A Survey Asked 1,150 People To Choose Their Favorite Laundry Detergent GMAT Problem-Solving

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
To determine the possible number of people who chose A as their favorite brand, we need to calculate the range of values for x percent when rounded to the nearest integer is 3.

When x is rounded to the nearest integer and the result is 3, we know that x must be between 2.5 and 3.5.

Let's calculate the range of values for x:
Lower bound: 2.5% of 1,150 = 0.025 * 1,150 = 28.75 (rounded to the nearest integer is 29)
Upper bound: 3.5% of 1,150 = 0.035 * 1,150 = 40.25 (rounded to the nearest integer is 40)

Therefore, the possible values for the number of people who chose A as their favorite brand are between 29 and 40.

Looking at the options provided:
I. 30 is within the range of 29 to 40.
II. 35 is within the range of 29 to 40.
​III. 45 is not within the range of 29 to 40.

Thus, the possible values are I and II only.
Therefore, the correct answer is option D. I and II only.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
Calculating the range of values for x percent when rounded to the next integer is 3 will help us determine the potential number of people who selected A as their preferred brand.

We can infer that x must be between 2.5 and 3.5 when x is rounded to the closest integer and the result is 3.

Let's determine the x value range:
Lower bound: If you round to the next integer, 29 is the result of 2.5% of 1,150, or 0.025 times 1,150.
Upper bound: 40.25 (rounded to the next integer is 40) is 3.5% of 1,150, or 0.035 * 1,150.

As a result, the range for the number of people who selected A as their preferred brand is 29 to 40.

Considering the available options:
I. 30 falls between the numbers 29 and 40.
II.The range of 35 is between 29 and 40.
III.The number 45 does not fall between 29 and 40.

Therefore, only I and II are viable values.
Option D, I and II, is the only one that is correct.

This is a GMAT Problem solving question. Here, the data given in the questions has to be analyzed to answer the question. Several areas of mathematics can be involved in the process. The way options are given is very close to correct answer, and normal guessing can lead to mistakes. Students need to understand the question properly and use proper methods to approach the answer.
Performing a computation backwards

From I, we get 2.6 to 3 from (30/1150) * 100.
II (35/1150)*100 results in approximately 3.0 = 3.
III (45 / 1150 * 100) results in 3.9 to 4

500. Just I and II.

The appropriate answer is D.