What is the cost to fence a rectangular plot at the rate of $20/meter?(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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What is the cost to fence a rectangular plot at the rate of $20/meter?

(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.

(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'C'. Can you explain this answer?

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Test: Rectangles And Squares- 1

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What is the cost to fence a rectangular plot at the rate of $20/meter?...

Steps 1 and 2 – Understand the question and draw inferences

To find – Cost to fence a rectangular plot at $20/meter

Given –

Rectangular plot
Rate of fencing -$20/meter

Approach –

Fencing a rectangular plot implies going around its perimeter.
So we need to find the perimeter of the rectangular plot.
For this we need the value of the sum of the length and the width.

Step 3 – Analyze Statement (1)

Statement (1): If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.

Let’s assume the length and the width of the plot as ‘a’ and ‘b’ meters.

New Length = a + 10

New Area = (a+10) * b

Original Area = a * b

According to Statement (1):

(a + 10) * b = a * b + 100

Simplifying this further we get:

ab + 10b = ab + 100
10b = 100
b = 10

Even though we know the value of b, we cannot find the value of a since no other information is provided about the rectangular plot.

Thus, this statement does not provide any information about the sum of the length and the width and hence the information is not sufficient to arrive at a unique answer.

Step 4 – Analyze Statement (2)

Statement II: If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.

Let’s assume the length and width of the plot as ‘a’ and ‘b’ meters.

Original perimeter = 2(a + b)

New Length = a + 0.1a = 1.1a

New Width = b -0.1b = 0.9b

New perimeter = 2(1.1a + 0.9b)

According to Statement (2):

2(1.1a + 0.9b) = 0.95 (2(a + b))

1.1a + 0.9b = 0.95a + 0.95b
0.15a = 0.05b
3a = b

Even though we know the relationship between a and b, we cannot find the value of sum of a and b since no other information is provided.

Thus, this statement does not provide any information about the sum of length and width and hence the information is not sufficient to arrive at a unique answer.

Step 5 – Analyze both Statements Together

Per Statement (1): b = 10
Per Statement (2): 3a = b

So combining these two statements, we can find individual values of a and b and hence we can find the sum of a and b.

Thus implies that we can find a unique answer to the question about determining the cost of fencing at the given rate.

Thus, Statements (1) and (2) together yield a unique answer.

Correct Answer Choice – Choice C

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Most Upvoted Answer

What is the cost to fence a rectangular plot at the rate of $20/meter?...

Analysis

Statement 1:

Increased Area with Increased Length

- Let the original length be L and width be W.
- The original area = L * W.
- The new length = L + 10 and new area = (L + 10) * W.
- Given that the new area is 100 sq. m more than the original area.

Statement 2:

Changes in Dimensions affecting Perimeter

- Let the original length be L and width be W.
- The new length = 1.1L and the new width = 0.9W.
- The new perimeter = 2(1.1L + 0.9W) = 2.2L + 1.8W.
- The original perimeter = 2L + 2W.
- Given that the new perimeter is 5% less than the original perimeter.

Solution

Using Both Statements Together

- From statement 1, we have the relationship between the original and new areas.
- From statement 2, we have the relationship between the original and new perimeters.
- We can now set up equations involving length, width, area, and perimeter to solve for the dimensions of the original rectangle.
- Once we have the original dimensions, we can calculate the cost to fence the plot at $20/meter.

Conclusion

- Both statements together provide enough information to determine the original dimensions of the plot and calculate the cost to fence it.
- Therefore, the correct answer is option C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answered by Talent Skill Learning · View profile

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What is the cost to fence a rectangular plot at the rate of $20/meter?(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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What is the cost to fence a rectangular plot at the rate of $20/meter?(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the cost to fence a rectangular plot at the rate of $20/meter?(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the cost to fence a rectangular plot at the rate of $20/meter?(1) If length of the plot is increased by 10 meters, the area of the plot increases by 100 sq. m.(2) If length of the plot is increased by 10% and width of the plot is decreased by 10%, the perimeter decreases by 5%.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.

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