10 second questions

Jai Ganesh · 2007-02-03 21:38:38

Excellent, kylekatarn!
Welcome back to the forum!

Toast · 2007-02-03 22:27:55

mathsyperson wrote:

Depending on where you are, the answer to 80. could also be 54 zeroes.
85. 500/log 2, rounded up.

Wow... that's amazing! Is there a reason why logging it will give you the number of digits?

mathsyperson · 2007-02-03 23:45:45

Yep. I made a mistake there, it should actually be 500*log 2, rounded up. But with the correction, it works.

You can see more easily why it works if we were asked how many digits were in 10^500. There are 501 digits in 500, just like there are 3 in 100 = 10², or 2 in 10 or whatever.
By definition, log (10^500) = 500, log 10² = 2, etc.
The reason that the results are all off by one is because they are all integers, so we can't round them up because they're already rounded.

Anyway, the laws of logs say that to take a different base of log of the number, you just need to take the log of the number and divide the result by the log of the base.

Rearranging that equation gives us the one that I used: {number of digits} = 500*log 2.

Jai Ganesh · 2007-02-04 16:20:00

86. How many distinct prime factors does 2400 have?

87. And how many distinct prime factors does 8400 have?

88. February 5, 2007 is a Monday. What day would February 5, 2008 be?

mathsyperson · 2007-02-05 01:39:59

86. Three: 2, 3, 5.
87. Four: 2, 3, 5, 7.
88. Tuesday.

Jai Ganesh · 2007-02-05 02:14:17

Excellent, mathsy and kylekatarn!

89. √2 + √3 + √4 + √5 is closest to which whole number?

90. What is the difference between (9x9x9x9) and (8x8x8x8)?

mathsyperson · 2007-02-05 04:23:53

89. (1 and a bit) + (1 and a big bit) + 2 + (2 and a little bit) = ~7?

90. (8+1)^4 = 8^4 + 4*8^3 + 6*8^2 + 4*8 + 1
∴ 9^4 - 8^4 = 4*512 + 6*64 + 32 + 1 = 2465.

Bit of a strange method, but that's the one that I think would be fastest for me.

Devantè · 2007-02-05 05:04:11

89. √2 + √3 + √4 + √5 ≈ 7
90. 6561-4096 = 2465

It really helps if you know your cube numbers. I just did (7³×7)-(8³×8). In other words, (729x7)-(512x8). Quick arithmetic, 6561-4096 = 2465.

Jai Ganesh · 2007-02-06 02:01:57

Well done, mathsyperson and Devante`.

I think I'd solve the second problem, viz. 90 the way Devante' did. Thats because I can tell from memory values of 9^4 and 8^4.

91. 3 feet is a yard, 220 yards a furlong and 8 furlongs a mile. How many feet is a mile?

92. Which of the two is greater? 100xpi or √100000?

93. How many numbers are there from 1 to 1000 which are divisible by 2, 3 and 5 but not divisible by 7?

Maelwys · 2007-02-06 02:15:50

Answers:

mathsyperson · 2007-02-06 03:14:51

Welcome to the forum, Maelwys!

Very impressive working out for 93. I think you might have made one small error though.

Incidentally, I read somewhere ages ago that the number of feet in a mile is closely approximated by

.
Completely useless, but still fun.

Jai Ganesh · 2007-02-07 16:30:04

I agree with mathsyperson. But I shouldn't have posted this question in the 10 seconds section. I am sure that would never have been enough.

Well done, mathsyperson!
Excellent, Maelwys! Welcome to the forum!!!

Jai Ganesh · 2007-02-08 16:19:02

94. Can you think of a triangle whose angles are in Arithmetic Progression?

95. A triangle cannot have angles (in whole numbers in degrees) in Gemoetric Progression. True of False?

Toast · 2007-02-08 18:09:00

94. 30, 60, and 90 degrees ^^

mathsyperson · 2007-02-09 01:24:06

There are actually lots of triangles that would work for 94. Equilaterals are another example. The only condition you need is that one of the angles is 60[sup]o[/sup], if that's true then the other angles will always fit.

95 is trickier. I'll have a think about that one.

Jai Ganesh · 2007-02-09 16:38:03

Yes, both Toast and mathsyperson are correct! Good work!

96. Irrespective of whether a year is a leap year or not, the months September and December have the same days for the same dates. Can you think of another such pair?

97. If a tyre 1 metre in daimeter runs at 60 revolutions per minute for an hour, what is the approximate distance covered?

98. How long would a train 200 metres long running at 10 metres/second take to cross a bridge 600 metres long?

Jai Ganesh · 2007-02-09 17:02:49

99. If Sn denotes the sum of n terms of an Arithmetic Progression and S1:S4 = 1:10, then what is the ratio of the first term to the fourth term?

100. The lengths of a triangle are x+1, 9-x and 5x-3. For how many values of x is the triangle isosceles?

mathsyperson · 2007-02-09 23:00:48

Jai Ganesh · 2007-02-10 17:28:27

Excellent, mathsyperson!!!!!

Jai Ganesh · 2007-02-10 18:02:59

101. (330x14)/5=?

102. 41.2 x 0.15 = ?

103. If 24 men can do a work in 40 days, in how many days would 30 men be able to do the same work?

104. A motorist tarvels at a constant speed of 82.6 Kilometers/hour. How many meters would he travel in 15 minutes?

105. $6200 amounts to $9176 in 4 years at simple interest. What is the rate of interest?

Jai Ganesh · 2007-02-11 00:23:27

106. Find the quadratic equation that has the roots 4 and -4.

107. What is the 16th term of the Arithmetic Progression 1, 6, 11, 16, 21......

108. If (5x³ - 2x + a) is divided by (x-2), the remainder is 7. What is the value of a?

Jai Ganesh · 2007-02-11 20:40:46

You are right, kylekatarn, Very well done!

Jai Ganesh · 2007-02-12 16:16:28

109. How many times the Principal would an amount deposited in a bank paying interest at 10% per annum compounded annually grow to?

110. Which of these would have the greatest volume? A spehere of radius 1 cm, a cube of side 1 cm or a cylinder of height 1 cm and radius 1 cm?

Toast · 2007-02-12 19:24:26

Jai Ganesh · 2007-02-13 16:28:13

And you thought right, Toast! Well done!

111. My mother is three times my age in years. 15 years later, she'd be double my age. What is the age difference between me and my mother?

112. If 1/a, 1/b and 1/c are in Harmonic Progression, what would (a+c)/2 be equal to?

Math Is Fun Forum

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