numbers aptitude questions

Aptitude Practice Paper Quantitative Railway Reasoning
51. 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred’s and ten’s places are respectively:
A. 7 and 4 B. 7 and 5
C. 8 and 5 D. None of these

Answer: Option C

Explanation:

 

Let the given number be 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) – (y + 6 + 4) = (xy -3) must be either 0 or 11.

xy – 3 = 0    y = x – 3

(17 + x + y) = (17 + x + x – 3) = (2x + 14)

x= 2 or x = 8.

x = 8 and y = 5.


52. If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
A. 3 B. 2
C. 1 D. 5
E. None of these

53. (112 + 122 + 132 + … + 202) = ?
A. 385 B. 2485
C. 2870 D. 3255

Answer: Option B

Explanation:

 

(112 + 122 + 132 + … + 202) = (12 + 22 + 32 + … + 202) – (12 + 22 + 32 + … + 102)

Ref: (12 + 22 + 32 + … + n2) = 1 n(n + 1)(2n + 1)
6
= 20 x 21 x 41 10 x 11 x 21
6 6

= (2870 – 385)

= 2485.


54. If the number 5 * 2 is divisible by 6, then * = ?
A. 2 B. 3
C. 6 D. 7

Answer: Option A

Explanation:

 

6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.

Then, (5 + x + 2) must be divisible by 3. So, x = 2.


55. Which of the following numbers will completely divide (4915 – 1) ?
A. 8 B. 14
C. 46 D. 50

Answer: Option A

Explanation:

 

(xn – 1) will be divisibly by (x + 1) only when n is even.

(4915 – 1) = {(72)15 – 1} = (730 – 1), which is divisible by (7 +1), i.e., 8.


56.  

9 + 3 + 7 + 2 9 + 1 = ?
4 17 15
A.
7 + 719
1020
B.
9 + 817
1020
C.
9 + 719
1020
D.
7 + 817
1020
E. None of these

Answer: Option D

Explanation:

 

Given sum
= 9 + 3 + 7 + 2 9 + 1
4 17 15
= (9 + 7 – 9) + 3 + 2 1
4 17 15
= 7 + 765 + 120 – 68
1020
= 7 + 817
1020

57.  

1 – 1 + 1 – 2 + 1 – 3 + … up to n terms = ?
n n n
A.
1 n
2
B.
1 (n – 1)
2
C.
1 n(n – 1)
2
D. None of these

58. On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
A. 10 B. 11
C. 12 D. 13

Answer: Option A

Explanation:

 

Clearly, (2272 – 875) = 1397, is exactly divisible by N.

Now, 1397 = 11 x 127

The required 3-digit number is 127, the sum of whose digits is 10.


59. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
A. 553681 B. 555181
C. 555681 D. 556581

Answer: Option C

Explanation:

 

987 = 3 x 7 x 47

So, the required number must be divisible by each one of 3, 7, 47

553681 (Sum of digits = 28, not divisible by 3)

555181 (Sum of digits = 25, not divisible by 3)

555681 is divisible by 3, 7, 47.


60. How many prime numbers are less than 50 ?
A. 16 B. 15
C. 14 D. 18

Answer: Option B

Explanation:

 

Prime numbers less than 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Their number is 15

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