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| Find the value of 1.1! + 2.2! + 3.3! + ......+n.n! |
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1.1! can be written as (2!-1!), likewise 2.2! = (3!-2!) , 3.3! = (4!-3!) and n.n! = (n+1)!-n! Thus by summing it up we get the result as given below. 1.1! + 2.2! + 3.3! + ......+n.n! = (2!-1!) + (3!-2!) + (4!-3!) +......+ (n+1)!-n! = (n+1)!-1.
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Fill in numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 into boxes to make the equations work.
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1 + 7 = 8, 9 - 5 = 4, 6 = 3 x 2
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| The height of a certain flagpole is 30 feet. Grease is applied to the pole. A monkey attempts to climb the pole. It climbs 3 feet every second but slips down 2 ft in the next second. When will the monkey reach the top of the flagpole? |
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Every two seconds the monkey gains 1 ft. Climbs 3 feet in 1st second and slips 2 feet in the next.
However, when it has reached 27ft, in the next jump (3ft upwards) it will reach the top. It will take 27*2 = 54 seconds to reach 27ft & then 1 sec to reach the top. Hence, 551
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Montu, Bantu, Chantu and Pintu have pets.
Montu says, "If Pintu and I each have a dog, then exactly one of Bantu and Chantu has a dog."
Bantu says, "If Chantu and I each have a cat, then exactly one of Montu and Pintu has a dog."
Chantu says, "If Montu and I each have a dog, then exactly one of Bantu and Pintu has a cat."
Pintu says, "If Bantu and I each have a cat, then exactly one of Bantu and I has a dog."
Only one of the four is telling the truth. Who is telling the truth? |
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For a IF-THEN statement to be false, IF part has to be true and THEN part has to be false.
Since only one statement is true and remaining three are false, IF part of three statements are true & THEN part of one statement is true. Let's put the given information in table. The pet-name in the normal text represents the IF part and the pet-name in round brackets represents the THEN part.
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Montu |
Bantu |
Chantu |
Pintu |
| Montu says |
Dog |
(Dog) |
(Dog) |
Dog |
| Bantu says |
(Dog) |
Cat |
Cat |
(Dog) |
| Chantu says |
Dog |
(Cat) |
Dog |
(Cat) |
| Pintu says |
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Cat
(Dog) |
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Cat
(Dog) |
It is clear that the IF part of the statements made by Montu, Chantu and Pintu are true as they do not contradict each other. And the IF part of the statement made by Bantu is false.
Thus, Bantu is telling the truth.
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Doo-Bee-Doo had born on 1468 B.C. He had lived one-fourth of his life as a boy, one-third of his life as a youth, one-fifth of his life as a man and the remaining 52 years as an old man. Which year did Doo-Bee-Doo die?
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Let's assume that Doo-Bee-Doo's age was N years when he died.
(life as a boy) + (life as a youth) + (life as a man) + (life as an old man) = (total life)
(N/4) + (N/3) + (N/5) + 52 = N
15N + 20N + 12N + 52*60 = 60N
13N = 52*60
N = 240 years
Thus, Doo-Bee-Doo was 240 years old, when he died. As he born in 1468 B.C., he died in (1468-240) 1228 B.C.
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