What is the sum of a certain pair of consecutive odd integers?

Two consecutive odd integers: a, a+2
The sum is 2a+2, a is the odd interger

(1) At least one of the integers is negative.
a can be -1, -3, -5, etc
Insufficient
(2) At least one of the integers is positive
a can be -1, 1, 3, ....
insufficient

1+2 => a=-1 => sufficient

Ans: C

What is the sum of a certain pair of consecutive odd integers?

(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

Sol. Let consecutive odd integers be 2x-1 and 2x+1
2x-1+2x+1=? or 4x = ?

1) let x=-2 so 2x-1 = -5 and 2x+1 = -3 sum is -8
let x =0 so -1 and 1 sum is 0
so not sufficient
2) let x = 2 so 2x-1 = 3 and 2x+1 = 5 sum = 8
let x = 1 so 2x-1 = 1 and 2x +1 = 3 sum = 4
so not sufficient

1) + 2) one is +ve and one is -ve
when x= 0 then only it is sufficient
so sum is 0

C is the correct answer

IMO E.

(1) At least one of the integers is negative. NS

We know at least one of the integers is -, means it can be -1, 1, or ..... or -3,-1 ,1

(2) At least one of the integers is positive. -5,-3,-1,1 or -5,-3,-1,1, or we do not have the exact number of integers. NS

What is the sum of a certain pair of consecutive odd integers?

(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

In my opinion, E. Please correct me if I am wrong.

1) At least one of the integers is negative.
-1, 3, 5, etc. We cannot find the sum. Not Sufficient.
2) At least one of the integers is positive.
-3, -1, 1, etc. We cannot find the sum. Not Sufficient.
1 & 2) We know that at least one has to be positive and at least one has to be negative. So at a minimum we have -1 and 1 with the sum of 0. But, we can also have -1, 1, and 3 with the sum of 3. This also, satisfies that at least one is odd integer is negative and at least one odd integer is positive. 0 does not equal 3, Not Sufficient. Without knowing how many positive odd integers and how many negative odd integers, we can't find the solution.

Here is my solution ->
As x and y are both consecutive odd
-> y =x+2 and x is odd

We need the sum x+y

Statement 1
Atleast one of them is negative
Test cases -> -101,-99
or -3,-1
Hence Insufficient
Statement 2
Atleast one of them is positive
Test cases -> 3,5
11,13
Hence insufficient
Combing the Two statements
Atleast one is negative and atleast one is positive
So one of them must be -1 and the other must be 1
Since (-1,1) is the only pair that will satisfy the conditions
Hence x+y must be Zero
Hence C

Target question: What is the sum of a certain pair of consecutive odd integers?
ASIDE: Some examples of pairs of consecutive ODD integers include -7 & -5, -13 & -11, 21 & 23, -1 & 1 etc.

Statement 1: At least one of the integers is negative.
So, one of the odd integers could be negative, or both of the odd integers could be negative.
There are several pairs of integers that meet this condition. Here are two:
Case a: the numbers are -3 and -1 in which case the sum is -4
Case b: the numbers are -1 and 1 in which case the sum is 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: At least one of the integers is positive.
So, one of the odd integers could be positive, or both of the odd integers could be positive.
There are several pairs of integers that meet this condition. Here are two:
Case a: the numbers are 5 and 7 in which case the sum is 12
Case b: the numbers are -1 and 1 in which case the sum is 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
In order to satisfy the conditions in statements 1 and 2, it MUST be the case that one of the odd integers is negative, and the other integer is positive.
The only way that this can happen is when the two integers are -1 & 1
So, the sum of the two integers must be 0

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer:
Cheers,
Brent

What is the sum of a certain pair of consecutive odd integers?

(1) At least one of the integers is negative --> infinite pairs are possible: ... (-3, -1); (-17, -15); ... (-1, 1); ... Not sufficient.
(2) At least one of the integers is positive --> infinite pairs are possible: ... (3, 5); (19, 21); ... (-1, 1); ... Not sufficient.

(1)+(2) One odd integer must be positive and another negative. As they are consecutive odd integers, there is only one pair possible (-1, 1) --> -1+1=0. Sufficient.

Answer: C.

We must determine the sum of a pair of consecutive odd integers.

Statement One Alone:

At least one of the integers is negative.

Using the information in statement one, we do not have enough information to answer the question. The two consecutive odd integers could be -1 and 1, with a sum of 0, or they could be -3 and -1, with a sum of -4. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

At least one of the integers is positive.

Using the information in statement two, we do not have enough information to answer the question. The two consecutive odd integers could be -1 and 1, with a sum of 0, or they could be 1 and 3, with a sum of 4. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the information from statements one and two, we know that at least one of the integers is negative and at least one of the integers is positive. The only pair of consecutive odd integers that includes one negative integer and one positive integer is -1 and 1, with a sum of 0. This is sufficient to answer the question.

Answer: C

watch out ! in question stem it is "certain pair of " not the "certain pairs of"

1) at least one integer is negative so it could be -1+1 or -5+(-3); Two different answrs. Insufficient.

2) One negative, other may be positive, or both can be positive of any consecutive odd values. (-1+1), (1+3), (2+3) Insufficient.

Considering both:
Must be \(-1+1\) definite Answer.

Ans is C.

1) at least one integer is negative so it could be -1+1 or -5+(-3); Two different answers. Insufficient.

2) One negative, others may be positive, or both can be positive of any consecutive odd values. Insufficient.

Considering both:
Must be -1+1 definite Answer.
Ans is C.

Video solution from Quant Reasoning:
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Answer: Option C

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