Official Quant thread for CAT 2013

MBA CAT 2024
16443
@blowcat13 said:
A jar full of milk contains 40% of water. a part of this milk is replaced by another containing 19%water and now the percentage of water is found to be 26%. The quantity of milk replaced is??A)1/3 B)2/3 C)2/5 D)3/5weak at alligations explain in detail plzzz

40% 19%
---26%--
7----14
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
Required quantity replaced = 2/3
16444

A 120 digit number is formed by writing first x natural numbers side by side as 1234567891011... Find the remainder when this number is divided by 8 ??


Answer according to book -6
Answer i am getting - 4 !
16445
@ananyboss said:
A 120 digit number is formed by writing first x natural numbers side by side as 1234567891011... Find the remainder when this number is divided by 8 ??Answer according to book -6Answer i am getting - 4 !
last three digit will be 646 so remainder will be rem (646 /8 ) = 6
16446
@hedonistajay said:
last three digit will be 646 so remainder will be rem (646 /8 ) = 6
9 ( single ) digit
+
( 64 - 10 +1 ) = 111 ( 2 digit numbers ) Make 120 digit
so last number becomes 64.
i.e. Last 3 digit = ....364 ?
16447
@hedonistajay

Ohh i got it thanks ! i was messing something :P
16448
@ananyboss said:
9 ( single ) digit +( 64 - 10 +1 ) = 111 ( 2 digit numbers ) Make 120 digitso last number becomes 64.i.e. Last 3 digit = ....364 ?
1-9 = 9
10 - 19 = 20
20 - 29 = 20
30 - 39 = 20
40 - 49 = 20
50 - 59 = 20
this constitute 109 digit now after that 646 will become the last three
16449
@ananyboss said:
A 120 digit number is formed by writing first x natural numbers side by side as 1234567891011... Find the remainder when this number is divided by 8 ??Answer according to book -6Answer i am getting - 4 !
1st 9 digits are single digit nos
So 120-9 = 111 digits remaining.
Now each next no. is 2 digit no.
So 111/2= 55.5
Means after 55 nos from 9, you will arrive at 119th digit.
check 54th no. from 9 to arrive at 117th digit.
= 9+ 54 =63.
Further it should be 646566...and so on. where '646' will be the 118th, 119th and 120th digit.
Hence answer is 6.
16450
@shattereddream said:
40% 19% ---26%-- 7----14 So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2 Required quantity replaced = 2/3
bhai how did you get quantity replaced ??
i mean we got only quantities of water na..
16451
Q: 12345.......3693/9, R?
16452
@viewpt said:
Q: 12345.......3693/9, R?
The question is not clear, is the 1,2,3....series till 3693 or what?
16453
@doctoriim said:
The question is not clear, is the 1,2,3....series till 3693 or what?
its a no. i.e. 1234......3693 is a no.
16454
@viewpt said:
Q: 12345.......3693/9, R?
remainder= rem(sum of digits/9)
= rem(3693(3694)2/9)=rem(1847*3693/9)=rem(2*3/9)=6
OA=6?
16455
@viewpt said:
its a no. i.e. 1234......3693 is a no.
Bro, I know this is a number, but while solving it I have to assusme this number is created by putting the numnerals 1,2,3, side by side....
Do you mean the number is like this: 12345........369136923693 ??
16456
@cynara said:
remainder= rem(sum of digits/9)
= rem(3693(3694)2/9)=rem(1847*3693/9)=rem(2*3/9)=6
OA=6?
@doctoriim said:
Bro, I know this is a number, but while solving it I have to assusme this number is created by putting the numnerals 1,2,3, side by side....
Do you mean the number is like this: 12345........369136923693 ??
If this assumption is considered, then OA is indeed 6.
16457
@cynara said:
remainder= rem(sum of digits/9)= rem(3693(3694)2/9)=rem(1847*3693/9)=rem(2*3/9)=6OA=6?
i guess smwhr smthing has got missed plz chk calc again..
16458
@pratskool said:
33 is neither a prime, nor it is 4*prime number... it can be written as 33 = 11*3a + b = 11 a - b = 3so a = 7, b = 433 = 7^2 - 4^2
@Logrhythm said:
let me try and take what uniquely here means....this question basically asks us to find out the number of numbers which can be expressed as the difference of squares of two number in exactly one way (uniquely)...for example x^2 - y^2 = 28 x and y have only 1 value (+ve integer) viz x=8 and y=6 8^2 - 6^2 = 28there is no other way of writing 28 in x^2-y^2 form except for this...whereas take any random non-prime odd number, say 33x^-y^2 = 33 can be expressed as 17^2-16^2 or 7^2-4^2 -> which are 2 ways and hence not unique...i hope kuch samaj gaye hoge bhai...
@dragster said:
a^2-b^2= (a+b)(a-b);and a , b are integers.. ; to be able to equate and find a, b - both (a+b) (a-b) should be either even or both odd ;even*even= multiple of 4 ; odd*odd= odd^2 or odd1*odd2(in case odd are different)but cases like 9 , 40 , 41 n many others do exist.. ; so we cant include just prime no.s but rather including all mutiples of 4 and odd no.s be inclusive
i think oa is 74 -8 =64
because all the odd terms and multiples of 4 can be expressed as difference of squares
odd terms excluding 1 = 49
multiples of 4 = 25
49+25 =74 - ( multiples of 12 coz they repeated )
74-8 =66
plz tell if iam right or wrong in appproach..
16459
@viewpt said:
i guess smwhr smthing has got missed plz chk calc again..
Nope. I'm not able to find any calc mistake. Is the OA something different?
16460

Vinay deposit 8000 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount that he receives after 15 months?


A = 8000(1 + (12/3*100))^5?? is it right?
16461

A makes a FD of Rs 20000 with the bank for a period of 3 years. If the rate of interest be 13%

SI per annum charged half yearly, what will he get after 42 months.
16462
x = sqrt(4+ sqrt(4 -sqrt(4 + sqrt(4 - sqrt(4 ......... to infinity

than x equals to ??