Math Revolution and GMAT Club Contest! If x and y are integers, are

Question

Math Revolution and GMAT Club Contest Starts!

QUESTION #15:

If x and y are integers, are they consecutive?

(1) x + y = 2
(2) x - y = 4

Check conditions below:

Math Revolution and GMAT Club Contest

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dayasantoshi · Answer

Given: x and y are integers,

Question: are they consecutive?
=> x=y+1 or x=y-1

First Approach  by Substituting numbers
(1) x + y = 2
 eg 1: 1+1=2
 eg 2: 0+2=2 or 2+0=2
 eg 3: -1+3=2 etc
We see that in any case x and y are not consecutive. Hence sufficient

(2) x - y = 4
 eg 1: 8 - 4 = 4
 eg 2: 4 - 0 = 4 or 0 - (-4) =4
 eg 3: 2-(-2)=4
We see that in any case x and y are not consecutive. Hence sufficient

Second Approach :
(1) x + y = 2
 0r x = 2 - y----(1)
If x and y are consecutive, x=y+1 or x=y-1 (ie x>y and y>x)
Case 1: On substituting for x = y+1 in (1)
 2-y = y+1
 y = 1/2 --- Not an integer
Case 2: On substituting for x=y-1
 2-y=y-1
 y=3/2----- Not an Integer

Hence, they do not satisfy the conditions, x and y are not consecutive.

(2) x - y = 4
 Or x = 4+y
If x and y are consecutive, x=y+1 or x=y-1 but x= 4+y indicates that they are not consecutive

Hence D

riteshgmat · Answer

Here I was having the doubt weather it is consecutive integers or is it even consecutive integers or is it odd consecutive integers .

I have assumed that it is consecutive integers i.e x and x + 1

Y = X + 1 ? Though they are number of ways to solve this . 
We can keep this value and test it or any other approach .

Statement (1) x + y = 2

The sum of any two consecutive integers is odd. 
For example ,

X = -1 , Y = 0 then X + Y is -1 which is odd.
X = 1 , Y = 0 then X + Y is 1 which is odd.
X = 1 , Y = 2 then X + Y is 3 which is odd.
X = 11 , Y = 12 then X + Y is 23 which is odd.

So they are not consecutive integers. 
may be they both are equal integers i.e X =1 and Y = 1

If the question was about even consecutive integers , then there would be chances that x = 0 and y = 2
Then x,y would be consecutive. But my current assumption is with normal consecutive integer.

(2) x - y = 4

The difference between any two consecutive integers is |1| 
So they are not consecutive integers.

Answer is D

CounterSniper · Answer

for x and y to be consecutive 
either x=y+1 or x=y-1
since neither of the statement doesn't give the required condition for x and y to be consecutive 
so D

WaitingSurprises · Answer

option D.
We need to find yes or no.

Statement 1- We cannot get any consecutive values of integer x and y such that x+y=2 
The only close value is when both are equal i.e. x=1 and y=1 but still they are not consecutive. => no. => sufficient.
Statement 2- We cannot get any consecutive values of integer x and y such that x-y=4 => no => sufficient.

Answer option D.

rockthegmat007 · Answer

QUESTION #15:

If x and y are integers, are they consecutive?

(1) x + y = 2
(2) x - y = 4

-- 
(1) x+y = 2 
the sum of any two consecutive integers is always ODD, so if sum of x and y is 2 (even), they cannot be consecutive, SUFFICIENT.
(2) x-y = 4
x is 4 units to the right to y on number line., so they are not consecutive. SUFFICIENT.
answer choice : D

appsy01 · Answer

I. x + y = 2 =>

Let's try some numbers - 
1+1 = 2 (Not Consecutive)
0+2 = 2 (NC)
-1+3=2 (NC)

We can see that x and y cannot be consecutive and solve the equation
Sufficient

II. x-y=4
x = y + 4
i.e; x is greater than y by 4 hence they are not concecutive
Sufficient

Answer is D

kingjamesrules · Answer

Answer is D. Both statements are sufficient to answer the question.

if x & y are integers, are they consecutive ?

1) x+y = 2 - this means both x and y are odd or both x and y are even as the result is even. This will never be possible if they are consecutive. Hence x and y are not consecutive. SUFFICIENT.

2) x-y=4 - same logic as above, either x and y both should be odd or both should be even for this to be true. Hence x and y are not consecutive. SUFFICIENT.

Answer is D - both are sufficient

Psiva00734 · Answer

if x and y are consecutive integers

If both integers are positive, then add a,a+1=2a+1,

If both integers are negative, then add= -a-a-1=-2a-1.

If consecutive integers substract then, a-a-1=1

or -a+a-1=1., if we use 0 and add equals 1 or -1

if we substitue addition in statment 1 and substraction statement 2 not satisfy as integers.

so both statements are sufficient that x and y are not consecutive integers.

so option D is correct.

nipunjain14 · Answer

statement 1: 
x+y = 2
this will be true for values: 1+1 =2 or 3-1 = 2 or 4-2 = 2 Thus in all cases x and y are not consecutive
Sufficient

Statement 2:
x- y = 2
this will be true for values : 5-1 = 4or 3+1 =4 or 2+2=4 or -4+8 = 4. Thus in all cases x and y are not consecutive
Sufficient

Ans: D

Kurtosis · Answer

St1: x + y = 2
If two integers are consecutive, one integer has to be even and the other integer has to be odd.
even + odd = odd. 
But according to statement 1, the sum of two integers is even. --> x and y are not consecutive integers.
Statement 1 alone is sufficient.

St2: x - y = 4. 
The 2 integers differ by 4 and hence are not consecutive integers.
Also, if x and y are consecutive, the difference between the 2 integers should be odd. But, since the difference is even x and y are not consecutive integers.
Statement 2 alone is sufficient

Answer: D

HieuNguyenVN · Answer

(1) x + y = 2
Since two consecutive integers contain 1 odd number and one even number, sum of two consecutive integers is always odd. -> x & y are not consecutive. Sufficient.
(2) x - y = 4
Since the different between two consecutive integers is always either 1 or - 1, it is sufficient to conclude that x & y are not consecutive.
Answer D.

anirbanroy · Answer

D
I No two consecutive integers can sum up to 2
II Two consecutive integers will either have a difference of +1 or -1.

Icecream87 · Answer

1) The sum of two consecutive integers is always ODD. If both x and y and negative, the sum will be a negative odd, if both positive, a positive odd is one of them is zero then the sum is 1 or -1. Sufficient x and y are not consecutive integers

2) The difference of 2 consecutive integers is always 1 or -1
- if x is 3 and y 4 ==> -1
-if x is 4 y 3 ==> 1
- if x is -3 y -4 ==> 1
- if x is -4 y -3 ==> -1
Sufficient x and y are not consecutive

Answer D

abhib3388 · Answer

Either statement alone is sufficient to answer this question
The answer is no. The numbers are not consecutive
x+y=2, by trial and error we can notice that none of the combinations are consecutive(1,1),(0,2),(2,0),(3,-1),(-1,3),(4,-2),(-2,4) and so on

By statement 2 , x-y=4, we can infer that x and y are seperated by 4 places on the number line and hence are not consecutive.

Ans) D

sri1sastra · Answer

x and y are integers, are they consecutive?

(1) x + y = 2
Lets say x , y are consecutive. Then their difference will be 1 .Therefore y should be either equal to x+1 or x-1
x+x+1 = 2 2x =1 x=1/2. Given x is integer. So not possible.
x+x-1= 2 2x=3 x=3/2 Given x is integer. So not possible.
Therefore with this equation, x and y can never be consecutive. So sufficient.

(2) x - y = 4
Lets say x , y are consecutive. Then their difference will be 1 .
which means x- y=1 or y-x =1 . Therefore x and y are not consecutive from this above equation. Hence sufficient.

As EACH statement ALONE is sufficient to answer the question asked, therefore choice D.

HKD1710 · Answer

Given: x and y are integers

(1) x + y = 2

sum of two consecutive integers will not be 2.

Sufficient.

(2) x - y = 4

Difference should be 1 in case of consecutive integers.

Sufficient.

Option D is the correct answer.

Bunuel · Answer

MATH REVOLUTION OFFICIAL SOLUTION:

Since we have 2 variables (x, y) in the original condition, we also need 2 equations to match the number of variables and the number of equations. Since we need both 1) and 2), the correct answer is likely C. Using both con 1) & 2), we get x=3, y=-1. Since they are not consecutive, it is not sufficient. Therefore the correct answer is C. However, since this is an “integer” question, which is one of the key questions, we should apply Common Mistake Type 4(A).

In case of con 1), if x+y=2, in any cases, there cannot be consecutive integers. So this is a “no” and sufficient (Adding two consecutive integers will always yield an odd number).

In case of con 2), the difference between two consecutive integers is always 1. So this is also a “no” and sufficient. Therefore, the correct answer is D. 
If D and C are both correct answers, then  D is the final correct answer . This type of question appears in a score range of 50 to 51.

Note 1 : Solving this type of question usually takes over 5 minutes during the actual exam. However, if you understand the relationship between Variable Approach Method and Common Mistake Types, you will be able to solve this type of question in just about 2 minutes.

Note 2 : For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

bumpbot · Answer

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