If a and b are consecutive negative integers, is b greater than a?

a=-4,b=-3 a+1=-3,b-1=-4 and b>a so yes statement 1 is sufficient,
Statement 2. suppose b=-3 or -5 but a is still unknown so can't answer. Answer A

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No This question asks whether b > a.

Given information from the question stem: a and b are consecutive negative integers.

On this question you can start with Statement 2 first since that statement is easier to evaluate.

Statement 2: b is an odd number. It should not matter if b is odd when determining if “b > a.” You can quickly Play Devil’s Advocate with a couple of consecutive negative integers. b could = -5 and a could equal -6. In this case b > a. Of course b could also equal -5 and a could equal -4, in which case b is not greater than a. Since you can get both a “yes” and a “no” for this statement it is not sufficient. Eliminate choices B and D (since you did Statement 2 first.)

Statement 1: a + 1 and b – 1 are consecutive negative integers. You already know from the facts that a and b are consecutive negative integers. Now when you add one to “a” and subtract one from “b” you also have consecutive negative integers. Playing Devil’s Advocate is a good strategy here to take the abstraction of variables and make it concrete with numbers. You can use the numbers from above: Let b = -5 and a = -6. Adding 1 to a and subtracting 1 from b changes it to b = -6 and a = -5, meaning that these are still consecutive negative numbers. So b can be greater (less negative) than a.

Can the opposite be true? Can a be larger than b? Try using the reverse numbers. Make a = -5 and b = -6. Now when you add one to a and subtract one from b the result is a = -4 and b = - 7, so this will not work with Statement 2. a cannot be larger than b; b must be the larger number. The statement is sufficient. The correct answer is A.

If a and b are consecutive negative integers, is b greater than a?

(1) \(a + 1\) and \(b – 1\) are consecutive negative integers.
(2) b is an odd number.

Consecutive numbers are numbers that are next to each other in a number line.
So either \(a=b+1\) or \(b=a+1\) i.e., \(a>b\) or \(b>a\)

Statement 1: a+1 and b-1 are consecutive numbers
i,e., \(a+1\) must be have a distance of +1 or -1 of \(b-1\) on numerical line of integers.
Thus \((a+1)=(b-1)+1\) or \((a+1)=(b-1)-1\)
\(a+1=b\) or \(a=b-3\)(here a,b have a difference of 3 i.e., these two cannot be consecutive numbers thus failing the given information in statement 1.)

Thus for \(a+1=b\) given that \(a, b\) are negative integers b is always greater than a.

Statement 2: b is an odd number.
b can be any odd negative number and there is no info regarding number a except that it is negative as mentioned.
So it we cannot determine whether b>a or not!
Not sufficient.

Answer choice A

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