Factor and Multiple

1. Find all the possible values of the digits X and Y if the six-digit number 123X4Y is divisible by 4 and 9 ?

2. Given a six-digit number 568XYZ, find the values of X, Y and Z such that the number is divisible by 3, 4 and 5 and is also the smallest six-digit number starting with 568 ?

3. Find the sum of first three prime numbers that end with a 9 ?

4. Paul has three pieces of rope with lengths of 140 cm, 168 cm and 210 cm. He wishes to cut the three pieces of rope into smaller pieces of equal length with no remainders.
What is greatest possible length of each of the smaller pieces of rope ?
How many of the smaller pieces of rope of equal length can he get ?

5. Two lighthouses flash their lights every 20 seconds and 30 seconds respectively. Give that they flash together at 8 p.m., when will they next flash together again ?

6. John , Peter and Paul were each given a piece of string of equal length. John cut his into equal lengths of 2 m; Peter cut his into equal lengths of 3 m; and Paul cut his into equal lengths of 5 m. If there was no remainder in each case, find the shortest length of string given to each of them.

7. Find the two number if their LCM is 120 and their HCF is 4. (Given three possible answers.)

8. Using prime factorization, find the square root of 148,225 ?

9. Using prime factorization, find the cube root of 74,088 ?

10. Insert +, -, X, : and brackets to make the following sentences true
5 5 5 5 5 5 = 7

Divisibility

1. Fill in the blank so the number can divisible by 3

3 4 7 …

2 5 … 7

5 … 4 2

… 2 4 7

7 … 2 0 4

2. Fill in the blank so the number can divisible by 9

3 7 4 …

2 8 … 5

6 … 3 7

… 8 7 4

4 … 5 7 2

3. Fill in the blank so the number can divisible by 11

3 7 8 4 …

4 1 3 … 5

2 8 … 5 2

8 … 8 2 6

9 6 7 4 …

Placement Test 2005-2006

1. If 1 cm­­­­­­­­­­­­­3 of water weighs 1 gram, what is the weight of 1 litre of water?
1000 kg c. 100 kg
100 kg d. 1 kg

2. A train leaves a station at 9.15 pm and arrives at its destination at 2.35 pm. The next day. How long does it take for the journey ?
a. 17 h 20 min c. 6 h 20 min
b. 5 h 20 min d. 11 h 50 min

3. Seven more than twice the sum of 6 and 3 is
a. 25 c. 22
b. 81 d. 47

4. Which one of the following numbers is nearest to 5?
a. 4.97 c. 4.79
b. 5.02 d. 5.21

5. There are 240 pages in a book. John has finished reading of them. How many more pages does he have to read to complete the book?
a. 80 c. 120
b. 180 d. 160

6. The smaller number which is divisible by 36 and 48 is …
a. 72 c. 144
b. 96 d. 288

7. Which of the following is the smallest?
a. c. 16 %
b. 60 % d. 0.075

8. A train cover 24 km in 20 minutes. How far will it go in hours?
a. 162 km c. 144 km
b. 180 km d. 216 km
9. Fifty pupils and two teachers went to the museum. Each pupil paid$1.80 for admission. Each teacher paid $3.60. How much did they pay altogether?
a. $ 90 c. $ 97
b. $95 d. $ 97.20

10. Seven yeas ago a man was twice as old as his sister. If his sister is now 15 years old, how old, in years, is the man?
a. 15 c. 19
b. 17 d. 23

11. The graph shows the distribution of mark gained in a test by a group of student.









How many student are there?
a. 5 c. 21
b. 16 d. 35

12. The area of a square is 400 cm2­­. The side of the square is …
a. 2 m c. 50 cm
b. 20 cm d. 24 cm

13. What is the most likely number needed to complete the following pattern?
2
5
19
14
8
13
18
15
1
6
12
…

a. 14 c. 9
b. 7 d. None of these

14. A strange signal is received from outer space :
MJKLMJKLMJKL …
The letter M, J, K, L are repeated over and over. If this pattern were to continue, what would the 5218th letter be?
a. M c. K
b. J d. L

15. In … , the missing sign is …
a. = c. >
b. < d. None of these

16. The value of + + is …
a. c.
b. d.

17. Two numbers multiply to give 84 and add to give 19. The smaller of the two numbers will be …
a. 1 c. 19
b. 12 d. 7

18. A bookseller bought for $20 and sold it for $25. Express the gain as a percentage of the cost price?
a. 125 % c. 25 %
b. 20 % d. 80 %

19. There are 24 pupils in Primary 6A. The number of girls is twice that of boys. Each girl donates $4 and each boy donates $2 to a particular charity. How much money is collected altogether?
a. $ 48 c. $ 80
b. $ 72 d. $ 144

20. If of a number is 24, then of the same number is …
a. 12 c.
b. 48 d. 27

21. The hypotenuse of a triangle is 13. If the height of this triangle is 5. Find the length of this triangle ?
a. 7 c. 14
b. 12 d. 18

22. In Math test, 5 students get 9 mark, 3 students get 8 mark and 2 students get 7 mark. What is the mean (average) of this test?
a. 8.3 c. 8.5
b. 8.4 d. 8.6

23. If the perimeter of a circle is 132 cm. Then the area of this circle is … cm2
a. 1384 c. 1386
b. 1385 d. 1387

24. Complete the series of numbers below.
225, 45, 9, …, 0.36
a. 4.5 c. 3
b. 1.8 d. 0.9

25. The front wheels of a cart have a circumference of 3 metres. The back wheels have a circumference of 4 metres. A white dot is painted on the rim of each wheel of each wheel where it touched the ground. The cart is then driven 100 metres. Including the starting position , how many times will the white dots be on the ground together?
a. 7 c. 9
b. 8 d. 10