Friday, 11 March 2016

[Q] Algebra Tricks - 2

Sometimes the equations are complex and you will find it difficult to assume values for the variables. Example -

Q . 1

Although the equation is symmetrical, we can't assume a=b=c, because that will make the LHS = 0. Such situations specially arise when the RHS is non-zero (here it is 1). Now what should we do? The trick is simple, there are three terms on the LHS, hence assume each term to be 1/3 (so that all the three terms will add up to give 1). Why have we taken 1/3, although it is obvious but still it comes from the formula - (value on RHS) / (No. of terms on LHS)
Here RHS = 1 and No. of terms on LHS = 3, hence we have assumed the value of each term as 1/3.
(a2 - bc)/(a2 + bc) = 1/3 ...      (1)
(b2 - ca)/(b2 + ca) = 1/3 ...      (2)
(b2 - ca)/(b2 - ca) = 1/3  ...      (3)
From (1), we get a2 = 2bc ...       (4)
. Similarly from (2) and (3), we get b2 = 2ca ...      (5)
and c2 = 2ab      ...    (6)

Put the values of a2, b2 and  c2 from (4), (5) and (6) in the expression whose value we have to find...
You will get 2 as the answer
Answer : (B)

Q. 2 
Here again, value on RHS = 3, No of terms = 3. Hence we assume each term to be 3/3 = 1
Therefore, (m – a2)/(b2 + c2) = 1
or m = a2 + b2 + c2
Answer : (B)

Please note that this hack is also applicable only for symmetrical equations.

Now let us see some other questions where you can assume the values.



Q. 3

Put x = 1, then since A is the average of x and 1/x, it's value will also be A = 1
The average of x3 and 1/ x3 = 1
Put A = 1 in all the 4 options to check which option will give '1' as the output.
Answer : (D)

Q . 4



Here on putting a=1, you will find that both the options A and B will give the same result. Hence put a = 4, then x = 1.25
The value of the expression = 3/2
Answer : (A)
Here, I have straight away put a=4, instead of 2 or 3 because in the question we have to calculate the square root of a. So if you will take a perfect square(like 4), the calculations will be much easier.
Note : In this question we calculated the square of 1.25, which is 1.5625. For those who don't know the trick for calculating the square of numbers ending with '5' (like 15, 65, 135, 225, etc.), let me share it.

In such cases, the last two digits are always 25.
E.g. the square of 65
The last two digits = 25
First 2 digits = 6*(6+1) = 42
Hence square of 65 = 4225
Similarly square of 125
The last two digits = 25
First 3 digits = 12*(12+1) = 156
Square of 125 = 15625

Q. 5.


Put x = 0
1st term = 1/a^2
2nd term = 1/a^2
3rd term = 0
1st term - 2nd term + 3rd term = 0
Answer : (D)
You can choose any value for 'x' and you would get the same answer. For e.g. let us take x = 1
= 1/(a^2 + a + 1) - 1/(a^2 - a + 1) + 2a/(a^4 + a^2 + 1)
= -2a/(a^4 + a^2 + 1) + 2a/(a^4 + a^2 + 1)
= 0

If you have any doubt in any question that has been asked by SSC, please drop a comment.

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51 comments:

  1. Replies
    1. Put x = 2 in x^4 + 2x^3 -2x - 1
      = 16 + 2*8 - 2*2 - 1
      = 32 - 5
      = 27

      Delete
  2. Sir one doubt for me plz reply me sir I applied for ssc cgl sir but I done a mistake in giving my dob can I reapply once again sir a fresh application some of them are saying ssc will reject both applications plz tel me sir whether I can apply second tym a new one

    ReplyDelete
    Replies
    1. SSC won't cancel your applications. You can fill the form 10 times if you want. Just do a new registration with correct DOB.

      Delete
    2. Sir I have by mistaken filled from two regions will my candidature get rejected?

      Delete
    3. @vishal...no problem...bus dono regions se exam dene mat chale jana :P

      Delete
  3. Where is question no 122?

    ReplyDelete
  4. Sir How do we identify that equation is symmetrical or not??
    is there any way to identify these types of equations?

    ReplyDelete
  5. Hi Prashant, I applied for SSC. In educational qualification, I have given only the graduation details. Is it necessary to specify school? I forgot to give details about my schooling(10th and 12th). What should I do now?

    ReplyDelete
    Replies
    1. If you have received your registration no., then no issue...

      Delete
    2. Yeah I got my registration number... Thanks a lot :)

      Delete
  6. Well thanks for making me feel like a dumbass 👍

    ReplyDelete
    Replies
    1. If you liked the blog, please don't forget to share it with others. After all sharing is caring :)

      Delete
    2. Awesomse hacks sir upload more plsssssssssssss

      Delete
  7. Sir in question 11 option b also gives 3 as output

    ReplyDelete
    Replies
    1. Thanks for pointing it out. Although x^2 -1 is the correct answer, but I shud just delete that question :)

      Delete
  8. Sir in question 11 option b also gives 3 as output

    ReplyDelete
  9. Sir ques 12 me why you a=4 directly after trying with 1

    ReplyDelete
    Replies
    1. Because we have to deal with square roots. Hence taking perfect squares like 4, 9, etc. will make the calculations simpler.

      Delete
  10. Thanks sir pls keep doing good work. Your blog is awesome :-)

    ReplyDelete
  11. Sir u forgot to post the hacks for solving asymmetrical algebric ques....

    please update those as well....


    and please some hacks related to geometry as well, as these days it is the most weighted section in SSC CGL


    and it will b realy helpful for us if u can create and manage a whatsapp grp

    I am asking a bit more frm you just becoz ur way of solving these questions have outclassed evry other blog out there in the jungles of internet.....
    as i m personally following so many blog, i nvr found any blog so superb as ur blog is....

    waiting for ur response regarding more tricks for Algebra, Trigo n geometry and also for whatsapp grp


    thanks in advance

    ReplyDelete
    Replies
    1. Thanks for the words...I will take up Geometry after Indo-Pak :)

      Delete
  12. I see only Q Nos. 1 , 10 ,12 and 13.bu6 in comments section i see guys having doubts on Q 11 ,i can't see it,neither i can see Q 2 to 8..

    ReplyDelete
    Replies
    1. I messed up the numbering...You didn't miss anything :)

      Delete
    2. SIR INDO -PAK OVER.WE ARE WAITING FOR RAJ VS SSC.

      Delete
  13. Yes sir i too cant see all questions

    ReplyDelete
    Replies
    1. I messed up the numbering...You didn't miss anything :)

      Delete
  14. Thank you for making this blog and sharing your knowledge. It is going to help us to crack cgl for sure. Personally, I am bit slow in QA section. I'll need these tricks to increase my speed. Your updates are highly awaited.

    Good day

    ReplyDelete
  15. x^4-1/x^4 = 119 find x^3 -1/x^3
    a) 36 b) -36 c) +- 36 d) +-33
    is there any short-cut to solve this type of sum.

    ReplyDelete
  16. Awesome sir !
    Waiting for ur nxt blog

    ReplyDelete
  17. In q.72 how can we assume x=0 directly ?? thank you in advance

    ReplyDelete
    Replies
    1. x is just a variable and that's the beauty of variables, you can assume anything as their value(in this context). Take x=1 and you will still get the value of the expression as zero...

      Delete
  18. Can i asked quetions without ssc cgl papers

    ReplyDelete
  19. sir all of these tricks are soo gud pls share some more......

    ReplyDelete
  20. This comment has been removed by the author.

    ReplyDelete
    Replies
    1. Put x=1, still you will get the same answer. 'x' is a variable, you can put anything as its value.

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  21. thank you SIR .........if possible make some awesome tricks Videos & upload youtube. It will take less time than writing Blog.BTW your tricks/HACKS really awesome. Thank you.

    ReplyDelete
  22. Sir...is there any short trick for chapters like ratios, average, partnership..if yes kindly update on these chapters.

    ReplyDelete
  23. x+1/x=5, thn value of x^6+1/x^6 is ?

    ReplyDelete
    Replies
    1. Apply the formula which I have mentioned in this article-
      http://sschacks.blogspot.in/2016/03/algebra-tricks-3.html

      Delete
  24. This comment has been removed by the author.

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  25. sir explain q.no 5
    thanks in advance.

    ReplyDelete
    Replies
    1. updated the explanation...please read again...

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  26. Sir Q.4 how did you solve taking x=1.25. I'm not getting the approach. Can you explain it lil bit more.

    ReplyDelete
  27. Thank u sir

    ReplyDelete
  28. oh God!, how simple you made algebra... I wish I would have visited your blog earlier...a thousand of thanks for sharing this...... God Bless you.

    ReplyDelete
  29. Sir any shortcuts for a/b+b/a=3 then a^3+b^3=?

    ReplyDelete