Test of Divisibility : XAT, TANCET Number Properties
The question is from the topic Number Systems. It is a question on tests of divisibility.
Question
What is the value of M and N respectively? If M39048458N is divisible by 8 and 11; where M and N are single digit integers?
- 7, 8
- 8, 6
- 6, 4
- 5, 4
- 4, 6
Correct Answer -
6, 4. Choice (3)
Explanatory Answer
Test of Divisibility by 8: If the last three digits of a number are divisible by 8, then the number is divisible by 8.
Here, last three digits 58N are divisible by 8 if N = 4 because 584 is divisible by 8.
Test of Divisibility by 11If the digits at odd and even places of a given number are equal or differ by a number divisible by 11, then the given number is divisible by 11.
Therefore, (M + 9 + 4 + 4 + 8) - (3 + 0 + 8 + 5 + N) = (M + 5) should be divisible by 11; this condition is satisfied when M = 6.
Correct answer choice (3)
Level of difficulty : Moderate
More Questions Answers on Number Theory
CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise