Math Problems : 2011 Gauss 8 - Part B
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Muhammad Yusuf
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1. Which of the following expressions is equal to 5?
(A) (2 x 3)2 (B) 3 + 22 (C) 23 - 1
(D) 32 - 22 (E) (3 + 2)2
2. Nick charges $7 for travel costs and then $10 per hour for babysitting. Which expression always represents the number of dollars that Nick charges for y hours of babysitting?
(A) 10y + 7 (B) y + 7 (C) 17y - 7 (D) 10y - 7 (E) 17y
3. Kalob's window measures 50 cm x 80 cm. Which of the following measurements would give an area that is exactly double the area of his window?
(A) 25 cm x 160 cm (B) 40 cm x 100 cm (C) 50 cm x 160 cm
(D) 100 cm x 160 cm (E) 50 cm x 120 cm
4. March 3, 2009 or 3/3/09 was called a “square root day" because the day and the month are both the square root of the last two digits of the year. The number of square root days between January 1, 2012 and December 31, 2099 is
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
5. In the diagram, AE and BD are straight lines that intersect at C. If BD = 16, AB = 9, CE = 5, and DE = 3, then the length of AC is
(A) 11
(B) 12
(C) 15
(D) 17
(E) 16
6. Beatrix is twice the height of Violet, and Violet is 2/3 the height of Georgia. What fraction of Georgia's height is Beatrix's height?
(A) 9/7 (B) 2/3 (C) 4/3 (D) 5/4 (E) 3/2
7. If x is a number between 0 and 1, which of the following represents the smallest value?
(A) x (B) x2 (C) 2x (D) √x (E) 1/x
8. Squares ABCD and EFGH are equal in area. Vertices B, E, C, and H lie on the same straight line. Diagonal AC is extended to J, the midpoint of GH. The fraction of the two squares that is shaded is
(A) 5/8
(B) 1/3
(C) 2/5
(D) 5/16
(E) 3/8
9. How many positive integers less than 400 can be created using only the digits 1, 2 or 3, with repetition of digits allowed?
(A) 30 (B) 33 (C) 36 (D) 39 (E) 42
10. The heights of 12 boys and 10 girls in a class are recorded. The average height of all 22 students in the class is 103 cm. If the average height of the boys is 108 cm, then the average height of the girls is
(A) 96 cm (B) 97 cm (C) 98 cm (D) 99 cm (E) 100 cm
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