bankers adda_ quant notes on inequalities for sbi prelims
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
http://www.bankersadda.com/2015/06/quant-notes-on-inequalities-for-sbi.html 1/9
Bankers Adda
SUNDAY, 7 JUNE 2015
Quant notes on Inequalities for SBI Prelims
In quadratic Equations We have the following options to choose from
:-
i. X >Y
ii. Y >X
iii. X >= Y
iv. Y>= X
v. X = Y or relationship cannot be established.
(i) Now, Suppose on solving the quadratic equation we get X = -1, 2
And Y = -2, -3
On putting these values on number line we will see that X lies on the
right of Y. Hence, We can say that X>Y or Y<X.
(ii) Now, Suppose if after solving the equation we get X = -1 , 2 and
Y= 3,4.
On putting these values on number line we see that Y lies to the right
of X without touching X at any point. Hence, We can say that
Y>X or X<Y.
(iii) If X= 3,4 and Y= 2,3. Putting this on number line we get X to the
right of Y but touching Y at one single point i.e., 3. Hence, X>=Y
or Y<=X.
(iv) If X=3,4 and Y=4,5. Putting these values on number line we will
see that Y lies to the right of X but touching X at 4. Hence, Y>=X
or X<=Y.
(v) Now, Suppose X= 2,4 and Y= 3,5. Putting these values on number
line we will see that X touches Y at all the points between 3 and 4
i.e., at 3, 3.1, 3.2, 3.3 etc. upto 4 hence, in this case we cannot
relate X and Y and Hence, Will answer as Relationship cannot be
established.
Also suppose if y=7 and X= 4,8 then X<y also X>y . Hence, in this
case also no relationship can be established.
Example some quadratic equation:
Example 1:
(i) 6X^2 +11X + 3 = 0
(ii) 6X^2 + 10X +4= 0
Answer :
(i) Shortcut tricks :
This equation +6 is coefficient of x2 .
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
http://www.bankersadda.com/2015/06/quant-notes-on-inequalities-for-sbi.html 2/9
This equation +6 is coefficient of x2 .
+ 11 is coefficient of x
+3 is constant term.
Step 1: we multiply (+6) x (+3) = +18 = 2x3x3
Step 2: we break 2x3x3 in two parts such that addition between
them is 11.
So, 2x3x3 = 2 x 9. Also, 9 +2 = 11
So , +9 and +2 = Sum of is +11 .
Step 3: Change the sign of both the factors , So +9 = -9 and +2 = -2 .
and divide by coefficient of x2 , So we get -9 / 6 = -3 / 2 and -2 / 6
= – 1 / 3 .
Therefore, X = -3/2 , -1/3
Similarly Solving (ii),
6x4= 24 = 2x2x2x3
Break 2x2x2x3 into two parts such that their sum becomes 10.
2x2 and 2x3 are two parts of 24 whose sum is 10.
Now, Change the sign of both the factors and divide by coefficient of
X^2.
So, +4 = > -4/6
And +6 = > -6/6
Y = --2/3 , -1
So, in all X= -1.5, -0.33
And, Y = -0.667, -1
Now, Putting these values on Number line we get to knw that from
-0.667 to -1
The values of X and Y coincides .
Hence, as X and Y coincides at more than 1 point,
We can Say X=Y or Relationship between X and Y cannot be
established.
EXERCISE
Give answer
(i). If x>y
(ii). If x>=y
(iii). If x<y
(iv). If x<=y
(v). x=y or relationship cannot be established
1) (a) 3X^2+8X+4 = 0 and (b) 4Y^2-19Y+12= 0.
2) (a) X^2 + X-20= 0 and (b) Y^2-Y-30= 0.
3) (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2).
4) (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
5) (a) x^2 = 729 and (b) Y= (729)^(1/2)
6) (a) 2x^2 + 11x + 14 = 0 and (b) 4y^2 + 12y +9 =0
7) (a) x^2-7x+12=0 and (b) y^2+y-12=0
8) (a) x^4- 227= 398 and (b) y^2 + 321=346
9) (a) x^2-1=0 and (b) y^2+4y+3=0
116-125126-135136-145Above 145
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
http://www.bankersadda.com/2015/06/quant-notes-on-inequalities-for-sbi.html 3/9
Labels: inequalities, quant notes, SBI PO 2015
9) (a) x^2-1=0 and (b) y^2+4y+3=0
10)(a) x^2-7x+12=0 and (b) y^2-12y+32=0
Answers:
1) (iii) x<y2) (v) No relationship can be established between x and y 3) (iv) x<=y4) (v) No relationship can be established5) (iv) X<= Y 6) (iii) x<y7) (ii) X>=Y8) (v) No relationship between X and Y.9)(ii) X>=Y 10) (iv) x<=y
Solution:- Solving we get X= -2/3 or -2Y= 3/4 or 4
Solution:- X=4,-5Y= -4,6
Solution:- X= +27, -27Y= +27
Solution:- X= +2/15 and -2/15Y= 4/225Comparing we get X>Y and X<YHence, no relationship can be established
Solution:- X=+27, -27 and Y= +27Comparing we get X<=Y
Solution:-X=-7/2 or -2Y=-3/2
Solution:- X=4,3Y=-4,3So, X>=Y
Solution:- X=+5,-5 and Y= +5,-5Comparing, we get X=Y, X<Y, X>Y.Therefore, no relationship can be established between X and Y.
Solution:- X=+1,-1 and Y= -1,-3Comparing we get X>=Y
Solution:- X=3,4 and Y= 4,8X<= Y
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Vartika • 4 months agoThis Quiz is provided by Hemant Ahuja ,a regular readerof bankers adda.Thanks Hemant :)
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
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Join the discussion…
• Reply •
Vartika • 4 months agoFeatured by Bankers Adda
This Quiz is provided by Hemant Ahuja ,a regular readerof bankers adda.Thanks Hemant :)
81△ ▽
• Reply •
Gabbar is back.. • 4 months ago> Vartika
Mam in 2nd answer it should be -5,4 and 6&-5. 12△ ▽
• Reply •
dreamy suman • 4 months ago
> Gabbar is back..
Yes....i thik ..ans is 4 3△ ▽
• Reply •
AB • 4 months ago
> dreamy suman
No ans is 5..no relationship 4△ ▽
• Reply •
Waiting For My turn • 4 days ago
> dreamysuman
yes 4 correct △ ▽
• Reply •
ashish • 4 months ago
> dreamy suman
u r ryt.... its 4 △ ▽
• Reply •
ravi • 4 months ago> Gabbar is back..
Sorry yar ur right 1△ ▽
• Reply •
ashish • 4 months ago
> Gabbar is back..
answr is iv
y>=x 1△ ▽
• Reply •
Meraj, The target achiever • 4 months ago
> Gabbar isback..
Here also same 1△ ▽
• Reply •
aman verma • 12 days ago
> Meraj, The targetachiever
yes ur right △ ▽
• Reply •
Don*******Chase the Game IBPS • a month ago
>Gabbar is back..
4/5 which is true answer..veryconfusious..plz help △ ▽
• Reply •
NIKITA PATEL • 3 months ago
> Gabbar is back..
ya u r correct △ ▽
• Reply •
Gabbar is back.. • 3 months ago
> NIKITAPATEL
Thanx nikita △ ▽
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
http://www.bankersadda.com/2015/06/quant-notes-on-inequalities-for-sbi.html 5/9
• Reply •
Siva Nandi Reddy • 4 months ago
> Gabbar is back..
sahil try to compare x=4 and y=6& -5 thereis no relationship so the ans is 5 △ ▽
• Reply •
Gabbar is back.. • 4 months ago
> Siva NandiReddy
Where is ur another x's digit ?Which is -5 △ ▽
• Reply •
Siva Nandi Reddy • 4 months ago
> Gabbar isback..
first u compare with -5 so u gety>=x but second time compare with4 there is no relationship so howcan u tell y>=x u compare with both terms △ ▽
• Reply •
Gabbar is back.. • 4 months ago
> Siva NandiReddy
First compare with -5 and -5 its x=ythen 4 and 6 its y>x so y>=x. Hopeu catch me.
2△ ▽
• Reply •
jeet • 3 days ago
> Gabbar is back..
In order to better understand. letsus list down all the possibilities.
x | y-5 -5-5 64 -54 6
for 3rd row the condition y>= x don'tsatisfy , so please atleast considerall the possibilities , tell me if i amwrong. △ ▽
• Reply •
Siva Nandi Reddy • 4 months ago
> Gabbar isback..
but what about x=4 and y=-5 u didn't compare this here x>y △ ▽
• Reply •
Siva Nandi Reddy • 4 months ago
> Siva NandiReddy
first u compare x=-5 with y=6 and-5and then u compare x=4 with y=6and -5 now how can u tell y>=x
1△ ▽
• Reply •
Gabbar is back.. • 4 months ago
> Siva NandiReddy
Sorry reddy u need to work on itsbasic then only u can underdtand. △ ▽
• Reply •
Praveen MCV • 4 days ago
> Gabbar is back..
Fst u understand the basics.. reddyis right.. △ ▽
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
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• Reply • △ ▽
• Reply •
ravi • 4 months ago> Gabbar is back..
Bhai -5,4$ 5 ,6 hoga △ ▽
• Reply •
raju patel • 4 months ago
> Gabbar is back..
-6, 5 △ ▽
• Reply •
Gabbar is back.. • 4 months ago
> raju patel
i dnt think so.. △ ▽
• Reply •
raju patel • 4 months ago
> Gabbar is back..
Y^2 - y - 30Y^2 -(6-5)Y -30Y^2 -6y + 5y -30Y(y-6)+5 (y-6)(Y-6) (Y+5)Y-6 =0 ya Y+5=0Y=6 or y= -5
4△ ▽
• Reply •
Arun Kumar • 4 months ago
> raju patel
Raju sir ur method easy tounderstand and also get correctanswer. ......!! △ ▽
• Reply •
raju patel • 4 months ago
> Arun Kumar
Sir nahi friend kaho △ ▽
• Reply •
Ramesh • 4 months ago
> Gabbar is back..
If u have any shartcurt △ ▽
• Reply •
Gabbar is back.. • 4 months ago
> Ramesh
(+)+(+)=(-)(-)(-)+(+)=(+)(+)(+)+(-)=(-big digit)(+small digit)(-)+(-)=(+big digit)+(-small digit)
5△ ▽
• Reply •
Kuldeep Shaw • 2 months ago
> Gabbar isback..
gabbar brother.. plz explain yehkya.. yeh maths ki inequalitysamajh me nahi aati mujhe plzbatao yeh kya likha hai tumne △ ▽
• Reply •
lokesh • 4 months ago
> Gabbar is back..
sahil i cant understand the short cutcan u explain me △ ▽
Gabbar is back.. • 4 months ago
> lokesh
Observe in this pic..specially thesigns viz. Positive and negative.
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
http://www.bankersadda.com/2015/06/quant-notes-on-inequalities-for-sbi.html 7/9
• Reply • 2△ ▽
• Reply •
Snehal • 10 days ago
> Gabbar is back..
Is it applicable for all equations? △ ▽
• Reply •
Gabbar is back.. • 10 days ago
> Snehal
Yes △ ▽
• Reply •
kk • 18 days ago
> Gabbar is back..
trick ok h but jb X^ ke multiple mekuchh aaye tb normal method jyadaeasy rhta h △ ▽
• Reply •
poonam • 4 months ago
> Gabbar is back..
5,-4 and 6,-5 △ ▽
• Reply •
Sasidhar Reddy Venna • 4 months ago
>poonam
No....4,-5&6,-5 is rightX^2+5x-4x-20=0Then it is 4&-5... △ ▽
• Reply •
poonam • 4 months ago
> Sasidhar ReddyVenna
ok..got it △ ▽
• Reply •
Gabbar is back.. • 4 months ago
> poonam
No poonam u r wrng it should be -5& 4 and 6 & -5. △ ▽
• Reply •
CASA .... • 4 months ago
> poonam
No relatoion cam be made △ ▽
• Reply •
Chotu • 16 days ago> Vartika
helw mam, am new to ba and feelng very happyso, whenX= -5,6Y= 4,6relationship betwn them is?
1△ ▽
• Reply •
answer me..!!! • 14 days ago> Chotu
x<=y 2△ ▽
• Reply •
pravin vyawahare • 4 months ago> Vartika
Thanks 4 the trick... △ ▽
• Reply •
HEMANT AHUJA. • 4 months ago> Vartika
ok mam dont thanks me △ ▽
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10/8/2015 Bankers Adda: Quant notes on Inequalities for SBI Prelims
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Raju Khangare • 4 months ago> Vartika
mam plz suggest a practice set for sbi po mains △ ▽
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ritu • 4 months ago> Vartika
Mam 2,5,6,me x ki value +ive me aa rhi h only △ ▽
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mam plz suggest new pattern quant apti book △ ▽
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Mam..I ask abt online practice set paper onbankersadda.com do u charge fees for practiceset or not? △ ▽
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$$KUNMUN$$ • 4 months ago> Vartika
ge mam also a big thanks to u:)))))) △ ▽
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