1. Which is the least number when it is divided by 7, 13 and 28 the remainder becomes 6:
[a] 365
[b] 370
[c] 376
[d] 388

Least number = LCM + Remainder
LCM of 7, 13, 28 is 364
Number = 364 + 6 = 370
2. Find the least number which when divided by 16, 18, 20, 25 leaves 4 as reminder in each case but when divided by 7 leaves no remainder:
[a] 18000
[b] 17004
[c] 18004
[d] 18002

LCM of 16, 18, 20, 25 is 3600
In the option, when divided by 3600, got remainder 4 is 18004
3. The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 6:10:00 hours then they will again change simultaneously at :
[a] 6:17:17
[b] 6:17:10
[c] 6:17:12
[d] 6:17:13

LCM of 48, 72, 108 ➝ 432
432
60 = 7.2 minutes 7 minutes & 0.2 x 60 seconds
7 minutes 12 seconds
traffic light will change simultaneously at 6:17:12
4. The greatest number of three digit which is divisible by 5, 15, 21 and 49 is:
[a] 715
[b] 765
[c] 785
[d] 735

LCM of 5, 15, 21, 49 is 735
The greatest three digit number which can be divided with 5, 15, 21, 49 is 735
5. Find the largest number of four digits which is exactly divisible by 27, 18, 12, 15 is:
[a] 9740
[b] 9730
[c] 9720
[d] 9710

LCM of 27,18,12,15 is 540 from given options, the largest number which can be divided by 540 is 9720
6. The LCM of two numbers is 864 and HCF is 144. If one of the number is 288 The other number is:
[a] 432
[b] 576
[c] 1296
[d] 144

x x 288 = LCM x HCF
x = 864 x 144/288 = 432
7. HCF of two numbers is 24 and their LCM is 1344. If difference between number is 24. The their sum is:
[a] 364
[b] 356
[c] 332
[d] 360

If HCF is 24, then number be
24x, 24y
24x x 24y = 24 x 1344
24xy = 1344
xy = 56
i.e x = 7, y = 8
Number = 24 x 7 = 168, 24 x 8 = 192
sum = 168 + 192 = 360
8. The difference between the simple interest and the compound interest at the rate of 12% per annum on Rs. 5000 for 2 years will be:
[a] Rs. 17.50
[b] Rs. 36
[c] Rs. 45
[d] Rs. 72

SI - CI = P(r/100)2
= 5000 x (12/100)2 = 5000 x 0.144 = 72
9. What least number should be subtracted from 26492528, so that the resulting number is divisible by 3 but not by 9?
[a] 1
[b] 2
[c] 4
[d] 7

sum of all digits in the number 26492518
= 2+6+4+9+2+5+1+8 = 37
Obviously 4 is the least number which should be subtracted from the number 26492518. So that the resulting number is divisible by 3 but not by 9
10. Which one of the following three digit number divides 9238 and 7091 with the same remainder is each case?
[a] 113
[b] 209
[c] 317
[d] 191

When we divide the number 9238 and 7091 by 113, we get the same reminder 85