Official Quant thread for CAT 2013

MBA CAT 2024
11341
@19rsb said:
Let S be the set of real numbers that can be represented as repeating decimals of the form 0.(abc) where a,b,c are distinct digits. Find the sum of the elements of S. Here () indicates recurring.
X = .abcabcabc
1000X = abc.abc...

999X = abc
3.3.111.X = abc
oops i read it wrongly...
11342
@19rsb said:
Let S be the set of real numbers that can be represented as repeating decimals of the form 0.(abc) where a,b,c are distinct digits. Find the sum of the elements of S. Here () indicates recurring.
N = 0.abcabc....
1000N = abc.abcabc....

N= abc/999

Sum = (1/999)*[ 72*(1 + 2 + 3 + 4 + 5)*100 + 64*(1 + 2 + 3 + 4 + 5)*(10 + 1) ] = 118.678..

A bit sleepy, might be terribly wrong :splat: ..

11343
If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is
11344
@Aman.Malhotra said:
If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is
2 ?
11345
@gs4890 explanation bhai??
11346

@Aman.Malhotra said:
@gs4890 explanation bhai??


The funda is minimum value of square of a number is zero as it should not be negative”So convert the given expression into sum of squares.
x^2+4xy+6y^2-4y+4 = x^2+4xy+4y^2+2y^2-4y+4= (x^2+4xy+(2y)^2)+ ½ (4y^2-8y+8)= (x+2y)^2 + ½ {(2y)^2-2*2y*2+22+4}=
(x+2y)^2 + ½ {(2y-2)^2+4}= (x+2y)^2 + ½ (2y-2)^2 + 2
Minimum value of (x+2y)^2 is zero
Minimum value of (2y-2)^2 is zero
The remaining part is '2' which is the minimum value of the whole expression

11347
@Aman.Malhotra said:
If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is
x^2 + 4xy + 6y^2 - 4y + 4
=(x+2y)^2+2(y-1)^2+2

put x=-2y, y=1
minimum value =2
11348
@Aman.Malhotra said:
If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is
x^2 + 4xy + 6y^2 - 4y + 4

partial differentiation w.r.t x => 2x + 4y = 0
partial differentiation w.r.t y =>4x + 12 y = 4

x + 2y = 0
x + 3y = 1

y = 1
x = -2

Substitute this to get 2 as the value
11349
@vbhvgupta said:
Q7
Both statements are insuficient
11350
mr meter was going from kashmir to kanyakumari by his car...when he started his journey odometer of his car showed 00000.on the way mr meter found that odometer was nt working properly and displayed p in between 4 & 5(ie between say 34 and 35 we get 3p).odometer at the end of journey showed 009p5.find the distance travelled by mr meter
11351
@Aman.Malhotra said:
mr meter was going from kashmir to kanyakumari by his car...when he started his journey odometer of his car showed 00000.on the way mr meter found that odometer was nt working properly and displayed p in between 4 & 5(ie between say 34 and 35 we get 3p).odometer at the end of journey showed 009p5.find the distance travelled by mr meter
addition of p in between 4 and 5 has shifted the system to base 11.
thus System goes like this.
1=1, 2=2,3=3,4=4,p=5,5=6,6=7,7=8,8=9,9=10
thus 009p5 shud look like 01056
convert into base 11.
6+5*11+10*121= 1210+55+6= 1271

Not sure for the ans though. Please confirm
11352

1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???


A 2
B 3
C 4
D 1

2) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??

A 121
B 321
C 212
D 231
11353
@dream_IIMA dd?
11354

@ audiq7 nope

11355
audiq7 OA given CAďťż
11356
@dream_IIMA said:
1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231
1D
2A
11357
@dream_IIMA
d
a?
11358

19rsb explain 2nd

and oa of 1st C

11359
@dream_IIMA said:
1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231


abc;b-a=1
100a+10b+c=11(10a+c)
10(a-b)+10c=0
10c=-10*-1;c=1

---
b-c=1, b=1+c=2
a=b-1=1, Number 121

11360
@dream_IIMA said:
19rsb explain 2ndand oa of 1st C
bhai 1st u explain one thing that if in 2nd we are getting 121 as answer then how come in 1st it could be 4 at unit place.......a little discrepancy in the OA I think .......