Official Quant thread for CAT 2013

MBA CAT 2024
16283
@bs0409 said:

If the minimum value of 4(x^2) + px - 3 is realized for x=a, where a>0, which of the following is necessarily true?a) 8a+p0c) 11a+2p>0d) 15a+2p
4(x^2) + px - 3
= 4(x^2+p/4*x) -3
= 4(x + p/8)^2 -3 - p^2/64
Minimum value of expression would be at x=-p/8
=> a= -p/8
=> 8a+p =0
=> 16a+2p = 0
==> 15a+2p a > 0, p )

Alternate solution:
By differentiating the given expression, 8*x+p = 0
now, x = a ==> 8*a+p = 0

=> 16a+2p = 0
=> 15a+2p

16284
@bs0409 said:
Correct.............If the minimum value of 4(x^2) + px - 3 is realized for x=a, where a>0, which of the following is necessarily true?a) 8a+p0c) 11a+2p>0d) 15a+2p
d) 15a + 2p
Since 8a + p = 0 and 16a + 2p = 0
16285
@bs0409 said:
Correct.............If the minimum value of 4(x^2) + px - 3 is realized for x=a, where a>0, which of the following is necessarily true?a) 8a+p0c) 11a+2p>0d) 15a+2p
Minimum value occurs when first derivative is 0
So 8x+p=a => 8a+p=0 => 16a+2p=0 =>a + (15a+2p) = 0
Now a>0 so 15a+2p(d)
16286
@Logrhythm said:
d/dx -> 8x+p=0=> x = -p/8 = ahence, option a and c = 0 (not true)option b -> 6a+p = 6a+(-8a) = -2a is not > 0 option d -> 15a+2(-8a) = -a hene, option d holds true...Guys can someone tell me where do they study VA at (forum link) on PG?? I searched but found no thread.....VA bi toh padhni hai
http://www.pagalguy.com/forums/verbal-ability/official-verbal-ability-thr-t-90385/p-3615881?page=1
16287
If f(x) = b(x^2) -a mod(x)-c and f(0)=f(1)=2, f(-2)=32, find the sum of the cubes of the roots of the equation f(x)=0
16288
@cynara said:
numbers divisible by 2, 200, by 3 - 133, by 5 - 80, by 7 - 57divisible by 6 - 66, by 10 - 40, by 14 - 28.by 15- 26, 21 -19, 35 -11by 30- 13, 42 - 9by105 - 3.,by 70 - 5by 210 - 1Numbers not divisble= 400 - (div by 2,3,5,7) + (div by 6,10,14,15,21)- (div by 30, 42,105,70) +(div by 210)= 400-470+190-30+1=91? -please let there bhi no calc mistake
This is Quite a method... full proof i would say 😛 Thanks
16289
@bs0409 said:
If f(x) = b(x^2) -a mod(x)-c and f(0)=f(1)=2, f(-2)=32, find the sum of the cubes of the roots of the equation f(x)=0
6742
16290
@vishcat said:
guys a TSD problem...A and B start at the same end of the pool which is 50m long.The one who completes 20 laps is the winner.The ratio of speed of A and B is 3:4.How many times would they meet or cross each other by the time the faster one finishes the race..?....p.s- whoever solves it please explain the solution too.
40 times
16291
@bs0409 said:
If f(x) = b(x^2) -a mod(x)-c and f(0)=f(1)=2, f(-2)=32, find the sum of the cubes of the roots of the equation f(x)=0
0..??
16292
@ishu1991 said:
6742
@dragster said:
0..??
dont hv oa......
16293
@bs0409 said:
dont hv oa......
16294
@bs0409 said:
Correct.............If the minimum value of 4(x^2) + px - 3 is realized for x=a, where a>0, which of the following is necessarily true?a) 8a+p0c) 11a+2p>0d) 15a+2p
4x^2 + px - 3 = 0
differentiating
8x + p = 0
x = a
8a + p = 0
p = -8a
15a + 2(-8a)
-a
d holds true
16295
@bs0409 said:
If f(x) = b(x^2) -a mod(x)-c and f(0)=f(1)=2, f(-2)=32, find the sum of the cubes of the roots of the equation f(x)=0
9/15??
16296

mr X calculated his profit on sp and it is 30 % .if he calculates as usal on cp what is profit %

16297

For even natural number,the highest number that n*(n^2-1)*(5n+2) is always divisible by is????


16298
@Pradeep_Rss said:
mr X calculated his profit on sp and it is 30 % .if he calculates as usal on cp what is profit %
42.85%....?
16299
@bs0409 said:
If f(x) = b(x^2) -a mod(x)-c and f(0)=f(1)=2, f(-2)=32, find the sum of the cubes of the roots of the equation f(x)=0
y= b|x|^2-a|x|-c
f(0)=-c=2, c=-2
f(1)=b-a-(-2)=2, so b=a
f(-2)= 4b-2a-c= 4b-2a+2=2b+2=32
b=15=a
roots of f(x)=0, (obtain by replacing x^2, by |x|^2)
|x|=15+root(345)/30 (negative rejected)
values of x= +|x|, -|x|
sum of roots =0
sum of cubes of roots=p^3+q^3= (p+q)(p^2+q^2-pq) if p,q are roots!
so sum of cubes of roots =0
Have to say, never expected this answer :neutral:
16300
How many zeroes will be there in the end of 25! when expanded in base 14?
16301
@TootaHuaDil said:
How many zeroes will be there in the end of 25! when expanded in base 14?

3?

16302
@Pradeep_Rss said:
mr X calculated his profit on sp and it is 30 % .if he calculates as usal on cp what is profit %
42.85%?