Grass on a lawn grows everyday by a fixed percent of the height on the

Question

Grass on a lawn grows everyday by a fixed percent of the height on the previous day. However, cows graze and reduce the height of the grass by 1 mm every day. What was the height of the grass on the first day before the cows started grazing? Assume that the cows graze at the end of the day, after which the grass grows in the beginning of the next day.

(1) The grass grows every day by 2 percent of the height on the previous day.
(2) The grass is completely grazed in 3 days.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects:

Problem Solving Butler  
  Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!

ManifestDreamMBA · Answer

Let the initial height of grass be x

S1
Day 1 growth = 1.02x
Day 1 end = 1.02x - 1
Day 2 growth = 1.02(1.02x -1)
Day 2 end = 1.02(1.02x -1)-1
....

We don't know any information to know x
Insufficient

S2
Number of days = 3
We don't know any information to know x
Insufficient

Combined, we have 1.02(1.02(1.02x -1)-1)-1 = 0
We can calculate the value of x
Sufficient

Answer C

shwetakoshija · Answer

Question Stem: 
 
 Grass grows by a fixed percentage of its height at the beginning of each day. 
 Then at the end of the day, cows graze 1 mm of it. 
 This process continues day by day.

To find : The initial height of the grass on Day 1, before cows grazed.

Statement 1:  The grass grows every day by 2 percent of the height on the previous day.
 
 This gives us the daily growth rate; however, we do not know how long the grass was allowed to grow and be grazed. 
 We also don’t know the final grass height at any point. 
 Without a starting or ending value — or the number of days over which the process occurred — we cannot apply this 2% growth rate meaningfully.

Statement 1 alone is not sufficient.

Statement 2:  The grass is completely grazed in 3 days.
 
 So, now we know that the grass reaches 0 mm at the end of Day 3. 
 But we have no idea how much it was growing each day, so we can’t figure out how much was being added before grazing. 
 Without the growth rate, we cannot work backwards to the original height.

Statement 2 alone is not sufficient.

Statements 1 and 2 Combined: 
Let’s logically work backward from the end of Day 3:
 
 At the end of Day 3, grass height = 0 mm. 
 That means just before cows grazed on Day 3, the grass must have been 1 mm (because cows grazed 1 mm to make it 0). 
 That 1 mm was the result of 2% growth on the grass height at the end of Day 2.
 
 So, if x = height at the end of day 2, then x + 2% of x = 1 mm.  
 We can find x

This same logic can be applied again to find Day 1 values.

Statements together are sufficient.

Shweta Koshija  
 GMAT, GRE, SAT, AP Coach for 10+ Years

ravi1522 · Answer

Grass on a lawn grows everyday by a fixed percent of the height on the previous day. However, cows graze and reduce the height of the grass by 1 mm every day. What was the height of the grass on the first day before the cows started grazing? Assume that the cows graze at the end of the day, after which the grass grows in the beginning of the next day.
statement 1
The grass grows every day by 2 percent of the height on the previous day. So this is giving me the percentage growth but we can't get anything from it .
not sufficient

statement 2
The grass is completely grazed in 3 days.
it means with addition and grazing the height of grass will be 3mm in 3 days

Not sufficient

when we combine

we know the rate and no of days we can easily calculate the initial height

Hence option C is correct

Grass on a lawn grows everyday by a fixed percent of the height on the

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 Data Sufficiency (DS) Questions

Grass on a lawn grows everyday by a fixed percent of the height on the

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