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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

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.

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

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25 Jul 2013, 11:55

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.

Answer: D.

Hope it's clear.

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

Rgds, 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, 07:56

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

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

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02 Jan 2014, 03:14

1

This post received KUDOS

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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02 Feb 2016, 14:04

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