Throughout last week, water was leaking from a certain tank at a const

Question

Throughout last week, water was leaking from a certain tank at a constant rate of \(\frac{1}{4}\) gallon per hour, and 14 gallons of water were added to the tank every day at 1 o'clock in the afternoon. If there were \(32 \frac{3}{4}\) gallons of water in the tank at 2 o'clock last Tuesday afternoon, at what time last week were there \(46 \frac{3}{4}\) gallons of water in the tank?

A. 2 o'clock Wednesday afternoon
B. 1 o'clock Thursday morning
C. 6 o'clock Thursday morning
D. 10 o'clock Thursday evening
E. 2 o'clock Friday morning

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A. 2 o'clock Wednesday afternoon
B. 1 o'clock Thursday morning
C. 6 o'clock Thursday morning
D. 10 o'clock Thursday evening
E. 2 o'clock Friday morning

Guntabulla · Accepted Answer

Every 24 hours there is a total addition of 8 gallons to the tank ( 14 gallons at 1:00 pm and a leak of 6 gallons (24/4) ).
We need a total addition of 14 gallons in the tank to make the required number (187/4 - 131/4).
Lets say two days have passed. Therefore at 2:00 pm on Thursday there is a total of 16 gallons in the tank. We need to let the leak continue from here until 2 gallons have been drained.
Therefore 2/(1/4) = 8 hours.

The answer is 10:00 pm on Thursday

KarishmaB · Answer

Rate of leak = 1/4 gallon per hr = 1 gallon per 4 hours = 6 gallons per day
Water added to tank = 14 gallons per day

Hence, every day, the tank gained 14 - 6 = 8 gallons.

32 \frac{3}{4}  gallons of water in the tank at 2 o'clock last Tuesday afternoon
means
33 gallons at 1:00 PM on Tuesday.
Hence 41 gallons at 1:00 PM on Wednesday and 49 gallons at 1:00 PM on Thursday.
to reach 47 gallons, it would take 4*2 = 8 hrs
to reach 46(3/4) gallons, it would take another 1 hour.

So 9 hrs after 1' o clock i.e. at 10:00 PM on Thursday, the tank had 46(3/4) gallons.

Answer (D)

sachi-in · Answer

Each 24 hours 24/4 = 6 gal is lost
Each day at 2 O'clock 14 gal is gained

Days:  Tue 2      Wed 2    Thu 2
Galln:  32.75      40.75     48.75

Each hour 0.25 or 1/4 gal is lost
hence to lose 2 gallons it will take 8 hrs from Thursday 2 O'clock

sheriffs · Answer

The tank starts with 32.75 gallons of water at 2 o'clock last Tuesday afternoon.
Water is leaking from the tank at a constant rate of 0.25 gallons per hour, so the tank loses 0.25 gallons of water per hour.
Every day at 1 o'clock in the afternoon, 14 gallons of water are added to the tank.
We want to find out when there were 46.75 gallons of water in the tank.
Now, let's create a equation to represent the situation:

Let T be the time in hours since last Tuesday afternoon.

The amount of water in the tank at time T is:

32.75 + 0.25T (since the tank starts with 32.75 gallons and loses 0.25 gallons per hour)

We want to find when the amount of water in the tank reaches 46.75 gallons:

32.75 + 0.25T = 46.75

Subtract 32.75 from both sides:

0.25T = 14

Divide both sides by 0.25:

T = 56

So, it will take 56 hours for the tank to go from 32.75 gallons to 46.75 gallons.

Now, we need to find the time when this happens.

56 hours is equal to 2.33 days (since there are 24 hours in a day).

So, the tank will have 46.75 gallons of water after 2.33 days from last Tuesday afternoon.

The correct answer is D. 10 o'clock Thursday evening.

thr3at · Answer

Hello,

Can you please correct me where I am wrong.

Combined efficiency of the pipes  ( in and Out) per hour = 14/24 (14g every 24 hours) - 1/4 ( ever hour gallons of water removed)
= 1/3

We have to fill 14G of water (46.75 - 32.75)

Time (in Hours)= 14/0.33= 42

In terms of days= 42/24=~ 1.8 
 1.8 days = 1 day + 18 hours.

Please correct me where I am wrong.

jpmendgon · Answer

I believe this is wrong, the question is misleading.
At Thursday 1pm 14 gallons were added to 35 existing gallons to make 49 gallons.
So, at the moment the 14 gallons were being added the tank came to a moment with 46,75 gallons.
Am I making a mistake here?

hchnr · Answer

let x be the days to reach our goal to  46 \frac{3}{4} 
we know that for one day (starting from 1pm) we have 8 gallons of water every day (14-24* \frac{1}{4} =8)
so we want to know  32 \frac{3}{4}  +8x =  46 \frac{3}{4} 
x= 7/4 days
7/4 days *24 = 42 hours
so 14:00 Tuesday + 42 hours = 22:00 Thursday

ndwz · Answer

same doubt.. can someone please explain why we don't add 42 hrs to 2PM Tuesday to get an answer of 8AM Thursday

DanTheGMATMan · Answer

Good rate problem. Take it one episode at at time:
 https://www.youtube.com/watch?v=wiqnFaA2x7E

ManifestDreamMBA · Answer

My understanding is this isn't correct because we don't know if we will have full 24hr cycle for both, as assumed in the highlighted step here

Think of it this way.

If you get a box of 12 candies every 2 hour starting 10AM, and eat 4 candies every hour.

10AM - 12 candies
11AM - 8 candies left (ate 4)
12PM - 4 candies left + 12 candies = 16 candies left
You ate 12*2 - 16 = 8 candies, i.e. 4 per hour

But as per the formula below, 12/2 - 4 = 2 candies consumed every hour is not the same

DonBosco7 · Answer

If you see how this question mocks your intelligence, you will probably feel so stupid because the answer is so simple and right there.
if you subtract 187/4 and 131/4, what do you get 56/4.
and the answer is exactly this figure i.e 56 hrs from 2 o'clock last tuesday, which comes out to be 10:00 PM thursday evening.

DrMock · Answer

This was the very first question I got in my mock 6 (and I start with quant). Was this an outlier or does GMAC rate problems differently?

WhitEngagePrep · Answer

Hi DrMock ! Not sure what you mean by an outlier? Usually the first question you see is going to be a somewhat middle-level difficulty, but that isn't exact! Let me know what makes you think this might be an outlier? The issue is that you're considering the once-a-day fill in as an hourly change, which it isn't. That 14 gallons hits the tank all at once at 1pm each day, not little by little throughout the day the way the leak is occurring (0.25 gallons / hour = 6 gallons for each 24 hour period. So you can't roll the two together into one step - you must treat this problem step by step! I actually also found this easier if I backed up from 2pm on Tuesday to 1pm on Tuesday (since that's the moment that we add the 14 gallons each day). I also like to use the answer choices rather than being precise at first! Tuesday 1pm = Tues 2pm + the 0.25 gallon that was lost in the hour = 32.75 + 0.25 = 33 gallons. Tues 1pm = 33 g Wed 1pm = 33 - 6 + 14 = 41 g What can we eliminate now? We are still lower than 46.75 but for the next 24 hours we're just going to keep dropping... so we won't have another shot at getting an add until Thursday at 1pm. We can eliminate A, B, and C - since those are all before Thursday at 1pm.) Thu 1pm = 41 - 6 + 14 = 49 g What can we eliminate now? We've overshot, meaning, we need to lose gallons and not get another add. So we could eliminate anything from Friday 1pm onwards, but that isn't an option. From 49g we need to lose just over 2.25 gallons = 9 hours later, or 10pm! Hope this helps!

Whit

DrMock · Answer

Just that I'm getting an 805+ difficulty question off the top seems uncharacteristic.

rak08 · Answer

whats wrong if i think like this :

let x = no. of days

32 3/4 + 14x - 6x = 46 3/4

when i solve this i get x = 1.75

adding this to 2:00 tuesday
+1 day = 2:00 wednesday
+0.75 * 24 = 18 hrs
which comes out 8:00 AM Thursday..

please guide.

dhruvie · Answer

Leak:  0.25 Gal/h
 Add:  14 Gal ---> 1:00 pm every day

Particulars  
  Water Present (Gal)  
 
   Tues @ 2:00 pm  
  32.75  
 
  Consumed till Wed @ 1:00 pm
(0.25 * 23 hrs) 
 (5.75) 
 
  Added on Wed @ 1:00 pm 
 14.00 
 
   Wednesday @ 1:00 pm  
  41.00  
 
  Consumed till Thursday @ 1:00 pm
(0.25 * 24 hrs)  
 (6.00) 
 
  Added on Thurs @ 1:00 pm  
 14.00 
 
   Thursday @ 1:00 pm  
  49.00  
 
   Actually required level  
  46.75

The reason we calculated this till Thursday is because water to decrease from 32.75 or 41.00 gallons will never result in 46.75 till there's enough addition.

Now,  water level to be depleted  (to reach answer): 49.00 - 46.75 =  2.25 Gal

How much time till 2.25 gallons leaked:  \frac{2.25}{0.25} , i.e.   9 hours.

Hence answer is 10 pm on Thursday -  Option D

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=87147 Harsha GMAT-Club-Forum-mrytwkn8.png

Wadree · Answer

Ayoo.....i just thought bout dis...ur right....then answer would be 1 o'clock Thursday afternoon.....but it isn't in da options.....so it doesn't contradict that much......but if 1 o'clock in Thursday afternoon WAS in da options.....it would've been misleading.....🥀💔😭

Wadree · Answer

Leak in 1 hour = 1 / 4 gallon 
Leak in 24 hour = 24 ×   = 6 gallon 
Added in 24 hour = 14 gallon 
Net gain in 24 hour = 14 - 6 = 8 gallon

Lets think from 2 o'clock tuesday afternoon........
So.... current time 2 o'clock tuesday afternoon = 32.75 gallon.....after 24 hour.....its now 2 o'clock wednesday 
afternoon = 32.75 + 8 = 40.75 gallon...... after another 24 hour goes by like this ........its now 2 o'clock thursday 
afternoon = 40.75 + 8 = 48.75 gallon ......but we gotta make 46.75 gallon....so...extra at 2 o'clock thursday 
afternoon = 48.75 - 46.75 = 2 gallon......
Now....time to leak 0.25 gallon = 1 hour
So...... time to leak 2 gallon = 8 hour ........
So....after 2 o'clock thursday afternoon.....it will take 8 more hour to leak extra 2 gallon and reach 46.75......
So......46.75 gallon will reach at 10 o'clock thursday evening.....

! nah id win!

Throughout last week, water was leaking from a certain tank at a const

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Particulars	Water Present (Gal)
Tues @ 2:00 pm	32.75
Consumed till Wed @ 1:00 pm (0.25 * 23 hrs)	(5.75)
Added on Wed @ 1:00 pm	14.00
Wednesday @ 1:00 pm	41.00
Consumed till Thursday @ 1:00 pm (0.25 * 24 hrs)	(6.00)
Added on Thurs @ 1:00 pm	14.00
Thursday @ 1:00 pm	49.00
Actually required level	46.75

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Throughout last week, water was leaking from a certain tank at a const

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