A cylindrical tank has a base with a circumference of GMAT Problem-Solving

Question: A cylindrical tank has a base with a circumference of 4√(π√3) meters and an equilateral triangle painted on the interior side of the base. A grain of sand is dropped into the tank, and has an equal probability of landing on any particular point on the base. If the probability of the grain of sand landing on the portion of the base outside the triangle is 3/4, what is the length of a side of the triangle?

A. √(2√6)
B. √(6√6)/2
C. √(2√3)
D. √3
E. 2

Answer: E

Solution and Explanation:

Approach Solution 1:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to powers and exponents. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate.
Assume that the base's radius is r,
and then the circumference is equal to 4√(π*√3) = 2πr.
Through consolidating, we r = 4√3/√π
Area of base = πr² = 4√3
If the triangle has a side of length x, then its area is √3x²/4
Very likely, the stone will land within the triangle. 1 - (3/4) = (1/4) = (triangle's area) (Area of base)
Substituting the aforementioned areas: (√3x²/4) / 4√3
Which makes it easier to say: x² = 4
Hence, x = 2.
Correct option: E

Approach Solution 2:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to powers and exponents. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate
Given: circumference = 4√(π*√3) and P(out) = ¾
Now, since there is a 3/4 chance that the sand grain will land on the base portion outside the triangle, the base portion (circle) outside the triangle must be 3/4 of the base's area and the triangle itself must be 1/4 of the base's area.
Next:
Circumference = 4√(π*√3) = 2πr
16π√3 = 4π²r² squares both sides.
4√3 = πr²
Areabase = πr² = 4√3.
The equilateral triangle's area is one-fourth that of the base:
areaequilateral=¼ ∗ 4√3
Also, area(equilateral) = a² * 3/4 is used to calculate the area of an equilateral triangle, where a is the length of a side;
areaequilateral=a²∗3√4 = √3
a=2
Correct option: E

Approach Solution 3:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to powers and exponents. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate.
Given: circumference equals 4√(π*√3) and P(out) equals three-quarters,
As there is a 3/4 chance that the sand grain will land on the base portion outside the triangle, the area of the base portion (circle) outside the triangle must be 3/4 of the area of the base, while the area of the triangle itself must be 1/4 of the area of the base.
Next:
Circumference = 4*3 = 2πr
Both sides are 16π√3 = 4π²r² squares.
4√3 = πr²
Areabase equals πr² = 4√3.
The area of the equilateral triangle is one-fourth the area of the base:
areaequilateral=¼ ∗ 4√3
Also used to determine the area of an equilateral triangle is area(equilateral) = a² * 3/4, where an is the length of a side;
areaequilateral=a²∗√3/4 = √3
a=2
Correct option: E

“A cylindrical tank has a base with a circumference of" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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