If x and y are non-negative integers such that x + y = 2, then which a

Question

If x and y are non-negative integers such that x + y = 2, then which among the following can be the value of 7x + 3y?

I. 6
II. 10
III. 14

(A)  II only
 (B)  I and II
 (C)  I and III
 (D)  II and III
 (E)  I, II and III

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-header3-e1532524244114.jpg

Aprajita760 · Answer

Given x+y=2 and both x and y are positive numbers. 
This means that 2 can be the value only if x=y=1.

Now, substitute the value of x and y in 7x+3y which will give the answer as 10.
But that is not provided in the option.

Can you please tell the method of solving it?

BrentGMATPrepNow · Answer

The key here is that x and y are non-negative  integers 
This means there are only 3 possible solutions to the equation x + y = 2

case i: x = 0, y = 2, in which case, 7x + 3y = 7(0) + 3(2) = 6
case ii: x = 1, y = 1, in which case, 7x + 3y = 7(1) + 3(1) =10
case iii: x = 2, y = 0, in which case, 7x + 3y = 7(2) + 3(0) = 14

So, 7x + 3y can equal 6, 10 or 14

Answer: E

Cheers,
Brent

Aprajita760 · Answer

Got it! Thanks! :D

Arro44 · Answer

X and Y can be either 0, 1 or 2 respectively.

If we plug in the different possible values we get

7(1) + 3(1) = 10
7(0) + 3(2) = 6
7(2) + 3(0) = 14

Therefore, I would go with AC E, all results are possible.

urshi · Answer

It is not positive. It is stated that it is non-negative integer. Which means the options for x and y can be

X + Y = 0,2 or 2,0 or 1,1

Hope it clears the air.

Posted from my mobile device

Archit3110 · Answer

non -ve integers ; 0,1,2,3,... so on 
so for x+y=2
we can have (1,1),(2,0),(0,2)
so 7x+3y can be 6,10,14
IMO E

nick1816 · Answer

7x+3y= 4x+3x+3y= 4x+3(x+y)=4x+6

x can have 3 values 0.1 and 2

At x=0, 4x+6= 4*0+6=6
At x=1, 4x+6= 4*1+6=10
At x=2, 4x+6= 4*2+6=14

EgmatQuantExpert · Answer

Solution 
  Given:  
 • x and y are non-negative integers
• x + y = 2

To find:  
 • The value of 7x + 3y

Approach and Working Out:   
 • We are given that x and y are non-negative integers. 
 o Implies, x = {0, 1, 2, 3, 4 …….} and y = {0, 1, 2, 3, 4 ………..}

• And we know that, x + y = 2
• Thus, the possible values of (x, y), which satisfy the above conditions are (0, 2), (1, 1), (2, 0)

Case 1 : (x, y) = (0, 2)
 • Implies, 7x + 3y = 7*0 + 3*2 = 6

Case 2 : (x, y) = (1, 1)
 • Implies, 7x + 3y = 7*1 + 3*1 = 10

Case 3 : (x, y) = (2, 0)
 • Implies, 7x + 3y = 7*2 + 3*0 = 14

Hence, the correct answer is Option E.

Answer: E

https://e-gmat.com/blogs/wp-content/uploads/2018/07/FT-GC-FB-event-e1532524398949.jpg

ScottTargetTestPrep · Answer

Solution:

Since x and y are non-negative integers, the solutions for the equation x + y = 2 are (x, y) = (0, 2), (1, 1) and (2, 0).

If (x, y) = (0, 2), then 7x + 3y = 7(0) + 3(2) = 6.

If (x, y) = (1, 1), then 7x + 3y = 7(1) + 3(1) = 10.

If (x, y) = (2, 0), then 7x + 3y = 7(2) + 3(0) = 14.

We see that all of them can be the values of 7x + 3y.

Alternate Solution:

Let’s first treat the two equations as a linear system after re-expressing the equation x + y = 2 as 3x + 3y = 6:

For statement I, we have:

7x + 3y = 6
3x + 3y = 6

Subtracting the second equation from the first yields:

4x = 0

x = 0

Thus, statement I can be true (since x is a non-negative integer).

For statement II, we have:

7x + 3y = 10
3x + 3y = 6

Subtracting the second equation from the first yields:

4x = 4

x = 1

Thus, statement II can be true (since x is a non-negative integer).

For statement III, we have:

7x + 3y = 14
3x + 3y = 6

Subtracting the second equation from the first yields:

4x = 8

x = 2

Thus, statement III can be true (since x is a non-negative integer).

Answer: E

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If x and y are non-negative integers such that x + y = 2, then which a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x and y are non-negative integers such that x + y = 2, then which a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards