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What is wrong with this proof?
2 = 1 ; a = b
a2 = ab
a2 – b2 = ab – b2
(a+b) (a-b) = b (a-b)
a+b = b
2b = b
2 = 1 |
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Since a = b, a-b = 0. Hence division by zero.
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| The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel? |
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The circumference of the front wheel is 30 ft and that of the rear wheel is 36 feet. Let the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions. As both the wheels would have covered the same distance, n*36 = (n+5)*30
36n = 30n + 150
6n = 150 or n = 25.
Distance covered = 25*36 = 900 ft.
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| There are 3 boxes labeled as box A, box B, and box C. Only one box has the gift you wanted, the other 2 are empty. Assume you pick the box A, you will have one third (1/3) of chance to win the gift. If I open the box B and show you the box B is empty, do you want to exchange your Box A for Box C in order to get a better chance to win? |
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Yes, because originally the possibility to win by picking the box C was one third (1/3). By knowing the fact the box B is empty its chance of having gift is transferred to box C, the chance to win gets increased to be two third (2/3).
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| I have a half-cup of tea and a half-cup of coffee. I take one teaspoon of tea and mix it with my coffee, then I take one teaspoon of this mixture and mix it with the tea. Which cup contains more of its original contents? |
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Each will have the same amount of its original content. How much liquid is being moved does not matter (whether it is a teaspoon, half a cup, or, in extreme case the full cup does not make any difference).
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For which n is the remainder largest when the number 817,380 is divided by n?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
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The correct answer is (D). 817,380 is divisible by all the numbers in the list except 8. Hence, 8 must give the largest remainder.
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