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

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Director
Joined: 29 Nov 2012
Posts: 765
If a and b are non-zero integers, and a/b > 1, then which of  [#permalink]

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Updated on: 21 Jun 2013, 23:34
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69% (01:54) correct 31% (01:31) wrong based on 452 sessions

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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

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Originally posted by fozzzy on 21 Jun 2013, 21:26.
Last edited by fozzzy on 21 Jun 2013, 23:34, edited 3 times in total.
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Posts: 50610
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
6
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 , 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.
Director
Joined: 29 Nov 2012
Posts: 765
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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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.

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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
2
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?
Math Expert
Joined: 02 Sep 2009
Posts: 50610
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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Joined: 22 Jan 2017
Posts: 2
Re: If a and b are non-zero integers, and a/b > 1, then which of  [#permalink]

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19 Jun 2017, 18:48
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.

Hi Brunel,

I am still confused. I can't see the connection between the question asking : a/b>1 , and the answers below

Could you or anyone kindly explaain this

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 50610
Re: If a and b are non-zero integers, and a/b > 1, then which of  [#permalink]

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19 Jun 2017, 21:20
whoisjon2 wrote:
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.

Hi Brunel,

I am still confused. I can't see the connection between the question asking : a/b>1 , and the answers below

Could you or anyone kindly explaain this

Thank you

The question does not asks whether a/b > 1. It says that a/b > 1. So, the question is: given that a/b > 1, which of the following options must be true?
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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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20 Jun 2017, 18:15
1
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

If a/b > 1, then a and b must have the same sign, with |a| > |b|. For example, a = 3 and b = 2 OR a = -3 and b = -2.

Let’s analyze each given answer choice.

A. a > b

Let a = -3 and b = -2; we can see that A is not true.

B. 2a > b

Let a = -3 and b = -2; we can see that B is not true.

C. a^2 < b^2

Let a = 3 and b = 2; we can see that C is not true.

D. ab > b

Let a = 3 and b = 2; we have ab > b. Let a = -3 and b = -2; we have ab > b. We see that D can be true, but let’s also analyze choice E before we conclude that choice D is definitely true.

E. a^3 < b^3

Let a = 3 and b = 2; we can see that E is not true.

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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 Dec 2017, 11:33
my .02:

* MUST BE TRUE questions tend to be D or E. so even if you're running out of time or trying to burn the Q, you have a 50/50 here.

we're told that:
1) a & b = integers AND ARE NOT 0 (aka NO FRACTIONS)
2) $$\frac{a}{b}$$>1

Let's make sense of (2): for a fraction to be GREATER THAN 1, what needs to be true?
a) The numerator must be greater than the denominator
b) The numerator AND denominator must share the same sign (i.e. both must be POSITIVE or NEGATIVE)

KEYS TO THE PROBLEM:
> if b = positive (let's say b=2), then we can say a=4. that way, 2>1.
> if b = negative (let's say b=-2), then we can say a=-4. that way, 2>1.
** Both of these conditions match the above proofs.
** Very helpful to PICK #s to solve

Let's plug in these sets of #s for A/C A->E.
A) a>b --> what if a=-4, b=-2? Incorrect.
B) 2a>b --> what if a=-4, b=-2? Incorrect.
C) $$a^{2}$$<$$b^{2}$$ --> what if a=-4, b=-2? Incorrect.
D) ab>b --> try: a=-4, b=-2. then, 8>-2. or: a=4, b=2. then, 8>2. Correct.
E) $$a^{3}$$<$$b^{3}$$ -->what if a=4, b=2? then 64<8. Incorrect.
Re: If a and b are non-zero integers, and a/b > 1, then which of &nbs [#permalink] 05 Dec 2017, 11:33
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