Here are various 2010 Math Prelim questions.

Do try them before checking on the worked solutions.

We will go through more of them in class.

Persis

**Question 1**

Water from 3 taps was used to fill an empty tank. Tap A, B and C could fill the tank completely in 3 hours, 4 hours and 5 hours respectively.

(a) What fraction of the tank was filled with water after half an hour when all taps were turned on at the same time?

Now only Tap A and B were both turned on to fill another empty tank. After 20 minutes, Tap C was also turned on. Both Tap A and B were turned off at the same time after turning on for an hour and only Tap C was left to fill the tank completely.

(b) How much longer would Tap C take to fill the tank completely with water after Tap A and B were turned off?

**Question ****2**

Rainy and Minnie had 1260 beads altogether. Rainy gave 2/3 of her beads to Minnie. Minnie then gave 3/8 of her beads to Rainy. Finally, they had the same number of beads. How many more beads had Rainy than Minnie?

**Question 3**

Kaylene was asked to number the pages of a book. When she had numbered the last page, she had counted a total of 822 digits.

(a) How many 3-digit numbered pages were there?

(b) What is the last page of the book?

**Question 4**

Mei and Jane bought a camera and a watch each. Mei spent ½ of her money on the camera and ¼ of the remaining money on a watch.

(a) What fraction of her money did Mei spend?

Jane spent 3/5 of her money on a camera. Her camera cost $280 more than Mei’s camera. They paid the same amount for their watch and had the same amount of money left.

(b) How much money had they altogether at first?

**Question 5**

Mom bought some muffins and tarts in the ratio 4:5. Each muffin cost $2.80. Each tart was $1.90. After giving away 5/8 of the muffins and 144 tarts, the ratio of the remaining items was 3:2.

(a) Find the total muffins and tarts left.

(b) How much more did the muffins cost than tarts?

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**Question 6**

Jay and Wei bought the same type of notebooks. Jay bought a few for $80. Wei enjoyed a discount of 20% and bought 4 more notebooks than Jay with the same amount of money. Find the usual price of one notebook.

**Question 1**

Water from 3 taps was used to fill an empty tank. Tap A, B and C could fill the tank completely in 3 hours, 4 hours and 5 hours respectively.

(a) What fraction of the tank was filled with water after half an hour when all taps were turned on at the same time?

Now only Tap A and B were both turned on to fill another empty tank. After 20 minutes, Tap C was also turned on. Both Tap A and B were turned off at the same time after turning on for an hour and only Tap C was left to fill the tank completely.

(b) How much longer would Tap C take to fill the tank completely with water after Tap A and B were turned off?

**Question ****2**

Rainy and Minnie had 1260 beads altogether. Rainy gave 2/3 of her beads to Minnie. Minnie then gave 3/8 of her beads to Rainy. Finally, they had the same number of beads. How many more beads had Rainy than Minnie?

**Question 3**

Kaylene was asked to number the pages of a book. When she had numbered the lat page, she had counted a total of 822 digits.

(a) How many 3-digit numbered pages were there?

(b) What is the last page of the book?

You can find the full solution here.

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