OG QR 2nd Ed. DS #86

[tofubeans]

If m and n are consevutive positive integers, is m greater than n?

1) m-1 and n+1 are consecutive positive integers.

2) m is an even integer.

Solution: A

The book's explanation is confusing me. They give two different outcomes for solution A yet it is still sufficient. I thought when there are two different outcomes/choices...that the data is insufficient?

[neelgandham]

If m and n are consevutive positive integers, is m greater than n?

1) m-1 and n+1 are consecutive positive integers.

Let us assume that m<n. Since, m and n are consecutive positive integers and n>m, the value of n = m+1. The value of n+1 is m+2. but m+2(n+1)and m-1 are not consecutive integers(contradicts statement I). So, our assumption that the value of m is less than n is wrong.

Now, let us assume that m>n. Since, m and n are consecutive positive integers and m>n, the value of m = n+1. and m(n+1)and m-1(n)are consecutive integers. So, our assumption that the value of m is greater than n is correct. So, statement I is sufficient to answer the question.

Let me explain the same with an example.
Let m<n, m=5 and n=6. Then the value of m-1 is 4 and that of n+1 is 7. Since 4 and 7 aren't consecutive integers, the value of m cannot be less than the value of n.

Let m>n, m=6 and n=5. Then the value of m-1 is 5 and that of n+1 is 6 (consecutive positive integers).

2) m is an even integer.

Irrelevant!

[pemdas]

this question is very precise in its formulation. You are given double constraints here: one in prompt m,n consecutive positive integers and the other in statement(1) m-1,n+1 are consecutive positive integers. The only way this is possible must be when m>n and two consecutive integers interchange their places.

If m and n are consevutive positive integers, is m greater than n?

1) m-1 and n+1 are consecutive positive integers.

2) m is an even integer.

Solution: A

The book's explanation is confusing me. They give two different outcomes for solution A yet it is still sufficient. I thought when there are two different outcomes/choices...that the data is insufficient?

[ronnie1985]

Assume m<n => n=m+1, then using the info in S1, we get m<n, hence not possible
Assume m>n => m=n+1, then using the info in S1, we get m>n, hence possible and sufficient..

[Anurag@Gurome]

If m and n are consevutive positive integers, is m greater than n?

1) m-1 and n+1 are consecutive positive integers.

2) m is an even integer.

Solution: A

The book's explanation is confusing me. They give two different outcomes for solution A yet it is still sufficient. I thought when there are two different outcomes/choices...that the data is insufficient?

(1) m - 1 and n + 1 are consecutive positive integers implies m > n.
If m < n, then m - 1 and n + 1 wouldn't be consecutive; SUFFICIENT.

(2) m is an even integer; clearly NOT sufficient.

The correct answer is A.

[shagalo]

the problem in this question is , in the choice # 1 , they said : m-1 and n+1 are consecutive positive integers.
How do i know that m-1 is before n+1 or after ,,,, they said just ( consecutive integers)