10 second questions

Jai Ganesh · 2008-05-28 23:11:13

Answers to #737, #738, and #739:

Excellent work, JaneFairfax and JohnnyReinB! All the three answers are correct!

Jai Ganesh · 2008-05-29 03:25:57

#740. The product of three consecutive Natural numbers is 3360. What is their sum?

#741. What are the last three digits of

?

#742. Out of a total of one hundred dozen employees, one more than twelve dozen are illiterate. Out of a total of thirty dozen female employees 305 are literate. Find the percentage of illiterate males with respect to literate males.

#743. For positive values of θ, what is the minimum value of

?

JaneFairfax · 2008-05-29 04:12:12

Jai Ganesh · 2008-05-29 18:22:22

Answer to #740:
You are correct, JaneFairfax! Very well done!!!

Jai Ganesh · 2008-05-29 18:59:01

#744. In a proportion the multiplication of Ist and 4th terms
is 40 and that of 2nd and 3rd terms in 2.5x then what is the value of x?

#745. How many small cubes, each of 96 cm² surface area,
can be formed from the material obtained by melting a larger
cube of 384 cm² surface area?

#746. The ratio of Albert’s age to Richard’s age is 4 : 3. Albert
will be 26 years old after 6 years. How old is Richard now?

Jai Ganesh · 2008-05-29 19:05:54

#747. A student scored 30% marks in the first paper of
Physics out of 180 marks. He has to get an overall score of at
least 50% in two papers. The second paper is carrying 150
marks. What is the percentage of marks he should score in the second paper to get the overall average score of 50%?

JohnnyReinB · 2008-05-29 20:11:51

JaneFairfax · 2008-05-29 21:53:33

Jai Ganesh · 2008-05-30 20:13:18

Answers to #745, #746, and #747:

JohnnyReinB, You are correct! Well done!

Answer to #745:
Please check your answer, JaneFairfax!

JaneFairfax · 2008-05-30 22:28:11

Oops! I didnt know what I did there I must have temporarily gone crazy.

Jai Ganesh · 2008-05-31 20:00:49

JaneFairfax · 2008-06-02 08:48:58

Last edited by JaneFairfax (2008-06-02 08:54:04)

Jai Ganesh · 2008-06-05 20:05:20

#748. The angles of elevation of the top of a tower, from the top and the foot of a pole of height
10 m are 30° and 60° respectively. What is the height of the tower?

#749. From the monthly salary of an officer, 10% is deducted as house rent, 15% of the rest he spends on childrens education and 10% of the balance, he spends on clothes. After this expenditure he is left with $1377. What is his monthly salary?

#750. A mixture of 40 litres of milk and water contains 10% water. How much water should be
added to this so that water may be 20% in the new mixture?

#751. What is the amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol?

#752. The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then what is the number of the candidates, who passed the examination?

JohnnyReinB · 2008-06-05 20:33:01

JaneFairfax · 2008-06-06 00:25:13

ZHero · 2008-07-08 00:12:27

ganesh wrote:

(1) Is 1298045602 a perfect square?
(2) Is 6719247 a prime number?

would someone please tell me how to solve such problems 'mentally'??

mathsyperson · 2008-07-08 00:58:07

There are useful shortcuts you can use for both of these.

For the first one, ignore most of the number and concentrate on the last digit. You just have to show that there are no square numbers the end in 2.

For the second one, use the division by 3 check (adding its digits up) to show that it is not prime.

10 seconds is perhaps a bit of an underestimate, but they certainly don't take as long as you'd expect at first glance.

ZHero · 2008-07-08 01:44:51

Thanks mathsyperson!
However, i was wondering if there are some 'common for all' rules which can be used to check for the conditions given above!?
For example, say the given numbers were 'actually' perfect square & prime (respectively), then??

Last edited by ZHero (2008-07-08 01:49:51)

mathsyperson · 2008-07-08 03:07:43

There's certainly no way to tell if a number is prime or not, other than exhaustively checking that it's not divisible by any prime number less than its square root.
For very large numbers (around googol-sized) proving that they are prime is next to impossible, and it's that fact that's exploited in protecting information that's sent over the web.

As for checking if a number is square or not, the only way I can think of is to take the square root and see if it's an integer. I can't think of a way to take square roots by hand, but I'm pretty sure there is one.
That, or use trial and improvement to find a number n such that either n² = k or n² < k < (n+1)², where k is the number you're checking.

cushydom · 2008-07-08 05:16:25

there is a way to tell if a number is prime or not. it just isnt very practical for large numbers. if x divides (x-1)! then it is not a prime. so all prime numbers,p, do not divide (p-1)!

ZHero · 2008-07-08 05:41:11

Sorry to bother you all once again but there's no other way for me to know...

ganesh wrote:

84. How many digits does 100! contain?
85. And how many digits does 2^500 contain?

I did understand the solution to 85th but don't know how you get 84.?
The answer to 84. is given to be 158... How?

mathsyperson · 2008-07-08 05:59:06

cushydom wrote:

there is a way to tell if a number is prime or not. it just isnt very practical for large numbers. if x divides (x-1)! then it is not a prime. so all prime numbers,p, do not divide (p-1)!

4 doesn't divide 3!, but 4 isn't prime. I think that's the only counter-example though.

To Zhero, the only way I can think of to answer #84 is to get a computer to tell you log(100!).
(Or just print out 100! and then you can count the digits)

ZHero · 2008-07-08 06:22:52

Aaah!
Is 84. wrongly put in '10 second questions'?
May the author 'Ganesh' have some solution!
Calling out to Ganesh...

Jai Ganesh · 2008-09-16 00:46:17

ZHero,
Solution to #84 is got by approximation using the only possible approximation for factorials available, the James-Sterling formula. If you want for the formula, look for elsewhere in this forum. I conceded, you'd have to perform the claculation at lightning speed to get the correct answer. But 10-second questions is a mixed bag, some are easy and some are difficult

To JohnnyReinB and JaneFairfax:
I shall check the answers from #749 to #752 and soon let you know whether you're right!

Jai Ganesh · 2008-09-16 00:52:50

#753. Find the volume of a right circular cone of radius 6 cm and height 7 cm.

Math Is Fun Forum

#676 2008-05-28 23:11:13

Re: 10 second questions

#677 2008-05-29 03:25:57

Re: 10 second questions

#678 2008-05-29 04:12:12

Re: 10 second questions

#679 2008-05-29 18:22:22

Re: 10 second questions

#680 2008-05-29 18:59:01

Re: 10 second questions

#681 2008-05-29 19:05:54

Re: 10 second questions

#682 2008-05-29 20:11:51

Re: 10 second questions

#683 2008-05-29 21:53:33

Re: 10 second questions

#684 2008-05-30 20:13:18

Re: 10 second questions

#685 2008-05-30 22:28:11

Re: 10 second questions

#686 2008-05-31 20:00:49

Re: 10 second questions

#687 2008-06-02 08:48:58

Re: 10 second questions

#688 2008-06-05 20:05:20

Re: 10 second questions

#689 2008-06-05 20:33:01

Re: 10 second questions

#690 2008-06-06 00:25:13

Re: 10 second questions

#691 2008-07-08 00:12:27

Re: 10 second questions

#692 2008-07-08 00:58:07

Re: 10 second questions

#693 2008-07-08 01:44:51

Re: 10 second questions

#694 2008-07-08 03:07:43

Re: 10 second questions

#695 2008-07-08 05:16:25

Re: 10 second questions

#696 2008-07-08 05:41:11

Re: 10 second questions

#697 2008-07-08 05:59:06

Re: 10 second questions

#698 2008-07-08 06:22:52

Re: 10 second questions

#699 2008-09-16 00:46:17

Re: 10 second questions

#700 2008-09-16 00:52:50

Re: 10 second questions

Board footer