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A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
- a)11236
- b)11025
- c)14400
- d)12696
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A lady grows cabbages in her garden that is in the shape of a square. ...
The shape of the area used for growing cabbages has remained a square in both the years.
Let the side of the square area used for growing cabbages this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing cabbages this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing cabbages last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of cabbages grown has increased by 211, the area would have increased by 211 sq ft because each cabbage takes 1 sq ft space.
Hence, X2 - Y2 = 211
(X + Y)(X - Y) = 211.
211 is a prime number and hence it will have only two factors. i.e., 211 and 1.
Therefore, 211 can be expressed as product of 2 numbers in only way = 211 * 1
i.e., (X + Y)(X - Y) = 211 * 1
So, (X + Y) should be 211 and (X - Y) should be 1.
Solving the two equations we get X = 106 and Y = 105.
(X + Y)(X - Y) = 211.
211 is a prime number and hence it will have only two factors. i.e., 211 and 1.
Therefore, 211 can be expressed as product of 2 numbers in only way = 211 * 1
i.e., (X + Y)(X - Y) = 211 * 1
So, (X + Y) should be 211 and (X - Y) should be 1.
Solving the two equations we get X = 106 and Y = 105.
Therefore, number of cabbages produced this year = X2 = 1062 = 11236.
The area in both the years are squares of two numbers.
That rules out choice D. 12696 is not the square of any number.
Check Choice A: If this year's produce is 11236, last year's produce would have been 11236 - 211 = 11025
11025 is the square of 105.
So, 11236 is the answer.
The area in both the years are squares of two numbers.
That rules out choice D. 12696 is not the square of any number.
Check Choice A: If this year's produce is 11236, last year's produce would have been 11236 - 211 = 11025
11025 is the square of 105.
So, 11236 is the answer.
Most Upvoted Answer
A lady grows cabbages in her garden that is in the shape of a square. ...
Problem:
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
Solution:
Given:
- Each cabbage takes 1 square feet of area in the garden.
- The garden is in the shape of a square.
- The number of cabbages grown this year is 211 more than last year.
Let's assume that the lady grew x cabbages last year. Therefore, the area of the garden would be x square feet.
Since the garden is in the shape of a square, the length and width of the garden would be equal. Let's assume that the length and width of the garden are y feet.
Therefore, we can write:
- Area of the garden last year = x = y^2 (since the garden is a square)
- Number of cabbages grown last year = x (since each cabbage takes 1 square foot)
This year, the lady grew 211 more cabbages than last year. Therefore, the total number of cabbages grown this year would be:
- Number of cabbages grown this year = x + 211
Since the garden is still in the shape of a square, the area of the garden would also be y^2 square feet. We know that each cabbage takes 1 square foot of area. Therefore, the total number of cabbages that can be grown in the garden this year would be:
- Total number of cabbages that can be grown = y^2
Equating the above two equations, we get:
- y^2 = x + 211
Substituting the value of x from the first equation, we get:
- y^2 = y^2 + 211
- 211 = 0
This is not possible. Therefore, the answer cannot be determined.
However, if we assume that the area of the garden has increased by a certain amount, then we can find the answer. Let's assume that the area of the garden has increased by k square feet. Therefore, the new area of the garden would be y^2 + k square feet.
We know that each cabbage takes 1 square foot of area. Therefore, the total number of cabbages that can be grown in the garden this year would be:
- Total number of cabbages that can be grown = y^2 + k
Equating the above two equations, we get:
- y^2 + k = x + 211
Substituting the value of x from the first equation, we get:
- y^2 + k = y^2 + 211
- k = 211
Therefore, the lady produced 211 more cabbages this year than last year, and the total number of cabbages produced this year is:
- Total number of cabbages produced this year = x + 211 = y^2 + 211 = (y^2 + k) = (y^2 + 211) = (y + 14)^2
- Since the area of the garden has increased by 14 feet (k = 14^2),
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
Solution:
Given:
- Each cabbage takes 1 square feet of area in the garden.
- The garden is in the shape of a square.
- The number of cabbages grown this year is 211 more than last year.
Let's assume that the lady grew x cabbages last year. Therefore, the area of the garden would be x square feet.
Since the garden is in the shape of a square, the length and width of the garden would be equal. Let's assume that the length and width of the garden are y feet.
Therefore, we can write:
- Area of the garden last year = x = y^2 (since the garden is a square)
- Number of cabbages grown last year = x (since each cabbage takes 1 square foot)
This year, the lady grew 211 more cabbages than last year. Therefore, the total number of cabbages grown this year would be:
- Number of cabbages grown this year = x + 211
Since the garden is still in the shape of a square, the area of the garden would also be y^2 square feet. We know that each cabbage takes 1 square foot of area. Therefore, the total number of cabbages that can be grown in the garden this year would be:
- Total number of cabbages that can be grown = y^2
Equating the above two equations, we get:
- y^2 = x + 211
Substituting the value of x from the first equation, we get:
- y^2 = y^2 + 211
- 211 = 0
This is not possible. Therefore, the answer cannot be determined.
However, if we assume that the area of the garden has increased by a certain amount, then we can find the answer. Let's assume that the area of the garden has increased by k square feet. Therefore, the new area of the garden would be y^2 + k square feet.
We know that each cabbage takes 1 square foot of area. Therefore, the total number of cabbages that can be grown in the garden this year would be:
- Total number of cabbages that can be grown = y^2 + k
Equating the above two equations, we get:
- y^2 + k = x + 211
Substituting the value of x from the first equation, we get:
- y^2 + k = y^2 + 211
- k = 211
Therefore, the lady produced 211 more cabbages this year than last year, and the total number of cabbages produced this year is:
- Total number of cabbages produced this year = x + 211 = y^2 + 211 = (y^2 + k) = (y^2 + 211) = (y + 14)^2
- Since the area of the garden has increased by 14 feet (k = 14^2),
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Question Description
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for GMAT 2026 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for GMAT 2026 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?a)11236b)11025c)14400d)12696e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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