An old woman sits on a park bench and begins dropping rice on the grou

Question

An old woman sits on a park bench and begins dropping rice on the ground at a constant rate of 7 grains per second. Initially, there is no rice on the ground and no pigeons are present, but after the woman has been dropping rice for 10 seconds, a pigeon shows up and begins eating rice at a constant rate of 3 grains per second. If the woman continues dropping rice at the same rate, if one new pigeon shows up every 10 seconds, if no pigeons leave, and if all pigeons eat at the same constant rate as long as there is rice on the ground, how many pigeons will be present the next time there is no rice on the ground?

A. 3
B. 4
C. 5
D. 6
E. 7

A. 3
B. 4
C. 5
D. 6
E. 7

emockus · Accepted Answer

To start: 70 grains

Next 10:140 grains
First Bird: 30
Rice Left: 110

Next 10: 180 grains
Two Birds: 60
Rice Left: 120

Next 10: 190 grains
Three Birds: 90
Rice Left: 100

Next 10: 170
Four Birds: 120
Rice Left: 50

Next 10: 120
 FIVE BIRDS : 150
Rice Left: ZERO

Answer Choice "C"

rohit8865 · Answer

pushpitkc · Answer

Grains being dropped = 7 grains/second
Pigeon's rate of eating grains = 3 grains/second

The woman drops  70 grains  in the first 10 seconds.

After 10 seconds, as a pigeon joins & starts to eat the rice grains on the road, there is a net addition of  40 grains

From the 10-20 second period, since there are 2 pigeons, there is a net addition of  10 grains  (70 - 2*30). Total: 120

From the 20-30 second period, since there are 3 pigeons, there is a net loss of  20  grains (70 - 3*30). Total: 100

From the 30-40 second period, since there are 4 pigeons, there is a net loss of  50  grains (70 - 4*30). Total: 50

Therefore, somewhere between 40 and 50 seconds, after the 5th pigeon joins, there is a net loss s.t there is no grain on the ground.(Option C)

evillasis · Answer

First 10s: +70 (= 7x10) -> Total grain: 70
Next 10s: +40 (=(7-3)x10) -> Total grain: 70+40=110
Next 10s: +10 (=7-3-3)x10) -> ...

As we can see we have the following sequence +70,+40,+10,-20,-50,-80.
If we add the sequence we can see that in the 6th period we became negative.

Given that in the first period we had 0 pigeons it means that in the 6th period we have 5 pigeons.

ishaan.wares · Answer

70+7n=(10+20+....+n)3
solving, n=140/30= max 5
ans:5

KarishmaB · Answer

In every 10 secs, work done (rice thrown) = 7*10 = 70 grains
In every 10 secs, negative work (rice eaten) = 30*n grains (where n is the number of pigeons)

For each time period of 10 secs, 1 extra pigeon is added. Say after t time periods, there are no grains of rice left.

70 * t = 0 + 30 + 30*2 + 30*3 + ... + 30*(t - 1)
70t = 30((t-1)*t/2)
t = 0 or 17/3
After 5 time period and 7 seconds, there will be no grains of rice. At that time, the 6th time period would be going on so there will be 5 pigeons.

Answer (C)

dcummins · Answer

Its easier to take the net rate on these types of questions

Initially
Woman(+) 
7g/s x 10sec = 70g

Woman- 1 Bird
7g-3g/s =4g/s x 10sec = 40g *The rate is still positive so the net amount of seeds is still an increase

Woman - 2 Birds
4g/s-3g/s= 1g/s x 10sec = 10g *The rate is still positive so the net amount of seeds is still an increase

Our running total = 120g

Woman - 3 Birds
1g/s-3g/s= -2g/s x 10sec = -20g *The rate is now negative so the net amount of seeds is decreasing

Our running total = 100g

Woman - 4 Birds
-2g/s-3g/s= -5g/s x 10sec = -50g

Our running total = 50g

Woman - 5 Birds
-5g/s-3g/s= -8g/s x 10sec = -80

Thus, when 5 birds turn up, the seeds will be gone.

GMAThunterr · Answer

Question asks about "how many pigeons will be present the next time there is no rice on the ground?"
Next time does not mean the next interval which implies the Number should be 5+1=6

As the question states "one new pigeon shows up every 10 seconds and there are no other restrictions." So after the rice finished next time one pigeon will come and the count for the next time will be 7.

Posted from my mobile device

gmatapprentice · Answer

I found the accounting approach to be quite helpful for this question:

For each 10s period, start with opening balance, net addition (additional rice grain-intake from new pigeons) and closing balance (helps put things in perspective).

soubhagya2906 · Answer

Let's form an equation.

each of the 10 sec interval

till first 10 secs 70 Grains 70x1

at 20Second 70x2 - 30 ( 3 grains/sec by a Pigeon)

at 30 sec 70x3 - 30 - 30x2

So forming and equation 70xn = 30(1+2+...+n-1)

7n = 3 nx(n-1) / 2

14 = 3n-3 => n = 17/3 ~ 6th 10sec block => 60th Sec at 60th sec Pigeon will be n-1 => Pigeon=5

fireagablast · Answer

base rate = 7/60
first 10 seconds (no pigeons) = 70/60
next 10 (1 pigeon) = 7/60-3/60 -->70/60+40/60
next 10 (2 pigeons) = 7/60-6/60 --> 70/60+40/60+10/60
next 10 (3 pigeons) = 7/60-9/60 -->70/60+40/60+10/60 - 20/60
next 10 (4 pigeons) = 7/60-12/60 -->70/60+40/60+10/60 - 20/60 - 50/60
next 10 (5 pigeons) = 7/60-12/60 -->70/60+40/60+10/60 - 20/60 - 50/60 - 80/60

at 5 pigeons, the rate consumed is beyond the rate provided + initial

mdanieletto · Answer

Every 10 mins:
- Woman drops 70 grains
- Each pigeon eats 30 grains.

NR OF GRAINS FOR AFTER 10 sec: +70------------------------1st pigeon arrives
NR OF GRAINS FOR AFTER 20 sec: +70+(70-30)=110--------2nd pigeon arrives
NR OF GRAINS FOR AFTER 30 sec: 110+(70-60)=120--------3rd pigeon arrives
NR OF GRAINS FOR AFTER 40 sec: 120+(70-90)=90---------4th pigeon arrives
NR OF GRAINS FOR AFTER 50 sec: 90+(70-120)=40---------5th pigeon arrives
NR OF GRAINS FOR AFTER 60 sec: 40+(70-150)=-40

CORRECT ANS: C

ShankSouljaBoi · Answer

What is the meaning of next time in this problem. With the 5th bird , the amount of rice is zero. So, the next time will be when 6th bird will be there. I went with 5 but still next time is confusing . VeritasKarishma could you please clarify

Best

Best

KarishmaB · Answer

When the woman sits down, there is no rice on the ground. The "next time" there is no rice on the ground will be when the pigeons have finished it all. 
Note that once there are 3 pigeons, the rate of consumption is higher than the rate of throwing rice. So once all rice is over, there will never be enough rice to feed all the pigeons.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An old woman sits on a park bench and begins dropping rice on the grou

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

An old woman sits on a park bench and begins dropping rice on the grou

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards