Q. 4

Let abc be a thre A. 9

B. 11

C. 18

D. 33

Answer :

General form of abc is 100a + 10b + c and general form of cba is 100c + 10b + a .

Now abc – cba = (100a + 10b + c) – (100c + 10b + a)


abc – cba = 100a – a + 10b – 10b + c – 100c.


abc – cba = 99a -99c = 99(a-c)


abc – cba is divisible by 99 because 99 is factor of abc – cba.


Hence all numbers which are factors of 99 will also be divisible by abc – cba.


Option (a) 9 is the factor of 99 ( 11 x 9 = 99). Therefore abc-cba is divisible by 9.


Option (b) 11 is the factor of 99 ( 11 x 9 = 99). Therefore abc-cba is divisible by 11


Option (c) 18 is not the factor of 99 because does not give 0 remainder. Therefore abc - cba is not divisible by 18.


Option (d) 33 is the factor of 99 (33 x 3 = 99). Therefore abc-cba is divisible by 33.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz on Divisibility TestQuiz on Divisibility TestQuiz on Divisibility Test32 mins
Smart Revision | Playing with NumbersSmart Revision | Playing with NumbersSmart Revision | Playing with Numbers54 mins
Divisible or notDivisible or notDivisible or not41 mins
NCERT | Divisibility TestNCERT | Divisibility TestNCERT | Divisibility Test43 mins
Mastering Divisibility TestMastering Divisibility TestMastering Divisibility Test42 mins
Smart Revision | Complete Chapter QuizSmart Revision | Complete Chapter QuizSmart Revision | Complete Chapter Quiz45 mins
Quiz | Who will Win the Game?Quiz | Who will Win the Game?Quiz | Who will Win the Game?41 mins
Quiz | Imp. Qs. on Playing With NumbersQuiz | Imp. Qs. on Playing With NumbersQuiz | Imp. Qs. on Playing With Numbers45 mins
Quiz | Imp Qs. on Properties of Rational NumbersQuiz | Imp Qs. on Properties of Rational NumbersQuiz | Imp Qs. on Properties of Rational Numbers45 mins
Extra Questions on Laws of Rational NumbersExtra Questions on Laws of Rational NumbersExtra Questions on Laws of Rational Numbers40 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Fill in the blankNCERT - Mathematics Exemplar

Fill in the blankNCERT - Mathematics Exemplar

If abc is a threeNCERT - Mathematics Exemplar

Let abc be a threNCERT - Mathematics Exemplar

The sum of all nuNCERT - Mathematics Exemplar

Fill in the blankNCERT - Mathematics Exemplar

Fill in the blankNCERT - Mathematics Exemplar

Fill in the blankNCERT - Mathematics Exemplar

Fill in the blankNCERT - Mathematics Exemplar

Let abc be a threNCERT - Mathematics Exemplar