COMPACT (Playing with the Numbers)

1) In a 2 digit number, the units digit is four times the tens digit and the sum of the digits is 10. Find the number.     28

2) In a 2 digit number, the units digit is double the tens digit. The number exceeds the sum of the digits by 18. Find the number.            24

3) In a 2 digit number 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.                     35

4) The sum of the digits of a two digit number is 8. The number obtained by interchanging its digits is 18 more than the original number. Find the original number.                         35

5) The unit digit of a two digit number is 3 and seven times the sum of the digits is the number itself. Find the number.  63

6) The sum of the digits of a two digit number is 15. The number obtained by interchanging its digits exceeds the given number by 9. Find the original number.                           78

7) The difference between a 2-digit number and the number obtained by interchanging its digits is 63. What is the difference between the digits of the number?             7

8) In a 3 digit number , the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Also, the sum of its digits is 16. Find the number.                862

9) In a 3 digit number , the hundreds digit is twice the tens digit while the units digit is thrice the tens digit. Also, the sum of its digits is 18. Find the number.   639









++++++++

* A given number is divisible by 2 only when its unit digits is 0,2,4,6 or 8

* A given number is divisible by 3 only when the sum of its digits is divisible by 3.

* A given number is divisible by 4 only when the number formed by its last two digits is divisible by 4.

* A given number is divisible by 5 only when its unit digit is 0 or 5.

* For divisibility by 7
Step-1: Double the unit digit of the given number
Step-2: Substract the above number from the number formed by excluding the unit digit of the given number.
Step-3: If the number so obtained is divisible by 7 then the given number is divisible by 7.

* A given number is divisible by 8 only when the number formed by its last three digits is divisible by 8.

* A given number is divisible by 9 only when the sum of its digits is divisible by 9.

* A given number is divisible by 10 only when its digits is 0.

* A given number is divisible by 11, if the difference between the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.

Note: A number which is divisible by 9 is always divisible by 3. But , a number divisible by 3 may not be divisible by 9.

EXERCISE

1) 94
2) 95
3) 205
4) 83
5) 327
6) 6132
7) 2222
8) 693
9) 570
10) 285
11)  2398
12) 79532
13) 13576
14) 46821
15) 84663
16) 66669
17) 470
18) 1056
19) 2735
20) 55053
21) 35790
22) 98765 
23) 42658
24) 77990
25) 90
26) 1174 
27) 57930
28) 60005
29) 378
30) 474
31) 1693
32) 20345
33) 67035
34) 591282
35) 903164 
36) 100002
37) 7524
38) 32022
39) 64302
40) 89361
41) 14799
42) 66888
43) 30006
44) 33333
45) 618
46) 3928
50) 50176
51) 39392
52) 56794
53) 86102
54) 66666
55) 99918
56) 77736
57) 7304
58) 59312
59) 66664
60) 44444
61) 154360
62) 998818
63) 265472
64) 7350162
65) 444444
66) 379654
67) 1057982
68) 6543207 
69) 818532
70) 900163
71) 7531622
72) 7896
73) 3467
75) 12873
76) 65436
77) 54636
78) 98175
79) 88777
80) 18657
81) 967458
82) 263705
83) 27971
84) 869517
85) 937546
86) 336899
87) 35692
88) 41328
89) 10874
90) 154326
91) 49104
92) 570312
93) 685218
94) 739514
95) 672
96) 5341
96) 1067
97) 7305
98) 863478
99) 4832718
100) 5436708

Exercise

1) Find all possible values of x for which the 4-digit number 754x is divisible by 3.         7542,7545,7548

2) Find all possible values of x for which the 4-digit number 51y3 is divisible by 9.       5103,5193

3) Find all possible values of x for which 7 x3 is divisible by 3.          723,753,783

4) Find all possible values of y for which the number 53y1 is divisible by 3.     5331, 5361, 5391

5) Find the values of x for which the number x806 is divisible by 9. Also find the number .            4, 4806

6) Find the values of z for which the number 471z8 is divisible by 9. Also find the number .                   7,  47178

7) Give five examples of numbers, each one of which is divisible by 3 but not divisible by 9.               21,24,30,33,39

8) Give five examples of numbers, each one of which is divisible by 4 but not divisible by 8.            28,36,44,52,60



EXERCISE

1) Replace A, B, C, or  D by suitable numerals in the following: 

A) 6A B 5 + D 5 8 C = 9351.        7,6,6,2
B) 3 5 A - C B 8= 183.                       1,6,1
C) 4 A × 6 = 2B4.                                 4,6
D) A B x B A = BCB.                          1,2,5
E) 

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