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If a, a+2 and a+4 are prime numbers, then the number of possible solutions for a is

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Important Questions on Numbers and Their Properties

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Let a, b, c, d and e be integers such that a=6b=12c, and 2b=9d=12e. Then which of the following pairs contain a number that is not an integer?
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In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely 2001,2002 and 2003. If floods are again expected in 2004, the number of huts expected to be destroyed is:
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Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is: 
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Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is 
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When 2256 is divided by 17 the remainder would be?

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Three pieces of cakes of weights 412 lbs, 634 lbs and 715 lbs, respectively, are to be divided into parts of equal weights. Further, each must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained?
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After the division of a number successively by 3,4 and 7, the remainders obtained are 2,1 and 4 respectively. What will be the remainder if 84 divides the number?
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At a bookstore, 'MODERN BOOK STORE' is flashed using neon lights. The words as individually flashed at the intervals of 212 s,414 s and 518 s respectively, and each word is put off after a second. The last time after which the full name of the bookstore can be read again is: