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# If a and b are non-zero integers, and a/b > 1, then which of

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If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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21 Jun 2013, 21:26
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If a and b are non-zero integers, and a/b > 1, then which of the following must be true?

A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3
[Reveal] Spoiler: OA

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Last edited by fozzzy on 21 Jun 2013, 23:34, edited 3 times in total.
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Re: If a and b are non-zero integers, and , then which of the fo [#permalink]

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21 Jun 2013, 21:55
fozzzy wrote:
If a and b are non-zero integers, and , then which of the following must be true?

$$a>b$$

$$2a>b$$

$$a^2< b^2$$

$$ab> b$$

$$a^3 < b^3$$

A & B are non zero integers then,
a>b .. Assume a = 10 & b = 20. Not true2a>b.. assume a = 10 and b =40
20>40?? Not true.

B^2 > a^2. assume a = 5 and b = 2.
4 > 25?? Not true

ab > b assume a = -3 and b =7
-21>7?? Not true

a^3 < b^3.. assume a = 3 and b = 2
9 < 8??
Not true.
I guess question is not correctly worded or i am making a mistake somewhere.
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Kudos [?]: 1090 [0], given: 543

Re: If a and b are non-zero integers, and , then which of the fo [#permalink]

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21 Jun 2013, 22:12
navigator123 wrote:
fozzzy wrote:
If a and b are non-zero integers, and , then which of the following must be true?

$$a>b$$

$$2a>b$$

$$a^2< b^2$$

$$ab> b$$

$$a^3 < b^3$$

A & B are non zero integers then,
a>b .. Assume a = 10 & b = 20. Not true2a>b.. assume a = 10 and b =40
20>40?? Not true.

B^2 > a^2. assume a = 5 and b = 2.
4 > 25?? Not true

ab > b assume a = -3 and b =7
-21>7?? Not true

a^3 < b^3.. assume a = 3 and b = 2
9 < 8??
Not true.
I guess question is not correctly worded or i am making a mistake somewhere.

Sorry I have updated the question!
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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22 Jun 2013, 12:43
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Expert's post
If a and b are non-zero integers, and a/b > 1, then which of the following must be true?

A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3

If b is positive, then we have that a>b>0.
If b is negative, then we have that a<b<0.

A. a > b. Not necessarily true.

B. 2a > b. Not necessarily true.

C. a^2< b^2 --> |a|<|b|. Not necessarily true.

D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.

E. a^3 < b^3 --> a<b. Not necessarily true.

Hope it's clear.
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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25 Jul 2013, 10:55
Bunuel wrote:
If a and b are non-zero integers, and a/b > 1, then which of the following must be true?

A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3

If b is positive, then we have that a>b>0.
If b is negative, then we have that a<b<0.

A. a > b. Not necessarily true.

B. 2a > b. Not necessarily true.

C. a^2< b^2 --> |a|<|b|. Not necessarily true.

D. ab > b. If a>b>0, then ab>b (the product of two positive integers is obviously greater than either one of them) and if a<b<0, then ab=positive>negative=b. So, this statement is always true.

E. a^3 < b^3 --> a<b. Not necessarily true.

Hope it's clear.

I Aspire to learn even 10% of the approaches you use to solve a math question.

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TGC !!
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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01 Jan 2014, 06:56
fozzzy wrote:
If a and b are non-zero integers, and a/b > 1, then which of the following must be true?

A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3

Yeah very good question a bit complicated, maybe I took the long way home but let's see

We get a-b/b > 0

One has to scenarios

1) If a-b>0, then b>0, therefore a>0. So all in all a>b>0
2) If a-b<0, then b<0, therefore a<0. So all in all 0>b>a

Let's check out the answer choices

A. a > b Not always true, could be scenario 2
B. 2a > b Not true at all
C. a^2< b^2 Too many different possibilities
D. ab > b This is equal to b(a-1)>0

Now we have two scenarios as well

If b>0, then a>1. Note that we are told that a.b are integers. Therefore b>0 means that b has to be 1 at least and therefore a>1.
If b<0, then a<-1. Same as above

So it works for both of our scenarios

E. a^3 < b^3 This is the same as to say b>a, which is not always true

Hope it helps

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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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02 Jan 2014, 02:14
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fozzzy wrote:
If a and b are non-zero integers, and a/b > 1, then which of the following must be true?

A. a > b
B. 2a > b
C. a^2< b^2
D. ab > b
E. a^3 < b^3

Lets plug in here

a = -3, b = -2
A - Eliminated
B - Eliminated
C - Eliminated
D - True
E - Eliminated
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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08 Jun 2014, 07:35
If a = 0.5 and b = 0.1

Then a/b = 0.5/0.1 = 5

When I tried to plug in the values into the d) option I got a*b = (0.5)(0.1) = 0.05 which isn't greater than b = 0.1

So option D also wouldn't hold true.

Am I doing something wrong?
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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08 Jun 2014, 09:24
Enael wrote:
If a = 0.5 and b = 0.1

Then a/b = 0.5/0.1 = 5

When I tried to plug in the values into the d) option I got a*b = (0.5)(0.1) = 0.05 which isn't greater than b = 0.1

So option D also wouldn't hold true.

Am I doing something wrong?

Yes. We are told that a and b are non-zero integers.
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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05 Jan 2015, 10:18
I guess the best approach here would be to Plug in values...
Try a=-3 and b = -2

All get eliminated except for D
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Re: If a and b are non-zero integers, and a/b > 1, then which of [#permalink]

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Re: If a and b are non-zero integers, and a/b > 1, then which of   [#permalink] 02 Feb 2016, 13:04
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