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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• Reply •

Raju Khangare • 4 months ago> Vartika

mam plz suggest a practice set for sbi po mains △ ▽

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Mam 2,5,6,me x ki value +ive me aa rhi h only △ ▽

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ge mam also a big thanks to u:)))))) △ ▽

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