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
