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King Octopus has servants with six, seven, or eight legs. The
servants with seven legs always lie, but the servants with either six or
eight legs always say the truth.
One day, 4 servants met :
The blue one says: “Altogether we have 28 legs”;
the green one says: “Altogether we have 27 legs”;
the yellow one says: “Altogether we have 26 legs”;
the red one says: “Altogether we have 25 legs”.
What is the color of the servant that says the truth?
"I'm telling the truth and my color is..."
What others making statements?
Since, each of 4 servants telling different numbers then only 1 of them must be telling the truth & other must be lying.
In that case, all 3 must be having 7 legs i.e. 21 legs while the one who is making true statement must have either 6 or 8 legs. Therefore, there must be 21 + 6 = 27 or 21 + 8 = 29 legs altogether.
Nobody is saying that they altogether have 29 legs but the green octopus is saying that they altogether have 27 legs. Hence, the green octopus must be telling the truth.
A pearl necklace has 33 pearls with the largest and most valuable in the middle.
Starting from one end, each successive pearl is worth $100 more than
the one before (up to the middle one), but starting from the other end
each pearl is worth $150 more than the one before, up to the big pearl.
The whole necklace is worth $65 000.
What is the value of the middle pearl?
Here is the calculation of it's cost!
What is the question?
Let X be the cost of the middle pearl of the necklace.
There are 33 total pearls in the necklace meaning that 16 pearls are on the left and 16 are on the right.
The values of the pearls at the left must be ( X - 100 ), ( X - 200 ),..........( X - 1600 ) and those which are right must have value ( X - 150 ), ( X - 300 ),................( X - 2400 ).
The total value of the pearls at left = ( X - 100 ) + ( X - 200 ) + .......... + ( X - 1600 )
= 16X - 100 ( 1 + 2 + ...... + 16)
The total value of the pearls at left = 16X - 100 (136)
The total value of the pearls at right = ( X - 150 ) + ( X - 300 ) +............... + ( X - 2400 )
= 16X - 150 ( 1 + 2 + ...... + 16)
The total value of the pearls at right = 16X - 150 (136)
Therefore,
The total cost of necklace = The total value of the pearls at left + The cost of middle pearl + The total value of the pearls at right
The total cost of necklace = 16X - 100 (136) + X + 16X - 150 (136)
= 33X - 250 (136)
The total cost of necklace = 33X - 34000
But, the total cost of the necklace given is $65000,
The total cost of necklace = 33X - 34000 = 65000
33X = 99000
X = 3000.
Hence, the cost of the middle pearl is $3000. So the cost of the leftmost pearl is 3000 - 1600 = 1400 and the rightmost pearl is 3000 - 2400 = 600.
If a car had increased its average speed for a 210 mile journey by 5
mph, the journey would have been completed in one hour less. What was
the original speed of the car for the journey?
Here is the calculation of averages speed!
What was the question?
Let S1 be the original speed and S2 be the modified speed and T1 be the time taken with speed S1 and T2 be the time taken with speed S2.
As per given data,
T1 - T2 = 1 hr.
D/S1 - D/S2 = 1 hr.
Here, D = 210 miles, S2 = S1 + 5,
210/S1 - 210/(S1+5) = 1
210(S1+5) - 210s = 1S1(S1+5)
S1^2 + 5S1 - 1050 = 0
(S1-30)(S1+35) = 0
S1 = 30 or S1 = -35.
Since speed can't be negative, S1 = 30 mph.
Hence, the original speed is 30 mph and average speed is 30 + 5 = 35 mph.
With the original speed it would have taken 210/30 = 7 hours but with average speed it took only 210/35 = 6 hours saving 1 hour of time.
99 unique numbers between 1 and 100 are listed one by one, with 5
seconds pause between every two consecutive numbers. If you are not
allowed to take any notes, what is the best way to figure out which is
the missing number?
This is how to correctly guess the missing number!
