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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, 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.

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, 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

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

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02 Feb 2016, 13:04

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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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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.

Answer: D.

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

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.

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?
_________________

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.

Answer: D
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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.