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

1.

Can you find the the missing number in the below series
117, 90, 63, X , 9, -18

   A.) 36
   B.) 34
   C.) 35
   D.) 39

Answer: Option 'A'

The given series is -- 117, 90, 63, X , 9, -18
Consequtive numbers decreases by 27
Following this pattern, the Missing Number X should decrease by 27 from the previous number.
When we subract 27 to the number before X (i.e 63) we get 63--27=36

2.

What is the diffference between the place value and face value of 3 in the numeral 1375? 

   A.) 300
   B.) 3
   C.) 297
   D.) 303

Answer: Option 'C'

place value of 3 = 3 × 100 = 300 
face value of 3 = 3
300 - 3 = 297

3.

On dividing a number by 357, we get 39 as remainder. On dividing the same number by 17, what will be the remainder?

   A.) 0
   B.) 3
   C.) 5
   D.) 11

Answer: Option 'C'

Let X be the number and y be the quotient. Then, X = 357 x y + 39 =(17x21xy)+(17x2)+5 =17 x (21y+2)+5 So, required number = 5

4.

Find the greatest five digit number that is exactly divisible by 7, 10, 15, 21 and 28 

   A.) 99840
   B.) 99900
   C.) 99960
   D.) 99990

Answer: Option 'C'

The number should be divisible by 10 (2, 5), 15 (3, 5), 21 (3, 7), and 28 (4, 7).
Hence, it is enough to check whether the number is divisible by 3, 4, 5 and 7.
Test of divisibility by 3: Sum of the digits will be divisible by 3 if a number is divisible by 3.
Test of divisibility by 4: The rightmost two digits viz., the units and tens digits will be divisible by 4 if a number is divisible by 4.
For e.g, 1232 is divisible by 4 because 32 is divisible by 4.
Test of divisibility by 5: The unit’s digit is either 5 or 0.
99960 is the only number which is divisible by 3, 4, 5 and 7.

5.

3 + 33 + 333 + 3.33 = ?

   A.) 372.33
   B.) 362.3
   C.) 702.33
   D.) 702

Answer: Option 'A'

3 + 33 + 333 + 3.33 ------ 372.33 ------

6.

Find the LCM of 42 , 20?

   A.) 504
   B.) 360
   C.) 1680
   D.) 420

Answer: Option 'D'

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.

7.

If the product of two successive positive integers is 5328, which is the smallest integer?

   A.) 78
   B.) 72
   C.) 76
   D.) 74

Answer: Option 'B'

72 x 74 = 5328

8.

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

9.

If the number 97215 × 6 is completely divisible by 11, then the smallest whole number in place of × will be:

   A.) 1
   B.) 2
   C.) 3
   D.) 4

Answer: Option 'C'

Given number = 97215 x 6 (6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11. x = 3

10.

Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

   A.) 1050
   B.) 1440
   C.) 1590
   D.) 1240

Answer: Option 'C'

Let the number that Anita wanted to multiply be x. She was expected to find the value of 35x. Instead, she found the value of 53x. The difference between the value that she got (53x) and what she was expected to get (35x) is 540. i.e., 53x – 35x = 540 => or (53 - 35) × x = 540 => x = 30 Therefore, the correct product = 53 × 30 = 1590

11.

Let N be the sum of first 100 natural numbers, then N is divisible by

   A.) 2, 4 and 8
   B.) 2 and 4
   C.) 2
   D.) 100

Answer: Option 'C'

N= 1 + 2 + … + 100 = 100 x (101/2) = 50 x 101 => N is divisible by 2 only

12.

How many numbers from 10 to 100 are exactly divisible by 9. 

   A.) 8
   B.) 11
   C.) 10
   D.) None of these

Answer: Option 'C'

10/9 = 1 and 100/9 = 11 ==> 11 - 1 = 10. Therefore 10 digits.

13.

Which of the following numbers is divisible by each one of 3, 7, 9 and 11? 

   A.) 639
   B.) 2079
   C.) 3791
   D.) 37911

Answer: Option 'B'

Given
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
So, 2079 is a correct answer.

14.

( 112 x 54) = ?

   A.) 67000
   B.) 70000
   C.) 76500
   D.) 77200

Answer: Option 'B'

(112 x 54) = 112 x ( 10/2 )4 = 112 x 104 / 24 = 1120000 / 16 = 70000

15.

Which one of the following numbers is completely divisible by 45 ?

   A.) 202860
   B.) 2033555
   C.) 331145
   D.) 181560

Answer: Option 'A'

45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.

16.

Which one of the following is not a prime number?

   A.) 31
   B.) 91
   C.) 61
   D.) 71

Answer: Option 'B'

91 is divisible by 7. So, it is not a prime number.

17.

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

18.

Output of a particular program follows the below pattern. Can you find the next number ? 
173, 151, 129, 107, _____

   A.) 84
   B.) 83
   C.) 87
   D.) 85

Answer: Option 'D'

The given series is -- 173, 151, 129, 107
Consequtive numbers decreases by 22
Following this pattern, the Missing Number should decrease by 22 from the previous number.
When we subract 22 to the last number (i.e 107) we get 107-22 = 85

19.

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number? 

   A.) 69
   B.) 78
   C.) 96
   D.) Cannot be determined

Answer: Option 'D'

Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3,
we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69. Hence, the number cannot be determined

20.

A number when divided by 216 leaves remainder 36 and the value of the quotient is 11. Find the number

   A.) 2412
   B.) 2212
   C.) 3312
   D.) 1922

Answer: Option 'A'

Number = Divisor x Quotient + Remainder = 216 x 11 + 36 = 2376 + 36 = 2412


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