A warehouse is equipped with identical packing machines

Question

A warehouse is equipped with identical packing machines, each operating at the same constant rate. If 12 of these machines can package a shipment in x hours, how many hours would it take y of these machines to package the same shipment?

(1) y = 3x
(2) One machine can package the shipment in 60 hours.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A warehouse is equipped with identical packing machines, each operating at the same constant rate. If 12 of these machines can package a shipment in x hours, how many hours would it take y of these machines to package the same shipment?

Let's measure the total work in machine hours:

If 12 machines finish in x hours, total work = 12 * x.
If y machines do the same work, required time = (12 * x)/y.

(1) y = 3x

Then required time = (12 * x)/(3 * x) = 4 hours. Sufficient.

(2) One machine can package the shipment in 60 hours.

1 machine finishes in 60 hours, so total work = 60 machine hours. Then 12 * x = 60, so x = 5. But y is still unknown, so (12 * x)/y is not fixed. Not sufficient.

Answer: A.

vasu1104 · Answer

all machines have identical rate.

say work = P
now we are given that 12 machine take X hrs to finish this task.
so rate for these 12 machines = P / X

from this we can find that rate of 1 machine = P / 12X

now we have Y machines
rate of Y machines = YP / 12X
we need to find how many hours for the same job
time = work / rate 
P / (YP/12X)
time = 12X / Y (find this)

so if we can find Y in terms of X, we get the ans.

S-1
y = 3x
we get the ans. time = 4 hrs
sufficient.

S-2
rate of 1 =p/60
so for 12 =p/5
for y machine rate = YP / 5

time for these y machines = 5 / Y

still unknowns with Y.
not sufficient

Option A

dp1234 · Answer

12 machine work together for x hours to finish a work. That means 12x hrs required for 1 job. 
So for y machines, time required will be t= (12x/y) hours. Need to find t, its a value question. 
(1) if y=3x, t=12x/3x = 4 hrs. SUFFICIENT
(2) 1 machine can do it in 60 hours. But we dont know no of y ? so cant find time for y machines. NOT SUFFICIENT.

ANS. A

Edskore · Answer

Great question — this is a classic Work and Rate Problems question in Data Sufficiency, and it's tricky because both statements look like they give you "useful" information. Let me walk through it carefully.

Step 1 — Set up the relationship.
Since all machines are identical, 12 machines complete the job in x hours. So:
Total work = 12 × x = 12x (machine-hours)
For y machines, the time t = Total work ÷ y = 12x/y
Our target: find the value of 12x/y.

Step 2 — Evaluate Statement (1): y = 3x
Substitute: t = 12x / (3x) = 12/3 = 4 hours.
The x values cancel, and we get a definite answer of 4 hours. SUFFICIENT.

Step 3 — Evaluate Statement (2): One machine can package the shipment in 60 hours.
This tells us the rate of 1 machine = 1 job per 60 hours.
So 12 machines take 60/12 = 5 hours → this means x = 5.
Now t = 12(5)/y = 60/y. But y is still unknown. INSUFFICIENT.

Step 4 — Combining won't help here either: Statement (2) fixes x = 5, so y = 3(5) = 15, giving t = 4 hours — but we already got 4 from Statement (1) alone. Answer: A.

Common trap: Students see Statement (2) and think "I know x now, that should be enough!" The trap is that knowing x alone (or the rate of one machine) doesn't pin down y, which is the other unknown you need. The sufficiency question is always whether you can reach a unique numerical answer — here y is still floating freely with Statement (2) alone.

Takeaway: In Work and Rate DS problems, first write out what the target expression actually depends on (here it's x and y together as a ratio), then check whether each statement pins down that ratio. If a statement gives you a direct relationship between the unknowns in the target, it's likely sufficient.

Dereno · Answer

Rate is constant. And 12 machines takes x hours.

So, total work = 12x

Time taken by y machines = ?

Statement 1:

y = 3x

Time taken by 3x machine = 12x / 3x = 4

Sufficient

Statement 2:

One machine can package the shipment in 60 hours.

1 machine takes 60 hours.

then , y machine takes (60/y) hours.

Hence,  Insufficient

Option A

chloreton · Answer

This is quite easy

We know that the work done is same in both. We will equate the Workdone = rate * time in both cases.
12 * x = y * t, we need to find t=?

From statement 1: y= 3x
As we can see above we can substitute and find the value of t. Sufficient

From statement 2 : One machine can package the shipment in 60 hours.
This is not going to be useful since we dont know what y is. Not sufficient.

Therefore, Option  A

A warehouse is equipped with identical packing machines

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GMAT Data Sufficiency (DS) Questions

A warehouse is equipped with identical packing machines

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