Official Quant thread for CAT 2013

@bhatkushal said:
Q)K and T are moving along two straight roads that intersect perpendicularly at X. When K is at X.T is 500 m from X.After 2 mins both K and T are at equidistant from X,again after 8 mins both are equidistant from X.What is ratio of K and T's speed?Bhailog explaination needed....
let T be z times faster than K

say K is 'a' m away from x, after 2 min

a=k*2
=> zk*2 = 500-a
=> 2kz = 500-2k ------------ (i)

say K is 'b' m away from X, after 8 min

b=k*8
=> zk*8 = 500+b
=> 8kz = 500+8k ------------(ii)

from (i) and (ii)

2000-8k=500+8k
=>k=1500/16

z = 500*8/1500 - 1
z = 2500/1500 = 5/3

so ratio => 3:5
Rajnish buys 30 books and 65 pens. What money does he have to pay for this?
A. At a profit of 20% he sells all the objects for Rs.3,828.
B. The CP of one book and one pen is Rs. 90.
C. The difference of sum and difference of buying price of one pen and one books is Rs. 28.
a)Only A alone is sufficient
b)B and C together are sufficient
c)A alone or B and C together are sufficient
d)All together are necessary
e) None of the statements either individually or together are sufficient
Rajnish buys 30 books and 65 pens. What money does he have to pay for this?
A. At a profit of 20% he sells all the objects for Rs.3,828.
B. The CP of one book and one pen is Rs. 90.
C. The difference of sum and difference of buying price of one pen and one books is Rs. 28.
a)Only A alone is sufficient
b)B and C together are sufficient
c)A alone or B and C together are sufficient
d)All together are necessary
e) None of the statements either individually or together are sufficient
@Cat.Aspirant123 said:
Rajnish buys 30 books and 65 pens. What money does he have to pay for this?A. At a profit of 20% he sells all the objects for Rs.3,828.B. The CP of one book and one pen is Rs. 90.C. The difference of sum and difference of buying price of one pen and one books is Rs. 28.a)Only A alone is sufficientb)B and C together are sufficientc)A alone or B and C together are sufficientd)All together are necessarye) None of the statements either individually or together are sufficient
c
@Cat.Aspirant123 said:
Rajnish buys 30 books and 65 pens. What money does he have to pay for this?A. At a profit of 20% he sells all the objects for Rs.3,828.B. The CP of one book and one pen is Rs. 90.C. The difference of sum and difference of buying price of one pen and one books is Rs. 28.a)Only A alone is sufficientb)B and C together are sufficientc)A alone or B and C together are sufficientd)All together are necessarye) None of the statements either individually or together are sufficient
c
@Cat.Aspirant123 said:
Rajnish buys 30 books and 65 pens. What money does he have to pay for this?A. At a profit of 20% he sells all the objects for Rs.3,828.B. The CP of one book and one pen is Rs. 90.C. The difference of sum and difference of buying price of one pen and one books is Rs. 28.a)Only A alone is sufficientb)B and C together are sufficientc)A alone or B and C together are sufficientd)All together are necessarye) None of the statements either individually or together are sufficient
c?
@bhatkushal said:
Q)K and T are moving along two straight roads that intersect perpendicularly at X. When K is at X.T is 500 m from X.After 2 mins both K and T are at equidistant from X,again after 8 mins both are equidistant from X.What is ratio of K and T's speed?Bhailog explaination needed....
4/5
(500-x)/x=t/k-----1
Also (500-x)/2=t
Put in 1 to get
k+t=250
Again
(x+y)/y=t/k-----2
(x+y)/8=t
Put in 2 to get
5t-4k=250
k=1000/9 mts/min
t=1250/9 mts/min
Ratio 4/5
@bhatkushal
@deedeedudu said:
4/5
method...
@vijay_chandola said:
Let the speed of T is t m/min and that of K is v m/minin two minutes, T will cover 2t and K will cover 2vso, 2v=500-2t=> v+t=250in next 8 minutes, T will cover 8t and K will cover 8vso, 8v+2v=8t-(500-2t)=> -v+t=50=> v=100 m/min, t=150 m/min
8v+2v=8t-(500-2t)=> -v+t=50 please explain this step @vijay_chandola
@rkshtsurana : f(x) and g(x) are two quadratic functions such that f(3) = 0 , g(5) = 0 . If they have a common root and f(5) * g(7) = 12, what is the value of common root?1) 4
2) 8
3) either 4 or 8
4) NOT
Can you explain ?
@bhatkushal said:
8v+2v=8t-(500-2t)=> -v+t=50 please explain this step @vijay_chandola
in next 8 minutes, K will go further 8v distance.
so, a total of 8v+2v=10v distance from X

in next 8 minutes, t would pass X and go up.
So, it's distance from X=8t-(500-2t)
@kleptomaniac_20 said:
@rkshtsurana : f(x) and g(x) are two quadratic functions such that f(3) = 0 , g(5) = 0 . If they have a common root and f(5) * g(7) = 12, what is the value of common root?1) 42) 83) either 4 or 84) NOTCan you explain ?
f(x) = p(x - a)(x - 3)
g(x) = q(x - a)(x - 5)

So, f(5) = 2p(5 - a)
g(7) = 2q(7 - a)

pq(5 - a)(7 - a) = 3

So, none of these, as value of a depends on p and q
@kleptomaniac_20 said:
@rkshtsurana : f(x) and g(x) are two quadratic functions such that f(3) = 0 , g(5) = 0 . If they have a common root and f(5) * g(7) = 12, what is the value of common root?1) 42) 83) either 4 or 84) NOTCan you explain ?
NOT..? getting 3 variables and one equation. :neutral:
Consider points A(1, €“3) and B(5, 2). Let P is a point on the line y = x. Find co-ordinates of P for which |AP + PB| is minimum.
OPTIONS

1) 10/9,10/9
2) 11/9,11/9
3) 11/7,11/7
4) 13/7,13/7
@sauravd2001 said:
Consider points A(1, €“3) and B(5, 2). Let P is a point on the line y = x. Find co-ordinates of P for which |AP + PB| is minimum.OPTIONS1) 10/9,10/9 2) 11/9,11/9 3) 11/7,11/7 4) 13/7,13/7
11/7, 11/7

Take the mirror image of any one point w.r.t. y=x and then compare the slopes
@chillfactor said:
You missed the case (a - b)/b = -2/5From here you will get a/b = 3/5So, (3k, 5k)
yeah.Sorry i missed it.Thanks
@vijay_chandola said:
11/7, 11/7Take the mirror image of any one point w.r.t. y=x and then compare the slopes
ye kya logic bola?? 😲
@vijay_chandola badiya 😛 samjh ni kaise kiya bt answere sahi hai
@Brooklyn said:
ye kya logic bola??
@sauravd2001 said:
@vijay_chandola badiya samjh ni kaise kiya bt answere sahi hai

if the two points in the given question are on different side of the line x=y then we would simply join the points and point of intersection with line y=x would give the coordinates of P. But in this case both the points are on same side of x=y. So we take reflection of point A about line x=y (In order to find the a similar distant point on different side)

~ Courtesy @anytomdickandhary Sir :)
@chillfactor : find the remainder when 50^51^52 is divided by 11?