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

1.

Four prime numbers are written in ascending order. The product of the first 3 numbers is 105. The product of the last 3 is 385. Find the second number

   A.) 7
   B.) 9
   C.) 5
   D.) 25

Answer: Option 'C'

Let the numbers a, b, c and d.
abc = 105
bcd = 385 
HCF(abc, bcd) = bc 
Since a and d are prime.
105 = 3 × 5 × 7
385 = 5 × 7 × 11
HCF(105, 385) = 35 = 5 × 7 
The second number is 5.

2.

In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is: 

   A.) 89
   B.) 88
   C.) 86
   D.) 85

Answer: Option 'C'

Divisor = (6 × 3) + 2 = 20
5 × Quotient = 20 
Quotient = 4. 
Dividend = (Divisor × Quotient) + Remainder
Dividend = (20 × 4) + 6 = 86

3.

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

   A.) 2 or 6
   B.) 4
   C.) 4 or 8
   D.) 8

Answer: Option 'A'

80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8, so 13x should be divisible by 8. This happens when x = 6. x + y = (6 + 0) = 6.

4.

217 x 217 + 183 x 183 = ?

   A.) 79698
   B.) 80578
   C.) 80698
   D.) 81268

Answer: Option 'B'

(217)2 + (183)2 = (200 + 17)2 + (200 - 17)2 = 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] = 2[40000 + 289] = 2 x 40289 = 80578.

5.

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

   A.) 12
   B.) 11
   C.) 9
   D.) 10

Answer: Option 'D'

10/10 = 1 and 100/10 = 10
==> 10 - 1 = 9 
==> 9 + 1 = 10 Numbers

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