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If a and b are integers and b ≠ 0 which of the following CANNOT equal

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If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 09 Nov 2015, 00:58
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(A) ab
If a=0 , then ab=0
(B) a - b
If a=b , then a-b= =0
(C) a + b
If a=-b , then a+b=0
(D) ab - b^2
If a=b , then ab-b^2= 0
(E) a^2 + b^2
Can't be equal to zero .
If a=0 , then a^2 + b^2 =b^2
if a=-ve , then a^2 + b^2 not equal to 0

Answer E
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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 20 Jan 2017, 06:38
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a and b are integers a could be 0,1,-1
On plugging In
Eliminate ABCD
E : B # 0 , results always a number
E
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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 01:55
i am struggling with this question,
all answers = 0 or some are positive some are negative,
how the hell is this E?

for E, a could = b so it doesn't make sense.

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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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mrcentauri wrote:
If a and b are integers and b ≠ 0 which of the following CANNOT equal 0 ?

(A) ab
(B) a - b
(C) a + b
(D) ab - b^2
(E) a^2 + b^2

i am struggling with this question,
all answers = 0 or some are positive some are negative,
how the hell is this E?

for E, a could = b so it doesn't make sense.


The square of a number is always more then or equal to 0. Since we are told that b ≠ 0, then b^2 > 0.

So, a^2 + b^2 = (0 or positive) + (positive) = (positive).

Answer: E.

Hope it's clear.
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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 04:30
but in the other questions a = b which equals 0? so that doesn't make sense either.

for example

If a and b are integers and b ≠ 0 which of the following CANNOT equal 0 ?

(A) ab --> this one makes sense anything times 0 = 0

(B) a - b --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer

(C) a + b --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer

(D) ab - b^2 --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer

(E) a^2 + b^2 --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer

what am I doing wrong here?

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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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mrcentauri wrote:
but in the other questions a = b which equals 0? so that doesn't make sense either.

for example

If a and b are integers and b ≠ 0 which of the following CANNOT equal 0 ?

(A) ab --> this one makes sense anything times 0 = 0

(B) a - b --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer------if a=3, then this will be 0

(C) a + b --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer------if a=-3, then this will be 0

(D) ab - b^2 --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer------if a=b, then this will be 0

(E) a^2 + b^2 --> b ≠0 so say b is 3 and a is either 0,1 or -1, this results in a non-zero integer

what am I doing wrong here?


Hi mrcentauri, kindly check the highlighted parts.

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If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 05:25
so what I have done wrong here is assume both were the same integers?
is this how a problem like this should be solved? according to manhattan prep strategy, you should try different numbers i.e. -/+ even/odd within the constraints of the problem (although this is a data sufficiency strategy)

how am I able to deduce a = b?, why could a not equal 3 and b = 5?

the question asks if and b ARE integers,

does this mean they are both the same or could be different?

do you see where I am coming from?

are you saying the trick is the wording of the question? a AND b are integers meaning or implying they are the same? because if so then the first answer would be non-zero

where am I going wrong here?

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If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 05:34
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mrcentauri wrote:
so what I have done wrong here is assume both were the same integers?
is this how a problem like this should be solved? according to manhattan prep strategy, you should try different numbers i.e. -/+ even/odd within the constraints of the problem (although this is a data sufficiency strategy)

how am I able to deduce a = b?, why could a not equal 3 and b = 5?

the question asks if and b ARE integers,

does this mean they are both the same or could be different?

do you see where I am coming from?

are you saying the trick is the wording of the question? a AND b are integers meaning or implying they are the same? because if so then the first answer would be non-zero

where am I going wrong here?


Hi mrcentauri

First you need to understand the language of the question. The question specifically says, which of the following \(CANNOT\) be \(0\)

So any choice which CAN or CANNOT be 0 must be eliminated. We only need option which will NEVER be \(0\) irrespective of the value of \(a\) or \(b\)

Now you can test as many values as you may like for a & b but in all the options except E, there is a possibility to get 0. Hence E is our answer because it CANNOT be 0 for any combination of a & b.

as the question does not provide any restriction between a & b so a=b is a possible assumption

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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 05:36
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mrcentauri wrote:
so what I have done wrong here is assume both were the same integers?
is this how a problem like this should be solved? according to manhattan prep strategy, you should try different numbers i.e. -/+ even/odd within the constraints of the problem (although this is a data sufficiency strategy)

how am I able to deduce a = b?, why could a not equal 3 and b = 5?

the question asks if and b ARE integers,

does this mean they are both the same or could be different?

do you see where I am coming from?

are you saying the trick is the wording of the question? a AND b are integers meaning or implying they are the same? because if so then the first answer would be non-zero

where am I going wrong here?


Yes, a and b could be the same integer but this is not the point here. I think you are misinterpreting the question.

If a and b are integers and b ≠ 0 which of the following CANNOT equal 0 ?

(A) ab
(B) a - b
(C) a + b
(D) ab - b^2
(E) a^2 + b^2

We know that b ≠ 0.

(A) ab --> this could be 0 of a = 0. Discard.

(B) a - b --> this could be zero if a = b. Discard.

(C) a + b --> this could be zero if a = -b. Discard.

(D) ab - b^2 = b(a - b) --> this could be zero if a = b. Discard.

(E) a^2 + b^2 --> this CANNOT be 0 because a^2 + b^2 = (0 or positive) + (positive) = (positive).

Answer: E.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal [#permalink]

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New post 24 Dec 2017, 05:42
niks18 wrote:
mrcentauri wrote:
so what I have done wrong here is assume both were the same integers?
is this how a problem like this should be solved? according to manhattan prep strategy, you should try different numbers i.e. -/+ even/odd within the constraints of the problem (although this is a data sufficiency strategy)

how am I able to deduce a = b?, why could a not equal 3 and b = 5?

the question asks if and b ARE integers,

does this mean they are both the same or could be different?

do you see where I am coming from?

are you saying the trick is the wording of the question? a AND b are integers meaning or implying they are the same? because if so then the first answer would be non-zero

where am I going wrong here?


Hi mrcentauri

First you need to understand the language of the question. The question specifically says, which of the following \(CANNOT\) be \(0\)

So any choice which CAN or CANNOT be 0 must be eliminated. We only need option which will NEVER be \(0\) irrespective of the value of \(a\) or \(b\)

Now you can test as many values as you may like for a & b but in all the options except E, there is a possibility to get 0. Hence E is our answer because it CANNOT be 0 for any combination of a & b.

as the question does not provide any restriction between a & b so a=b is a possible assumption


ok this makes sense so basically I have to force the equation as such that the variables in the expression will result in an equation that equals 0,

This makes complete sense now, thank you

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Re: If a and b are integers and b ≠ 0 which of the following CANNOT equal   [#permalink] 24 Dec 2017, 05:42
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