Tutor MathsGuru: Ask me for your burning Maths questions!

[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.

[Dharma]

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.

Qn 7 - For every 2 x 2 square grid, the top left square is the sum of the other 3 squares.

x = 89 - 35 - 35 = 19
Check 9 + 7 + 19 = 35 - ok
x = 19

Qn 21 - 7 squares

http://www.postimage.org/image.php?v=aV12mae0

Q23 - X = 7

http://www.postimage.org/image.php?v=Ts1UOXA

[fudgemum]

Hi Dharma, Thank you very much for the solutions.

[Dharma]

fudgemum:

Hi Dharma, Thank you very much for the solutions.

No pbm, fudgemum