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 | Re: previous CAT question |
Hi babloo, First of all 1001 has factor 7, 11 , 13 now, 3^1001 / 7 ----> 3^5/7 , remainder - 5 3^1001/11 ----> 3/7 ,remainder - 3 3^1001/13 ----> 3^5/13 , remainder - 9 so we get 7a + 5 = 11b + 3 = 13c+9 now what is word interpretation of the above statement .. find the smallest number which when divided by 7 gives remainder 5 , when divided by 11 leaves remainder 3 and when divided by 13 leaves remainder 9? first take any two condition , i always prefer big numbers 11b + 3 = 13c + 9 divisor of 13 + 9 = 9,22,35,48,61,74,87,100,113,126,139 divisor of 11 + 3 - 3,14,25,36,47,58,69,80,91,102,113 so smallest number is 113 whats the next number then ? its of form LCM(11,13) + 113 = 143k + 113 so we have combined two conditions so now our job is to compare this with third one 143k + 113 = 7a + 5 143k + 108 = 7a 140+ 3k + 105 + 3 = 7a so 3k + 3 should give 0 remainder when divided by 7 so k = 6 final remainder is hence 143(6) + 113 = 971  |
