.

I) a/b>0. Yes . This option is correct for all integers. If we consider positive values , the result will be the same.

II) a - b>0. Not always. a=-2 and b=-4, The answer will be negative. a=4 b=2. The answer is positive.

III) a + b> 0. What if both a and b are negative. NOT always.

Thus, only I is correct.

The best answer is A.


Hi KSBGC,
Could you please explain how the highlighted portion is correct? I think a-b>0 is always true.
TIA!


Typo it was. Thanks for notification.

Not always true as u don't know about the signs of a and b. both can be positive or both can be negative.

Given,

ab>b.

no sign is mentioned in question. Thus , both of the scenario must be verified.

Thanks.
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If a & b are non-zero integers and a × b >b, which of the following   [#permalink] 23 May 2019, 04:00
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If a & b are non-zero integers and a × b >b, which of the following

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