    Question

# When a number 'N' is divided by a proper divisor D' then it leaves a remainder of 14 and if the thrice of that number i.e., 3N is divided by the same divisor D, the remainder comes out to be 8. Again if the 4 times of the same number i.e., '4N' is divided by D the remainder will be :

A
35
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B
22
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C
5
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D
can't be determined
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Solution

## The correct option is C can't be determinedIn the first case N = DQ + 14. In the second case 3N = 3(DQ + 14) = 3DQ + 42 = 3DQ + 34 + 8 3N = (3DQ + 34) + 8 It shows that 34 must he divisible by 34 or its factor i.e., 1,2, 17,34. But 1 and 2 can't be values of D. Since the divisor D must be greater than the remainder (viz. 8, 14) Hence we are now left with two possible values of D viz. D = 17 and D = 34 Now, if remainder D = 17, then N = 17Q + 14 4N = 4(17 Q + 14) = 4 × 17Q + 56 =17 × 4Q + 17 × 3 + 5 4N = 17 (4Q + 3) + 5 Thus the remainder will be 5. But if we consider D = 34, then N = 34Q + 14 4N = 4(34Q + 14) = 34 × 4Q + 56 = 34 × 4Q + 3 + 22 4N = 34 (4Q + 1) + 22 Thus the remainder will be 22. Hence we can't say exactly whether the remainder will be 5 or 22. So (d) is the correct option.  Suggest Corrections  1      Similar questions  Related Videos   Factorising Numerator
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