Official Quant thread for CAT 2013

@krum said:
cp - 100mp - 150discount - 3xprofit/loss - 2xsay profit=>(150(100-3x)/100-100)/100*100=2x=>150(100-3x)/100=100+2x=>15000-450x=10000+200x=>x=5000/650=100/13say loss=>(150(100-3x)/100-100)/100*100=-2x=>x=5000/250=20so 20% loss
x=20 => loss = 2x = 40% wot say ?

[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.


a) -2.03 b) -1.97 c) -2.97 d) -1.7

I can't understand the Question also. Please explain the Qestion and answer.
@catter2011 said:
3)1 & 1)believing, credibility
3)1 and 4) pursuing, scrutiny
@sujamait said:
The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined Though the matter of the existence of ghosts in that house might not be worth _____________, some observations from the neighbours may merit _____________ in the light of the deaths that have taken place there.OPTIONS1) believing, credibility2) proving, refutation3) examination, integrity4) pursuing, scrutiny
1)1
2)pursuing, scrutiny

happy diwali sir
@sujamait said:
The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined Though the matter of the existence of ghosts in that house might not be worth _____________, some observations from the neighbours may merit _____________ in the light of the deaths that have taken place there.OPTIONS1) believing, credibility2) proving, refutation3) examination, integrity4) pursuing, scrutiny



f(0).f(0)=f(0+0)+0.0
=> f^2(0) = f(0)
=>f(0)[ f(o)-1] = 0
=> f(0) = 0 or 1
thus (d) cannot be uniquely determined


Though the matter of the existence of ghosts in that house might not be worth believing , some observations from the neighbours may merit credibility in the light of the deaths that have taken place there.
@sujamait said:
The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined Though the matter of the existence of ghosts in that house might not be worth _____________, some observations from the neighbours may merit _____________ in the light of the deaths that have taken place there.OPTIONS1) believing, credibility2) proving, refutation3) examination, integrity4) pursuing, scrutiny
3) 1
confused between 1) and 4) :banghead:
scrutiny fit nahi ho raha so going with 1) believing and credibility [but pursuing zyada chha baithta hai]
@padmanabhan1989 said:
[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.a) -2.03 b) -1.97 c) -2.97 d) -1.7 I can't understand the Question also. Please explain the Qestion and answer.
greatest integer function - [4.2]=4, [5.0]=5, [-2.3]=-2 hope u get the picture
{x}, should be clear

[-2.03]^3+{-2.03}^2
=>-2^3+.03^2
=>-8+.0009
=>-7.9991

only this one comes closest, if i'm not making any mistake


@padmanabhan1989 above is wrong, [-2.3]=-3

are u sure about the value -7.91?
@padmanabhan1989 said:
[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.a) -2.03 b) -1.97 c) -2.97 d) -1.7 I can't understand the Question also. Please explain the Qestion and answer.
[x]^3 + {x}^2 = -7.91

by options x = -2.03
{x} = 0.03
[x] = -2

so -8 + 0.9x = -7.9

so option A
@krum said:
greatest integer function - [4.2]=4, [5.0]=5, [-2.3]=-2 hope u get the picture{x}, should be clear[-2.03]^3+{-2.03}^2=>-2^3+.03^2=>-8+.0009=>-7.9991only this comes closest, if i'm not making any mistake
KRUM, approach for dis..

The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined
@krum said:
greatest integer function - [4.2]=4, [5.0]=5, [-2.3]=-3 ?hope u get the picture{x}, should be clear[-2.03]^3+{-2.03}^2=>-2^3+.03^2=>-8+.0009=>-7.9991only this comes closest, if i'm not making any mistake
@catter2011 said:
KRUM, approach for dis..The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined
f(1)f(0)=f(1)+0
=>f(0)=1

f(2)f(0)=f(2)+0
=>f(0)=1

...
@catter2011 said:
A two-digit number, with non-zero digits, has its units digit divisible by its tens digit. The number is divisible by the average of its digits. How many possible values can the ratio of the units digit and the tens digit assume?
4 values ?
@catter2011 said:
A two-digit number, with non-zero digits, has its units digit divisible by its tens digit. The number is divisible by the average of its digits. How many possible values can the ratio of the units digit and the tens digit assume?
ab be the number
a5
when a = 1 b = 2...9 total 8 values
when a = 2 b= 4 6 8 total 3 values
when a = 3 b = 6 9 total 2 values
when a = 4 b = 8 only 1 value
so total 8+3+2+1 = 14 values
now when (a,b) = (1,3) (1,4) (1,6) (1,7)(1,9) the number is not divisble
in other cases the ratio = (1,2) ratio = 6
(1,5) = 5
(1,8) = 4
(2,4) = 8
(2,6) = not possible
(2,8) = not possible
(3,6) = 8
(3,9) not possible
(4,8) = 8
so 8 6 5 4 total 4 values??
@catter2011 said:
KRUM, approach for dis..The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined
f^2(0)-f(0)=0
f(0)(f(0)-1) =0
f(0)=0,f(0) =1....cant be uniquely
@padmanabhan1989 said:
[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.a) -2.03 b) -1.97 c) -2.97 d) -1.7 I can't understand the Question also. Please explain the Qestion and answer.
i think question is that sum is -7.51
anyway greatest integer function [x] means u take the integer just less than x. eg : [273.8484]=273 similarly for -ve values [-4.23] = -5 (note the diff)

thus observe that answer gives -7. something.
this means if u have something like -8 +something...
now u can get -8 only if [x] where x= something like -1.yy which will give u [x] = -2

also fractional value is nothing but the decimal part (with decimal ofcourse) eg for {5.46}=.46

thus if u work out answer in my opinion is -1.7 ( n i think question should be sum is -7.51 instead of -7.91)

do clarify
@surajmenonv said:
f(0).f(0)=f(0+0)+0.0=> f^2(0) = f(0)=>f(0)[ f(o)-1] = 0=> f(0) = 0 or 1thus (d) cannot be uniquely determinedThough the matter of the existence of ghosts in that house might not be worth believing , some observations from the neighbours may merit credibility in the light of the deaths that have taken place there.
i had a doubt

applying the given rule

f(1)f(0)= f(1)

=> either both f(1) and f(0)=0 or f(1)=0 or f(0)=1

but f(1)^2 =f(2)+1

Case 1
considering f(1)=0
f(2)=-1
but same principle

f(2)f(0)=f(2)
=> either both f(2) and f(0)=0 or f(2)=0 or f(0)=1
2 cases not possible , only f(0)=1

case 2
considering both f(1)=0 and f(0)=0
same calculating f(2) leads to f(0) =1
contradiction

case 3
f(0)=1

so it can be uniquely determined

PS : point me if i am wrong :P
@milestogo3 said:
han bhai, made a blunder, in that case, none of the options match :p

[x] denotes the greatest integer value just below x and {x} its fractional value. The sum of [x]^3 and {x}^2 is -7.91. Find x.a) -2.03 b) -1.97 c) -2.97 d) -1.7


@sujamait said:
The real function f(x) satisfies the equation f(x) f(y) = f(x + y) + xy for all real numbers x and y. What is the value of f(0)?OPTIONS1) ˆ'1 2) 0 3) 1 4) 2 5) Cannot be uniquely determined

option 5 ?? cannot be uniquely determined
f(0)*f(0) = f(0)
now f(0) can be 0 or 1
@sujamait said:
Though the matter of the existence of ghosts in that house might not be worth _____________, some observations from the neighbours may merit _____________ in the light of the deaths that have taken place there.OPTIONS1) believing, credibility2) proving, refutation3) examination, integrity4) pursuing, scrutiny

option 3? examination , integrity ?

@surajmenonv said:
i think question is that sum is -7.51anyway greatest integer function [x] means u take the integer just less than x. eg : [273.8484]=273 similarly for -ve values [-4.23] = -3 (note the diff)thus observe that answer gives -7. something.this means if u have something like -8 +something...now u can get -8 only if [x] where x= something like -1.yy which will give u [x] = -2also fractional value is nothing but the decimal part (with decimal ofcourse) eg for {5.46}=.46thus if u work out answer in my opinion is -1.7 ( n i think question should be sum is -7.51 instead of -7.91)do clarify
I didnt get this step buddy " for -ve values [-4.23] = -3 (note the diff)" why -3?
Sun Life Insurance Company issues standard, preferred, and ultra-preferred policies. Among the company €™s policy holders of a certain age, 50% are standard with a probability of 0.01 of dying in the next year, 30% are preferred with a probability of 0.008 of dying in the next year, and 20% are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the deceased being a preferred policy holder?
A. 0.1591 B. 0.2727
C. 0.375 D. None of these

Soln also plz