Reserve tank 1 is capable of holding z gallons of water. Water is pump

capacity of tank 2 is u = 2*(x-y)

time it takes for tank 2 to get filled is 2*(x-y)/y
time it takes for tank 1 to get filled is z/(x-y)

z/(x-y) - 2*(x-y)/y < 0? equivalent (since y > 0 , x-y > 0)

zy < 2*(x-y)^2 = 2*x^2-4*x*y + 2*y^2 (1) is sufficient
2 is irrelevant

I'd say A.

1 tells us that if Z was 100, x and y were 10 and 5 respectively, 1 would not be true. for 1 to be true, x and y will be 10 and 1 or around that area.

B tells us nothing about the rate at which water is flowing into the second tank.

Any other thoughts?

Another "lone wolf". Here the complex equation is A

Nice problem. Got to the answer but took more than 3 mins... Problem statement itself took very long to read and understand

I did not get why did you use yz< 2x^2-4xy-y^2 in the above solution. The solution is sufficient without the usage of this equation.

+1 Kudos if you like the post

T1 - Water is being filled at the rate of X Gallons/Minute and leaking at the rate of Y G/M
In one minute T1 is getting filled at (X-Y) G/M
Z Gallons would get filled in Z/(X-Y)

Capacity of T2 = 2(X-Y) G/M
T2 water is being filled at Y G/M
Therefore, T2 would get filled = 2(X-Y)/Y

A) 2 (X-Y)^2 > ZY
=> 2(X-Y)/Y > Z/(X-Y)
Therefore A is sufficient

B) The total capacity of tank 2 is less than one half that of Tank 1
This doesn't specify the relationship between the rates at which the tanks are being filled. Only the relationship between the capacities.

Therefore, Only A is sufficient.

Hope this helps.

HOW DO WE SOLVE SUCH QUES IN 2 MIN . IT TOOK ME MORE THAN 2 MIN TO UNDERSTAND AND SOLVE THE SAME.CAN SOME PLS SUGGEST ME WITH HIS OR HER APPROACH

Bunuel - Please can you help suggest if is there any method in which we can approach to solve in 2 mins ??

Thanks in advance

What is the difficulty level of this question.

Dear GMATGuruNY

Can you share your thoughts on this question?
Thanks in advance

Statement 1: zy < 2x² - 4xy + 2y²
To see the implications of this inequality, plug in values for x and y and solve for z.
Let x=10 and y=2.
Then:
z(2) < 2(10²) - 4(10)(2) + 2(2²)
2z < 128
z < 64.
Here, the capacity of tank 1 is LESS than 64 gallons.

Tank 1:
Since tank 1 receives x=10 gallons per minute and loses y=2 gallons per minute, the net gain for tank 1 = 10-2 = 8 gallons per minute.
Since the capacity of tank 1 is LESS than 64 gallons, the time to fill tank 1 at a rate of 8 gallons per minute must be LESS than 64/8 = 8 minutes.

Tank 2:
After one minute, the volume in tank 1 = 8 gallons.
Since the capacity of tank 2 is twice the volume in tank 1 after one minute, the capacity of tank 2 = 2*8 = 16 gallons.
Time to fill tank 2 at a rate of y=2 gallons per minute = 16/2 = 8 minutes.

While tank 1 requires LESS than 8 minutes, tank 2 requires EXACTLY 8 minutes.
The case above illustrates that tank 1 will fill up before tank 2.
SUFFICIENT.

Statement 2: The total capacity of tank 2 is less than one-half that of tank 1.
In statement 1 above, it is possible that the capacity of tank 2 = 16 gallons, while the capacity of tank 1 = 63 gallons.
These values also satisfy statement 2.
As we saw above, the result will be that tank 1 fills up before tank 2.
But if we increase the capacity of tank 1 to 1000 gallons and leave all of the other values the same, tank 2 will fill up before tank 1.
INSUFFICIENT.

Do we have any other approach to this question
GMATinsight
VeritasKarishma

I manage to get this problem correct by pluging numbers, can someone please try to explain me differently with algebra ? I don't really understand the solutions above

Tank 1:
Since water is PUMPED IN at x gallons per minute but LEAKS OUT at y gallons per minute, the net gain per minute = x-y.
Since the z-gallon tank is filled at a net rate of x-y gallons per minute, we get:
Time fill tank 1 \(= \frac{capacity}{rate} = \frac{z}{x-y}\)

Tank 2:
The total capacity of tank 2 is twice the number of gallons that remains in tank 1 after 1 minute.
After 1 minute, the number of gallons in tank 1 = (net gain per minute)(one minute) = (x-y)(1) = x-y.
Since the capacity of tank 2 is twice this number of gallons, we get:
Capacity of tank 2 = 2(x-y) = 2x-2y.

The water that leaks out of tank 1 drips into tank 2.
Since water leaks from tank 1 into tank 2 at a rate of y gallons per minute, we get:
Time to fill tank 2 \(= \frac{capacity}{rate} = \frac{2x - 2y}{y}\)

Does tank 1 fill up before tank 2?
In other words:
Is the time fill tank 1 less than the time to fill tank 2?
Original question stem:
Is \(\frac{z}{x-y}< \frac{2x-2y}{y}\)?

Simplifying the question stem, we get:
\(zy < (2x-2y)(x-y)\)
\(zy < 2x^2-4xy+2y^2\)

Question stem, rephrased:
Is \(zy < 2x^2-4xy+2y^2\)?

Statement 1: \(zy < 2x^2-4xy+2y^2\)
The answer to the rephrased question stem is YES.
SUFFICIENT.

Statement 2:
Since the capacity of tank 2 = 2x-2y and the capacity of tank 1 = z, we get:
\(2x-2y < \frac{1}{2}z\)
\(4x-4y < z\)
\(4 > \frac{z}{x-y}\)
\(\frac{z}{x-y} < 4\)
No way to answer the original question stem or the rephrased question stem.
INSUFFICIENT.

Please find the solution as depicted in figure

Answer: Option A

Capacity of tank 1 = \(z\) gallons ... (i)
Effective filling rate of tank 1 = \((x - y)\) gallons/min

=> Time taken to fill tank 1 = \(\frac{z}{(x-y)}\) minutes ... (ii)

Volume of water in tank 1 after 1 minute = \((x - y)\) gallons

=> Volume of tank 2 = \(2(x - y)\) gallons ... (iii)

Filling rate of tank 2 = \(y\) gallons/min

=> Time taken to fill tank 2 = \(\frac{2(x - y)}{y}\) minutes ... (iv)

We need to verify if: tank 1 fills up before tank 2

i.e. if \(\frac{z}{(x-y)} < \frac{2(x - y)}{y}\)

i.e. if \(yz < 2(x - y)^2\)

i.e. if \(yz < 2x^2 - 4xy + 2y^2\) ... (v)

From statement 1: The exact condition in (iii) above is mentioned in this statement --- Sufficient

From statement 2: Capacity of tank 2 is less than one half that of tank 1

=> \(2(x - y) < z/2\)

=> \(z > 4(x - y)\)

However, this is not enough to verify condition (v) above - Insufficient

Answer A

Statement 2 - Capacity of tank 2 is less than one half that of tank 1

2(x−y)<z/2, over here why are we saying Capacity of tank 2 is 2(x-y) as that's not the overall capacity but the capacity after 1 min. How do we infer that total capacity of tank 2 will follow the same equation as after 1 min