Viraj_Deshpande's posts

Viraj_Deshpande
commented on an article

Dressed in shorts and a crumpled white t-shirt and sitting coyly in his apartment in Dombivali, on the outskirts of Mumbai, Shashank Prabhu looks more like the teenager next door who you'd see rushing to his tuition classes. But once he begins to speak, the confidence and command of a topper are quite evident. Prabhu topped t...

281
117 Comments

drvispute
C u in IIM next yr !.
04 Sep '10.

anonymous
[...] (US 10 1/2)WINTERSCHUHE STIEFELSchuhe Gunstig Kaufe....
21 Mar '12.

Viraj_Deshpande
replied to Quant by Arun Sharma

My solution:

Every no. can be expressed in the form of 9k or 9k+1 or 9k-1 or 9k+2 or 9k-2 or 9k+3 or 9k-3 or 9k+4 or 9k-4, where k is an integer.

2998 = 9 * 337 + 1

Thus, 1 to 3000 (Excluding 1 and 3000) has

334 nos. of type 9k+2 (because of no. 2999) and

333 nos. of type 9k+1, 9k,...

Every no. can be expressed in the form of 9k or 9k+1 or 9k-1 or 9k+2 or 9k-2 or 9k+3 or 9k-3 or 9k+4 or 9k-4, where k is an integer.

2998 = 9 * 337 + 1

Thus, 1 to 3000 (Excluding 1 and 3000) has

334 nos. of type 9k+2 (because of no. 2999) and

333 nos. of type 9k+1, 9k,...

3

Viraj_Deshpande
replied to Revant aka Profootball25 getting hitched!

Congrats Revant!

Viraj_Deshpande
replied to Number System

6711+4179 is possible.

First_timer's solution (above) is correct.

First_timer's solution (above) is correct.

1

Viraj_Deshpande
replied to Number System

Test of divisibility by 11 is that sum of odd-placed nos = sum of even-placed nos.

Looking at the options, their (sum of even-placed nos. - sum of odd placed nos.) = (8-7=)1, (14-7=)7, (8-10=)-2 and (14-10=)4 respectively.

y=1, z=7, w=3 or 6 or 9, x=2 or 4 or 6 or 8

Thus the nos. (and t...

Looking at the options, their (sum of even-placed nos. - sum of odd placed nos.) = (8-7=)1, (14-7=)7, (8-10=)-2 and (14-10=)4 respectively.

y=1, z=7, w=3 or 6 or 9, x=2 or 4 or 6 or 8

Thus the nos. (and t...

1

Viraj_Deshpande
replied to Quantagious

(x+y)^2 = x^2+2xy+y^2 = 2007 - 54X^2 = 9 (223 - 6X^2)

Thus, (x+y) = 3k, where k is an integer

9k^2 = 9(223-6x^2) gives 6x^2=223-k^2

Since 3 divides (223 - k^2), k^2 should be of the form (3p+1).

k^2 of the form (3p+1) where (223-k^2)/6 is also a perfect square are found by listing the...

Thus, (x+y) = 3k, where k is an integer

9k^2 = 9(223-6x^2) gives 6x^2=223-k^2

Since 3 divides (223 - k^2), k^2 should be of the form (3p+1).

k^2 of the form (3p+1) where (223-k^2)/6 is also a perfect square are found by listing the...

1

Viraj_Deshpande
replied to Geometry

Area of triangle = 0.5*b*c*sinA

b=4,c=5

Thus area = 10sinA

Clearly, this is <=10, equality existing when A=90 degrees.

Bound means the maximum value it can attain.

b=4,c=5

Thus area = 10sinA

Clearly, this is <=10, equality existing when A=90 degrees.

Bound means the maximum value it can attain.

1

Viraj_Deshpande
replied to official quant thread for CAT 2009

RHS is not 22752*x. It is only one no. with x in its units place. Hope this clears the confusion

1

Viraj_Deshpande
replied to official quant thread for CAT 2009

Their HCF is 45 means they dont have any other common factor except 45, otherwise it would've figured in the HCF. Hence, once we divide both by 45, what remains should be a pair of co-prime nos.

Clear?

Clear?

Viraj_Deshpande
replied to official quant thread for CAT 2009

No. of divisors of 21600 with HCF 45 = No of co-prime divisors of 21600/45 (=480). This should help.

There is some formula for no. of pairs of co-prime divisors. Cant recollect now. Will post here if I manage to recollect in time.

There is some formula for no. of pairs of co-prime divisors. Cant recollect now. Will post here if I manage to recollect in time.