Q. 34.1( 57 Votes )

# If 24x is a multiple of 3, where x is a digit, what is the value of x?

(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... . But since x is a digit, it can only be that6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values)

Answer :

Since 24*x* is a multiple of 3, the sum of its digits is a multiple of 3

Sum of digits of 24*x* = 2 + 4 + *x* = 6 + *x*

Hence, 6 + *x* is a multiple of 3

This is possible when 6 + *x* is any one of these numbers 0, 3, 6, 9, and so on …

Since *x* is a single digit number, the sum of the digits can be 6 or 9 or 12 or 15 and the value of *x* comes to 0 or 3 or 6 or 9 respectively

Thus, *x* can have its value as any of the four different values 0, 3, 6, or 9

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If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is

NCERT - Mathematics ExemplarTest the divisibility of each of the following numbers by 11:

(i) 22222

(ii) 444444

(iii) 379654

(iv) 1057982

(v) 6543207

(vi) 818532

(vii) 900163

(viii) 7531622

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 4:

(i) 134

(ii) 618

(iii) 3928

(iv) 50176

(v) 39392

(vi) 56794

(vii) 86102

(viii) 66666

(ix) 99918

(x) 77736

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 8:

(i) 6132

(ii) 7304

(iii) 59312

(iv) 66664

(v) 44444

(vi) 154360

(vii) 998818

(viii) 265472

(ix) 7350162

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 9:

(i) 327

(ii) 7524

(iii) 32022

(iv) 64302

(v) 89361

(vi) 14799

(vii) 66888

(viii) 30006

(ix) 33333

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 5:

(i) 95

(ii) 470

(iii) 1056

(iv) 2735

(v) 55053

(vi) 35790

(vii) 98765

(viii) 42658

(ix) 77990

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 3:

(i) 83

(ii) 378

(iii) 474

(iv) 1693

(v) 60005

(vi) 67035

(vii) 591282

(viii) 903164

(ix) 100002

RS Aggarwal - MathematicsTest the divisibility of each of the following numbers by 10:

(i) 205

(ii) 90

(iii) 1174

(iv) 57930

(v) 60005

RS Aggarwal - MathematicsWhich of the following numbers are divisible by 9?

(i) 524618

(ii) 7345845

(iii) 8987148

RS Aggarwal - Mathematics