# Aptitude - Numbers

### Exercise :: Numbers - General Questions

91.

Which one of the following is a prime number ?

 A. 161 B. 221 C. 373 D. 437 E. None of these

Explanation:

437 > 22

All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.

161 is divisible by 7, and 221 is divisible by 13.

373 is not divisible by any of the above prime numbers. 373 is prime.

92.

The smallest 6 digit number exactly divisible by 111 is:

 A. 111111 B. 110011 C. 100011 D. 110101 E. None of these

Explanation:

```The smallest 6-digit number 100000.

111) 100000 (900
999
-----
100
---

Required number = 100000 + (111 - 100)
= 100011.
```

93.

The largest 5 digit number exactly divisible by 91 is:

 A. 99921 B. 99918 C. 99981 D. 99971 E. None of these

Explanation:

```Largest 5-digit number = 99999

91) 99999 (1098
91
---
899
819
----
809
728
---
81
---

Required number = (99999 - 81)
= 99918.
```

94.

 768 x 768 x 768 + 232 x 232 x 232 = ? 768 x 768 - 768 x 232 + 232 x 232

 A. 1000 B. 536 C. 500 D. 268 E. None of these

Explanation:

 Given Exp. = (a3 + b3) = (a + b) = (768 + 232) = 1000 (a2 - ab + b2)

95.

The smallest 5 digit number exactly divisible by 41 is:

 A. 1004 B. 10004 C. 10045 D. 10025 E. None of these

Explanation:

```The smallest 5-digit number = 10000.

41) 10000 (243
82
---
180
164
----
160
123
---
37
---

Required number = 10000 + (41 - 37)
= 10004.
```

96.

How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?

 A. 8 B. 9 C. 10 D. 11 E. 7

Explanation:

 Here a = 3 and r = 6 = 2. Let the number of terms be n. 3

Then, tn = 384 arn-1 = 384 3 x 2n - 1 = 384 2n-1 = 128 = 27 n - 1 = 7 n = 8 Number of terms = 8.

97.

If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?

 A. 4x + 6y B. x + y + 4 C. 9x + 4y D. 4x - 9y

Explanation:

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11. (4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

98.

9548 + 7314 = 8362 + (?)

 A. 8230 B. 8410 C. 8500 D. 8600 E. None of these

Explanation:

```  9548          16862 = 8362 + x
+ 7314          x  = 16862 - 8362
-----             = 8500
16862
-----
```

99.

In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?

 A. 0 B. 12 C. 13 D. 20

Explanation:

Number = (12 x 35)

Correct Quotient = 420 � 21 = 20

100.

2 + 22 + 23 + ... + 29 = ?

 A. 2044 B. 1022 C. 1056 D. None of these

Explanation:

 This is a G.P. in which a = 2, r = 22 = 2 and n = 9. 2 Sn = a(rn - 1) = 2 x (29 - 1) = 2 x (512 - 1)   = 2 x 511   = 1022. (r - 1) (2 - 1)