If x and y are integers, what is the value of x + y?

The key for me after getting the question wrong was to understand the question is not asking for X and Y, but 'X + Y'.

I had at first ousted A due to the possibility of X and Y being combinations like 1+6, 2+5, 3+4. The key was in the wording...they all add up to 7 and it is therefore the combinations don't actually matter.

x and y are INTEGERS (point to be noted)
x+y = ?
from stat 1
3<(x+y)/2 < 4
multiplying by 2
6 < x+y < 8
only possible integer between 6 and 8 is 7
so x+y = 7
sufficient .

stat 2
2<x<y<5
since x and y are integers
x= 3 and y =4 are the only possible values.
x+y = 7
sufficient .

correct choice - D

Bunuel, can we safely assume that X and Y have to be a DISTINCT number? X and Y cannot be 3, for instance?

Thanks!

No we cannot assume that: unless it is explicitly stated otherwise, different variables CAN represent the same number.

Thanks Bunuel for your prompt response. My bad, I misunderstood the question!

Video solution from Quant Reasoning:

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is key questions.

StepIII: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of 'x + y' - where 'x' and 'y' are integers.

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that \(3 < \frac{(x + y)}{2} < 4\) .

=> \(3 < \frac{(x + y)}{2} < 4\) = 6 < (x + y ) < 8

=> 'x' and 'y' are integers and hence x + y = integer. The only integer between '6' and '8' will be 7 and therefore, x + y = 7

Since the answer is unique, the condition(1) is sufficient by CMT 2.


Condition(2) tells us that 2 < x < y < 5.

=> 'x' and 'y' are integers and x < y = integer. The only integer between '2' and '5' will be x = 3 and y = 4 and therefore, x + y = 7

Since the answer is unique , the condition(2) alone is sufficient by CMT 2.

Each condition alone is sufficient.

So, D is the correct answer.

Answer: D

SAVE TIME: By Variable Approach, when you know that value of Con(1) = Con(2), then 'D' is the correct answer.

Solution:

Question Stem Analysis:

We need to determine the value of x + y, given that x and y are integers.

Statement One Alone:

Simplifying the inequality, we have:

6 < x + y < 8

Since x and y are both integers, their sum is also an integer. Since there is only one integer value between 6 and 8, we see that x + y = 7. Statement one alone is sufficient.

Statement Two Alone:

Since x and y are integers, the only values that satisfy the inequality 2 < x < y < 5 are x = 3 and y = 4. Therefore, x + y = 7. Statement two alone is sufficient.

Answer: D

Answer: Option D

Video solution by GMATinsight



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1. multiply by 2 on both sides
6<(x+y)<8
i.e. x+y = 7

2. 2<x<y<5
i.e. 2<3<4<5
x+y=7

Correct Answer is D

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