Orchade grower

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mgmt_gmat: Master | Next Rank: 500 Posts; Posts: 221; Joined: Mon Dec 22, 2008 6:24 pm; Thanked: 2 times

by mgmt_gmat » Fri Feb 12, 2010 2:54 am

Based on this year's costs, an orcharde grower budgets P dollars for planting N new trees next year.
If the average cost of planting each tree were to increase 25 percent from this year's cost ,then the
greatest number of trees that the orchard grower could plant next year using P dollars would be.
A. 20% less than N
B. 25%less than N
C. equal to N
D. 20%greater than N
E. 25% greater than N

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Source: Beat The GMAT — Problem Solving | Fri Feb 12, 2010 2:54 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 12, 2010 3:40 am

mgmt_gmat wrote:Based on this year's costs, an orcharde grower budgets P dollars for planting N new trees next year.
If the average cost of planting each tree were to increase 25 percent from this year's cost ,then the
greatest number of trees that the orchard grower could plant next year using P dollars would be.
A. 20% less than N
B. 25%less than N
C. equal to N
D. 20%greater than N
E. 25% greater than N

We can reduce the question to...

By what percent must an end user trim down the utilization of a certain article of trade devoid of shifting a preset financial plan to it, if the price of the article of trade is raised by 25 percent?

And "100-theory" would by far work now...

When rate is 100 and demand is 100, the preset financial plan is 100 Ã— 100 = 10000.

When rate is 125 and demand is X (let's say), the preset financial plan is still 100 Ã— 100 = 10000 such that 125 X = 10000 or X = 80, a cut of [spoiler]20[/spoiler].

[spoiler]A[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 12, 2010 11:32 am

mgmt_gmat wrote:Based on this year's costs, an orcharde grower budgets P dollars for planting N new trees next year.
If the average cost of planting each tree were to increase 25 percent from this year's cost ,then the
greatest number of trees that the orchard grower could plant next year using P dollars would be.
A. 20% less than N
B. 25%less than N
C. equal to N
D. 20%greater than N
E. 25% greater than N

Say costs for planting 1 tree is C

C*N = P

Now if is goes up by 25% the new cost NC becomes 1.25C
The new Number of trees NN is?

NC*NN = P
1.25C*NN = P
NN = P/C* 1/1.25
NN = N *0.8

The new no is 20% less than the old num

Always borrow money from a pessimist, he doesn't expect to be paid back.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue May 15, 2018 3:34 pm

mgmt_gmat wrote:Based on this year's costs, an orcharde grower budgets P dollars for planting N new trees next year.
If the average cost of planting each tree were to increase 25 percent from this year's cost ,then the
greatest number of trees that the orchard grower could plant next year using P dollars would be.
A. 20% less than N
B. 25%less than N
C. equal to N
D. 20%greater than N
E. 25% greater than N

If it's on budget, then the cost per tree is P/N. Since the average cost were to increased by 25%, the cost per tree will the be 1.25(P/N) = 1.25P/N. Therefore, the number of trees that can be planted is:

P/(1.25P/N) = PN/(1.25P) = N/1.25 = 4N/5 = (80/100)N

We see that only 80% of the trees can be planted with P dollars, which is a 20% decrease from the original number of trees.

Alternate Solution:

Let's assume that the grower budgets $100 this year for planting N = 100 trees. Thus, it will cost $1 per tree for planting. Next year, a 25% increase raises the cost per tree to $1.25. With the budget still at $100, it means that the grower can plant only 100/1.25 = 80 trees, which is 20% less than what he can plant this year.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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