Q&A - PSLE Math
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Hi
How u know Annie’s age was 17. Her mother’s age was 45 ??? -
wow…this is amazing…how do u derive that ans? why is it so difficult for a p6?
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If the final number is 4489 then…
1. Annie’s mum is 45 years old.
1a. If Annie’s mum was aged 44, Annie must be 10 years or below younger than her mum, but then Annie would have the numbers 89-99 for her age!
1b. If Annie’s mum was aged 46, then Annie would need to be more than 111 in difference to get 4489.
2. If Annie’s mum is 45, then the original number is 45xx.
2a. Since the final number is 4489, Annie must be at least 11 years younger than her mum (but 4500-4489 = 11 doesn’t make sense, since Annie isn’t 00 years old and surely her mum wasn’t 11 when Annie was born).
2b. If Mum - Annie = 12, original number = 4533, difference = 4533-4489 = 44.
The ‘gap’ is too big. How to make the gap smaller?
2c. If Mum - Annie = 30, original number = 4515, difference = 4515-4489 = 26.
Now that’s very close. Need to adjust by 2 years less.
2d. If Mum - Annie = 28, original number = 4517, difference = 4517-4489 = 28.
3. Yay, problem solved! -
huh?
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oh…ok…got it…
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Which math topic does this question test? :?
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Andrew Lee:
Annie’s mother’s age must be 45. (Annie’s mum’s age cannot be 44 otherwise Annie will be older than her mum)Hi ...
Annie wrote her mother's age followed by her own age to form a 4-digit number. She used the diff between their ages to subtract from the 4-digit number. Then Annie obtained the number 4489. What was Annie's age ?
Let Annie’s age be ab
45ab – (45 – ab) = 4489
4000 + 500 + 10a + b – 40 – 5 + 10a + b = 4000 + 400 + 80 + 9
4000 + 500 + 20a + 2b = 4000 + 400 + 80 + 9 + 40 + 5
4000 + 500 + 20a + 2b = 4000 + 500 + 30 + 4
2b = 4
b = 2 or 7
If b = 2
20a = 30
a = 1.5 ( a is a whole number) – reject
If b = 7
2b = 14 (leave 4 in ones place and carry forward 10 to the tens place)
20a + 10 = 30
20a = 20
a = 1
Annie’s age = 17 -
Hi Dharma
Good Morning.
Wishing you a fabulous 2011.
Perhaps, another way to solve this question in an algebraic way is to consider ab as equal to a single unit
4500 + ab – (45-ab) = 4489
4455 + ab + ab =4489
ab = 34
Hence ab = 17
However for this question, it isn’t too tedious to solve it with logical reasoning and Guess and Check for students who prefer not to use algebra.
Best wishes -
Belle2011:
HiDear tianzhu,
Once again, thanks very much for your solution.
Cheers,
Belle.
You're welcome.
Best wishes -
tianzhu:
Hi Dharma
Good Morning.
Wishing you a fabulous 2011.
Perhaps, another way to solve this question in an algebraic way is to consider ab as equal to a single unit
4500 + ab – (45-ab) = 4489
4455 + ab + ab =4489
ab = 34
Hence ab = 17
This type of question, guess and chk method is recommended than using algebra. The latter should only be used at sec 1 level. Pupils need to come up with the ans fast under exam condition.
As it is not too complicated, the mark awarded is probably btw 2/3 marks.
However for this question, it isn’t too tedious to solve it with logical reasoning and Guess and Check for students who prefer not to use algebra.
Best wishes
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