# Aptitude - Numbers

Exercise : Numbers - General Questions
46.
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
24
144
292
584
Explanation:
``` 5 | x                z = 13 x 1 + 12  = 25
--------------
9 | y - 4            y = 9 x z + 8  = 9 x 25 + 8  = 233
--------------
13| z - 8            x = 5 x y + 4  = 5 x 233 + 4  = 1169
--------------
| 1 -12

585) 1169 (1
585
---
584
---

Therefore, on dividing the number by 585, remainder = 584.
```

47.
In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
4236
4306
4336
5336
None of these
Explanation:

Divisor = (5 x 46) = 230

 10 x Quotient = 230     = 230 = 23 10

Dividend = (Divisor x Quotient) + Remainder

= (230 x 23) + 46

= 5290 + 46

= 5336.

48.
4500 x ? = 3375
 2 5
 3 4
 1 4
 3 5
None of these
Explanation:
 4500 x x = 3375      x = 337575 = 3 4500100 4

49.
What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
4
3
2
1
None of these
Explanation:
``` 6) 4456 (742
42
---
25
24        Therefore, Required number = (6 - 4) = 2.
---
16
12
---
4
```

50.
What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?
23
31
29
37
49
Explanation:
``` 87) 13601 (156
87
----
490
435
----
551
522
---
29
---

Therefore, the required number = 29.
```