If x and y are positive integers, are they consecutive?

Question

(1) x + y = 3
(2) x - y = 1

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iamsachin · Answer

Is X & y consecutive?
1)X+y = 3, x and y are +ve integers so they can be 1,2,3....infinite. For the given option it can only be possible by 1+2.
Sufficient
2)X-Y=1, for any numbers to be consecutive there diff should be 1 and here is also one.
sufficient

answer is D

C0nst1 · Answer

If we take both Statements together the answer to the question would be "no". So if it ask If something is the case, then we should look out for options that respond "yes" to that?

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are if positive integers x and y are consecutive it not

Statement 1:   x + y = 3
  Since x and y are positive ingtegers, x + y = 3 is only possible when x and y are 1 and 2 
 This makes them consecutive  
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:   x - y = 1
  Since the difference between x and y is 1, we can be sure they are consecutive 
 Thus,  statement 2 alone is also sufficient

Hence the right answer is    Option D

vivek920368 · Answer

Bunuel  we do not know if x>y or visa versa.

so the difference could be 1 or -1.

how do we look past this? please advise.

Bunuel · Answer

The question asks whether x and y are consecutive integers. Each statement gives an YES answer to this question and we are not concerned whether x > y or not.

ScottTargetTestPrep · Answer

Statement One Alone:

\Rightarrow  x + y = 3

Since x and y are positive integers, the only way the sum of x and y can equal 3 is if x = 1, y = 2, or if x = 2, y = 1. In either case, x and y are consecutive integers. Statement one alone is sufficient.

Eliminate answer choices B, C, and E.

Statement Two Alone:

\Rightarrow  x - y = 1

Since x is one more than y, x and y are consecutive integers. Statement two alone is sufficient.

Answer: D

If x and y are positive integers, are they consecutive?

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