Official Quant thread for CAT 2013

MBA CAT 2024
9461
@Cat.Aspirant123 said:
How much simple interest is earned after 2 years? I. The difference between the simple interest and the corresponding compound interest is 12. II. The compound interest on the same sum for the 2 years at the same rate is 252.A alone, B alone, either alone, neither, Both required
Both required??
R = 10% and P= 1200..
9462
@Cat.Aspirant123 said:
How much simple interest is earned after 2 years? I. The difference between the simple interest and the corresponding compound interest is 12. II. The compound interest on the same sum for the 2 years at the same rate is 252.A alone, B alone, either alone, neither, Both required
Both Required

Using I:- Px^2 = 12, where x = r/100
Using II:- P(1 + x)^2 - P = 252

Dividing the two we will get
x^2/(x^2 + 2x) = 12/252
252x = 12x + 24 or x = 0
So, x = 1/10

r = 100x = 10%
9463
@Cat.Aspirant123 said:
How much simple interest is earned after 2 years?
I. The difference between the simple interest and the corresponding compound interest is 12.
II. The compound interest on the same sum for the 2 years at the same rate is 252.

A alone, B alone, either alone, neither, Both required
Let P be the prinicpal
SI = 2Pr/100
CI = P[(1-r/100)^2-P]
1)SI - CI = 12
we get an equation with 2 unkonws so cannot be solved
2) again 2 unkonws and 1 eq.
so both are required to answer
9464
@bullseyes said:
Consider the set P = {–5, –3, –1, 1, 3, 5….} consisting of 1998 numbers. If 'a' be the average of the elements in P and 'b' be twice the average of the first 1998 natural numbers, then find the value of (a – b)?
(1995^2 - 9)/1998 - 1999 = -7
9465
Let f(n) denote the sum of the digits of n. Find f(f(f(4444^4444))).


9466

Three VP's regularly visit the plant on different days. Due to labour unrest, VP(HR) regularly visits the plant after a gap of 2 days . VP(operations) regularly visits the plant after a gap of 3 days. VP(sales) regularly visits the plant after a gap of 5 days. The VP's dont devaiate from their individual scheules. The CEO of the comapny meets them when all the three VPs meet. CEO is on leave from Jan 5 2012 to Jan 28 2012. Last time CEO met them was on Jan 3 2012. When is the next time CEO meet all the Vp's (1mark) (XAT 2012)

Options : 1) Feb 2 2012 2)Feb 7 2012 3) Feb 8 2012 4) Feb 3 2012 5) None of these

9467
a, b, c, d are integers such that:
a
Then a is :
1. Prime
2. Perfect square
3. Not a perfect square
4. CBD
9468
@chandrakant.k said:
Three VP's regularly visit the plant on different days. Due to labour unrest, VP(HR) regularly visits the plant after a gap of 2 days . VP(operations) regularly visits the plant after a gap of 3 days. VP(sales) regularly visits the plant after a gap of 5 days. The VP's dont devaiate from their individual scheules. The CEO of the comapny meets them when all the three VPs meet. CEO is on leave from Jan 5 2012 to Jan 28 2012. Last time CEO met them was on Jan 3 2012. When is the next time CEO meet all the Vp's (1mark) (XAT 2012)Options : 1) Feb 2 2012 2)Feb 7 2012 3) Feb 8 2012 4) Feb 3 2012 5) None of these
Option 3) Feb 8 2012 ?

Gap of 2 days -> Visits every 3rd day
Gap of 3 days -> Visits every 4th day
Gap of 5 days -> Visits every 6th day

So, Together they visit every LCM(3,4,6) = 12 days

So, after Jan 3,2012 -> (Jan 15, Jan 27)[on holiday] and They meet with the CEO on Feb 8th 2012 ?

PS: There could be calculation mistakes :splat:
9469
@ScareCrow28 said:
Let f(n) denote the sum of the digits of n. Find f(f(f(4444^4444))).
7?
mod by 9 gives sum of digits

ps: @YouMadFellow welcome back....:)
9470
@chandrakant.k said:
Three VP's regularly visit the plant on different days. Due to labour unrest, VP(HR) regularly visits the plant after a gap of 2 days . VP(operations) regularly visits the plant after a gap of 3 days. VP(sales) regularly visits the plant after a gap of 5 days. The VP's dont devaiate from their individual scheules. The CEO of the comapny meets them when all the three VPs meet. CEO is on leave from Jan 5 2012 to Jan 28 2012. Last time CEO met them was on Jan 3 2012. When is the next time CEO meet all the Vp's (1mark) (XAT 2012)Options : 1) Feb 2 2012 2)Feb 7 2012 3) Feb 8 2012 4) Feb 3 2012 5) None of these
Feb 8 2012?
9471
@ScareCrow28 said:
Let f(n) denote the sum of the digits of n. Find f(f(f(4444^4444))).


f(4444^4444) = 16*4444 = 71104
f(71104) = 13
f(13) = 4
correct?
9472
@chandrakant.k said:
f(4444^4444) = 16*4444 = 71104f(71104) = 13f(13) = 4correct?
I am afraid bhai. Correct answer is 7.
Sum of digits is calculated by taking the mod of number with 9
4444^4444mod9 = 7
9473
Five years ago, the average age of a family consisting five members was 40 years. Four years ago, a child was born. If a year ago, a man aged 60 years died, what is the present average age (in years) of the family?


42.5
33.6
66.5
77.5
9474
@YouMadFellow welcome back bhai 😃
@ScareCrow28 said:
Feb 8 2012?
correct
@ScareCrow28 said:
I am afraid bhai. Correct answer is 7.
Sum of digits is calculated by taking the mod of number with 9
4444^4444mod9 = 7
wrong logic wrong method 😛 😛
9475
@Cat.Aspirant123 said:
Five years ago, the average age of a family consisting five members was 40 years. Four years ago, a child was born. If a year ago, a man aged 60 years died, what is the present average age (in years) of the family? 42.533.666.577.5
Sum of ages 5 years ago = 200
Sum of ages 4 years ago = 205
Sum of ages a year ago = 205 + 3*6 -60 = 163

Present Sum of ages = 163+5 = 168

Avg = 168/5 = 33.6
9476
@ScareCrow28 said:
Let f(n) denote the sum of the digits of n. Find f(f(f(4444^4444))).
444^4444 mod 9
=7^4444 mod 9
=7^4 mod 9
=7 mod 9
==> f(f(f(4444^4444)))=f(f(4444^4444))=f(4444^4444)=7



@Cat.Aspirant123 said:
Five years ago, the average age of a family consisting five members was 40 years. Four years ago, a child was born. If a year ago, a man aged 60 years died, what is the present average age (in years) of the family? 42.533.666.577.5
present sum of ages=200-56+4+20=168

==> average =168/5=33.6

P.S. @YouMadFellow : _/\_ welcome back!! :D
9477
@Cat.Aspirant123 said:
Five years ago, the average age of a family consisting five members was 40 years. Four years ago, a child was born. If a year ago, a man aged 60 years died, what is the present average age (in years) of the family?

42.5
33.6
66.5
77.5
total age 5 years ago = 200
currently if the old man had not died = 45*5+4 = 229
but he has dies at 60 1 year back so 229-61 = 168
avergae = 168/5 = 33.6
9478
@YouMadFellow @vijay_chandola Please check the 5th post on this page.
@chandrakant.k
9479
@Cat.Aspirant123 said:
How much simple interest is earned after 2 years? I. The difference between the simple interest and the corresponding compound interest is 12. II. The compound interest on the same sum for the 2 years at the same rate is 252.A alone, B alone, either alone, neither, Both required
Both required
9480

can anyone provide me the links for downloading TISS NET sample papers???