Official Quant thread for CAT 2013

@gs4890 said:
-64x8 => -512
plzz explain
@Ashmukh said:
plzz explain
[-8,8]
for lowest magnitude take lowest and highest numbers, -8*8=-64
same for all 8 pairs ,so -64*8=-512

@Ashmukh its not mentioned they are distinct
@krum umm don't u think we need to have disitnct no in multiplication after we are done with -8*8,like after that -7*7
@akansh_1 said:
The value of (222)baseX in base 'X' when converted to base 10 is 'P'. The value of (222)baseY in base 'Y' when converted to base 10 is Q. If (P – Q)base10 = 28, then what is the value of (Q – X)base10?(a) 10(b) 92(c) 79(d) Cannot be determined
P=2+2x+2x^2
Q=2+2y+2y^2

=>2*(x-y)*(1+x+y)=28
=>(x-y)*(1+x+y)=1*14=2*7

x-y=1
1+x+y=14
=>x=7,y=6

x-y=2
1+x+y=7
=>x=4,y=2 ; but 222 is not possible in base 2

so Q-X=2(1+6^1+6^2)-7=79
@akansh_1 said:
a1, a2, a3.....a8 are eight real numbers belonging to the interval [–8, 8]. What is the minimum possible value of a1a2 + a2 a3 +...... a7a8 + a8a1?a) –64 (b) 0(c) –512 (d) –16
a1=8
a2=-8
a3=8
a4=-8
a5=8
a6=-8
a7=8
a8=-8

-64*8=-512
Raj works part time in three different organisations €“ P, Q and R €“ everyday. Each of these
organisations pays a fixed salary on hourly basis. On any day, Raj earned Rs. 3,850 by working for
4 hrs, 5 hrs and 6 hrs respectively and on the next day, he earned Rs. 5,350 by working for 5 hrs,
3 hrs and 7 hrs respectively. If the hourly salaries paid by the three organisations are in Arithmetic
Progression, find the difference between the hourly salaries of the highest and the lowest paying
organisations?
A. Rs. 1,000 B. Rs. 500 C. Rs. 750 D. None of these

If 'p' and 'q' are prime numbers such that p = q + 2 and 'q' is greater than 100, then which of the
following is always true?
A. p^2 – q^2 is always divisible by 24.
B. p^3 + q^3 is always divisible by 24.
C. Both A and B
D. None of these

There are 8 poles on the same side of a straight road. Two of these poles are without flags; two of
these have a flag of the same country and each of the rest of the four poles has a plain flag of a
different colour. What is the probability that the first four poles from either end have two flags of the
country and two plain colored flags?
A.
1/
140
B.
6/
35
C.
1/
70
D. None of these

@sujamait said:
There are 8 poles on the same side of a straight road. Two of these poles are without flags; two ofthese have a flag of the same country and each of the rest of the four poles has a plain flag of adifferent colour. What is the probability that the first four poles from either end have two flags of thecountry and two plain colored flags?A.1/140B.6/35C.1/70D. None of these
6/35

(4c2*4!/2!)*(4!/2!)*2/(8!/(2!*2!))
@sujamait said:
If 'p' and 'q' are prime numbers such that p = q + 2 and 'q' is greater than 100, then which of thefollowing is always true?A. p^2 – q^2 is always divisible by 24.B. p^3 + q^3 is always divisible by 24.C. Both A and BD. None of these
only A

q is of the form 6k-1 p is of the form 6k+1

now substitution shows only 1 as the answer
@sujamait said:
There are 8 poles on the same side of a straight road. Two of these poles are without flags; two ofthese have a flag of the same country and each of the rest of the four poles has a plain flag of adifferent colour. What is the probability that the first four poles from either end have two flags of thecountry and two plain colored flags?A.1/140B.6/35C.1/70D. None of these
D ??

(2c1*4!*4!)/(8!)
@sujamait said:
Raj works part time in three different organisations €“ P, Q and R €“ everyday. Each of theseorganisations pays a fixed salary on hourly basis. On any day, Raj earned Rs. 3,850 by working for4 hrs, 5 hrs and 6 hrs respectively and on the next day, he earned Rs. 5,350 by working for 5 hrs,3 hrs and 7 hrs respectively. If the hourly salaries paid by the three organisations are in ArithmeticProgression, find the difference between the hourly salaries of the highest and the lowest payingorganisations?A. Rs. 1,000 B. Rs. 500 C. Rs. 750 D. None of these
1000

either P/R pays the middle term of the AP of the salaries..

LET a-d,a,a+d be the salaries in AP

assume P
15a+d=3850
15a+4d=5350

d=500
2d=1000

we wil get the same thing when we assume R as middle term
@sujamait said:
Raj works part time in three different organisations €“ P, Q and R €“ everyday. Each of theseorganisations pays a fixed salary on hourly basis. On any day, Raj earned Rs. 3,850 by working for4 hrs, 5 hrs and 6 hrs respectively and on the next day, he earned Rs. 5,350 by working for 5 hrs,3 hrs and 7 hrs respectively. If the hourly salaries paid by the three organisations are in ArithmeticProgression, find the difference between the hourly salaries of the highest and the lowest payingorganisations?A. Rs. 1,000 B. Rs. 500 C. Rs. 750 D. None of these
Is it option D?
Difference is 2*750=1500 ?
@wovfactorAPS said:
6/35(4c2*4!/2!)*(4!/2!)*2/(8!/(2!*2!))
y did u do 4c2 ??
@Brooklyn said:
y did u do 4c2 ??
4 different colours i have to choose 2

first bracket -first 4 places

second bracket-last four

2-interrchanging of them
@wovfactorAPS said:
4 different colours i have to choose 2first bracket -first 4 placessecond bracket-last four2-interrchanging of them
u dont have to choose 2 color :O

its 2plain and 2 country flag
@Brooklyn said:
u dont have to choose 2 color its 2plain and 2 country flag
nah the plain flags are of 4 different colours..

read the question again
@wovfactorAPS said:
nah the plain flags are of 4 different colours..read the question again
my bad :banghead:
@sujamait said:
Raj works part time in three different organisations €“ P, Q and R €“ everyday. Each of theseorganisations pays a fixed salary on hourly basis. On any day, Raj earned Rs. 3,850 by working for4 hrs, 5 hrs and 6 hrs respectively and on the next day, he earned Rs. 5,350 by working for 5 hrs,3 hrs and 7 hrs respectively. If the hourly salaries paid by the three organisations are in ArithmeticProgression, find the difference between the hourly salaries of the highest and the lowest payingorganisations?A. Rs. 1,000 B. Rs. 500 C. Rs. 750 D. None of these
___P_____Q_____R
___a____a-d____a+d
___4_____5______6 = 3850
___5_____3______7 = 5350

Solving 2 equations
d=500
Hence difference b/w highest and lowest = 2d = 1000 ??
@sujamait said:
There are 8 poles on the same side of a straight road. Two of these poles are without flags; two ofthese have a flag of the same country and each of the rest of the four poles has a plain flag of adifferent colour. What is the probability that the first four poles from either end have two flags of thecountry and two plain colored flags?A.1/140B.6/35C.1/70D. None of these
B. 6/35

{2*4C2*(4!/2!)*(4!/2!)} / {8!/(2!*2!)}