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primary 6 | Maths
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Here's a question that I found in a P6 2009 paper. Can any fellow tutors solve this?
Date Posted: 4 years ago
Views: 751
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Answer= 564?
this question is from CHIJ 2009 SA2 paper 2 Q17. it is possible that this question is missing some additional information / condition.
although the question can be solved, and the answer is given as 564 in some answer key, this answer is not unique!
based on the answer of 564, the no. of lorries & vans in car park P, and the no. of lorries & vans in car park Q, at the beginning, would be 60, 140, 160 & 180 respectively.
another possible answer is 4589, with the initial figures being 660, 1540, 1000 & 1125 respectively. these figures can satisfy all the conditions in the question. some students may argue that it is not reasonable for a car park to have so many lots, but on the internet, it says that suntec city car park has about 3100 lots.
if you ignore the physically impossibility with regards to the actual size of the car park, then the question as it is given here, has infinite solutions.
it is not reasonable for the teacher to set a question that has more than one possible answer, so it is likely that the question is missing some additional information / condition.
although the question can be solved, and the answer is given as 564 in some answer key, this answer is not unique!
based on the answer of 564, the no. of lorries & vans in car park P, and the no. of lorries & vans in car park Q, at the beginning, would be 60, 140, 160 & 180 respectively.
another possible answer is 4589, with the initial figures being 660, 1540, 1000 & 1125 respectively. these figures can satisfy all the conditions in the question. some students may argue that it is not reasonable for a car park to have so many lots, but on the internet, it says that suntec city car park has about 3100 lots.
if you ignore the physically impossibility with regards to the actual size of the car park, then the question as it is given here, has infinite solutions.
it is not reasonable for the teacher to set a question that has more than one possible answer, so it is likely that the question is missing some additional information / condition.
Yeah, I think there must be some missing information going on here. Not the first time this happens. That's why I am asking over here, wondering if there's some secret method to solve this question, despite the missing information. But I guess I will kick this question out from my list of HARD questions.
I'm pretty sure the correct and intended variation of the question is
"The number of lorries in carpark P to the number of vans in carpark P to the number of lorries in carpark Q to the number of vans in carpark Q is 3 : 7 : 8 : 9"
If the statements are split alone, we cannot assume that the 3 : 7 and the 8 : 9 can be directly compared.
It appears that the 20% of the vans being moved is a redundant information. This is a little weird, considering that in primary school questions, all the data in the question is used in some way. To combat this, I tried adding the condition that there were the same number of vans in both carparks at the end, but found that this did not lead anywhere at all.
"The number of lorries in carpark P to the number of vans in carpark P to the number of lorries in carpark Q to the number of vans in carpark Q is 3 : 7 : 8 : 9"
If the statements are split alone, we cannot assume that the 3 : 7 and the 8 : 9 can be directly compared.
It appears that the 20% of the vans being moved is a redundant information. This is a little weird, considering that in primary school questions, all the data in the question is used in some way. To combat this, I tried adding the condition that there were the same number of vans in both carparks at the end, but found that this did not lead anywhere at all.
This questions is unsolvable, lack of connection between car park p and q for lorries.
an unsolvable question should be one that has no possible answer. due to missing condition, this question has infinite answers. the question can still be solved as follows ...
consider if we let the initial no. of lorries & vans in car park P and no. of lorries & vans in car park Q be 3u:7u:8p:9p respectively. if we try to calculate 40% of 3u and 20% of 9p, we will end up with fractional units. to avoid fractional units, we start with ... 15u:35u:40p:45p.
at the end, we have ... 21u:(35u+9p):40p:36p.
given condition that 21u+76=40p, we have to look for numbers for 1u which make 21u+76 a multiple of 40.
1st answer: 1u=4 & 1p=4, gives final vehicles = 564.
next answer: 1u=44 & 1p=25, gives final vehicles = 4589.
subsequent answers can be found with 1u=4+40n and1p=4+21n, where n is any positive integer.
the 20% of vans moved adds the condition that no. of vans in Q at first must be a multiple of 5, and reduces the no. of possible answers. without this condition, there are 5 times as many possible answers.
although the question is still solvable, this level of analyzing may be a bit too much to ask from the majority of primary school students.
one possible way to make the 1st answer unique is to add condition "... at the end, there are 32 more vans at Carpark P than at Carpark Q".
consider if we let the initial no. of lorries & vans in car park P and no. of lorries & vans in car park Q be 3u:7u:8p:9p respectively. if we try to calculate 40% of 3u and 20% of 9p, we will end up with fractional units. to avoid fractional units, we start with ... 15u:35u:40p:45p.
at the end, we have ... 21u:(35u+9p):40p:36p.
given condition that 21u+76=40p, we have to look for numbers for 1u which make 21u+76 a multiple of 40.
1st answer: 1u=4 & 1p=4, gives final vehicles = 564.
next answer: 1u=44 & 1p=25, gives final vehicles = 4589.
subsequent answers can be found with 1u=4+40n and1p=4+21n, where n is any positive integer.
the 20% of vans moved adds the condition that no. of vans in Q at first must be a multiple of 5, and reduces the no. of possible answers. without this condition, there are 5 times as many possible answers.
although the question is still solvable, this level of analyzing may be a bit too much to ask from the majority of primary school students.
one possible way to make the 1st answer unique is to add condition "... at the end, there are 32 more vans at Carpark P than at Carpark Q".
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Date Posted:
4 years ago
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