Official Quant thread for CAT 2013

@hexagon

Akash, Bhanu and Sam work on a project. After they complete 1/4th of the project, Sam takes a break. For 7 days only Akash and Bhanu work on the project. After that Sam relieves both of them. He completes the project in 5 days. Bhanu works 50% faster than Akash while Sam alone can finish the entire project in 20 days, How long would Bhanu take to finish the entire project?



ans 23 1/3 days



1/2 of the work is done in 7 days.

Time taken by Akash= A
By Bhanu= 2A/3=B

Hence to complete the whole work time taken: 3B/5

To complete half: 3B/10

3B/10=7

B=23 1/3 days....


@hexagon

Akash, Bhanu and Sam work on a project. After they complete 1/4th of the project, Sam takes a break. For 7 days only Akash and Bhanu work on the project. After that Sam relieves both of them. He completes the project in 5 days. Bhanu works 50% faster than Akash while Sam alone can finish the entire project in 20 days, How long would Bhanu take to finish the entire project?



ans 23 1/3 days



(A + B)*7 + 5*(S) = 3/4


Now, it is given in the question that S can complete the entire project in 20 days, so S complete 1/20 of the work in one day.


Using above, (A + B)*7 + 1/4 = 3/4

(A + B)*7 = 1/2

(A + 3A/2)*7 = 1/2 ( Using B = 3A/2)

On solving above, we get A = 1/35

Hence, B = 3/70

This means that B completes 3/70 of the work in one day. So, he will take 70/3 days to complete the entire project on his own.😃

@hexagon

Akash, Bhanu and Sam work on a project. After they complete 1/4th of the project, Sam takes a break. For 7 days only Akash and Bhanu work on the project. After that Sam relieves both of them. He completes the project in 5 days. Bhanu works 50% faster than Akash while Sam alone can finish the entire project in 20 days, How long would Bhanu take to finish the entire project?



ans 23 1/3 days



(a+b)7 + 5s = 3/4 (work that remained to be completed)


and s = 1/20 , b = 1.5a

so we get a=1/35

b = 3/70


so b will take 70/3 = 23 1/3 days to complete the task

How many ordered sets of positive integer triples (a,b,c)are there such that a+b×c=100?

  • t
  • t

0 voters

How many ordered sets of positive integer triples (a,b,c)are there such that a+b×c=100?

If α, β are the roots of the equation x^2 - x + 1 = 0, then the value of α^16 - β^32 =


1

-1

0

2


@barneywaitforitstinson

How many ordered sets of positive integer triples (a,b,c)are there such that a+b×c=100?



is it 475 ?

@rnishant231

is it 475 ?



no its wrong


first divide the coins in to three groups. 10-10-8 . weight 10-10 together and you l get to know whether the heavier coin is in the group of 10-10 or 8. so we are done with one weighing. Now lets say the heavier coin is in the group of 10. divide it into three groups of 4-4-3. weigh 4-4 together and now u l get to know whether the coin is in the group of 4 or in the group of 3. if in group of 4 then weigh 2 -2 and then once more and you get the coin in fourth weighing. similar approach can be followed if the coin was in the group of 8.

@rnishant231

If α, β are the roots of the equation x^2 - x + 1 = 0, then the value of α^16 - β^32 =



1



-1



0



2



-1?

how would u divide 19 elephants in three people in the ratio of 2:4:5?

@barneywaitforitstinson

How many ordered sets of positive integer triples (a,b,c)are there such that a+b×c=100?



t



t



×

We have to count all factors of 1 to 99 and then add the no of factors of each number.
1 is factor of all numbers, so should be counted 99 times
2 will be counted 49 times
3, 33 times
4 - 24 times
5 - 19 times
6 - 16 times
7 - 14 times
8 - 12 times
9 - 11 times
10 - 9 times
11 - 9 times
12 - 8 times
13 & 14 - 7 times
15 & 16 - 6 times
17, 18, 19 - 5 times
20, 21, .., 24 - 4 times
25, 26, .., 33 - 3 times
34, 35, ..., 49 - 2 times
50, 51, .., 99 - 1 time

So, total will be 99 + 49 + 33 + 24 + 19 + 16 + 14 + 12 + 11 + 9 + 9 + 8 + 2*7 + 2*6 + 3*5 + 5*4 + 9*3 + 16*2 + 50*1 = 473

@barneywaitforitstinson

How many ordered sets of positive integer triples (a,b,c)are there such that a+b×c=100?



t



t



×

0 triplets would exist.

@chandrakant.k

Starting off with an easy question
III only

@chandrakant.k

Starting off with an easy question

@chandrakant.k

Starting off with an easy question
III only

@chandrakant.k

Starting off with an easy question

Please share the approach for this question:

Q. What is the probability of a random generator generating 10 consecutive numbers in ascending order (assume it is a perfect random generator)

@heylady

Please share the approach for this question:



1/10! ? 10 no.s gen by it can be arranged in 10! ways. That means in those many ways 10 no.s can be generated. Out of which only one way is there where 10 no.s are in ascending order. :)

@chandrakant.k

Starting off with an easy question
III only

@chandrakant.k

Starting off with an easy question

@chandrakant.k

take ths for example.. 472+559 = 1031 all conditions are statisified...



A mixture comprises two chemicals A and B. The price of A is Rs. 100/- per litre and that of B is Rs.200/- per litre. We can spend a maximum of Rs. 600/- for making the mixture. The densities of A andB are 10 kg/litre and 12 kg/litre respectively. The mixture must contain each of the chemicals to theextent of at least 25% by weight. The maximum weight of the mixture that can be made is closestto:a. 60 kg b. 51 kg c. 54 kg d. 48 kg



closest to 48 kg
100x+200y=600
we have to minimise liq b contents (too costly)
12y/10x=1/3
==> x=3.6y
==>y=6/5.6 for our optimal solution
and weight= 10X+12y=48y=48*6/5.6 which is closest to 48 kg


@chandrakant.k

Starting off with an easy question
III only

@chandrakant.k

Starting off with an easy question

@chandrakant.k

take ths for example.. 472+559 = 1031 all conditions are statisified...



A mixture comprises two chemicals A and B. The price of A is Rs. 100/- per litre and that of B is Rs.200/- per litre. We can spend a maximum of Rs. 600/- for making the mixture. The densities of A andB are 10 kg/litre and 12 kg/litre respectively. The mixture must contain each of the chemicals to theextent of at least 25% by weight. The maximum weight of the mixture that can be made is closestto:a. 60 kg b. 51 kg c. 54 kg d. 48 kg



closest to 48 kg
100x+200y=600
we have to minimise liq b contents (too costly)
12y/10x=1/3
==> x=3.6y
==>y=6/5.6 for our optimal solution
and weight= 10X+12y=48y=48*6/5.6 which is closest to 48 kg


@hexagon

new difference in interest will be around 397 but variation in interest with repectv to old one should be 397-198.7=198.3 approx. imo