If a and b are integers, and the sum of a and b is zero, which of the

a+b = 0

So, either a and b are of opposite signs or both a and b are 0

None of the options is always true.

Option E

If a and b are integers, and the sum of a and b is zero, which of the following statements must be true?
(A) The product of a and b is even.
(B) The product of a and b is odd.
(C) The product of a and b is negative.
(D) The product of a and b is zero.
(E) None of the above.


Solution

Given a+b =0 and a and b are integers , MBT needed


a + b = E we can have case1 (a odd and b odd ) or case2 ( a even and b even)

option A : Ruled out as product can be odd also as in Case 1
Option B : Ruled out as Product can be even also as in Case 2
Option c : Ruled out as we can have both a and b = 0 so product is not negative
option d :Ruled out as product can -ve also , a=2 and b=-2 Product =-4


Option E : by process of elimination therefore e is the answer - None of above

The two integers have to be the opposite sign of same integer. So the product of a and b is negative.
Answer is C.

Let's assume the following two possible solutions: 5, -5 and 4, -4. Answer A and B are negated because the product can be either even or odd. The answer C is true because in order to get the 0 we must have one positive and one negative numbers, and the product of these two are negative. For answer D, in order to get 0 we have to have at least one 0 but a and b are distinct integers so it is not true. So the answer is "C"

As a+b = 0 --> a = -b. Also, both a & b are integers.

As it is must be true question, we will evaluate each option, and will try to find any possible scenario while will contradict the option.

(A) The product of a and b is even. --> 3, -3 (negative numbers are neither odd, nor even)
(B) The product of a and b is odd. --> 2,-2 (negative numbers are neither odd, nor even)
(C) The product of a and b is negative. --> 0,0
(D) The product of a and b is zero. --> 2,-2
(E) None of the above. --> CORRECT ANSWER

Negating (A) -1 and +1
Negating (B) -2 and +2
Negating (C) 0 and 0.
Negating (D) -1 and +1.
Answer (E) None of the above.

Given A and B are integers and sum is zero. Our job is to find one value to prove statements wrong and eliminate each.
Let us take A = -1 and B = 1
a) product is even = > no . Eliminate
b) The product is odd => yes. Keep for now.
c) The product is negative => no. Eliminate
d) The product is zero => no. Eliminate

Now consider A = -2 and B = 2
b) the Product is odd => no(4) . Eliminate.


Hence answer is none of the above and E.

a+b=0;=>a=-b
If a and b are non zero, their product will be negative
If a and b are zero, their product will be 0
Hence non of these

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a + b = 0
It is a must true condition , so we have to find out one case which is not true.
a and b can either have opposite signs with same number or can be both zero.

A) Product of a and b is even => When a=2 and b = 4 but 2+4 is not equal to zero.
B) Product of a and b is odd => When a=3 and b = 3 but 3+3 is not equal to zero.
C) Product of a and b is negative => When a=2 and b = -3 but 2-3 is not equal to zero.
D) Product of a and b is zero => When a=0 and b=2 but 0+2 is not equal to zero.

Answer - Option 'E'

Since this is a MUST-BE true question, let's evaluate each statement and try to find a case that doesn't conform to the choice:
(A) The product of a and b is even. Consider -3 and 3, their sum = 0, but product = -9 (not even) OUT
(B) The product of a and b is odd. Consider -4 and 4, their sum = 0, but product = -16 (not odd) OUT
(C) The product of a and b is negative. Consider 0 and 0, their sum = 0, but product = 0 (not negative) OUT
(D) The product of a and b is zero. See (A) and (B) for examples.
(E) None of the above. TRUE

Thus, the correct answer is (E)

If a and b are integers, and the sum of a and b is zero, which of the following statements must be true?

numbers
a and b will be such a=+-b
three forms
i) a= 3 so b= -3
ii) a = 2 so b = -2
iii) a= 0 and b= 0

(A) The product of a and b is even. i) violates it
(B) The product of a and b is odd. ii) violates it
(C) The product of a and b is negative. iii) violates it
(D) The product of a and b is zero. i) and ii) violates it
(E) None of the above. should be the correct answer

E is the correct answer

which means a mode of a and b are equal
either a or b has to be negative to make the sum zero
so the correct answer is c

Given, a and b are integers (they can be -3, -7, 0 , 2, 3, any integer value)
a+b=0
case 1, a=b=0
->then,the sum of a+b=0+0=0
->the product of a*b=0

or, case 2, a=-b
->then, the sum of a+b=a-b=0
->the product of a*b=(-)ve integers

Correct Answer E ( Both C and D can be answer, so we can't choose one)

can be odd ( -1*1) or even (-2*2) and both of them could also be 0.

OA is E, None of the above

If a and b are integers, and the sum of a and b is zero, which of the following statements must be true?
(A) The product of a and b is even. - Incorrect ,
suppose a =-3 and b =+3 which gives a+b =0 but their product is -9 which is not even .so this must not be true for all cases.

(B) The product of a and b is odd. - Incorrect
suppose a =-4 and b =+4 which gives a+b =0 but their product is -16 which is not odd .so this must not be true for all cases.

(C) The product of a and b is negative. - Incorrect
suppose a=0 and b =0, here also sum a+b =0 , but their product is not negative. so this must not be true for all cases.

(D) The product of a and b is zero. - Incorrect
suppose a =-3 and b =+3 which gives a+b =0 but their product is -9 which is not zero .so this must not be true for all cases.

(E) None of the above. - Correct, As either of the option, must not be true in every case.

So Answer is none of the above

If a and b are integers, and the sum of a and b is zero, which of the following statements must be true?
(A) The product of a and b is even.
(B) The product of a and b is odd.
(C) The product of a and b is negative.
(D) The product of a and b is zero.
(E) None of the above.

a + b = 0. Therefore a = -b. The product of a and b is \(a*b = -b*b = -b^2\). Thus this product can be even if b is even, can be odd if b is odd, can be negative if b is positive, and can be 0 if b is 0. Then we can only choose E.

Ans: E

Let's go through the options with some counterexamples. Since it is a must be true question, every possible set of value should satisfy the condition, failure in which would deem the answer choice unacceptable.

A) The product need not be even, as we could add two odd numbers with opposite signs and get an odd product. For instance 3+(-3) does yield a sum of 0, but its product is not even. It is -9 (odd).

B)The opposite of answer choice A, we could add two even numbers with opposite signs and have an even product. Say 2+(-2) yields a sum of 0, but an even product.

C) Product need not be negative, we can add 0 and 0 to get a sum of 0, and a product 0, which is non negative.

D) The examples stated in options A and B show that the product need not always be 0.

E) Since we proved that none of the above options need not be always true, this is the only valid choice.

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