According to writers in forum.channelnewsasia.com, the correct question and answer can be found in http://forum.channelnewsasia.com/viewtopic.php?t=100831&postdays=0&postorder=asc&start=20. It is also based on the memory of children who had sat for the actual paper. This version seems more plausible in terms of difficulty level. The article below was published before I came across the correct version.
The method I've used is not one that the typical Pr 6 student can do. I suspect either MOE worded the question wrongly or the Sunday Times printed it wrong, or the student from whom they got the question remembered wrongly. At any rate, the answer in the article — 1568 is incorrect (if you assume the number of chairs in the rows of 13 and 7 are respectively completely divisible by 13 and by 7). If the numbers are NOT divisible by 13 or 7 (respectively) than the question should just say "Group A comprises 6/14 of the total num of chairs while Group B comprises half the total num of chairs"; and it should be followed up by "There are 112 more chairs in Group B than in Group A") . Otherwise, the rows of 13 and rows of 7 simply confuse the issue.
I encourage you to think through the method I've used below. It is by no means the only nor best method. If you come up with a better method, do mail me at coolitan@hotmail.com. I certainly look forward to that so I can learn something new!
(a). 6/14 of the chairs in a hall are in rows of 13.
(b). Half of the chairs are in rows of 7.
(c). There are 112 more chairs in rows of 7.
The rest of the chairs are stacked up.
Find the total number of chairs.
I. Let the total number of chairs be X. That is what we're trying to find out.
II. From (a) above, assuming 6/14 of the chairs are in complete rows of 13, than 6/14 of X is divisible by 13. That gives equation (1):
6/14 X = 13 A ...equation (1);
where A is some integer.
III. From (b) above, assuming half the chairs are in complete rows of 7, than 1/2 of X is divisible by 7. That gives equation (2):
1/2 X = 7B ...equation (2);
where B is another integer.
IV. From (c) above, an additional 112 chairs are in rows of 7 (note that it is16 complete rows). Here I interpret the word "more" to read "additional to those mentioned in statements (a) and (b); rather than that (b) is 112 more than (a). Now we make an observation here: if statement (b) has already accounted for half of the chairs, than those 112 chairs in (c) must be LESS THAN half the total. That gives equation (3):
1/2 X > 112 ...equation (3)
V. We don't know how many chairs are stacked up, but that does not matter. The diagram below illustrates how I have interpreted the question. We now have 3 variables (X, A, and B - all integers), in 3 equations (1,2 and 3), the last of which is an inequality equation, which hints there can be more than one answer.
VI. Now we try to solve the equations.
VII. From (2) and (3), we get:
7B >112, and therefore
B > 16 ...equation (4)
VIII. From (1) and (2), we get:
6/7 * X/2 = 13 A,
6/7 * 7B
=13 A,
B = 13/6 A ...equation (5)
IX. From (4) and (5), we get:
13/6 A >16,
A > 16 * 6 / 13,
A > 96/13
A > 7
...equation (6); since A must be an integer.
X. Given A and B have to be an integers, we look at the smallest integers that satisfies both (5) and (6). For B to be an integer in (5), A must be a multiple of 6. So by surveying, we can choose 12, since it is greater than 7 (see equation 6) and is a multiple of 6 (see equation 5).
XI. Putting A = 12 in (1), we get X = 364, and if A = 18 (the next integer that's a multiple of 6), we get X = 546 etc.
XII. As in all problem solving, don't forget to check the answer is really correct by substituting in the original equations. You'll find the answer bears out!
I'm no maths professor but the one big lesson that I tell all my students is not to delve too long on any ONE question. Some are just beyond your grasp, or some are simply wrong (and the invigilator will tell you it can't have been set wrong)! Imagine if you'd spent half your time on this question before deciding to move on, then you fail the paper because you didn't have enough time to complete the paper. Try telling MOE afterwords that the one wrong question caused you to spend 90% of your time figuring out THAT question and resulted in not having enough time to do the rest of the paper. They'll tell you to go pick a hobby - eg. flying kites?