RRB NTPC - Number System : Aptitude Test (200 Questions with Explanation)

41.

Which of the following numbers is divisible by 6? 
(i) 5647386  (ii) 8460398 (iii) 2385972

   A.) (i) and (ii) only
   B.) (ii) and (iii) only
   C.) (i) and (iii) only
   D.) (i) only

Answer: Option 'C'

For a number to be divisible by 6,
It should be divisible by both 2 and 3
1.) 5,64,386
Test for divisibility by 3
5 + 6 + 4 + 3 + 8 + 6 = 39
39 is divisible by 3.
2.) Test for divisibility by 2
The last digit of 5,647,386 is 6
The number is even
Therefore, 5,647,386 is divisible by two.

8,460,398 

Test for divisibility by 3
8 + 4 + 6 + 0 + 3 + 9 + 8 = 38
38 is divisible by 3.
2.) Test for divisibility by 2
The last digit of 8,460,398  is 8
The number is even
Therefore, 8,460,398 is divisible by two.

42.

What is the sum of all three digit numbers? 

   A.) 49550
   B.) 49455
   C.) 494450
   D.) 494550

Answer: Option 'D'

Sn = n/2[a + l] 
= 900/2 [100 + 999] 
= 450[1099] 
= 494550

43.

2720 / 2710 = 3k, then k = ?

   A.) 27
   B.) 30
   C.) 12
   D.) 15

Answer: Option 'B'

2720 / 2710 = 3k => 2710 = 3k => (33)10 = 3k => 330 = 3k.

44.

The unit digit in the product (784 x 618 x 917 x 463) is:

   A.) 2
   B.) 3
   C.) 4
   D.) 5

Answer: Option 'A'

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

45.

Find the HCF of 12 , 22?

   A.) 1
   B.) 2
   C.) 4
   D.) 132

Answer: Option 'B'

The fastest way to find the correct answer is by elimination rule : 
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers. 
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.

46.

(4300731) - ? = 2535618

   A.) 1865113
   B.) 1775123
   C.) 1765113
   D.) 1675123

Answer: Option 'C'

Let 4300731 - x = 2535618 Then x, = 4300731 - 2535618 = 1765113

47.

A Computer program gave the following output. Can you predict the Missing number in the computer output ?
117, 142, 167, X , 217, 242

   A.) 191
   B.) 192
   C.) 190
   D.) 194

Answer: Option 'B'

The given series is -- 117, 142, 167, X , 217, 242
Consequtive numbers increases by 25
Following this pattern, the Missing Number X should increase by 25 from the previous number.
When we add 25 to the number before X (i.e 167) we get 167+25=192

48.

How many numbers from 29 to 79 are exactly divisible by 11. 

   A.) 5
   B.) 6
   C.) 4
   D.) 7

Answer: Option 'A'

29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers

49.

A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition. 

   A.) 87.8%
   B.) 86.8%
   C.) 85.8%
   D.) 84.8%

Answer: Option 'A'

Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600 = 9000/100 = 90
Number of rotten bananas = 8% of 400
= 8/100 × 400 = 3200/100 =32
Therefore, total number of rotten fruits = 90 + 32 = 122
Therefore Number of fruits in good condition = 1000 - 122 = 878
Therefore Percentage of fruits in good condition = (878/1000 × 100)%
= (87800/1000)% = 87.8%

50.

Find the LCM of 25 , 30?

   A.) 150
   B.) 480
   C.) 300
   D.) 125

Answer: Option 'A'

The fastest way to find the correct answer is by elimination rule : 
Check whether each of the given choices is divisble by both the numbers. If any choice doesn’t get divided by both the numbers, then you can eliminate that particular choice and move to the next number. Answer will be the Number that is exactly divisble by both given numbers. 
Please Note : There may be a scenario when two or more numbers in the choice will be exactly divisible by both the numbers, in that case , please choose the lowest among the numbers.

51.

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is: 

   A.) 18
   B.) 24
   C.) 32
   D.) 81

Answer: Option 'B'

Let the ten's and unit's digit be x and 8 / x respectively.
Then, (10 x + 8 / x) + 18 = (10 x 8 / x) + x
=> 10x2 + 8 + 18x = 80 + x2
=> 9x2 + 18x - 72 = 0
=> x2 + 2x - 8 = 0
=> (x + 4)(x - 2) = 0
=> x = 2 => ten's digit
=> 8 / x = 8/2 = 4 => unit's digit
Hence the number is 24

52.

In the given series, can you find the Missing number ?
117, 94, 71, X , 25, 2

   A.) 47
   B.) 46
   C.) 50
   D.) 48

Answer: Option 'D'

The given series is -- 117, 94, 71, X , 25, 2
Consequtive numbers decreases by 23
Following this pattern, the Missing Number X should decrease by 23 from the previous number.
When we subract 23 to the number before X (i.e 71) we get 71--23=48

53.

Find the HCF of 19 , 8?

   A.) 1
   B.) 2
   C.) 3
   D.) 152

Answer: Option 'A'

The fastest way to find the correct answer is by elimination rule : 
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers. 
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.

54.

Find the LCM of 25 , 3?

   A.) 75
   B.) 150
   C.) 48
   D.) 100

Answer: Option 'A'

The fastest way to find the correct answer is by elimination rule : 
Check whether each of the given choices is divisble by both the numbers. If any choice doesn’t get divided by both the numbers, then you can eliminate that particular choice and move to the next number. Answer will be the Number that is exactly divisble by both given numbers. 
Please Note : There may be a scenario when two or more numbers in the choice will be exactly divisible by both the numbers, in that case , please choose the lowest among the numbers.

55.

What is the sum of all two digit numbers? 

   A.) 4900
   B.) 4895
   C.) 4905
   D.) None of these

Answer: Option 'C'

10 + 11 + 12 + 13 + 14 + 15 + - - - - - - - - + 97 + 98 + 99 + 100 
Sn = n/2[a + l] 
= 90/2[10 + 99] 
= 45[109] 
= 4905.

56.

Find the HCF of 19 , 14?

   A.) 1
   B.) 2
   C.) 3
   D.) 266

Answer: Option 'A'

The fastest way to find the correct answer is by elimination rule : 
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers. 
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.

57.

A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

   A.) 0
   B.) 1
   C.) 2
   D.) 3

Answer: Option 'D'

Let x = 6q + 3. Then, x2 = (6q + 3)2 = 36q2 + 36q + 9 = 6(6q2 + 6q + 1) + 3 Thus, when x2 is divided by 6, then remainder = 3.

58.

The LCM of two numbers is 280 and their ratio is 7 : 8. The two numbers are

   A.) 36, 40
   B.) 80, 90
   C.) 43, 49
   D.) 35, 40

Answer: Option 'D'

Let the number be 7x and 8x 
HCF = x 
We know HCF × LCM = product of two numbers
HCF × LCM = 7x × 8x
280x = 56x2
x = 5
Thus, numbers are 35 and 40

59.

What should come in place of _____ in the below number series?
173, 149, 125, 101, _____

   A.) 76
   B.) 77
   C.) 78
   D.) 79

Answer: Option 'B'

The given series is -- 173, 149, 125, 101
Consequtive numbers decreases by 24
Following this pattern, the Missing Number should decrease by 24 from the previous number.
When we subract 24 to the last number (i.e 101) we get 101- 24 = 77

60.

Output of a particular program follows the below pattern. Can you find the Missing number?
117, 146, 175, X , 233, 262

   A.) 203
   B.) 202
   C.) 206
   D.) 204

Answer: Option 'D'

The given series is -- 117, 146, 175, X , 233, 262
Consequtive numbers increases by 29
Following this pattern, the Missing Number X should increase by 29 from the previous number.
When we add 29 to the number before X (i.e 175) we get 175+29=204


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