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

Got it! Thanks! :D

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.

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

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

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

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

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

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.