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A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?
I. 30
II. 35
III. 45
II. 35
III. 45
- a)I only
- b)II only
- c)III only
- d)I and II only
- e)I, II and III
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A survey asked 1,150 people to choose their favorite laundry detergent...
Given:
- 1,150 people were surveyed
- The survey asked people to choose their favorite laundry detergent from brands A, B, and C
- x percent of the people chose A as their favorite brand, rounded to the nearest integer, the result is 3
To find:
Which of the following could be the number of people who chose A as their favorite brand?
Solution:
Let's assume the number of people who chose A as their favorite brand is "a".
Step 1: Find the percentage of people who chose A as their favorite brand
To find the percentage, we can use the formula:
Percentage = (Number of people who chose A / Total number of people surveyed) * 100
Step 2: Round the percentage to the nearest integer
We are given that the rounded percentage is 3. So, we can write:
Round(Percentage) = 3
Step 3: Solve the equation to find the value of a
Let's solve the equation:
Round((a / 1150) * 100) = 3
Step 4: Check which options satisfy the equation
We need to check which options for "a" satisfy the equation. Let's go through each option one by one:
Option I: a = 30
Plugging in the value of a in the equation:
Round((30 / 1150) * 100) = 3
Round(2.6087) = 3
3 = 3
This option satisfies the equation.
Option II: a = 35
Plugging in the value of a in the equation:
Round((35 / 1150) * 100) = 3
Round(3.0435) = 3
3 = 3
This option satisfies the equation.
Option III: a = 45
Plugging in the value of a in the equation:
Round((45 / 1150) * 100) = 3
Round(3.913) = 3
4 = 3
This option does not satisfy the equation.
Conclusion:
The options that satisfy the equation are I and II. Thus, the number of people who chose A as their favorite brand could be 30 or 35. Therefore, the correct answer is option (d) I and II only.
- 1,150 people were surveyed
- The survey asked people to choose their favorite laundry detergent from brands A, B, and C
- x percent of the people chose A as their favorite brand, rounded to the nearest integer, the result is 3
To find:
Which of the following could be the number of people who chose A as their favorite brand?
Solution:
Let's assume the number of people who chose A as their favorite brand is "a".
Step 1: Find the percentage of people who chose A as their favorite brand
To find the percentage, we can use the formula:
Percentage = (Number of people who chose A / Total number of people surveyed) * 100
Step 2: Round the percentage to the nearest integer
We are given that the rounded percentage is 3. So, we can write:
Round(Percentage) = 3
Step 3: Solve the equation to find the value of a
Let's solve the equation:
Round((a / 1150) * 100) = 3
Step 4: Check which options satisfy the equation
We need to check which options for "a" satisfy the equation. Let's go through each option one by one:
Option I: a = 30
Plugging in the value of a in the equation:
Round((30 / 1150) * 100) = 3
Round(2.6087) = 3
3 = 3
This option satisfies the equation.
Option II: a = 35
Plugging in the value of a in the equation:
Round((35 / 1150) * 100) = 3
Round(3.0435) = 3
3 = 3
This option satisfies the equation.
Option III: a = 45
Plugging in the value of a in the equation:
Round((45 / 1150) * 100) = 3
Round(3.913) = 3
4 = 3
This option does not satisfy the equation.
Conclusion:
The options that satisfy the equation are I and II. Thus, the number of people who chose A as their favorite brand could be 30 or 35. Therefore, the correct answer is option (d) I and II only.
Community Answer
A survey asked 1,150 people to choose their favorite laundry detergent...
Given that x percent of the 1,150 people surveyed chose A as their favorite brand and rounding x to the nearest integer results in 3, we can set up the following equation:
Round(x) = 3
To determine the possible values of x, we need to consider the range within which x can fall when rounded to the nearest integer. Since x is given as a percentage, it must be between 0 and 100.
Let's calculate the upper and lower bounds for x:
Upper bound:
If x = 3, then x rounded to the nearest integer is already 3.
If x = 3, then x rounded to the nearest integer is already 3.
Lower bound:
If x = 2.5, rounding it to the nearest integer would result in 3.
If x = 2.5, rounding it to the nearest integer would result in 3.
Therefore, x can be any value between 2.5 and 3.5, inclusive.
Now, let's calculate the number of people who chose A using the lower and upper bounds:
Lower bound:
(2.5/100) * 1150 = 28.75
(2.5/100) * 1150 = 28.75
Upper bound:
(3.5/100) * 1150 = 40.25
(3.5/100) * 1150 = 40.25
The number of people who chose A can vary between approximately 28.75 and 40.25.
Among the given answer choices:
I. 30: This falls within the possible range (between 28.75 and 40.25).
II. 35: This falls within the possible range.
III. 45: This does not fall within the possible range.
II. 35: This falls within the possible range.
III. 45: This does not fall within the possible range.
Therefore, the correct answer is D. I and II only.
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A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?I. 30II. 35III. 45a)I onlyb)II onlyc)III onlyd)I and II onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer?
Question Description
A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?I. 30II. 35III. 45a)I onlyb)II onlyc)III onlyd)I and II onlye)I, II and IIICorrect answer is option 'D'. 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 A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?I. 30II. 35III. 45a)I onlyb)II onlyc)III onlyd)I and II onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B, and C. Of the people surveyed, x percent chose A as their favorite brand. If x is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?I. 30II. 35III. 45a)I onlyb)II onlyc)III onlyd)I and II onlye)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
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