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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3256
If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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Difficulty:   15% (low)

Question Stats: 75% (01:09) correct 25% (01:19) wrong based on 85 sessions

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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

_________________

Originally posted by EgmatQuantExpert on 19 Jun 2019, 05:39.
Last edited by EgmatQuantExpert on 19 Jun 2019, 05:44, edited 2 times in total.
Intern  B
Joined: 05 May 2019
Posts: 21
If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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, 05:43.
Last edited by Aprajita760 on 19 Jun 2019, 05:44, edited 1 time in total.
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4355
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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1
Top Contributor
1
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

Cheers,
Brent
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Intern  B
Joined: 05 May 2019
Posts: 21
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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

Cheers,
Brent

Got it! Thanks! :D
LBS Moderator V
Joined: 04 Jun 2018
Posts: 692
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44 GPA: 3.4
WE: Analyst (Transportation)
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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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Intern  B
Joined: 21 Feb 2018
Posts: 16
If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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.

Posted from my mobile device
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5918
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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

VP  V
Joined: 19 Oct 2018
Posts: 1309
Location: India
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3256
Re: If x and y are non-negative integers such that x + y = 2, then which a  [#permalink]

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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.

_________________ Re: If x and y are non-negative integers such that x + y = 2, then which a   [#permalink] 26 Jun 2019, 02:41
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