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

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

Skywalker18 · Answer

(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

kanusha · Answer

a and b are integers a could be 0,1,-1
On plugging In 
Eliminate ABCD
E : B # 0 , results always a number
E

mrcentauri · Answer

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.

Bunuel · Answer

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.

mrcentauri · Answer

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?

niks18 · Answer

Hi  mrcentauri , kindly check the highlighted parts.

mrcentauri · Answer

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?

niks18 · Answer

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

Bunuel · Answer

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.

mrcentauri · Answer

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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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

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