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**1. Homework Statement**

ok, i've got several questions:

1. which integer is closest to [tex]\sqrt{1994 + \sqrt{1994}}[/tex]

A. 44

B. 45

C. 46

D. 47

E. 48

2. Four singers take part in a musical round of 4 equal lines, each finishing after singing the line through three times. The second singer begins when the first singer begins the second line, the third singer begins when the first singer begins the third line, the fourth singer begins when the first singer begins the fourth line. The fraction of the total singing time that all four are singing at the same time is:

A. 3/4

B. 3/5

C. 2/3

D. 5/6

E. 8/15

3. Our local baker sell small buns for 30c each, or 7 for $1, or $1.80 per dozen. My mother gives me $10 to bring home 60 buns and tells me I can keep the change. I want to be able to bring home at least 60 buns and have as much money left over as possible. What is the most change I can keep?

A. $0.90

B. $1.00

C. $1.10

D. $1.20

E. $1.30

4. Which pf the five numbers is not equal to any of the others?

A. [tex]\frac{1996}{1997}[/tex]

B. [tex]\frac{996}{997}[/tex]

C. [tex]\frac{1997996}{1998997}[/tex]

D. [tex]\frac{19971996}{19981997}[/tex]

E. [tex]\frac{996996}{997997}[/tex]

5. The number 119 is very curious.

When divided by 2, it leaves a remainder of 1

When divided by 3, it leaves a remainder of 2

When divided by 4, it leaves a remainder of 3

When divided by 5, it leaves a remainder of 4

When divided by 6, it leaves a remainder of 5

How many other 3-digit numbers have this property?

A. 0

B. 1

C. 3

D. 7

E. 14

**2. Homework Equations**

**3. The Attempt at a Solution**

1. i tried working with powers, i.e 1994[tex]^{\frac{1}{2}}[/tex] and then simplifying. i couldn't reach anything.

2. I found the total time as 7 lines. (4 lines for the first singer and then 3 lines after him for the last singer). The only time all the four all singing together is when the first singer sings the last line.

my answer [tex]1/7[/tex] is not ofund in the choices.

3. I calculated the maximum change as $1.00 when he either buys 63 buns (7 for $1) or when he buys 60 buns ($1.80 the dozen) But i think it was a bit tooo easy.

4. I don't know how to proceed

5. Again, I dunno

What is more important to me is learning the methodology to tackle these problems, so I need great help. thnks