Official Quant thread for CAT 2013

Consider the increasing sequence 1, 3, 4, 9, 10, 12, 13… and so on. The sequence consists of all those positive integers which are powers of 3 or sum of distinct powers of 3.

Find the 100th term of the sequence.

  • 932
  • 978
  • 981
  • 987
  • NOT

0 voters

In the following diagram, the length of diameter AB is a two digit integer. Reversing the digits of length of AB gives the length of perpendicular chord CD. The distance of their intersection point H to the center O is a positive rational number.

Determine the length OH.


  • CBD
  • 13.5
  • 15.5
  • 16.5

0 voters

The first 23 natural numbers are written in increasing order beside each other to form a single

number. What is the remainder when this number is divided by 18?
a)1
b)6
c)12
d)15

I am getting remainder 11 which is not in the option :(:(


two men and a woman are entrusted with a task. the second man needs 3 hours more to cope with the job than the 2nd man and the woman would need working together. the 1st man, working alone, would need as much time as the second man and the woman working together. the 1st man working alone, would spend 8hrs less than the double period of time the 2nd man would spend working alone. how much time would the two men and the woman need to complete the task if they all worked together?(A)1hr(B)3hrs(C)4hrs(D)5hrs


Can someone explain how to solve it.

what would be the remainder if 9876543298765432......80 terms is divided by 17 ?

options
a)3
b)0
c)4
d)5
e)2

approach please

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hello friends 2day i call 2 ibps for conforming that po 2 waiting list will come or not then reply that it will not come. ie koi waiting list nahi ayegi. it is conformed by them😠😠

@jasneetdua

In how many ways can two numbers be chosen from X such that sum of their squares are divisible by 9?

where X is a set of consecutive natural numbers from 1 to 20. Please exlain



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In trapezium ABCD, AB||CD and AB : CD = 1 : 2. AC and BD intersect at O. P and Q are mid points of AD and BC respectively such that PQ intersects BD and AC at M and N respectively. Given that area(MON) = 1, find area(ABCD).


A. 20 B. 36 C. 48 D. data insufficient

If the eight digit number 5668x25y is divisible by 48, find out the least value of x+y???? please solve completely

The roots of x^3-4x^2+x+6=o nd x^3 -3x^2-4x+k= o thn vch is value of k . If they have comn roots


@DieHard12 @jasneetdua sol. for trapezium prob. :drinking:

A car overtakes a bus traveling from Bangalore to Chennai at 6:30 a.m. The car reaches Chennai at 8 a.m. After stopping there for 1 hour, it starts back towards Bangalore and meets the same bus at 9:30 a.m., which was moving towards Chennai at that time. If both the car and the bus were traveling at uniform speeds on the same route, then what will be the time when the bus would reach Chennai?

Three milkmen Ramu, Kamu and Namu had 5L, 10L and 15L of milk-water solution respectively. In the solution that Kamu and Namu had, the ratio of milk and water were 2 : 3 and 1 : 4 respectively. All of them sat together and mixed their respective solutions together. They sold the combined mixture at Rs. 20 per liter and Ramu got Rs. 2.5 for every liter of mixture sold. What was the milk-water ratio in the solution that Ramu had with him? (Assume water comes free of cost and they share the revenue earned in the ratio of milk content

In a trapezium whose parallel sides have length 2 and 4 units, a circle is inscribed which touches all the four side lengths of trapezium. Find the diameter of the circle.


A. 3 B. 2√3 C. 2√2 D. data insufficient

P-A-B and P-C-D are two secants of a circle meeting the circle at four distinct points A B, C and D. Given that area(PAC) = 4 and area(ABCD) = 5,


find the ratio AC : BD.


A. 2 : 3 B. 4 : 5 C. 4 : 9 D. None of these

How long is the side of the largest equilateral triangle that can be inscribed in a square whose side has length 1 unit ?

Post approach as well 😃

options :

1
root(5)/2
3*root(5)/4
2-root(3)
root[8-4*root(3)]

How many real n's are there such that n! is a perfect square?

What is the highest power of 3 in 87! – 60!?

How many natural numbers N less than 100 satisfy the condition that the sum of the natural numbers from 1 to N is divisible by 15?

20

25

30

26