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Problem Of The Day - Filled each circle

8:48 PM

Muhammad Yusuf , Posted in Problem Of The Day , 0 Comments

Each of the integers 1 to 7 is to be written, one in each circle in the diagram. The sum of the three integers in any straight line is to be the same. In how many different ways can the centre circle be filled?

(A) 1 (B) 2 (C) 3

(D) 4 (E) 5

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Math Problems : Grade 7 (2)

10:43 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. A 4 x 4 x 4 cube consisting of smaller cubes is painted and then broken apart. How many of the smaller cubes will have exactly 2 painted sides?

(A) 8 (B) 16 (C) 20 (D) 24 (E) 32

2. How many three digit numbers can be constructed using the digits 1, 2, 3, 4 and 5 if the same digit cannot appear twice in a row in any of the numbers?

(A) 60 (B) 65 (C) 80 (D) 120 (E) None of these

3. A rectangular floor is completely covered with tiles whose size is 1 x 2. If the tiles are not cut and do not overlap, the size of the floor cannot be

(A) 4 x 9 (B) 8 x 8 (C) 11 x 7 (D) 16 x 5 (E) None of these

4. How many ways can the number 10 be written as the sum of exactly three positive and not necessarily different integers if the order in which the sum is written does not matter? For instance, 10 = 1 + 4 + 5 is one such sum. This sum is the same as 10 = 4 + 1 + 5.

(A) 5 (B) 6 (C) 7 (D) 8 (E) 10

5. Paul’s calculator can make only two operations: add 12 to the number displayed, or subtract 7 from it. Today, it shows the number 1998. What is the minimal number of steps needed to display the number 2000?

(A) 4 (B) 12 (C) 16 (D) 21 (E) 24

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Math Probems : Grade 7

10:41 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. Everyday, Lisa puts her spare change (nickels and dimes) in a piggy-bank. This weekend she decides to count her savings. She finds that she has 72 coins with a total value of $4.95. How many dimes does she have?

(A) 14 (B) 23 (C) 25 (D) 27 (E)

2. Ève has two more marbles than Solène. Solène has twice as many marbles as Steve. Steve has 7 less marbles than Ève. How many marbles do they have between them?

(A) 13 (B) 20 (C) 27 (D) 34 (E) None of these

3. One day in math class, Shelley asks the teacher: “Mr. Nelson, how old are you?” Mr. Nelson responds: “This year I am three times as old as my sister. However, six years ago, I was five times as old as she was.” How old is the mathematics teacher?

(A) 36 (B) 40 (C) 49 (D) 55 (E) None of these

4. Four tennis players enter a tournament. How many different ways can the pairings be made for the first round games?

(A) 3 (B) 6 (C) 8 (D) 12 (E) 24

5. A box contains some apples. Andrée takes ½ of them along with one extra apple. Beatrice takes 1/3 of the remaining apples along but put two apples back in the box and finally, Corrine takes 5/6 of the remaining apples along with one more apple. There are now seven apples left in the box. How many apples were in the box before Andrée took her share?

(A) 16 (B) 44 (C) 110 (D) 140 (E) None of these

6. The “floor” of a fraction is defined to be the largest integer which is not greater than that fraction. For instance, floor (10 / 3) = 3. Evaluate

floor ( floor ( 1000 / 7 ) / (floor ( 71 / 2 ) ).

(A) 4 (B) 5 (C) 7 (D) 10 (E) 500

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Math Problem 1

10:37 PM

Muhammad Yusuf , Posted in Problem Of The Day , 0 Comments

What is the value of

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Math Contest : ASMA - Senior Devision

6:06 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

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Math Problems : The Massachusetts Association of Mathematics Leagues (MAML)

5:39 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. A car is traveling at 70 miles per hour. To the nearest tenth, how many seconds does it take to travel one mile?

(A) 51.3 (B) 51.4 (C) 52.3 (D) 52.4 (E) 53.3

2. A square is folded into thirds along the dotted lines producing the rectangle shown. If the perimeter of the rectangle is 24, find the number of units in the perimeter of the original square.

(A) 36

(B) 42

(C) 48

(D) 27

(E) 28

3. In the 2010 World Cup of Soccer the goalkeeper of the Kenyan team stopped 80% of the shots on goal prior to the game against South Africa. Against South Africa he did not stop any of the 15 shots the South Africans took and his percentage dropped to 50%. How many shots on goal did he stop before the game against South Africa?

(A) 10 (B) 15 (C) 18 (D) 20 (E) 25

4. Shown is a figure with 100 teeth. Each tooth is a 1 by 1 square. Find the number of square units in the area enclosed by the figure.

(A) 1791

(B) 1890

(C) 1891

(D) 1900

(E) 1901

5. If a single digit is removed from the decimal expansion of 8/11, resulting in a new decimal, determine the largest possible result.

(A) 73/100

(B) 76/99

(C) 7/9

(D) 77/100

(E) 17/22

6. A father and son drove out to California. The father drove 80% of the time and covered 60% of the distance. Assuming that each drove at a constant rate, determine the ratio of the father's speed to the son's speed.

(A) 8/25

(B) 3/8

(C) 12/25

(D) 3/5

(E) 3/4

7. In the following list of 4 people, if exactly one person is telling the truth and exactly one person did it, then who did it?

Al: I didn't do it.

Betty: Carl did it.

Carl: Debby did it.

Debby: I did it.

(A) Al (B) Betty (C) Carl (D) Debby (E) Cannot be determined.

8. Simplify:

(A) − √3 (B) − √2 (C) √2 (D) √3 (E) – ½ √5

9. In circle O, AB ⊥ BO , AB + BO + OC = 10 and ( AB) (BO) = 5 . Find OC.

(A) 3

(B) 3.5

(C) 4

(D) 4.5

(E) 5

10. Determine the number of square units in the area of the region bounded by the graphs of ⎢x⎢ + y = 4 and x + 5y = −4 .

(A) 16 (B) 20 (C) 24 (D) 28 (E) 32

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Math Contest Problems : Eighth Grade Test - Excellence in Mathematics Contest – 2011

3:39 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. Included in the Rhind Papyrus from 3600 years ago, the Egyptians used the following rule to determine the area of a circle:

“From the diameter, subtract 1/9 of the diameter. Square your answer.”

Compared to the correct formula for computing the area of a circle, what is the per cent error when using this Egyptian formula? (Note: “per cent error” = “amount of error”/”correct answer”.)

A. 0.60% B. 0.73% C. 0.92% D. 1.28% E. 1.31%

2. In mentioning the phenomenal growth of the Internet, a computer scientist wrote that the capacity is now reaching one yottabyte. If one yottabyte equals one thousand zettabytes; one zettabyte equals one million pettabytes; one pettabyte equals one million gigabytes; one gigabyte equals 210 megabytes; and one megabyte equals 220 bytes; then one yottabyte equals approximately 10N bytes. What is N? (Personally, I’d say, “That’s a lotta bytes!”)

A. 15 B. 18 C. 21 D. 24 E. 27

3. It is 6:00 PM Tuesday in San Francisco when it is 2:00 AM Wednesday in London. Zan at the San Francisco Google office and Alec at the London Google office are scheduled to work together on a project on their computers. Zan contacts Alec at 7:40 AM San Francisco time and they begin working. They work together until Alec shuts down his computer at 7:15 PM London time. For how many minutes did they work together?

A. 35 B. 95 C. 155 D. 215 E. 275

4. One-Pile Nim is a two-person game. Pattie and Malik take turns. There is one pile of chips. On each turn, a player takes 1, 2, 3, 4, or 5 chips from the pile. The player to take the last chip wins. At one point of the game, it is Pattie’s turn and there are 1,000 chips remaining in the pile. If both players make their best plays, there is only one winning play for Pattie. What is it?

A. Take 1 chip B. Take 2 chips C. Take 3 chips D. Take 4 chips E. Take 5 chips

5. Alicia, Ben, and Camellia are each bicycling at a constant speed.