If each of three grocery stores receives 1/4 of a farmer’s potato crop

Question

If each of three grocery stores receives 1/4 of a farmer's potato crop, a farmer's market receives 1/3 of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer's crop?
Sol-
farmer's potato crop be x
three grocery stores -x/4 each
farmer's market = 1/3 (x-(3x/4)) = x/12
rest =200

total= 200+(x/12)+3x/4 = x
=> x= 1200 (D)

A. 300
B. 400
C. 900
D. 1,200
E. 1,400

u1983 · Answer

Bunuel .... please review ( and explain

) the question .... if possible.

Bunuel · Answer

______________________
Edited the stem. Thank you.

u1983 · Answer

Thanks a bunch Bunnuel for the help.

Each of three grocery stores receives 1/4 of a farmer’s potato crop. They receives in total =  3* \frac{1}{4} = \frac{3}{4} 
Hence remaining =  1 - \frac{3}{4} = \frac{1}{4}

According to the Q-stem : a farmer’s market receives 1/3 of the remaining, and a local fast food restaurant receives the remaining 200 pounds
Thus 200 pounds = 2/3 of the remaining after the 3 grocers= \frac{2}{3} * \frac{1}{4} =  \frac{1}{6}

Hence The total portal of the farmed potato= 6*200=1200 pounds
Hence I would go with  option D .

EgmatQuantExpert · Answer

Solution

Given:  
 • Each grocery store receives  \frac{1}{4}  of a farmer’s potato crop
• A farmer’s market receives  \frac{1}{3}  of the remaining 
• A local fast food restaurant receives the remaining 200 pounds

To find:  
 • Total amount of potatoes (in pounds) in the farmer’s crop

Approach and Working:   
If we assume the total amount of potatoes to be x pounds, then
 • Grocery stores received =  3 * \frac{x}{4} = \frac{3x}{4} 
• Farmer’s market received =  \frac{1}{3} (x – \frac{3x}{4}) = \frac{1}{3} * \frac{x}{4} = \frac{x}{12} 
• Remaining crop =  x – (\frac{3x}{4} + \frac{x}{12}) = x – \frac{5x}{6} = \frac{x}{6}

Given that,  \frac{x}{6}  = 200
  Or, x = 200 * 6 = 1200 pounds

Hence, the correct answer is option D.

Answer: D

generis · Answer

(1)  Each of 3 grocery stores gets  \frac{1}{4}  of the potato crop
 3*\frac{1}{4}=\frac{3}{4}  is gone, 
and  \frac{1}{4}  remains

(2)   \frac{1}{3}  of the remaining  \frac{1}{4}  goes to a farmer's market

(\frac{1}{3}*\frac{1}{4})=\frac{1}{12}  more is gone

FRACTION GONE: (\frac{3}{4}+\frac{1}{12})=\frac{10}{12}  gone, and

FRACTION LEFT
 (1-\frac{10}{12})=(\frac{12}{12}-\frac{10}{12})=\frac{2}{12}=\frac{1}{6}  remains

(3)  How many pounds of potatoes, P, were there to begin with?

200 lbs of potatoes remain
 \frac{1}{6}  of  P  remains
 200=\frac{1}{6}P 
 P=1,200

Answer D

ScottTargetTestPrep · Answer

We can let n = the total number of pounds of potatoes in the farmer’s crop. Note that 3/4 of his crop went to the grocery stores, leaving 1/4 of the crop remaining. We know that 1/3 of this remaining 1/4 went to the farmer’s market, and the remaining 200 pounds went to the fast food restaurant. We can create the equation:

n = 3(1/4)n + 1/3(1/4)n + 200

n = (3/4)n +(1/12)n + 200

12n = 9n + n + 2400

2n = 2400

n = 1200

Alternate Solution:

We know that 3/4 of the crop went to grocery stores, and (1/3)(1/4) = 1/12 of the crop went to the farmer’s market. Thus, we see that 3/4 + 1/12 = 9/12 + 1/12 = 10/12 of the crop went to these endeavors, leaving 2/12 = 1/6 of the crop, which is equal to 200 pounds, to go to the fast food restaurant. Thus, if we let n = the number of pounds of potatoes in the crop, we see that:

(1/6)n = 200

n = 1200

Answer: D

CounterSniper · Answer

let the total be x

1. each of the three grocery stores receives 1/4 = 3x/4
2. a farmer's market receives 1/3 of the remaining = (x/4)*1/3 = x/12
remaining = x - (3x/4 + x/12) = 200 
 x -(10x/12) = x/6 = 200 
 x=1200

D

Gmat2Cracker · Answer

If each of three grocery stores receives 1/4 of a farmer's potato crop, a farmer's market receives 1/3 of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer's crop?
Sol-
farmer's potato crop be x
three grocery stores -x/4 each
farmer's market = 1/3 (x-(3x/4)) = x/12
rest =200

total= 200+(x/12)+3x/4 = x
=> x= 1200 (D)

If each of three grocery stores receives 1/4 of a farmer’s potato crop

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

If each of three grocery stores receives 1/4 of a farmer’s potato crop

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