Official Quant thread for CAT 2013

the thread is going so fast today couldn't catch up at all!! Keep it on !👏👏

P and Q are two villages on the bank of a river. Q is 24 km downstream of P. Veeru lives in P, while his friend Chiru lives in Q. Both have clocks at their houses but Veeru's clock runs ahead of Chiru's by a certain constant period. One day Veeru sets off at 5:00 p.m. (by his clock) and reaches Q at 6:00 p.m. (by Chiru's clock). The next morning, he sets off from Q at 6:00 a.m. (by Chiru's clock) and reaches P at 10:00 a.m. (by his own clock). The speed of the current in the river is 2 km/hr.


What is the time shown by Veeru's clock when Chiru's clock shows 6:00 p.m.?

4:00 p.m.

5:00 p.m.

7:00 p.m.

7:30 p.m.


Find the speed (in km/hr) of the boat in still water.

6.5

7.5

8

10

A, B and C run a race. A gives B a head start of y m and C a head start of 2y m. A beats B by y m and C by 2y m. The ratio of the speeds of A and B equals half the ratio of the speeds of B and C. Which of the following can be concluded about the distance that C would have run when A finishes the race?

It is less than y.

It is more than y.

It is equal to y.

None of the above

what is the process one should follow to find out for ex. largest five digit multiple of 72 ?
how to approach this?

Three natural numbers a, b and c are such that a2 + b2 = c2. If a = 20, how many ordered pairs (b, c) are possible?

1

2

3

4


plz post solution for this geometry question

A ball is thrown down on the flat surface from a height of 100 meters. Every time it bounces to a height of 50% of its previous height. Another ball is thrown up from the same flat surface to a height a 100 meters. It comes down and bounces to a height of 40% of its previous height. Find the ratio of distance covered by first and second ball.

India fielded 'n' ( >3) bowlers in a test match, and they operated in pairs. If a particular bowler did not bowl in pair with at least two other bowlers in the team, then at most how many bowlers could have bowled in pair with every other bowler in the team?

What is the effective way of finding remainders when 11111 is divided by 72. Or any multiple of 11111 like 99999/72. Any general concepts for numbers of the kinds 11111 , 1111 , 111 ?

If N = 1223334444..... and is a 100 digit number. find the remainder when N is divided by 16?




  • 11
  • 15
  • 13
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0 voters

solution plz

Q) the coefficient of x^15 in the product (1-x)(1-2x)(1-2^2x)..... (1-2^15x) ???

Options -
a) 2^105 - 2^121
b) 2^121 - 2^105
c) 2^120 - 2^104
d) None of these

Q) the coefficient of x^49 in the product (x-1)(x-3)(x-5)..... (x-99) ???

Options -
a) -99^2
b) 1
c) -2500
d) None of these

Sum of 10th, 20th and 30th terms of an AP is equal to the 58th term, what is the ratio of the sum of the 10th,20th and 30th term to the sum of 5th,10th and 15th terms, when the common difference is not equal to 0 ??

the nth term of an AP is p and mth term of the same AP is q, then (m+n)th term of the AP is :-

a) p+q
b) p+q-a +d
c) p+q-a-d
d) p+q-d+a

F(x) = 2x+1, where x = 1,2,3,4,.... 100
G(x) = 3x-2, where x = 1,2,3,4 .... 100

for how many values of x, F(x) = G(x) ??



find the number of positive integers N
  • 3
  • none of these
  • 34
  • 17
  • 0

0 voters

find the sum:-

1x2 + 2x2 + 3x2^2 + 4x2^3 + ......... 100x2^99 ??

find the sum of the series :-
7+26+63+124 ..... +999 ??

if m times the mth term of an AP is equal to p times the pth term, find (m+p)th term ??