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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?

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by BTGModeratorVI » Wed May 13, 2020 11:00 am

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Answers

A

B

C

D

E

Stats

Difficulty—

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


Answer: E
Source: e-GMAT
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Re: 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

by Jay@ManhattanReview » Thu May 14, 2020 11:27 pm
BTGModeratorVI wrote: ↑
Wed May 13, 2020 11:00 am
 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

Answer: E
Source: e-GMAT
Given that x and y are non-negative integers such that x + y = 2, the pair of values for x and y are

1. x = 0 and y = 2. thus, 7x + 3y = 7*0 + 3*2 = 6
2. x = y = 1. thus, 7x + 3y = 7*1 + 3*1 = 10
3. x = 2 and y = 1. thus, 7x + 3y = 7*1 + 3*0 = 14

The correct answer: E

Hope this helps!

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Re: 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

by Scott@TargetTestPrep » Sat May 16, 2020 9:17 am
BTGModeratorVI wrote: ↑
Wed May 13, 2020 11:00 am
 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


Answer: E
Source: e-GMAT
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

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