Official Quant thread for CAT 2013

the biggest possible cube is taken out of arigid solid cylinder of radius 15 cm and height 20 cm.

what will be the volume of the cube??

a)375

b)800

c)375*2^(1/2)

d)none of these

@gudda1122 said:
A certain pair of used shoes can be repaired for $12.50 and will last for 1 year. A pair of the same kind of shoes can be purchased new for $28.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?I don't have OA so we needed to discussPlease provide approach
The average cost per year of the new shoes is greater than the cost of repairing the used shoes =1.5/12.5*100=12 %


@swapnil4ever2u said:
@Logrhythm what am i doing wrong !! i am trying by that formula for 3 digit.. then subtracting the ones in 1-99, 801-899, 900-999.. (total 19*3) if u could try like that ..

For counting any digit in base b (1 to b-1) in 3 digit numbers, the formulae is 3b^2-5b+2

So, for base 10, it is 300-50+2=252.

Since u want from 100 to 800, we have to subtract 20+2*9=38

So ANS=252-38=214
@bs0409 kya baat h .. bhai har marj ki dwa rahke ho ...
@Logrhythm said:
avg cost per year of repaired shoe = 12.50avg cost per year of a new shoe = 14so, (14-12.5)/12.5 = 0.12 or 12% ??
@Logrhythm said:
I guess you are right....karni padegi wo wali cost bhi consider...
kyon consider karenge....repair cost?...new cost par hi to poocha hai?...mera bhi 12% hi aa raha hai?
@bs0409 said:
x^2+x+1=0 has imaginary roots only. No real roots....a,b,c,d,e-primea is min and e is maxa+b+c+d+e=350Find a
a+b+c+d+e=350
exept 2 all primes are odd .. since sum is even =>this means odd numbers are odd number of times .. ie out of the a,b,c,d,e .. 4 are odd and 1 even
since a is the smallest .. so a must be 2

@getupsid said:
the biggest possible cube is taken out of arigid solid cylinder of radius 15 cm and height 20 cm. what will be the volume of the cube??a)375b)800c)375*2^(1/2)d)none of these
volume of cylinder = 22/7 * 225 * 20
volume of cube = volume of cylinder
side of cube = (22/7 * 225 * 20) ^ (1/3) -------> (A)
factorizing and simplifying (A) we get, 10*((99/7) ^ (1/3))
so 7 * 14 = 98 therefore (14.XX)^1/3 wud be between 2 and 3
hence 10 * 2.XX
so side of cube is between 20 and 30
cube of side would be greater than provided options so d) none of these
correct me if i am wrong

the number of positive integral solutions of the equation a+b+c+d+e=30 is

@pavimai said:
the number of positive integral solutions of the equation a+b+c+d+e=30 is
a' +1 +b' +1 +c'+1 +d'+1 +e'+1 = 30 ==> a'+b'+c'+d'+e' = 25 ==> (25+5-1)C ( 5-1 ) = 29c4
@pavimai said:
the number of positive integral solutions of the equation a+b+c+d+e=30 is
as given positive integers, give a,b,c,d,e each min of 1.
so a'+b'+c'+d'+e' = 25

(25+5-1) C (5-1) = 29C 4
Guppy has a watch that shows the date without the month and the year. By default, the watch displays 31 days in each month. Therefore, at the end of all the months with less than 31 days the date on the watch needs to be readjusted. On 10th March 2001 it showed the right date as €˜10 €™. What date would it show on 15th May 2002, if it is known that Guppy never readjusted his watch during this period?
(a) 23 (b) 7 (c) 8 (d) 22
@swapnil4ever2u said:
how many whole numbers between 100 and 800 contain the digit 2 ??
BW 100 to 199 --- we have 19 numbers having 2 as a digit in them.
200 to 299 --- 119 numbers having 2 as a digit in them.
300 to 499 --- 19
.
.
.
700 to 799 --- 19

19 * 6 + 119 = 233??

@Faruq said:
Guppy has a watch that shows the date without the month and the year. By default, the watch displays 31 days in each month. Therefore, at the end of all the months with less than 31 days the date on the watch needs to be readjusted. On 10th March 2001 it showed the right date as 창€˜10창€™. What date would it show on 15th May 2002, if it is known that Guppy never readjusted his watch during this period?(a) 23 (b) 7 (c) 8 (d) 22
actual no.of day 365 + 21 +30 + 15 = 431.

but the watch shows 31 * 13 + 21 + 15 = 439.

watch shows 8 days more soon 15th ==> 23 will be shown.. @joyjitpal check dis bhai..
@veertamizhan said:
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
11 ! / (4! *4!*2! ) - 8! /(4! * 2! )
@swapnil4ever2u said:
how many whole numbers between 100 and 800 contain the digit 2 ??
20*6 + 100 + 20 = 240

A is the set of the first 100 natural numbers. What is the minimum number of elements that should be picked from A to ensure that atleast one pair of numbers whose difference is 10 is picked?
@Faruq said:
A is the set of the first 100 natural numbers. What is the minimum number of elements that should be picked from A to ensure that atleast one pair of numbers whose difference is 10 is picked?
51??

If a circle is provided with a measure of 19 deg on centre, is it possible to divide the circle into 360 equal parts ?
please provide explanation .

@Faruq said:
A is the set of the first 100 natural numbers. What is the minimum number of elements that should be picked from A to ensure that atleast one pair of numbers whose difference is 10 is picked?
51 :neutral:
P.S. Sir kahan ho ajkl? :splat:
@somnathbhatta said:
If a circle is provided with a measure of 19 deg on centre, is it possible to divide the circle into 360 equal parts ?
please provide explanation .
It is always possible :)
18*19 = 342 :mg: