Official Quant thread for CAT 2013

@techgeek2050 said:
a cryptarithmatic problemSEND + MORE = MONEY how is that? and is there any convention that is generally followed in such questions?
9 5 6 7
1 0 8 5
1 0 6 5 2

have to take cases, it is always a bit time consuming

not aware of any shortcut, if you find one, share it with us too...

@vbhvgupta said:
the square of the sum of the roots of a quadratic equation E is 8 times the product of its roots. Find the value of the square of the sum of the rootsdivided by the product of the roots of the equation whose roots are reciprocals of those of E.
eqn 1 (x-a)(x-b) = 0
eqn 2 (x-1/a)(x-1/b) = 0

we get req value as 8
@jain4444 said:
34692 (2 numbers) 23469 ( 2 numbers) 46923 69234 92346 there is a cyclicity of 5 digits in each case 2007 mod 5 = 2 now here we can make extra case by having last 2 digits as 17 or 51 which is only possible in 1st two cases so , in total 7 such numbers are possible @Logrhythm@ScareCrow28@RDN
OA is 9

source :
http://www.mayk.fi/sites/default/files/2008_JuniorRatkaisut_0.pdf
question 30
@RDN said:
yeah it will be 9

34692 (2 numbers)
23469 (2 numbers)
46923
69234 (2 numbers)
92346 (2 numbers)

total 9
@skt. said:
@albiesriramIs it (c) 6 ?For first two no's 12 , difference is 1.for first four no's 1234, diff is 2,for first 6 no's 123456, diff is 3..for 100 no's diff is 5050/11 = 6.
if i calculate manually i am getting difference as 41..

sum of odd positioned digits
1+3+5+7+9+(0+1+2+...9)*9
=430
sum of even positioned digits
2+4+6+8+(1+1+...10times)+(2+2+...10times)+....+(9+9+..10times) + 1
=471

so diff is 41

where i m going wrong ?
@rnishant231 said:
if i calculate manually i am getting difference as 41..sum of odd positioned digits 1+3+5+7+9+(0+1+2+...9)*9 =430sum of even positioned digits 2+4+6+8+(1+1+...10times)+(2+2+...10times)+....+(9+9+..10times) + 1=471so diff is 41where i m going wrong ?
correct hai.. now divide the 41 by 11.. remiander kya aayega?
@iLoveTorres said:
correct hai.. now divide the 41 by 11.. remiander kya aayega?
but is method se

For first two no's 12 , difference is 1.
for first four no's 1234, diff is 2,
for first 6 no's 123456, diff is 3
.
.
for 100 no's diff is 50


difference 50 aa raha hai..but i m getting 41..

@rnishant231 said:
but is method seFor first two no's 12 , difference is 1.for first four no's 1234, diff is 2,for first 6 no's 123456, diff is 3..for 100 no's diff is 50difference 50 aa raha hai..but i m getting 41..
41mod 11 rem 8
answer is 8
6 vala wrong tha,nobody edited that but oa is 8
@abhishek.2011 said:
41mod 11 rem 8answer is 86 vala wrong tha,nobody edited that but oa is 8
is this the ques where all nos from 1 to 100 are written and we have to calculate mod 11?
@Subhashdec2 said:
is this the ques where all nos from 1 to 100 are written and we have to calculate mod 11?
yup it is, the answer provided by ever1 first was 6 but it is 8, chillfactor , me and 1 more guy gave 8 as answer which lead to confusion but later it was confirmed that the answer is 8 :)

@abhishek.2011 said:
yup it is, the answer provided by ever1 first was 6 but it is 8, chillfactor , me and 1 more guy gave 8 as answer which lead to confusion but later it was confirmed that the answer is 8
how is it 8
10^n=-1 if n is odd
+1 if n is even
tell me where m i wrong

12345......100
-1+2-3+4-5+6-7+8-9+(-10-11-12-....-99) +100 mod 11
-5-(45*109) +100 mod 11
-5 +1+1
-3
8

@abhishek.2011 got it
i took 109 mod 11 as +1 but it should be -1

@Koushik98 said:
In the figure given below, ABCD is a rectangle, DE : EC = 5 : 4 and CF : FD = 8 : 1. If the area of the quadrilateral APFD is 49 square units, then find the area of the quadrilateral BPEC (in square units). a 86 b 87 c 88 d 85
is it 88
area of rectangle 234
area of the required quadilateral 88
@neerajspiky said:
0

a-5d + a- 4d+...+ a+4d+ a+5d = a-9d+ a-8d+....+a+8d+ a+19d

=> a = 0,
d= 0;

Sum= 0
@albiesriram said:
3?
@Subhashdec2 said:
3?
there will be 4 such instances right? we can do a 10*9*8*7 in 4 different suites.. #confused i guess its NOTA
@albiesriram said:
there will be 4 such instances right? we can do a 10*9*8*7 in 4 different suites.. #confused i guess its NOTA
yea it should be multiplied with 4

@albiesriram

3

Edit: 4

@albiesriram said:
Ans - 4*10*9*8*7/ 40c4

1st selecting 4 suit - 4 different ways, next select other 4 cards with different denomination in 10 * 9 * 8 * 7 ways.

question Plse answer-
25 independent, fair coins are tossed in a row. What is the expected number of consecutive HH pairs?
Details
If 6 coin tosses in a row give HHTHHH, the number of consecutive HH pairs is 3.