Mia is "helping" her mom pick up 30 toys that are strewn on the floor GMAT Problem-Solving

Question: Mia is "helping" her mom pick up 30 toys that are strewn on the floor. Mia’s mom manages to put 3 toys into the toy box every 30 seconds, but each time immediately after those 30 seconds have elapsed, Mia takes 2 toys out of the box. How much time, in minutes, will it take Mia and her mom to put all 30 toys into the box for the first time?

(A) 13.5
(B) 14
(C) 14.5
(D) 15
(E) 15.5

Approach Solution 1

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.
Only one of the five options is correct.
After her mother had placed three toys in the toybox for 30 seconds, Mia promptly removes two of them.

3 in the toy box at 30 seconds
30 seconds later: 1 in the toybox.
4 in the toy box at 60 seconds
30 seconds later: 2 in toybox; 30*n seconds (n=1, 2, 3...) later: 3+n-1 in toybox.
Now, determine 3+n-1=30 n+2=30 n=28.

Therefore, it will take 14 minutes to first assemble the box with all 30 toys.
The solution is (B).

Approach Solution 2

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.
Only one of the five options is correct.
We are aware that Mia's mother places three toys into the box every thirty seconds, and that Mia then removes two of those items immediately after her mother does so. Therefore, one additional toy is added to the box approximately once every thirty seconds.

We know that once the total number of toys in the box reaches 27, followed by a delay of 30 seconds, the box will contain all 30 toys because there are 30 toys in total.
When we divide 27 by 2, we get the number of minutes it will take us to reach 27 toys, given that 30 seconds is equivalent to half a minute: 27÷2=13.5
27 ÷ 2 = 13.5

It will take 13.5 minutes before there are 27 toys in the box, and then it will only take 30 seconds after that before there are 30 toys in the box, thus the entire process will take 14 minutes.

Therefore, the correct answer is B.

Approach Solution 3

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.
Only one of the five options is correct.
After Mia's mother places three toys in the toy box for 30 seconds, Mia promptly removes two of them.

At 30 seconds: 1 toy in the toy box
At 60 seconds: 2 toys in the toy box

Now, we can see that after every 60 seconds, the number of toys in the box increases by 1. Therefore, we need to find the value of n when 3 + (n - 1) = 30, where n represents the number of 60-second intervals.

Simplifying the equation:
3 + n - 1 = 30
n + 2 = 30
n = 28

Since each interval is 60 seconds, the total time required is 28 * 60 seconds = 1680 seconds.
Converting 1680 seconds to minutes, we have 1680 seconds / 60 seconds per minute = 28 minutes.

Therefore, the correct answer is (B) 14 minutes.

“Mia is "helping" her mom pick up 30 toys that are strewn on the floor" - 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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