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At a warehouse, the daily output of Machine Orion is two-thirds of the daily output of Machine Vega. What is the daily output of Machine Orion, in units per day?
(1) If each machine produced 12 more units per day, then Machine Orion’s output would be three-fourths of Machine Vega’s output.
(2) If each machine produced 12 fewer units per day, then Machine Orion’s output would be one-half of Machine Vega’s output.
(1) If each machine produced 12 more units per day, then Machine Orion’s output would be three-fourths of Machine Vega’s output.
(2) If each machine produced 12 fewer units per day, then Machine Orion’s output would be one-half of Machine Vega’s output.
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22 Apr 2026, 02:45
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GMAT Club Official Solution:
At a warehouse, the daily output of Machine Orion is two-thirds of the daily output of Machine Vega. What is the daily output of Machine Orion, in units per day?
(1) If each machine produced 12 more units per day, then Machine Orion’s output would be three-fourths of Machine Vega’s output.
Let Orion = 2x and Vega = 3x. Then this statement implies:
2x + 12 = (3/4)(3x + 12)
x = 12
So Orion = 2x = 24.
Sufficient.
(2) If each machine produced 12 fewer units per day, then Machine Orion’s output would be one-half of Machine Vega’s output.
Again let Orion = 2x and Vega = 3x. Then this statement implies:
2x - 12 = (1/2)(3x - 12)
x = 12
So Orion = 2x = 24.
Sufficient.
Answer: D.
At a warehouse, the daily output of Machine Orion is two-thirds of the daily output of Machine Vega. What is the daily output of Machine Orion, in units per day?
(1) If each machine produced 12 more units per day, then Machine Orion’s output would be three-fourths of Machine Vega’s output.
Let Orion = 2x and Vega = 3x. Then this statement implies:
2x + 12 = (3/4)(3x + 12)
x = 12
So Orion = 2x = 24.
Sufficient.
(2) If each machine produced 12 fewer units per day, then Machine Orion’s output would be one-half of Machine Vega’s output.
Again let Orion = 2x and Vega = 3x. Then this statement implies:
2x - 12 = (1/2)(3x - 12)
x = 12
So Orion = 2x = 24.
Sufficient.
Answer: D.
General Discussion
15 Apr 2026, 20:15
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Let Orion’s output = O and Vega’s output = V
Given: O = (2/3)V
Statement (1):
If both produce 12 more,
O + 12 = (3/4)(V + 12)
Substitute O = (2/3)V
(2/3)V + 12 = (3/4)(V + 12)
Simple equation with One variable,
You can skip the calculation, as we will get fixed value
Multiply by 12 to clear fractions:
8V + 144 = 9(V + 12)
8V + 144 = 9V + 108
144 − 108 = 9V − 8V
36 = V
So V = 36
Then O = (2/3)*36 = 24
Statement (1) alone is sufficient.
Statement (2):
If both produce 12 less,
O − 12 = (1/2)(V − 12)
Substitute O = (2/3)V
(2/3)V − 12 = (1/2)(V − 12)
Simple equation with One variable,
You can skip the calculation, as we will get fixed value
Multiply by 6:
4V − 72 = 3(V − 12)
4V − 72 = 3V − 36
4V − 3V = −36 + 72
V = 36
Then O = (2/3)*36 = 24
Statement (2) alone is also sufficient.
Both statements are independently sufficient.
Answer option: D
Given: O = (2/3)V
Statement (1):
If both produce 12 more,
O + 12 = (3/4)(V + 12)
Substitute O = (2/3)V
(2/3)V + 12 = (3/4)(V + 12)
Simple equation with One variable,
You can skip the calculation, as we will get fixed value
Multiply by 12 to clear fractions:
8V + 144 = 9(V + 12)
8V + 144 = 9V + 108
144 − 108 = 9V − 8V
36 = V
So V = 36
Then O = (2/3)*36 = 24
Statement (1) alone is sufficient.
Statement (2):
If both produce 12 less,
O − 12 = (1/2)(V − 12)
Substitute O = (2/3)V
(2/3)V − 12 = (1/2)(V − 12)
Simple equation with One variable,
You can skip the calculation, as we will get fixed value
Multiply by 6:
4V − 72 = 3(V − 12)
4V − 72 = 3V − 36
4V − 3V = −36 + 72
V = 36
Then O = (2/3)*36 = 24
Statement (2) alone is also sufficient.
Both statements are independently sufficient.
Answer option: D
