## Pri School Exam Hub

Discussions on tuition centres/enrichment services that specialise in Mathematics.

### Pri School Exam Hub

Dear Parents,

If you have any Math questions, please feel free to post here. I will get back as soon as possible. I will also post common exam questions weekly so do check out my post frequently.

1) Concept: External unchanged (Ratio)

On a train, the ratio of the male to the number of female passengers was 5:9. After 20 female alighted, the ratio became 1:3. How many female passengers were there on the train at first?

Note: The number of male passengers remained unchanged. Only female passengers alighted.
Before -> 5:9
After -> 1:3 = 3:9 (muliply by 3 to make both male units the same)
Now we can compare the female units, notice there was a decrease from 5 units to 3 units (difference of 2 units)

Thus, the 2 units equates to the 20 female passengers.
2 units -> 20
5 units -> 50

There are 50 female passengers on the train at first.

OrangeBelt

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### Re: Pri School Exam Hub

2) Concept: Constant difference (Ratio)

The ratio of Martin's age to Jeremy's age is 1:4. In 15 years time, the new ratio is 2:3. How old is Martin now?

Note: The age difference/ age gap always remain the same.
Thus, we have to make both difference the same.
1:4 (difference is 3 units)
2:3 = 6:9 (multiply by 3 to have the difference of 3 units)

Difference:
Martin: 1 unit to 6 units (Diff: 5u)
Jeremy: 4 units to 9 units (Diff: 5u)
Thus, the 5 units will be the growth of 15 years
5 units => 15
1 unit => 3
Martin is 3 years old now.

OrangeBelt

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### Re: Pri School Exam Hub

besides guess and check, what is the shortcut solution for below question. tks

A stapler cost \$8. A dictionary cost \$12.50. Tom bought 9 staplers and dictionaries. He paid \$31 more for the staplers than the dictionaries. How many dictionaries did tom buy?

jwxh
GreenBelt

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### Re: Pri School Exam Hub

Hi jwxh,

Thank you for the qn. I welcome more questions =)

A stapler cost \$8. A dictionary cost \$12.50. Tom bought 9 staplers and dictionaries. He paid \$31 more for the staplers than the dictionaries. How many dictionaries did tom buy?[/quote]

Method 1: Algebra
Let the number of stapler be x. Let the number of dictionary be y.
Equation 1: x + y =9
Equation 2: 8x - 12.5y = 31

From eqn 1, we can say that x = 9 - y
Then we substitute x = 9 - y into eqn 2.
8 (9 - y) - 12.5y = 31
72 - 8y - 12.5y = 31
12.5y + 8y = 72 - 31
20.5y = 41
y = 2
Thus, he bought two dictionaries.

Method 2: Assumption method
Assume that Tom has spent all his money on staplers
9 x \$8 = \$72

Take out the \$31 more that he spent on staplers
\$72 - \$31 = \$41

Now we can add up the amount of a stapler and a dictionary
\$12.50 + \$8 = \$20.50 (1 set of stapler and dictionary)

Divide
\$41 / \$20.50 = 2
Thus, he bought two dictionaries.

EXAM TIPS: If you have time, you can check the answer.
Dictionary: 2 x \$12.50 = \$25
Staplers: 7 x 8 = \$56
Difference: \$56 - \$25 = \$31

OrangeBelt

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### Re: Pri School Exam Hub

Concept: Repeated Identity

Mary and Jenny had a number of stickers in the ratio 4: 1. Jenny and Grace had a number of stickers in the ratio 2: 3. If they have a total of 169 stickers altogether, how many stickers does Mary have?

Exam tips!!
1. Highlight the key words
2. Identify the concept: Repeated identity
3. Write down the info provided in the question

Whose name is repeated twice? JENNY!!
M : J
4 : 1 (multiply by 2 to make Jenny's ratio the same)

J : G
2 : 3

Put the ratio together to compare
M : J : G
8 : 2 : 3

Total units = 8 + 2 + 3 = 13

13 units -> 169 stickers
1 unit -> 13 stickers
8 units -> 104 stickers
Mary has 104 stickers

** Repeated identity questions can be in the form of percentages, fractions and ratio.

OrangeBelt

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### Re: Pri School Exam Hub

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