Official Quant thread for CAT 2013

MBA CAT 2024
24048
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
B)32
24049
@amresh_maverick said:
Q1> see attachement
guess 8 - (2 + (1/4)*4pi) = 6 - pi
24050
@Dexian said:
B)32
how?

24051
@sachisurbhi said:
how?
he tore pages from 7 to 38.....
sum till 38 = 38*39 /2=39*19=741
sum till 6 = 6* 7/2=21
741-21=720
24052
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
720 = 32*22.5

As 720 is sum of even number of consecutive integers, so it's average must be a number of the form xx.5. I've explained it earlier also.

Thus the answer is 32 and the page numbers are 7, 8, ....., 22, 23, .... 37, 38

Team BV
24053
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
38*39/2 - 6*7/2 = 720

hence he tore 38-6 = 32 pages...
24054
@bodhi_vriksha said:
720 = 32*22.5As 720 is sum of even number of consecutive integers, so it's average must be a number of the form xx.5. I've explained it earlier also.Thus the answer is 32 and the page numbers are 7, 8, ....., 22, 23, .... 37, 38Team BV
can you explain the concept again, or direct me to the page where u had explained it earlier. i have somewhat got the hold of this but need a more descriptive explanation....
24055
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
Suppose the n pages are a, a + 1, ...., a + (n - 1)

Sum = n(2a + n - 1)/2 = 720

n(2a + n - 1) = 1440
Now, one of n and (n + 2a - 1) will be even and other will be odd and n

1440 = 32*45 (in all other cases n will be odd)
=> n = 32
24056
@amresh_maverick said:
Q1> see attachement
c) 6-pi
24057
@chandrakant.k Better try I - is not true, II - not true. Obviously III is true. 😃
24058
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
2nx + n(n-1) = 1440
--> n(2x + n-1) = 1440
n has to be even, and x has to be odd, therefore it should be like even*odd
n has to have all the powers of 2... therefore n = 32 ...
24059
@sachisurbhi said:
pradip tore a certain number of consecutive leaves from his book.Each leaf is numbered on either side and is considered to be two pages.if the sum of pages which he tore off was 720.how many pages did he tear offa)16b)32c)42d)45
basically we have to write 720 as sum of consecutive numbers

720/32 = 22.5

22 = 16th term and 23 = 17th term

so ,we can write 720 as the sum of 32 consecutive numbers
24060

q2>

24061
@amresh_maverick said:
q2>
38degrees
24062
@amresh_maverick said:
q2>

Edit:
38 degrees...........

180-(2*(90-x))+x+66=180
3x+66=180
x=38.
24063
@amresh_maverick said:
Q1> see attachement
TP=AP=x
TB^2=2x^2
TB=rt2*x

By pythagoras x=2rt2

angle PAB=45
Area APB=2+pie
traingle ATB=8

remaining area 6-pie
24064
@amresh_maverick said:
q2>
ans seems to be 38 degre
24065
@sachisurbhi said:
if y (y>=4) is an even natural number and x=y^2 -2y, then the largest natural number that divides x^2 - 8x isa)192b)144c)384d)96
(y-4)(y-2)(y)(y+2)
y>=4 is even natural number

2*4*6*8=384
24066
@gnehagarg said:
(y-4)(y-2)(y)(y+2) y>=4 is even natural number2*4*6*8=384
could you elaborate this pls
24067
@amresh_maverick said:
Q1> see attachement
6 - pi ?

PA^2 = AO^2 + PO^2 = 2^2 + 2^2 --> PA = 2rt2
so TB = 4
area of triangle = 1/2*4*4 = 8
area of shaded region = 8 - (1/2*2*2 + pi/4*(2)^2) = 8 - (2 + pi) = 6 - pi