Question Number 5:
5. A number when divided by a certain divisor leaves a remainder of 19; if twice the number is divided by the same divisor, then the remainder is 7. Then which of the following is true?
- (A) The divisor is 31
(B) The number can only be 50.
(C) The number lies between 10 and 20.
(D) Both (A) and (B).
(E) Can't Determine
Say, the number is n and the divisor is d.
Therefore, (n = ad + 19) and (2n = bd + 7), where a and b are constant integers.
We can easily conclude that d is greater than 19.
If we multiply the first expression by 2, we get (2n = 2ad + 38)
Which must be equal to (2n = bd + 7). Therefore, d = 38 - 7 = 31
(This is a bit tricky. Think about it! As we multiply n by 2, the remainder becomes 7. Whereas multiplication results in 38. Therefore 38 must be greater than than d and of the form (md + 7) => md = 31 => Only possible integer value of m is 1. Thus d = 31)
One possible value of n is 50. But n may be any integer of the given forms, i.e (31a + 1)
The correct answer is A.