M01-29

Question

After passing away, a farmer divided his entire land among his three sons. Alfred received 20% more acres than James and 25% more than Stephen. If James inherited 3,600 acres, how many acres did Stephen receive?

A. 2400
B. 3456
C. 3600
D. 3750
E. 4320

Show Answer

Official Answer

B

A. 2400
B. 3456
C. 3600
D. 3750
E. 4320

Bunuel · Accepted Answer

Official Solution:

After passing away, a farmer divided his entire land among his three sons. Alfred received 20% more acres than James and 25% more than Stephen. If James inherited 3,600 acres, how many acres did Stephen receive?

A. 2400
B. 3456
C. 3600
D. 3750
E. 4320

Show Answer

Official Answer

B

A. 2400
B. 3456
C. 3600
D. 3750
E. 4320

Given that James received 3,600 acres, and Alfred received 20% more acres than James, Alfred received  3,600*1.2 = 4,320  acres. Since Alfred also received 25% more than Stephen, Stephen received  \frac{4,320}{1.25} = 3,456  acres.
 
Another approach is to observe that Alfred got the largest share (20% more than James and 25% more than Stephen), while Stephen got the smallest share, which is less than James's 3,600 acres. Among the answer choices, A seems too low (33% less than 3,600), so the correct answer is B.

Answer: B

nickimonckom · Answer

Hi Fantaisie,

Here below is a quick way to solve this :

A=\frac{6}{5}J=\frac{5}{4}S

\frac{6}{5}J*\frac{4}{5}=S

\frac{24}{25}J=S

3600-\frac{3600}{25}=S

fantaisie · Answer

Any suggestions on a quicket way to solve this equation? Many thanks!

AndrewN · Answer

The  quickest  way is up for debate, but another way you can solve the question with mental math and a little test-specific technique is to understand from the question stem that  Alfred must have the greatest number of acres  and employ the 10% rule to quickly work your way through the percentages:

20% more than 3,600 = 2 * 10% of 3,600, or 2 * 360, which is 720

That is, to get 10% of any number, just push the decimal one place to the left. We can determine in a matter of seconds that Alfred received 3,600 + 720 acres, or 4,320 acres. Now take a look at the answer choices:

A. 2400
B. 3456
C. 3600
D. 3750
E. 4320

Since the question is asking about  Stephen  and not Alfred, and we know that the two did not receive the same amount of land, choice (E) is gone. You can use the remaining choices to evaluate which one, with an additional 25%, would match 4,320 from before. Because we calculated that 20%, not 25%, of 3,600 equals that very amount, we can get rid of choice (C), but we also know that a greater value such as 3,750 would lead to an even greater number of acres, and that would violate the known fact that Alfred was bequeathed the most land. Choice (D) is gone as well. Of the remaining two answer choices, 25% of 2,400 is much easier to gauge than 25% of 3,456. Remember, we are just looking to match 4,320, so 25% plus the base value (or 125% altogether) needs to equal this number. Test the easier value to help with timing:

25% of 2,400 = 600

You can either take one-fourth of 2,400 off the top of your head or you can use the 10% rule again, understanding that 5% is just half of 10%:

25% of 2,400 = 10% + 10% + 5% of 2,400, or 240 + 240 + 120, which is 600

Clearly, 600 + 2,400 will get us only to 3,000, and we need a larger base from which to calculate our 25%.  Only choice (B) remains, so it must be the answer.  I took a long time typing out the entire thought process, but the chain of logic--using the 10% rule and the process of elimination--can break the question down in a minute or so, with the added benefit that you will know you have the correct answer.

Good luck with your studies.

- Andrew

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

mhGupta · Answer

Alfered received 20% more than James: A=J+.20J=1.2J
Alfered recived 25% more than Stephen: A=S+.25S=1.25S

Now solve for A=A
                    1.2J=1.25S
J is given 3600 Acres

S= (1.2*3600)/1.25
S=3456

kouassidrissa047 · Answer

I don’t quite agree with the solution. in my mind the result is 3240: 
When i calculate 25% of 4320 , i that is 1080 , and the difference yield 3240. Whereas, when i check the difference between 4320 and 3456, that yield 864 , that is 20% of 4320 and not 25%. The amount that is effectively 25% more than Stephan share is 1080.

Bunuel · Answer

Please review the question and the solution again. You're confusing  "25% more than"  with  "25% of."  If Alfred received 25% more than Stephen, it means:
 
Alfred = Stephen + 25% of Stephen = 1.25 × Stephen 
 
So  Stephen = 4320/1.25 = 3456

You're subtracting 25%  of Alfred , which is wrong. The comparison must be based on  Stephen’s share , not Alfred’s.

M01-29

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