What least value should be given to * so that the number 145*603 is exactly divisible by 9?

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DSSSB Grade 4 Previous Paper 1 (Held on: 3 Sept 2019 shift 1)

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Number System

Aptitude

1. What least value must be assigned to ‘*’ so that the number 451 * 603 is exactly divisible by 9?

1. 1. 7
   2. 8
   3. 5
   4. 9

Correct Option: B

If the sum of the digits of a number be divisible by 9, the number is divisible by 9.
Sum of the digits of 451 * 603 = 4 + 5 + 1 + * + 6 + 0 + 3
Sum of the digits of 451 * 603 = 19 + *
If * = 8, then 19 + 8 = 27 , which is divisible by 9.

• Aptitude
• Number series

Correct Answer:

Description for Correct answer:
451*603 to divide by 9 must be (4 + 5 1 * + 6 + 0 + 3)

exactly divide by 9 to (19 + *) divide by 9

*must be equal to = 8, 17,.....

For min. valye = 8

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Multiple Choice Questions

41.

If 

B.

68 Views

42.

The sum of the cubes of two numbers in the ratio 3 : 4 is 5824. The sum of the number is 

• (5824)1/3

• 28

• 24

• 24

B.

28

Let the numbers be 3x and 4x respectively.
According to the question,
   (3x)3 + (4x)3 = 5824
   27x3 + 64x3 = 5824
     91x3 = 5824
       x3 = 64   
     ⟹  x = 4
∴       Sum of the numbers = 3x + 4x = 7x = 7 x 4 = 28

138 Views

43.

A number when divided by 361 gives a remainder 47. If the same number is divided by 19, the remainder obtained is

• 3

• 8

• 9

• 9

C.

9

Shortcut Method:
Divide the remainder 47 by 19 i.e. Required remainder = 9

259 Views

44.What least value must be assigned to '*' so that the number 451*603 is exactly divisible by 9?7855

B.

8

A number is divisible by 9 if the sum of its digits is divisible by 9.
     

201 Views

45.

The missing term in the sequence
2, 3, 5, 7, 11, .......17, 19 is

• 16

• 15

• 14

• 14

D.

14

Sequence of prime numbers is followed in the pattern.

135 Views

46.

A number, when divided successively by 4, 5 and 6 leaves remainders 2, 3 and 4 respectively. The least such number is

• 50

• 53

• 58

• 58

D.

58

216 Views

47.

If the sum of the digits of a three-digit number is subtracted from that number, then it will always be divisible by

• 3 only

• 9 only

• Both 3 and 9

• Both 3 and 9

C.

Both 3 and 9

Let the 3-digit number be 100x + 10y + z.
Sum of the digits  = x + y + z
According to the question,
  Difference
     = 100x + 10y + z - (x + y + z)
     =  99x + 9y
     = 9(11x + y)
Clearly, it is a multiple of 3 and 9.

254 Views

48.

The sum of the areas of the 10 squares, the lengths of whose sides are 20 cm, 21 cm,....29 cm respectively is

• 6085 cm2

• 8555 cm2

• 2470 cm2

• 2470 cm2

A.

6085 cm2

Required sum = 202 + 212 + ......292
 = (12 + 22 +.......+292) - (12 + 22+........+192)

183 Views

49.

The wrong number in the sequence
8, 13, 21, 32, 47, 63, 83 is

• 32

• 47

• 63

• 63

B.

47

207 Views

50.

The unit digit in the product (2467)153 x (341)172 is

• 7

• 8

• 4

• 4

A.

7

Unit digit in (2467)153 
Cancel all (power digits except unit & ten's digit) and take it power to unit digit
Thus, we can write (7)53, 
Now divide power 53 by 4, we get remainder 1.  Make this remainder the  power of (7) i.e. (7)1 = 7
∴ Unit digit in (2467)153  = 7  ...(i)
Similarly,
(341)72 = (1)72 on dividing power 72 by 4 we get remainder zero, when remainder is zero, take power 4
i.e. (1)4 = 1
∴ Unit digit in (341)72  = 1    ...(ii)

∴ Unit digit (2467)153 x (341)72 = 7 x 1  = 7

263 Views

What least value must be assigned to * so that the number 279 4423 is divisible by 9?

What is the least number that must be added to 5234?