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

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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

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

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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

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

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).

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

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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

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,