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
• B. 22
• C. 5
• D. can't be determined

Answer 1

The correct option is D can't be determined

In 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 $\times$ 17Q + 56
=17 $\times$ 4Q + 17 $\times$ 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 $\times$ 4Q + 56
= 34 $\times$ 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.