**UMTCMS**

Mu Alpha Theta

Quiz Bee

Mu Alpha Theta

Quiz Bee

**December 4, 2012**

12:30pm

UM Matina Auditorium

12:30pm

UM Matina Auditorium

Each question is for 60 seconds.

Each correct answer is worth 5 points.

Each question is for 2 minutes.

Each correct answer is worth 7 points.

5. Aling Rosa bought 12 dozen oranges at P45 per dozen. She found 18 bad oranges, and she sold the rest of them at 6 oranges for P25. Did she lose or gain? By how much?

2. The area of a rhombus is 300 in , and the lengths of its diagonals are in the ratio of 2 : 3. Compute the length of a side of the rhombus.

7. The ratio of the areas of the two similar triangles is 4:5. If the legs of the smaller

triangle are 3 cm and 4 cm long, how long

is the hypotenuse of the larger triangle?

**10 Easy Round Questions**

5 Questions for the Average Round

5 Questions for the Difficult Round

Each question is for 30 seconds.

Each correct answer is worth 3 points.

3. An arithmetic progression and a geometric progression have the same first term, which is 4. Their third terms are also equal, but the second term of the arithmetic progression exceeds the second term of the geometric progression by 2. Find the second term of the geometric progression.

**The Mechanics**

10. Ricky was told to add 4 to a certain number, and then divide the sum by 5. Instead, he first added 5, and then divided the sum by 4. He came up with the wrong answer of 9. What should be the correct answer?

1. The larger angles of a

rhombus are doubled the

smaller angles.

The length of the shorter

diagonal is 10 cm. What is the perimeter of the rhombus?

2. If the price of a diamond varies

as the square of its weight, and a

diamond weighing 2 grams is worth

PhP 10 000, what is the value of a

10-gram diamond?

If 36 = 6 , find x.

4. A boy's club decides to build a

cabin. The job can be done by

3 skilled workmen in 4 days

or by 5 of the boys in 6 days.

How long will it take if all

work together?

5. Mr. Lee borrowed PhP 25 000 on March 10, 2011 and paid it back with the interest at 5% on March 10, 2012. How much is the amount he paid?

6. For x 2,

what is the minimum value of y in

y=3x-x ?

8. Bill and Chris have the same favorite barbershop. Bill goes to this barbershop after every 8 days, while Chris after every 6 days. If they met one Tuesday afternoon, on what day will they possibly meet again?

9. On the clock’s face, what is the smaller angle between the segments joining the center to the 2 o’clock and to the

7 o’clock marks?

2. Let ABCD be a convex quadrilateral with

AB = AD = 25 cm,

CB = CD = 10 13 cm, and

DB = 40 cm. How long is AC?

3. Two times the father's age is 8 more than six times his son's age. Ten years ago, the sum of their ages was 44. How old is his son now?

4. Two negative numbers differ by 3 and their squares differ by 63. Find the larger number.

1. If x = 3, what is the average of 2x - 11x, 12x, and 2x - 2x ?

The sum of the lengths of the three sides of a right triangle is 18. The sum of the squares of the lengths of the three sides is 128. Find the area of the triangle.

4. Ella has two-thirds as much money as Jake. If Jake gives one-third of his money to Ella, and Ella gives Jake one-sixth of what she has then, then Jake will have P1 less than Ella. How much had each at first?

5. Let x and y be two 2-digit integers, where y is the number obtained by reversing the digits of x. If x - y = 495, Find x and y.

THE BREAK

Clincher Round

3. A man calculates that if he continues at the present speed, to drive the remaining 100 km of his trip, he will arrive 30 minutes late. In order to arrive on time, he must travel at an average rate of 10 kph faster. What is his present speed?

2. In ABC, with AB = AC, let D be a point on side BC such that AD = BD. If DAC = 90, what is BAD?

1. After working for the required number of hours, Mary Lou works 4 hours overtime each at 150% of her regular hourly pay. Her total pay that day is equivalent to 12 hours at her regular hourly salary. What is her required number of working hours each day?

4. A fair die is tossed three times. Given that the sum of the first two tosses equals the third, what is the probability that at least one \1" is tossed?

The area of a right triangle and the length of its hypotenuse are both numerically equal to 5. What are the lengths of its legs?

1.

40 cm

2.

PhP 250 000

3.

2/3

4.

12/5 days

5.

PhP 26 250

2

6.

2

7.

5 5

2

8.

Friday

9.

150 degrees

10.

7

2

3

2

1.

19

2.

45 cm

3.

15 years old

4.

-9

5.

Aling Rosa lost

PhP 15.

1.

9 square units

2.

5 13 in

3.

8

4.

Jake has PhP 9

while Ella has PhP 6.

2

2

5.

x = 32

y = 23

3.

40 kph

2.

30 degrees

1.

6 hours

per day

4.

3/5

2

1 - x

x

cm