Official Quant thread for CAT 2013

@iLoveTorres said:
x
nahi bhai x>3 hoga..

-3x

now when u multiply both sides with -1, the sign gets reversed...

3x > 9
x > 3

-------------

u can also validate your result by putting it in the child equation...
@scrabbler said:
Solve this:-3x +2 Phir batata hoon.regardsscrabbler
@iLoveTorres said:
x
So plug x = 1 or x = 0 into the original and check? According to your solution they should satisfy...

regards
scrabbler

@scrabbler said:
Solve this:-3x +2 Phir batata hoon.regardsscrabbler
x>3 ??
@scrabbler said:
So plug x = 1 or x = 0 into the original and check? According to your solution they should satisfy...regardsscrabbler
so you mean to say only if there is a -ve sign on both the sides of the > or
@iLoveTorres said:
so you mean to say only if there is a -ve sign on both the sides of the > or
Fundamentally!
@scrabbler said:
Solve this:-3x +2 Phir batata hoon.regardsscrabbler
-3x
x > 3 ??
@iLoveTorres said:
so you mean to say only if there is a -ve sign on both the sides of the > or
No I mean that if there is a negative multiplied (or divided) on both sides, the inequality will change. Suppose you have more money than me (ilt > scr), and we multiply both our values by -1 then you will now have less right? (Take actual values and see...)

In practice since we are solving for x, if there is a -ve coefficient for x we will have to multiply by -1 at some point which will reverse the inequation.

So even if it is -3x > 11 for example, it should be x
regards
scrabbler

@ScareCrow28 said:
Fundamentally!
then how do you deal with a variable say "x". Now if i take the variable to the other side of the > or case 1) when x>0 you can straight away move simplify the equation
case 2) when x or is this the appproach?
@scrabbler said:
No I mean that if there is a negative multiplied (or divided) on both sides, the inequality will change. Suppose you have more money than me (ilt > scr), and we multiply both our values by -1 then you will now have less right? (Take actual values and see...)In practice since we are solving for x, if there is a -ve coefficient for x we will have to multiply by -1 at some point which will reverse the inequation.So even if it is -3x > 11 for example, it should be x regardsscrabbler
samajh mein aa gaya.. thanks :)
@iLoveTorres said:
then how do you deal with a variable say "x". Now if i take the variable to the other side of the > or case 1) when x>0 you can straight away move simplify the equation case 2) when x or is this the appproach?
Something like that, yes. Try to do it with your approach and see what happens (I alwasys get these wrong, myself, by that kind of approach, which is why I tried graph instead 😛 )

regards
scrabbler

Solve: ||x-2|-2| = 4

@Logrhythm said:
Solve: ||x-2|-2| = 4
x= -4 or 8
@Logrhythm said:
Solve: ||x-2|-2| = 4
-4 and 8? Graphically again :(

regards
scrabbler

@jain4444 said:
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
first pipe effciency =x
second pipe efficiency=x-5
thrd pipe effciency=x-9

1/(x)+1/(x-5)=1/(x-9)
x^2-18x+45=0
x=3 or 15
@Logrhythm said:
Solve: ||x-2|-2| = 4
8 or -4.
@iLoveTorres said:
then how do you deal with a variable say "x". Now if i take the variable to the other side of the > or case 1) when x>0 you can straight away move simplify the equation case 2) when x or is this the appproach?
Yes that's how we do it.. Sorry 😛 Movie dekhra hun..
Waise bhi @scrabbler ne sab samjha dia h sabko as always :mg:
@scrabbler said:
-4 and 8? Graphically again regardsscrabbler
aapne fir graph kara, meine 4 case bana kar kara...

1) -ve -ve
-x+4=4
x=0 (does not satisfy)

2) -ve +ve
x-2+2=4
x=4 (does not satisfy)

3) +ve -ve
-x+2-2=4
x=-4 (satisfies)

4) +ve +ve
x-2-2=4
x=8 (satisfies)

so, x=-4 and 8

but aese toh bohot time jaa rhaa hai mera....kuch graph sikhna padega... 😞
@Logrhythm said:
aapne fir graph kara, meine 4 case bana kar kara...1) -ve -ve -x+4=4x=0 (does not satisfy) 2) -ve +vex-2+2=4x=4 (does not satisfy)3) +ve -ve-x+2-2=4x=-4 (satisfies)4) +ve +ve x-2-2=4x=8 (satisfies)so, x=-4 and 8but aese toh bohot time jaa rhaa hai mera....kuch graph sikhna padega...
@scrabbler bhai mujhe bhi thode graph wale classes de do so that i am able to save time while solving such questions
@Logrhythm said:
aapne fir graph kara, meine 4 case bana kar kara...1) -ve -ve -x+4=4x=0 (does not satisfy) 2) -ve +vex-2+2=4x=4 (does not satisfy)3) +ve -ve-x+2-2=4x=-4 (satisfies)4) +ve +ve x-2-2=4x=8 (satisfies)so, x=-4 and 8but aese toh bohot time jaa rhaa hai mera....kuch graph sikhna padega...
Graphically, was well under 1 min. Worth trying.

regards
scrabbler

Given that x and y are positive integers, solve x^y = y^x