math

This was on my test and have a few more question that is from my test.

18.The Sum of five unequal natural numbers is 90. The second largest of these five numbers can be at the most?
A.19
B.41(41 is the right answer)
C.44
D.43
E.42
please show work.

22.In what month does the 301st day of the year occur?
The answer is October,but is there a work for this problem?
A.August
B.September
C.October
D.November
E.December

32.For how many positive integers for "n" in the following inequality?
4.2<3n<57
A.16
B.17
C.18
D.15
E.14
the answer is 17, but i'm not sure how.

42. If a=-9 and b=10, what is the value of a^2+4a(divide)2+3b?
A.93
B.-69
C.52.5
D.7.5
E.32
the answer is 93, but i got -69. Please help me with this question.

asked by Mat
  1. Making the first 3 as small as possible, they would have to be 1, 2, and 3
    let the 4th be x and the 5th be y
    then
    1+2+3+x+y = 90
    x+y = 84
    remember, y has to be the largest
    we want x to be as large as possible but still be less than y
    x y
    .. ..
    .. ..
    40 44
    41 43
    42 42 --->but they can't be equal
    43 41 ---> x is no longer less than y

    so it looks like x = 41 and y = 43
    the largest that the second largest number can be is 41

    22. The average number of days per month is 30
    301/30 = 10.0333
    and the 10th month is October
    or
    365-301 = 64 days left
    but Dec + Nov = 31+30 = 61
    so that puts you back into October

    32.
    4.2 < 3n < 57
    divide by 3
    1.4 < n < 19
    So n can be 2,3,4, ... , 17,18
    Count them, there are 17

    42.
    a^2 + 4a/2 + 3b
    = 81 + 4(-9)/2 + 3(10)
    = 81 - 18 + 30
    = 93

    posted by Reiny

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