Thursday, 10 March 2016

[Q] Algebra Tricks - 1

Algebra is the easiest topic for SSC because you don't have to memorize any formula for it and all the questions can be solved within 10 seconds with jugaad.
First let me share with you the concept of symmetrical expressions(as I call it). A symmetrical expression is the one in which the weight of all the variables (a, b, c, etc.) is equal. Examples will make things clear.
Examples of symmetrical expressions -

  • a3 + b3 + c3
  • 3a + 3b + 3c
  • a2 + b2 + c2
  • a + b + c
  • ab + bc + ca

Examples of non - symmetrical expressions -
  • a - b + c
  • 2a + 3b + 3c
  • a3 + b2 + c3
  • a + b + c2

Hack - 1 : "Whenever you encounter a symmetrical equation in any question, you can safely assume : a = b = c (even if it is not given in the question)"


Let's solve previous year questions -


Q . 1.

Here you can see that the LHS as well as the RHS of the equation is symmetrical, hence a = b = c
Answer : (A)



Q .2. 


We put a = b = c, hence (a+c)/b becomes (a+a)/a, or 2
Answer : (B)

Q . 3.

In this question we have to find the value of x.
Here the equation is completely symmetrical, hence we assume a = b = c
Put b=a, c=a (so that the whole equation is in terms of 'a')
Now LHS becomes 3(x - a2)/2a
RHS = 12a
Solving this, you will get, x = 9a2
From here we get that the value of x is 9a2

Now put a = b = c in all the 4 options and check which option gives you the value 9a2

A) 9a2
B) 3a2
C) 3a2
D) 0

Answer : (A)


Q . 4. 


bc + ab + ca = abc is symmetrical and hence we can assume a=b=c
Now put b=a and c=a in this equation. We will get -
3a2a3
So a = 3
Now put a=b=c=3 in the expression whose value we have to find. You will get the answer as 1.
Answer : (B)

Hack - 2 : "When only a single equation is given and based on that you have to find the value of an expression, you can assume the value of variables yourself. But make sure to assume only such values that will not make the denominator zero"


Examples :
Q . 5

In this question, only a single equation is given, i.e., x + y + z = 0, and based on this equation we have to find the value of an expression
We can assume x = -1, y = 1 and z = 0 (such that x + y + z = 0)
Now on putting these values in the expression, we get the answer as 2

Answer : (D)

           Q . 6. 

a + b = 1
Let's assume a = 1 and b = 0
Put the values in the expression, and you will get 0.
Answer : (A)

      Q . 7.

In this question the values of x and y both depend on a constant 'a'. We can assume any value for 'a' and this will give the values of x and y. Let us assume a=1
This will give x = 2 and y = 0
Put these values in the expression and you will get the answer as 16.
Answer : (A)

Q . 8

Pick values for a, b and c, such that their sum is 2s. Let us assume a = 2s, b = s and c = -s (here you should not assume a,b or c to be zero because that will make the elimination of options difficult)
Put these values in the expression and you will get 2s2
Now check all the four options to see which of them will give the value 2son putting a=2s, b=s and c=-s
Answer : (C)


Don't forget to read Algebra Tricks - 2, 3 and 4

To buy the super-hit SSC Hack-Book, follow the below link-


48 comments:

  1. it was really helpfull...please share more shortcuts

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  2. Great work sir

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  3. Amazing work, going through the blog was way more productive than spending a couple of hours with Arihant ๐Ÿ˜Š๐Ÿ˜Š. Really appreciated

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  4. Thanks a lot...u r a really great educator..

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  5. If a/b=c/d=e/f=3 , then 2a^2+3c^2+4e^2/2b^2+3d^2+4f^2= ?
    how to solve this question???

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  6. put some geometry tricks also , i will be indebted sir... and also some unsymmetrical condition ..

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  7. This comment has been removed by the author.

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  8. Sir how in Q3 symmetry is present in L. H. S?

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  9. Sir how in Q3 symmetry is present in L. H. S?

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    Replies
    1. Symmetry means if in any expression variable 'a' is used, then 'b' and 'c' should also be used in the same way. In Q3, (x - a^2) is there and with that (x - b^2) and (x - c^2) are also present. Hence it is symmetrical

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  10. sir, please provide some examples for solving assymetrical type of algebric questions also

    and some geometry tricks also

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  11. are there any tips n tricks for english section also
    if it is possible for u to share those also

    thanks in advance

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  12. Put more ques like this. Very hepful. Ur good work won't get unnoticed.!!

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  13. Really...awesome..Please post concepts in TIME AND DISTANCE, and other concepts also

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  14. This comment has been removed by the author.

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  15. Wow..unbelievable..M looking forward to you for englightenment Sir..Thnk you in advance

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  16. Great great help sir,earlier by ur paper cutting tricks I was able to solve all d questions of book easily N in vry less tym.I was vry afraid of paper cutting earlier,however. N today again ur algebra tricks r boon for non coaching students lyk me

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  17. Great great help sir,earlier by ur paper cutting tricks I was able to solve all d questions of book easily N in vry less tym.I was vry afraid of paper cutting earlier,however. N today again ur algebra tricks r boon for non coaching students lyk me

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  18. Great job your blog is really interesting

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  19. awesome blog i have ever seen on internet.......Its very useful....Thnks a Million

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  20. x+1/x=3 then value of x^5+1/x^5
    Pls provide short trick

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    Replies
    1. Apply the direct formula given at the end of this article-
      http://sschacks.blogspot.in/2016/03/algebra-tricks-3.html

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    2. (xcube+1byxcube * xsquare+1byxsquare)- x+1byx
      (18 * 7)-3
      123

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  21. sir in Q.no. 5
    if we take a=2 b=-1 c=-1 then answer does not as 0 it comes as 2.
    please explain ?

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    Replies
    1. Answer is 2 only. Dont go by the tick mark. I have clearly written Answer = (D)

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    2. sir in Q 8
      why cant we put a=1 b=1 c=1 and calculate value of s
      so that we can put all the values in the given equation

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    3. Ans couldn't get by putting a=b=c=1 in q.8...pls check

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    4. Sry...got the ans

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    5. But not so effective checking dis way...at the end left with two options

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  22. ab+bc+ca=0 then
    1/(a^2-bc) + 1/(b^2-ca) + 1/(c^2-ab)

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    Replies
    1. ab+bc+ca=0 .......... let a=b ...(1)
      it implies a^2 +2ac=0
      it implies a(a + 2c) =0 or a=-2c
      put c=1
      it implies a=b=-2 ... from (1)
      Therefore the evaluation of the expression
      1/(a^2-bc) + 1/(b^2-ca) + 1/(c^2-ab) =0

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  23. Great work. From now onwards I follow this blog only

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  24. sir , I have quatnum cat by sarvesh kumar verma for mathematics , its sufficient or not and also tell me should I purchase quickest mathematics also or should practice from quantum cat book ,

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  25. if 1/4*2/6*3/8*4/10.....31/64=1/2^x
    find the value of x.

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  26. Thank You Sir... Really Helpful... :D :D

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  27. b-c/a a c/b a-b/c =1 & a-b c not 0
    (1) 1/c = 1/a 1/b
    (2) 1/a = 1/b 1/c
    (3) 1/b = 1/a-1/c
    (4) 1/b = 1/b 1/c

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  28. What is the difference in Hack 1 and hack 2 in Algebra. I am not able to discrete between where to use Hack 1 and where to use Hack 2. Please elucidate.

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  29. Hi
    Can you please explain the concept of symmetrical/Asymmetrical equation in details?

    Thanks
    Chandan

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  30. a/bc+ca + b/ca+ab + c/ab+bc = 1 . find the value of a^2/bc+ca + b^2/ca+ab + c^2/ab+bc. sir , it is a symetrical equation but you method didn't work here.options are (A)1 (B)2 (C)0 (D)-1.

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  31. Your blog is of great help have to agree with my colleagues. This is way better than mugging up texts on books..please update for upcoming cgl 2k17 as well and add more topics.....Thank You

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  32. Thank you for this blog.
    Sir, I have a doubt.
    In Q.no:5 I felt there is symmetry in x+y+z=0 and so I took x=y=z and substituted them in the question equation and got answer as 0 because the denominator is becoming 0. But the correct answer is 2. But as you have shown the method is to assume any values in the place of x,y and z. Why didn't symmetry concept work there even though the given expression satisfies the symmetry concept and how can I come to know when to apply symmetry concept and when to assume any values for x,y and z.

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