September 10, 2024

SSC Simplification questions are a type of mathematical problem commonly found in exams conducted by the Staff Selection Commission (SSC) or similar competitive examinations. These questions are designed to assess a candidate’s ability to simplify complex mathematical expressions or equations using various arithmetic operations.

To solve simplification questions, candidates are expected to have a solid understanding of fundamental arithmetic operations such as addition, subtraction, multiplication, and division. They should also be familiar with the rules of precedence, including the order in which operations should be performed (commonly known as BODMAS or PEMDAS).

The simplification  questions  are among the most commonly asked in the quantitative aptitude component of the various Government tests. A candidate can achieve the highest score on this topic without committing mistakes. Here, I’m providing important  SSC simplification  questions and answers for competitive exam .  Try to solve questions of  simplification on your own to improve your preparation for competitive exams.

# SSC simplification questions :

Que. 1 Evaluate  $\large&space;\boldsymbol{\frac{\frac{1}{5}\div&space;\frac{1}{5}\times&space;\frac{1}{5}}{\frac{1}{5}\times&space;\frac{1}{5}\div&space;\frac{1}{5}}}$

(a) 1            (b) 125           (c) 25           (d) 5                   (e) none of these

Question 2.  Simplify : $\large&space;\mathbf{1-1\div&space;\left&space;\{&space;1+1\div&space;\left&space;(&space;1+\frac{1}{3}&space;\right&space;)&space;\right&space;\}}$

(a) $\large&space;\frac{3}{7}$                  (b) $\large&space;\frac{11}{7}$

(c) $\large&space;\frac{7}{3}$         (d)  $\large&space;\frac{7}{11}$
(e) none of these

Question 3: Simplify $\large&space;\mathbf{7\frac{1}{2}-\left&space;[&space;2\frac{1}{4}\div&space;\left&space;\{&space;1\frac{1}{4}-\frac{1}{2}\left&space;(&space;1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}&space;\right&space;)&space;\right&space;\}&space;\right&space;]}$

(a) $\large&space;2\frac{1}{2}$

(b) $\large&space;3\frac{1}{2}$        (c) $\large&space;4\frac{1}{2}$
(d) $\large&space;5\frac{1}{2}$      (e) none of these

Question 4: What is the value of $\large&space;\mathbf{\frac{5.6\times&space;0.36+0.42&space;\times&space;3.2}{0.8&space;\times&space;2.1}}$

?

(a) 2         (b) 1          (c)  3           (d)$\large&space;\frac{3}{2}$

Question 5 : What is the value of $\large&space;\frac{(1.2)^{3}&space;+(0.8)^{3}+(0.7)^{3}-2.016}{(1.35)[(1.2)^{2}&space;+(0.8)^{2}+(0.7)^{2}-0.96-0.84-0.56])}$

?

(a) $\large&space;\frac{1}{4}$             (b)$\large&space;\frac{1}{2}$

(c) 1      (d) 2

Question 6: What is the value of  $\large&space;\sqrt{4600+\sqrt{540+\sqrt{1280+\sqrt{250+\sqrt{36}}}}}$   ?

(a) 69             (b) 68            (c) 70          (d) 72

Question 7: If 47.2506= $\large&space;4A+\frac{7}{B}+2C+\frac{5}{D}+6E$

, then the value of (5A+ 3B+6C+D+3E) is

(a) 53.6003             (b)53. 603            (c) 153.6003           (d)  213.0003

Question 8: If $\large&space;1^{3}+2^{3}+.........+9^{3}=2025,$ then the value of  $\large&space;(0.11)^{3}+(0.22)^{3}+(0.33)^{3}+........+(0.99)^{3}$

is close to   (a) 0.2695            (b) 0.3695             (c) 2.695         (d) 3.695

Question 9: The value of $\large&space;\sqrt{\frac{(0.1)^{2}+(0.01)^{2}+(0.009)^{2}}{(0.01)^{2}+(0.001)^{2}+(0.0009)^{2}}}$ is

(a) 0.01          (b) 0.1             (c) 10          (d) 100

Question 10: Simplify $\large&space;\left&space;(&space;4.8\times&space;1.8&space;\div&space;3.6+5.4&space;\,&space;\,&space;of&space;\,&space;\,&space;\frac{1}{9}-\frac{1}{5}\right&space;)$

(a) 2.8           (b)  2                 (c) 3.9            (d) 3

For further information on how to master the numerical ability section of the various competitive tests, applicants can click on the links provided below:

Question 11 : $\mathbf{\frac{1}{5}+999\frac{494}{495}\times&space;99}$

(a) 99000                   (b) 9900          (c) 990         (d) 99

Question 12 : Simplify $\large&space;\mathbf{\frac{1}{1+\frac{(2/3)}{1+\frac{2}{3}+\frac{(8/9)}{(1-\frac{2}{3})}}}}$

(a) $\large&space;\frac{13}{15}$             (b)  $\large&space;\frac{15}{13}$

(c)  $\large&space;\frac{13}{14}$             (d) $\large&space;\frac{14}{15}$

Question 13 : $\large&space;\mathbf{999\frac{995}{999}\times&space;999&space;=?}$

(a) 990809        (b) 998996           (c) 998999                 (d) 999824

Question 14 : $\large&space;\mathbf{\frac{3\frac{1}{4}-\frac{4}{5}\,&space;\,&space;of\,&space;\frac{5}{6}}{4\frac{1}{3}\div&space;\frac{1}{5}-\left&space;(&space;\frac{3}{10}&space;+21\frac{1}{5}\right&space;)}-\left&space;(&space;1\frac{2}{3}&space;\,&space;of\,&space;1\frac{1}{2}\right&space;)=?}$

(a) 9        (b) $\large&space;11\frac{1}{2}$       (c) 13          (d) $\large&space;15\frac{1}{2}$

Question 15. $\large&space;\mathbf{999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}}=?$

(a) 29997       (b) 5979       (c) 5997      (d) 5994

Question 16. $\large&space;\mathbf{7\frac{1}{2}-\left&space;[&space;2\frac{1}{4}&space;\div&space;\left&space;\{&space;1\frac{1}{4}-\frac{1}{2}\left&space;(&space;1\frac{1}{2}-\frac{1}{3}-\frac{1}{6}&space;\right&space;)&space;\right&space;\}\right&space;]}=?$

(a) $\large&space;\frac{2}{9}$              (b) 1           (c) $\large&space;4\frac{1}{2}$

(d) $\large&space;1\frac{77}{288}$

Question 17. $\large&space;\mathbf{\frac{1\frac{1}{7}-\frac{2}{3}+\frac{\frac{2}{5}}{1-\frac{1}{25}}}{1-\frac{1}{7}\left&space;(&space;\frac{1}{3}+\frac{\frac{2}{5}}{1-\frac{2}{5}}&space;\right&space;)}=?}$

(a) $\large&space;\frac{3}{4}$                     (b) $\large&space;\frac{24}{25}$

(c) 1                 (d) $\large&space;1\frac{1}{24}$

Question 18:  $\large&space;\mathbf{\frac{6^{6}+6^{6}+6^{6}+6^{6}+6^{6}+6^{6}}{3^{6}+3^{6}+3^{6}}\div&space;\frac{4^{6}+4^{6}+4^{6}+4^{6}}{2^{6}+2^{6}}}&space;=2^{n}$

then the value of n is

(a) -1         (b) 0                 (c) $\large&space;\frac{1}{2}$             (d) 1

Question 19 :  $\large&space;\boldsymbol{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}\div&space;\frac{1}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}=?$

(a) $\large&space;\frac{7}{29}$             (b) $\large&space;\frac{5}{6}$

(c) 1              (d) $\large&space;\frac{9}{13}$

Question 20 :  $\large&space;\mathbf{N=55^{3}+17^{3}-72^{3}},$

then N is divisible by

(a) 3 and 17              (b) 40 and 11             (c)  11 and 15              (d)  all of these

Question 21:  The value of the expression $\large&space;\mathbf{7777+7777\times&space;7777&space;\times&space;(5\div&space;77)\times&space;(11\div&space;35)}$

(a) 12344321                     (b) 12344321              (c) $\large&space;7^{7777}$

(d) 1242098

Question 22: The value of $\large&space;\mathbf{0.\overline{57}-0.4\overline{32}+0.3\overline{5}}$  is

(a)  $\large&space;0.\overline{494}$

(b) $\large&space;0.\overline{498}$                  (c)$\large&space;0.4\overline{98}$
(d) $\large&space;0.4\overline{94}$

Question 23 : If $\large&space;\boldsymbol{\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}}$

, where x, y and z are natural numbers, then the value of (2x+3y-z) is :

(a) 1        (b) 4         (c) 0         (d) 2

Question 24 :  The value of $\large&space;\mathbf{3\frac{1}{4}\div&space;4\frac{1}{2}\,&space;of\,&space;5\frac{1}{3}+\frac{1}{8}\div&space;\frac{1}{2}&space;\,&space;of\,&space;\frac{1}{4}-\frac{1}{4}\left&space;(&space;\frac{1}{2}\div&space;\frac{1}{8}\times&space;\frac{1}{4}&space;\right&space;)}$   is

(a) $\large&space;\frac{53}{60}$

(b) $\large&space;\frac{13}{15}$                 (c) $\large&space;\frac{7}{8}$
(d) $\large&space;\frac{3}{4}$

Question 25 :  The value of $\large&space;\mathbf{4\div&space;12\,&space;of\,&space;[3\div&space;4\,&space;of\{(4-2)\times&space;6\div&space;2\}]-2\times&space;6\div&space;8+3}$

is

(a) $\large&space;4\frac{1}{6}$                   (b) $\large&space;7\frac{1}{6}$

(c) $\large&space;2\frac{1}{3}$              (d) $\large&space;3\frac{1}{3}$

Question 26 : The value of $\large&space;\mathbf{\frac{7+3\sqrt{5}}{3+\sqrt{5}}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}}$   lies between

(a) 2   and 2.5              (b) 3 and 3.5            (c) 1.5 and 2         (d) 2.5 and 3

Question 27 : The value of $\large&space;\mathbf{\frac{27\times&space;(0.25)^{3}+125(0.05)^{3}}{(0.75)^{2}-0.25\times&space;0.5}}$

is

(a) 1             (b) 0.25         (c) 0.75              (d) 0.5

Question 28 :  $\large&space;\mathbf{(2-\frac{1}{3})(2-\frac{3}{5})(2-\frac{5}{7})&space;...............(2-\frac{999}{1001})}=?$

(a) $\large&space;\frac{999}{1001}$

(b) $\large&space;\frac{1003}{3}$                  (c) $\large&space;\frac{1001}{3}$
(d) none of these

Question 29 : $\large&space;\mathbf{\frac{1}{(1&space;\times&space;2)}+&space;\frac{1}{(2&space;\times&space;3)}&space;+\frac{1}{(3&space;\times&space;4)}+&space;.............+&space;\frac{1}{(100&space;\times&space;101)}=?}$

(a) $\large&space;\frac{1}{100}$

(b) $\large&space;\frac{100}{101}$              (c) $\large&space;\frac{101}{102}$
(d) $\large&space;9\frac{9}{10}$

Question 30 :  $\large&space;\boldsymbol{\frac{\frac{1}{3}.\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}.\frac{1}{4}-3.\frac{1}{3}.\frac{1}{5}.\frac{1}{4}+\frac{1}{5}.\frac{1}{5}.\frac{1}{5}}{\frac{1}{3}.\frac{1}{3}+\frac{1}{4}.\frac{1}{4}+\frac{1}{5}.\frac{1}{5}-\left&space;(&space;\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{3}.\frac{1}{5}&space;\right&space;)}}$

=?

(a) $\large&space;\frac{2}{3}$               (b) $\large&space;\frac{3}{4}$

(c) $\large&space;\frac{47}{60}$                   (d) $\large&space;\frac{49}{60}$

Answer : 1. (a)    2.(a)      3. (c)     4. (a)       5. (d)      6. (b)      7. (c)      8. (c)     9. (c )       10. (a)     11. (a)     12. (a)    13. (b)    14. (c)   15. (c)   16 (c)    17 .  (d)      18. (b)         19. ( c)        20. (d)        21. (d)        22. (c)    23. (d)       24. (a)     25.  (a)    26. (a)     27 .(a)    28. (b)  29. (b)   30.  (c)