Official Quant thread for CAT 2013

@Budokai001 said:
The sequence 1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, €Ś. has one odd number followed by the next twoeven numbers, then the next three odd numbers followed by the next four even numbers and so on.What is the 2003rd term of the sequence?

Is it 3943??
Row 1 -- 1
Row 2 --2,4
Row 3 --5,7,9
Row 4 --10,12,14,16
..... and so on

now observe that every row contains the same number of elements as the row number and ends with the square of the row number and also if row number is even then the elements are even and if odd then the elements are odd...
so we need to find 2003rd term
n(n+1)/2 = 2003
n ~ 62
so 62nd row will end with 62^2 ie 3844
we need 2003 - 1953 = 50 elements more...
63rd row's elemts wld be -> 3845, 3847,...
so 50th element wld be -> 3845 + 49*2 = 3943...

@Budokai001 ho gaya 3943

calculation mistake

@Budokai001 said:
The sequence 1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, €Ś. has one odd number followed by the next twoeven numbers, then the next three odd numbers followed by the next four even numbers and so on.What is the 2003rd term of the sequence?
2003th term ll require =1+2+3+4+...63=2016....alternations between odd and even groups....

fr each group we miss out on n+1 no starting with 2nd group...2nd grp misses 3..3rd grp misses 6 & 7..4th grp misses 11,13,15..so on..


by 62rd grp we have missed=1+2+3+....61=1891 trms...
last no of 62rd grp=1+2+3+..62=1953+1981=3934=1953rd term...2003rd term is the next 50th odd no. starting wid 3935....
=3935+49*2=4033....!!!

bhai bahoot gadbad lagta hai..:gm::drinking:
@happy3475 ans is 3943 bro.. !

In how many ways can 1000 be written as a sum of 'n' consecutive natural numbers, where 'n' is
greater than 1?

@Budokai001 said:
In how many ways can 1000 be written as a sum of 'n' consecutive natural numbers, where 'n' isgreater than 1?
it is given by the number of odd factors - 1
1000 = 5^3*2^3
hence 3 ways...
A circle is drawn inside a trapezium such that it touches all the four sides of the trapezium. The line
joining the midpoints of the non-parallel sides divides the trapezium in two parts with areas in the
ratio 3 : 5. If the lengths of the non-parallel sides are 6 cm and 10 cm, then what is the length (in cm)
of the longer parallel side of the trapezium?
(a) 8 (b) 10 (c) 12 (d) Cannot be determined

@Logrhythm said:
it is given by the number of odd factors - 11000 = 5^3*2^3hence 3 ways...
could u pls explain?
@Budokai001 said:
@happy3475ans is 3943 bro.. !In how many ways can 1000 be written as a sum of 'n' consecutive natural numbers, where 'n' isgreater than 1?
3 ways?
5^3*2^3
odd no. of factors-1
4-1=3
@Calvin4ever said:
could u pls explain?
Say, a + 1, a + 2, ..., a + n are the numbers, then
N = n(n + 2a + 1)/2
=> n(n + 2a + 1) = 2N

Now, one of n and (n + 2a + 1) will be odd, so basically we need to write 2N as product of even and odd natural numbers and smaller of the two will be n. So, we just have to look for odd factors of 2N or N (as they are same). But since n can not be 1, we need to subtract 1.

#Copied from somewhere...
@Budokai001 said:
A circle is drawn inside a trapezium such that it touches all the four sides of the trapezium. The linejoining the midpoints of the non-parallel sides divides the trapezium in two parts with areas in theratio 3 : 5. If the lengths of the non-parallel sides are 6 cm and 10 cm, then what is the length (in cm)of the longer parallel side of the trapezium?(a) 8 (b) 10 (c) 12 (d) Cannot be determined
12 ??
3 step of a ladder is immersed in water .if thickness of the steps is 1.5cm and distance between the steps is 8cm .the tide raise at the rate of 16cm per hour for first 6 hrs and then it ebbs at the rate of 8cm per hour .after 8 hrs how many steps will be immersed in water??

@sumit99 said:
3 step of a ladder is immersed in water .if thickness of the steps is 1.5cm and distance between the steps is 8cm .the tide raise at the rate of 16cm per hour for first 6 hrs and then it ebbs at the rate of 8cm per hour .after 8 hrs how many steps will be immersed in water??
11 ??
@sumit99 said:
3 step of a ladder is immersed in water .if thickness of the steps is 1.5cm and distance between the steps is 8cm .the tide raise at the rate of 16cm per hour for first 6 hrs and then it ebbs at the rate of 8cm per hour .after 8 hrs how many steps will be immersed in water??
logically the answer to this question should be CBD, as we do not know the number of steps the ladder has...but assuming that there are infinite steps then it should be 11...
@Logrhythm said:
logically the answer to this question should be CBD, as we do not know the number of steps the ladder has...but assuming that there are infinite steps then it should be 11...
I wonder if this is a trick question. what if this was the ladder of the boat or something ?? it wud be the same rite. (where else wud a ladder be in the sea?) :p
@sumit99 said:
3 step of a ladder is immersed in water .if thickness of the steps is 1.5cm and distance between the steps is 8cm .the tide raise at the rate of 16cm per hour for first 6 hrs and then it ebbs at the rate of 8cm per hour .after 8 hrs how many steps will be immersed in water??
11?
A and B are the two opposite ends of a swimming pool and the distance between them is
420 metres. Ankur and Manu start swimming towards each other at the same time from A and B,
with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns back
and starts swimming towards the other end. At what distance (in metres) from A will they meet when
Manu is in his 13th round? Note: A to B is considered one round and B to A another round.
(a) 405 (b) 330 (c) 240 (d) 280

@Budokai001 said:
A and B are the two opposite ends of a swimming pool and the distance between them is420 metres. Ankur and Manu start swimming towards each other at the same time from A and B,with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns backand starts swimming towards the other end. At what distance (in metres) from A will they meet whenManu is in his 13th round? Note: A to B is considered one round and B to A another round.(a) 405 (b) 330 (c) 240 (d) 280
330 ??
A fuel dealer mixes two brands of fuel which cost in the ratio 2:3. A solution of 30% brand A with brand B yields profit of 10% when sold at rs 297. what is the cost of brand B?
@nagpal9 said:
A fuel dealer mixes two brands of fuel which cost in the ratio 2:3. A solution of 30% brand A with brand B yields profit of 10% when sold at rs 297. what is the cost of brand B?
300 ??
@nagpal9 said:
A fuel dealer mixes two brands of fuel which cost in the ratio 2:3. A solution of 30% brand A with brand B yields profit of 10% when sold at rs 297. what is the cost of brand B?
A B
Cost/kg 2x 3x
let total kg=100 30 70

(60x+210x)/(30+70) = 297(1- 1/11)
=>x=100

3x=300 ?