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Some Math Questions from Gmatprep [#permalink]
12 Jun 2007, 17:57

If you know how to solve any of the following problems, please let me know.

1)For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount of the sale in excess of $500. If the total amount of one of her sales was $800, the saleswoman's commission was approximately what percent of the total amount of the sale?

a)22%
b)24%
c)25%
d)27%
e)28%

2) The residents of Town X participated in s survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watch television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched TV last week?

[u]Question # ![/u]
To find out that what % her total salary is to the sales we shall use the formula total salary/total sales*100. (simple % formula).
In this formula, we have total sales = 800, but dont have the total salary. To find this, we are given certain conditions. These conditions tell us that uptill the sales of 500, she will get 20% of the sales as her salary and any sales up & above 500 mark will fetch 30% of the sales. so 800=500+300.
therefore, 500*20%+300*30% = 100+90=190 shall be her total salary. So putting this information into the original formula, we get
190/800*100=23.75. Even though, we dont have any anwser choice of 23.75, the question asks us approximate value, and rounding 23.75 gives us 24. So we shall take choice b 24% which is a better approximation of 23.75% than 22%. SO the answer is B 24%
[u]Question # 2[/u]
This question is very simple if u know the concept of standard deviation. Standard deviation tells us how tightly or loosely packed a set of set of data is. One property of stadard deviation is that statisticians have found out, after studying loads of data and variables that data follow a symmetrical pattern. The pattern is that majority of the data points are located around the mean position and as u move away from the mean position, the data points become more and more scarce. This distribution of data points also follows a simple pattern. majority of data lies in the first standard deviation range(means if u add and subtract the standard deviation from the mean, u get the first standard deviation region). lesser data is found between 1st and 2nd s.d. (means u sbtract and add s.d. from 1 s.d. range) and only about 1% od data lies beyond 3rd s.d.
Now, if i have made clear it to u, u can see that from the question, the statement has given u both mean and s.d. and have asked u what figure lies between 1st and 2nd standard deviation.
The mean is 21 and s.d. is 6. so first s.d. range would be 21+-6 i.e., 15-27, the 2nd s.d. range would be 15-6 and 27+6.which would be 9-15 and 27-33. as the question has already stated that "below the mena" so v are not concerned with any value above the mean. so the answer should be between 9 & 15. only one answer choice lies in this range which is d=12.
so the answer is d, 12.
Hope this helps.

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