Official Quant thread for CAT 2013

pyashraj · January 23, 2013, 6:48pm

Even i was taken aback..bt the question is nt wrng..

logrhythm · January 23, 2013, 6:52pm

@pyashraj said:
A boat takes a total of 5 hrs to make a round trip btwn 2 points in a river which is 24 Km apart.Had the speed of the boat tripled, the boat wud had taken a total of 7.5 Hrs to make the same trip. Find the speed of the boat in still water.

Is it 10??

24/(u+v) + 24/(u-v) = 5

24/(u+3v) + 24/(u-3v) = 7.5

somnathbhatta · January 23, 2013, 6:54pm

@pyashraj said:
A boat takes a total of 5 hrs to make a round trip btwn 2 points in a river which is 24 Km apart.Had the speed of the boat tripled, the boat wud had taken a total of 7.5 Hrs to make the same trip. Find the speed of the boat in still water.

1.2 km/hr ?

calvin4ever · January 23, 2013, 6:55pm

@pyashraj said:
@Calvin4everEven i was taken aback..bt the question is nt wrng..

Okay, lets say that the speed of the boat is less than the current. How wud it go upstream then??

pyashraj · January 23, 2013, 6:56pm

@somnathbhatta

@Calvin4ever said:
Okay, lets say that the speed of the boat is less than the current. How wud it go upstream then??

OA is 10km/hr..

Let the speed of the Boat be v km/hr n speed of the river be u km/hr..

Thus, 24/(u+v) + 24/(u-v) = 5...(i)

Again, 24/(u+3v) + 24/(u-3v) = 15/2...(ii)

Solving (i) n (ii), we have 25v^2 = u^2

=>u = 5v..(iii)

Nw, From (i), we have v =2..Thus, the speed of boat in still water= 10 km/hr..

The Trick was that the speed of the boat was less than that of the current

somnathbhatta · January 23, 2013, 6:57pm

@Logrhythm said:
Is it 10??24/(u+v) + 24/(u-v) = 524/(u+3v) + 24/(u-3v) = 7.5

shouldn't the speed of the boat in still water be greater than the speed of the stream ?
i mean v>u ?

anitito123 · January 23, 2013, 6:58pm

the number of different prime number p>2 such that p divides (71^2)-(37^2)-51 is:
options:3,4,5,6

is there any trick or we have to check manually for each prime no.?

somnathbhatta · January 23, 2013, 6:58pm

@pyashraj said:
@somnathbhattaOA is 10km/hr..Let the speed of the Boat be v km/hr n speed of the river be u km/hr..Thus, 24/(u+v) + 24/(u-v) = 5...(i)Again, 24/(u+3v) + 24/(u-3v) = 15/2...(ii)Solving (i) n (ii), we have 25v^2 = u^2=>u = 5v..(iii)Nw, From (i), we have v =2..Thus, the speed of boat in still water= 10 km/hr..The Trick was that the speed of the boat was less than that of the current

if v

logrhythm · January 23, 2013, 6:59pm

@somnathbhatta said:
shouldn't the speed of the boat in still water be greater than the speed of the stream ? i mean v>u ?

han bhai...but abb kya karu options ni diye question post karne wale bhai ne. ni toh data inconsistent hota answer mera...

coz 5 hrs wale case mein upstream ni jaa pate..

pyashraj · January 23, 2013, 7:00pm

@somnathbhatta said:
if v

@Logrhythm said:
han bhai...but abb kya karu options ni diye question post karne wale bhai ne. ni toh data inconsistent hota answer mera...coz 5 hrs wale case mein upstream ni jaa pate..

Bhai TIME ke Material ka Ques hai..

calvin4ever · January 23, 2013, 7:01pm

@pyashraj said:
@somnathbhattaOA is 10km/hr..Let the speed of the Boat be v km/hr n speed of the river be u km/hr..Thus, 24/(u+v) + 24/(u-v) = 5...(i)Again, 24/(u+3v) + 24/(u-3v) = 15/2...(ii)Solving (i) n (ii), we have 25v^2 = u^2=>u = 5v..(iii)Nw, From (i), we have v =2..Thus, the speed of boat in still water= 10 km/hr..The Trick was that the speed of the boat was less than that of the current

v cannot be less than u !!

@Logrhythm

anitito123 · January 23, 2013, 7:01pm

the number of different prime number p>2 such that p divides (71^2)-(37^2)-51 is:
options:3,4,5,6

iska koi trick hai to batado koi.

somnathbhatta · January 23, 2013, 7:02pm

@pyashraj had a similar question in my today's mock test .. i got the mock test answer correct .. same question different values .

logrhythm · January 23, 2013, 7:03pm

@anitito123 said:
the number of different prime number p>2 such that p divides (71^2)-(37^2)-51 is:options:3,4,5,6is there any trick or we have to check manually for each prime no.?

3 primes??

{71^2 - 37^2} - 51 = {(71-37)(71+37)} - 51 = {(34)(108)} - 51 = 3621 = 3*17*71

logrhythm · January 23, 2013, 7:05pm

@pyashraj said:
Bhai TIME ke Material ka Ques hai..

bhai maar time walon ko :p

pyashraj · January 23, 2013, 7:05pm

@somnathbhatta

Dekha..Even i was taken aback while solving the question..bt what could be dne..I was myslf nt cnfdnce enuf with the validity of the ques..Hence posted here..to clear that whether i am wrng or wright..

@Calvin4ever

@Logrhythm

N i just wnted to clear thngs out..that whether the infrmtion in the ques was wright or wrng..

calvin4ever · January 23, 2013, 7:06pm

@anitito123 said:
the number of different prime number p>2 such that p divides (71^2)-(37^2)-51 is:options:3,4,5,6is there any trick or we have to check manually for each prime no.?

3 ?? Its just finding the prime factors after simplifying (71^2)-(37^2)-51 = 108*34-51 = 17*3*71 !!

anitito123 · January 23, 2013, 7:17pm

@Logrhythm @Calvin4ever ok..my bad.

calvin4ever · January 23, 2013, 7:25pm

In a certain mixed school, where a special feature was made of the inculcation of good manners, they had a curious rule on assembling every morning. There were twice as many girls as boys. Every girl made a bow to every other girl, to every boy, and to the teacher. Every boy made a bow to every other boy, to every girl, and to the teacher. In all there were nine hundred bows made in that model academy every morning. Now, can you say exactly how many boys there were in the school?

venomizer · January 23, 2013, 7:27pm

EACH ALPHABET RESEMBLES A UNIT DIGIT FROM 0-9.SUCH THAT NO SINGLE ALPHABET RESEMBLES TWO DIFFERENT DIGITS.
H O T
*G U N
P I U I
P O E T
P U N I
H I P P P I

FIND THE NUMERIC SUM OF T+O+N+G+U+E