questions

[vinita deswal]

Sumit committed a mistake in finding the LCM of three distinct positive integers greater than 1 namely A, B and C, and found it to be 840, which is a common multiple of A, B and C all, but is not the lowest. The HCF of A, B and C is 1. Find the maximum possible value of A + B + C.

 

plz give a short mthd....

 

There are “n” necklaces in a safe box (n > 1). Every necklace has the same number of diamonds. Each

necklace has at least 2 diamonds. The total number of diamonds in these “n” necklaces is between

500 and 600. If this data is sufficient to find the value of n, then what is the value of “n”?

(1) 19 (2) 23 (3) 29 (4) None of these

plz give a quick method

[Rohan Aggarwal]

q1 - i also took time in this... cnt find short soln :(

q2 - straight away it is NOT .. because 19,23,29 are not so large that a change of +/- 1 in them wil make the value of total number of diamonds exceed the range of 500-600.. so none of them can be n. in fact the value of n can be anywhre betwn 50-99 (both included) 

others please verify and let me know if im wrong

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Regards,
Suvrit Chadha

[Rohan Aggarwal]

for q1... i hav a soln which wil take 2-3 min... that shud be fine

[JATIN GUPTA]

What are the options for the 1st question( i.e .....max possible value of A+B+C)?

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Regards,
Jatin Gupta

[vinita deswal]

ans 1) 563

3+140+420

plz share ur quick method

 

ans 2) n=23, 529 lies b/w 500 n 600 it is d only perfect square of a prime no. in this range

[Rohan Aggarwal]

square ? where is it given that there are n diamonds in each necklace ?

[vinita deswal]

Just the data that the total number of diamonds is between

500 and 600 is enough to find n. This would mean that there

exists a number between 500 and 600 that can be uniquely

split into 2 factors. This can happen if the number is a product

of two prime numbers. But

“n” can be uniquely identified. This

implies that both the prime numbers are equal, otherwise we

would not know what is n and what is the number of diamonds

in each of the necklaces.

Hence look for a square of a prime number between 500 and

600. This happens to be 529. Hence the number of necklaces

= n = number of diamonds in each necklace = 23.

*this is the exact solution that has been specified

[Rohan Aggarwal]

clearly... lcm shud be 420, as it is the largest posible after 840 (we need largest lcm bcoz ques wants max posible value of numbers), and for 3 numbers to have hcf 1 , 2 cases are there

either all 3 are prime

or 1 is prime n other 2 are multiples of each other

taking 3,5,7 at a time (2 cnt be taken since it somes twice in 420)

and also taking max 2 posible numbers out of remaining factors.

we have 3+140+420, 5+84+420, 7+60+420

out of which 1st is largest.. this took 4 min max..

              

On Tue, Aug 3, 2010 at 9:46 AM, Rohan Aggarwal <jiit....@gmail.com> wrote:

[Rohan Aggarwal]

ohhh i got it i went wrong in my concept applied... ok thanks for sharing :) 

[shrinidhi k]

@vinita
But 576 is also asquare that lies between 500 and 600

>>>>>>>> *Sumit committed a mistake in finding the LCM of three distinct

>>>>>>>> positive integers greater than 1 namely A, B and C, and found it to
>>>>>>>> be 840,
>>>>>>>> which is a common multiple of A, B and C all, but is not the lowest.
>>>>>>>> The HCF

>>>>>>>> of A, B and C is 1. Find the maximum possible value of A + B + C. *
>>>>>>>> **
>>>>>>>> *plz give a short mthd.... *
>>>>>>>> **

>>>>>>>>
>>>>>>>> There are “n” necklaces in a safe box (n > 1). Every necklace has
>>>>>>>> the
>>>>>>>> same number of diamonds. Each
>>>>>>>>
>>>>>>>> necklace has at least 2 diamonds. The total number of diamonds in
>>>>>>>> these “n” necklaces is between
>>>>>>>>
>>>>>>>> 500 and 600. If this data is sufficient to find the value of n, then
>>>>>>>> what is the value of “n”?
>>>>>>>>
>>>>>>>> (1) 19 (2) 23 (3) 29 (4) None of these
>>>>>>>>
>>>>>>>> plz give a quick method
>>>>>>>>
>>>>>>>> --
>>>>>>>> You received this message because you are subscribed to the Google
>>>>>>>> Groups "Simple fundas" group.
>>>>>>>> To post to this group, send email to simple...@googlegroups.com
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>>>>>>>> simple-funda...@googlegroups.com<simple-fundas%2Bunsu...@googlegroups.com>

>>>>>>>> For more options, visit this group at
>>>>>>>> http://groups.google.co.in/group/simple-fundas?hl=en-GB
>>>>>>>>
>>>>>>>> Regards,
>>>>>>>> Suvrit Chadha
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> --
>>>>>> You received this message because you are subscribed to the Google
>>>>>> Groups "Simple fundas" group.
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>>>>>> For more options, visit this group at
>>>>>> http://groups.google.co.in/group/simple-fundas?hl=en-GB
>>>>>>
>>>>>> Regards,
>>>>>> Suvrit Chadha
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> Regards,
>>>>> Jatin Gupta
>>>>>
>>>>> --
>>>>> You received this message because you are subscribed to the Google
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>>>>> For more options, visit this group at
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>>>>>
>>>>> Regards,
>>>>> Suvrit Chadha
>>>>>
>>>>
>>>> --
>>>> You received this message because you are subscribed to the Google
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>>>> For more options, visit this group at
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>>>>
>>>> Regards,
>>>> Suvrit Chadha
>>>>
>>>
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>>>
>>> Regards,
>>> Suvrit Chadha
>>>
>>
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[vinita deswal]

plz read the soln i gave later ;

it has to be square of a prime no.