Tutor MathsGuru: Ask me for your burning Maths questions!

[david59]

My GEP student who had just left my centre after his PSLE, shown me this kind of questions from his maths homework. Once a while, Pri 6 students are given such kind of questions just to amuse them only. [/b]

[mathsguru]

Vikaesh:

Thanks for the solution mathsguru, BTW this is a Maths Olympiad Qn!

You're most welcome Vikaesh! And yeap...I thought so too...should be an Olympiad question.

[mathsguru]

Vikaesh:

Here's another one:

1/a + 1/b + 1/c = 57/58
What is the smallest possible sum of a+b+c

Hi Vikaesh,

Here's my solution. However, since the question does not say much of the numbers a, b and c, I made my own assumptions and obtained 2 answers for the 2 sets of assumptions. :lol:

http://www.postimage.org/image.php?v=Pq1gPFi9
Curious to know what the answer key says though... :?

Regards,
MathsGuru

[fudgemum]

The question is


Given that the value of the sum 1/a + 1/b + 1/c lies between 28/29 and 1, find the smallest possible value of a+b+c where a, b and c are whole numbers.

The answer for this question is 12. This is SMOPS 2009 first round question.

I tried using guess and check method starting with 1. 1 is not possible because the result will be more than 1. 2 and 3 are possible.
1/2 + 1/3 = 0.8333.
The other number cannot be 4 and 5. The sum will be more than 1. If it is 6, the sum will be exactly 1. So it should be 7.
1/2 +1/3 + 1/7 is less than 1 and greater than 28/29.

So the answer is 2+3+7 = 12.

[mathsguru]

fudgemum:

The question is


Given that the value of the sum 1/a + 1/b + 1/c lies between 28/29 and 1, find the smallest possible value of a+b+c where a, b and c are whole numbers.

The answer for this question is 12. This is SMOPS 2009 first round question.

I tried using guess and check method starting with 1. 1 is not possible because the result will be more than 1. 2 and 3 are possible.
1/2 + 1/3 = 0.8333.
The other number cannot be 4 and 5. The sum will be more than 1. If it is 6, the sum will be exactly 1. So it should be 7.
1/2 +1/3 + 1/7 is less than 1 and greater than 28/29.

So the answer is 2+3+7 = 12.

Hi Fudgemum,

Thanks for clarifying!! No wonder no matter how I solve, I can't seem to get the answer \"12 based on Vikaesh's original question...

Hi Vikaesh >> Is Fudgemum's question correct?

Regards,
MathsGuru

[david59]

fudgemum:

The question is


Given that the value of the sum 1/a + 1/b + 1/c lies between 28/29 and 1, find the smallest possible value of a+b+c where a, b and c are whole numbers.

The answer for this question is 12. This is SMOPS 2009 first round question.

I tried using guess and check method starting with 1. 1 is not possible because the result will be more than 1. 2 and 3 are possible.
1/2 + 1/3 = 0.8333.
The other number cannot be 4 and 5. The sum will be more than 1. If it is 6, the sum will be exactly 1. So it should be 7.
1/2 +1/3 + 1/7 is less than 1 and greater than 28/29.

So the answer is 2+3+7 = 12.

While I understand your rationale of 1/2 +1/3 + 1/7 is less than 1 and greater than 28/29, the total sum of the three is equal to 41/42 = 0.97619
but the value of 57/58 is 0.98275.
Since the question states that the value of the three is equal to 57/58, how then is the answer 2, 3 n 7 correct when they do not give the same equal value.
Sorry, pardon my ignorance. I would like to learn. :?

[tianzhu]

david59:

fudgemum:

The question is


Given that the value of the sum 1/a + 1/b + 1/c lies between 28/29 and 1, find the smallest possible value of a+b+c where a, b and c are whole numbers.

The answer for this question is 12. This is SMOPS 2009 first round question.

Since the question states that the value of the three is equal to 57/58,

Hi David

According to fudgemum's question, it should be 28/29 not 57/58.

Best wishes

[ChiefKiasu]

mathsguru:

Hi Fudgemum,


Thanks for clarifying!! No wonder no matter how I solve, I can't seem to get the answer \"12 based on Vikaesh's original question...

Hi Vikaesh >> Is Fudgemum's question correct?

Regards,
MathsGuru

MathsGuru's logic is impeccable. There has to be a mistake either in the question or answer provided by Vikaesh. So before we all go bald :frustrated: for nothing, can Vikaesh kindly state the source of your question and answer?

[Dharma]

ChiefKiasu:

mathsguru:

Hi Fudgemum,


Thanks for clarifying!! No wonder no matter how I solve, I can't seem to get the answer \"12 based on Vikaesh's original question...

Hi Vikaesh >> Is Fudgemum's question correct?

Regards,
MathsGuru

MathsGuru's logic is impeccable. There has to be a mistake either in the question or answer provided by Vikaesh. So before we all go bald :frustrated: for nothing, can Vikaesh kindly state the source of your question and answer?

Hi Chief,

The question can be found under SAPMOPS 2009 1st Round Q18. Check this http://www.hci.sg/aphelion/apmops/downloads.htm

[fudgemum]

I think the question was changed and this is only my guess.


Since the value of the sum 1/a + 1/b + 1/c lies between 28/29 and 1, he has assumed it as 28.5/29 which is 57/58. It is only inbetween and not the midpoint.

If anyone can provide the solution for Round 1 question numbers 7,21,23 and 30 from the above link provided by Dharma, it will be of great help.

Thanks.