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    1. David received his allowance on Sunday. He spends 1/4 of his allowance on Monday and 2/3 of the remainder on Tuesday. What part of his allowance is left for the rest of the week?

      If David spends 1.4 of his allowance on Monday then he is left with 1 – 1/4 = 3/4 of his allowance at the end of day Monday. If he spends 2/3 of the remainder then that is 3/4 (the remainder x 2/3 = 1/2 his allowance spent on Tuesday. If he starts with 3/4 and spends 1/2 then he is left with 3/4 – 1/2 = 1/4 of his allowance for the rest of the week.

    1. Hi Emma,

      That is a large volume of items to address. In order to process that many you should really be joining the tutoring course. You can enroll for the remaining period for only $44.95. Email customer service for the appropriate discount code. If you have a couple problems that are higher priority then please feel free to share the details of what is not clear to you (not just the questions number).

    1. 30 represents the original total of students so the new total/old total will be (old + added)/old = (30 + 10)/30. Another way to think about it is that there were 30 x 4 = 120 daily rations in total which now get divided by 40 students so there are only 3 days of rations after the addition of 10 more students.

  5. 35.

    I do no understand this problem. When I added them up, I got 240 which divided by 15 is 16. However, that is not an option can you help me?

    What is the average of the first 15 positive integers?
    A. 7
    B. 7.5
    C. 8
    D. 8.5
    E. 9
    Question 35 of 40

    1. Hi Jefferson,

      If you add up the 1st 15 positive integers {1…15} you should get 120. A quick method to do that is to note the sum of the positive integers from 1 to n is n(n+1)/2 = 15(16)/2 = 120. If you divide that by 15 then the result is 120/15 = 8. Another quick method is to note that the mean of the set which is symmetrical about the median is also equal to the median which is the middle number or 8 in this case.

      I always recommend making quick estimates and common sense checks to see if the result computed is in the right ballpark. For example, the average of the numbers 1 to 15 will be somewhere in between. I can assess your sum of 240/15 = 16 cannot possibly be correct even before I calculate a single number because your average is greater than any number in the set. Something must be wrong with that calculation.

  7. There is a video explanation that is beneath the explanation of PS 9, Question 32 which is Math Exam 04 – Q10. In that video, it says that -8/3 is “positive 64/9 at minute 1:00. How is that possible, please that -8/3 is +64/9?

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