| Q25) Find the smallest 6 digit number that is divisible by 13? 1) 100001 2) 99996 3) 100009 4) 999995 Divide 99999(Largest 4 digit number) by 13 and get remainder 'R'. R = 3. ∴ Largest 4 digit number divisible by 13 is (99999 - R) = (99999 - 3) = 99996 Required number = 99996 + 13 = 100009 Hence, Option 3. Q26) Which of the following pairs contains a number that is not an integer? 1) (a/b, b/e) 2) (c/e, a/d) 3) (de/6, a/d) 4) (c/b, a/4) a = 4b = 6c = 9d = 12e Hence, option 4. Q27) If c is a positive integer and (c + 1)(c + 3) is odd, then (c + 2)(c + 4) must be a divisible by which one of the following? 1) 16 2) 6 3) 3 4) 8 As (c + 1)(c + 3) is odd, so c + 1 and c + 3 must be odd. This, is possible only when c is even. Therefore, c = 2d , where d is a positive integer. (c + 2)(c + 4) = (2d + 2)(2d + 4) = 4(d + 1)(d + 2) Here, either d + 1 is even or d + 2 is even. So, (c + 2)(c + 4) must be divisible by 8. Hence, option 4. Q28) It is given that (224 + 1) is completely divisible by N. Which of the following numbers is completely divisible by N? 1) (212 - 1) 2) (236 - 1) 3) (248 - 1) 4) (272 - 1) (224 + 1) = y + 1 where y = 224 (248 - 1) = (y2 - 1) = (y + 1)(y - 1) Hence, option 3. |