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

Question

(1)  3<\frac{(x+y)}{2}<4

(2)  2<x<y<5

VeritasPrepRon · Accepted Answer

Hi OmniPrep, this is a good lesson that sometimes gets overlooked. Questions will often give you just enough information to solve X+Y (for example in difference of squares and such) but not for X and Y individually. Recognizing what the question is asking you is the difference between a correct D response and an incorrect E that you were sure was right when you selected it. As always, precision in wording is key. I recommend rereading the question before selecting an answer choice and clicking next, but some people feel they don't have the time to do that type of double check. Just remember that it can easily save you 1-2 traps on the exam, and that can be a big swing in the final score. What's the value of spending 2 minutes to get a question wrong when you can spend 2.2 minutes to get it right.

Hope this helps!
-Ron

Bunuel · Answer

If x and y are integers, what is the value of x + y? (1) 3<(x+y)/2<4 --> multiply by 2; 6 x=3 and y=4 --> x+y=7. Sufficient. Answer: D.

OmniPrep · Answer

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.

minhaz3333 · Answer

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

septwibowo · Answer

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

Thanks!

Bunuel · Answer

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

septwibowo · Answer

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

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=YBXhB9tLByM

MathRevolution · Answer

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.

ScottTargetTestPrep · 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

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=BlT3lZiGP2k

Snehaaaaa · Answer

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

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=pqGh1IY7lMQ Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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