# Solutions for Number System & Simplifications Practice Problems

Friends, here are the solutions with explanations for our Number System / Simplification Practice Problems. Please check the problems from here and try to solve them on your own before checking these solutions. Happy Reading :)
1.
Sum of first 'n' natural numbers is = n(n+1)/2

Total money is 1 + 2 + 3 +... + 30 = (30 x 31) / 2  = Rs. 465

2.
Number is = 76 Q + 26, where Q is the Quotient and will have values 1, 2, 3 etc..,

= 19 x 4 x Q + 19 x 1 + 7

When the number is divided by 19, the remainder will be 7

Shortcut : When the second divisor is a factor of first divisor, answer is obtained by dividing the first remainder by the second divisor. Here divide 26 by 19, the remainder is 7.

3.
LCM of 6 and 7 is 42. Divide 6869 by 42, the remainder is 23.
So, Required number is (42 - 23) = 19

4.
Dividing the power 438 by 4, the remainder is 2.

(36527)438 will also have the same digit in the unit place as (36527)2

The digit in the unit place of (36527)2 is 9.

So, the digit in the unit place of (36527)438 is 9.

5.
Let the third number be "X".  Then first number will be 2X and the second number will be 4X.

So, 2X + 4X + X = 126 => X = 18

Second number is 4 x 8 = 72

6.
Let the two digit number be 10X + y

so, 10X + y - (10Y + X) = 27

=> 9X - 9Y = 27  => X - Y = 3

So, Difference between the digits of the number is 3

7.
To divide a number by 72, it should be completely divisible by both 8 and 9.

6 + 2 + 7 + 3 + 5 + 9 + 7 + 2 = 41

The number, which is divisible by 9 after 41 is 45. 45-41 = 4 If we keep 4 in place of '#' symbol it is divisible by 9. also we have to check up whether it is divisible by 8, as the last 3 digits are divisible by 8, it is divisible by 8 also.

So, 4 should come in place of '#'

Set 1
1.
(1.87 x 1.87 x 1.87 + 0.13 x 0.13 x 0.13) / (1.87 x 1.87 + 0.13 x 0.13 - 0.13 x 1.87) = ?

This is like in the form of a3+ b3

(a + b) (a2- ab + b2)

So, answer is 1.87 + 0.13 = 2

2.
5(1/4) + 2(2/7) - 3(1/6) - 4(1/4) = ?

(1/4) + (2/7) - (1/6) - (1/4) = 5/42

3.
(18/100) x 1220 + (35/100) x 2750

=> 219.6 + 962.5 = 1182.1

5.
(16)1/2 + (√7 x √7 x √7)1/3+ (23)2= ?3+√7+21

=> 4 + √7 + 529 = ?3+ √7+21

?3 = 512  =>  ? = 8

6.
( √?- 1)2 = 8 - √28

=  ( √?- 1)2 = 7 + 1 - 2√7

=>  ( √?- 1)2 = ( √7- 1)2

=>  √? =  √7

=> ? = 7

7.
1755 % 27 % 5 = 2 x  √?

=> (1755 / (27 x 5))  = 2 x √?

=> √? = 13/2 = 6.5

=> ? = 42.25

8.
(0.6)2 %  (0.216)2 = (0.6)? % (0.36)3

(0.6)2 / (0.6)3 = (0.6) ? / ((0.6)2 )3

=  (0.6) ? /  (0.6)6

=> (0.6) 2-3 /  (0.6)?-6

=> 2-3 = ? - 6

=> ? = 5

### Set 2

1.
5 (1/8) x (8/9) % 2(1/21) x 7(1/13) = ?

5 x 1 % 2 x 7 = ?

=> ? = (5/2) x 7 = 17.5

2.
94.98% of 1299 - 12.49% of 1839.97 = ?

=> 95% of 1300 - 12.5% of 1840

=> 1235 - 230 = 1005

3.
13.604 x 21.009 x 18.971 = ?
13.6 x 21 x 19 = 5426.4

4.
17.978 - 21.008 + 32.981 - 12.968

= ? - 17.001

=> 18 - 21 + 33 - 13 + 17 = ?

=> ? = 34

5.

(249 /15) x (399 / 19) % (14 / 199)

=> (250 /15) x (400 /20) x (200/15)

1. all the best for ur results ..tc

2. 3. Q 7. How 6+2+7.......41 come?

4. Mam please post the Quick reference guide for SBI Associate PO Exam. I have on 9th.

5. mam pls upload the Quick reference guide for SBI Associate PO exam, I have on 9th

6. Karthika JanakiramanNovember 3, 2014 at 8:28 PM

how 1755% 27% 5 is solved?

7. i am in waiting list..score 42 in gd and 45in pi

8. Karthika JanakiramanNovember 3, 2014 at 8:29 PM

any one plz tel me howz it solved?

9. Tomorrow Every candidates who have applied for rrb are going to have their results. So I wish you all the best to every one.. God bless you....

10. tomorrow or 5th?

11. I think 23.69. Right ?

12. 5th i think

13. Actually 5th is tentative date. But ibps's routine is going declare the result before one or two days of given tentative date. As today they have not. But tomorrow may be...

14. sbi associates po mai simpification v ayegi kya

15. In SBI associates only DI will be focused...

16. i dont know abt it. thanks. any idea abt cut off scores for offficers and assiatants?

17. no simplications bro only di and series might come and and ineualities and 5 marks regarding data sufficeny

18. rrb po?

19. explanation is not correct or the question is not correct
it was wrong process

20. rrb po cut off

21. 22. This year's difficulty level of rrb exam was some what high in nature as compared to last year's. So cutoff will be + or - 4 to 5... That's it...

23. result not yet came

24. One suggestion from my side to candidates who are waiting results of rrb's. Please don't have over confidence on results and every selection process. It seems our weakness. So keep study. There are some exams in coming days that you are going to face.

25. 26. r u sure abt series, inequality and data sufficency bcoz in SBI PO i think only DI is there so i hope only DI in Associate too...??

27. WHAT'S YOUR NO IN WAITING LIST

28. What to attempt & what to leave in sbi associate po exam plz tell in detail. How many questions to b solved in each section???? Plz help..

29. Thanks a ton u have been very kind & helpful 😃

30. Set 2. 6th problem I couldn't understand from d third step can somebody help me out.

31. basically DI occupy more marks in 2014 PO i got 40questions in DI rest 10 all these sorry series is not given

32. Can anyone post ibps clerk 2013 chattisgarh sectional cut off?

33. Do what u are confirm of....dont fluke....15 per section is more than enough to clear section wise cut off and overall 80+ for merit but with accuracy.....good luck...

34. the solution for 8 (direction 1- 8) is wrong.

35. rrb cut-off????????

36. (y) correct

37. nope..postponed to 15th

38. happy to help u :)

39. Karthika JanakiramanNovember 7, 2014 at 11:43 AM

No..itz 43.2.... something..ans key is given lyk dat ly..!

40. 41. I tried logging in bankers adda disqus form but y is it no accepting.

42. hi kiran, i like ur explanations of the Qs, plz be in touch wid me. actually i m preparing on my own , no friend circle and no tuitor so facing difficulties. unnecessary comments at BA making important comments unseen.

now i have got 2 doubts. help me out wid explanation

1- A goes 4km north and stops and then again goes 6km in d same direction and turns right goes 4km and turnsleft and goes 4km . how far is he from starting point? ans= root 212. ans wid diag plz.

2=cost of pure milk is 16 per ltr. On adding water the mix is sold @15 per
ltr and milkman gains 25%. What is the ratio of milk and water. Ans 25:7

43. Hey I m so sorry that I saw ur comment today... Well I too preparing on my own n hv d same prblm as urs.. :D 2nd ques to mixture ka hai..jo k mjhe thik se Ni aaega..but I'll try n will explain u in evening cz m outside at dis tym...n if u got any doubt except this u can ask me anytime...here is my mail id... kiran.verma@live.in.. Although m a avg student n very poor in math bt I'll always happy to help everyone agr mjhe aaega to.. :)

44. 