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

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New post Updated on: 19 Jun 2019, 06:44
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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

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Originally posted by EgmatQuantExpert on 19 Jun 2019, 06:39.
Last edited by EgmatQuantExpert on 19 Jun 2019, 06:44, edited 2 times in total.
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If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post Updated on: 19 Jun 2019, 06:44
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?

Originally posted by Aprajita760 on 19 Jun 2019, 06:43.
Last edited by Aprajita760 on 19 Jun 2019, 06:44, edited 1 time in total.
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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 06:44
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EgmatQuantExpert wrote:
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


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
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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 06:45
GMATPrepNow wrote:
EgmatQuantExpert wrote:
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


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


Got it! Thanks! :D
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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 06:46
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.
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If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 06:54
Aprajita760 wrote:
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?



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.

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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 11:23
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


EgmatQuantExpert wrote:
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

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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 19 Jun 2019, 14:52
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 wrote:
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

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Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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New post 26 Jun 2019, 03:41

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


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Re: If x and y are non-negative integers such that x + y = 2, then which a   [#permalink] 26 Jun 2019, 03:41
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