A) 32 rolls | B) 54 rolls |

C) 108 rolls | D) 120 rolls |

Explanation:

Number of cuts made to cut a roll into 10 pieces = 9.

Therefore, Required number of rolls = (45 x 24)/9 = 120.

A) 2414 | B) 204 |

C) 87 | D) 8 |

Explanation:

Suppose there are 9 balls

Let us give name to each ball B1 B2 B3 B4 B5 B6 B7 B8 B9

Now we will divide all the balls into 3 groups.

Group1 - B1 B2 B3

Group2 - B4 B5 B6

Group3 - B7 B8 B9

Step1 - Now weigh any two groups. Let's assume we choose Group1 on left side of the scale and Group2 on the right side.

So now when we weigh these two groups we can get 3 outcomes.

Weighing scale tilts on left - Group1 has a heavy ball.

Weighing scale tilts on right - Group2 has a heavy ball.

Weighing scale remains balanced - Group3 has a heavy ball.

Lets assume we got the outcome as 3. i.e Group 3 has a heavy ball.

Step2 - Now weigh any two balls from Group3. Lets assume we keep B7 on left side of the scale and B8 on right side.

So now when we weigh these two balls we can get 3 outcomes.

Weighing scale tilts on left - B7 is the heavy ball.

Weighing scale tilts on right - B8 is the heavy ball.

Weighing scale remains balanced - B9 is the heavy ball.

The conclusion we get from this Problem is that each time weigh. We element 2/3 of the balls.

As we came to conclusion that Group3 has the heavy ball from Step1, we remove 6 balls from the equation i.e (2/3) of 9.

Simillarly we do the ame thing for the Step2.

Now going with this conclusion. We have 6561 balls.

Step - 1

Divided into 3 groups

Group1 - 2187Balls

Group2 - 2187Balls

Group3 - 2187Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 2

Divided into 3 groups

Group1 - 729Balls

Group2 - 729Balls

Group3 - 729Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 3

Divided into 3 groups

Group1 - 243Balls

Group2 - 243Balls

Group3 - 243Balls

Taking the similar steps as we did in the above example, we come to the conclusion that Group1 has the heavy ball.

Step - 4

Divided into 3 groups

Group1 - 81Balls

Group2 - 81Balls

Group3 - 81Balls

Step - 5

Divided into 3 groups

Group1 - 27Balls

Group2 - 27Balls

Group3 - 27Balls

Step - 6

Divided into 3 groups

Group1 - 9Balls

Group2 - 9Balls

Group3 - 9Balls

Step - 7

Divided into 3 groups

Group1 - 3Balls

Group2 - 3Balls

Group3 - 3Balls

Step - 8

So now when we weigh 2 balls out of 3 we can get 3 outcomes.

Weighing scale tilts on left - left side placed is the heavy ball.

Weighing scale tilts on right - right side placed is the heavy ball.

Weighing scale remains balanced - remaining ball is the heavy ball.

So the general answer to this question is, it is always multiple of 3 steps.

For 9 balls = 9. therefore 2 steps

For 6561 balls = 6561 therefore 8 steps

A) 17 & 9 | B) 9 & 11 |

C) 9 & 9 | D) 11 & 9 |

Explanation:

Let the number of apples in each tree of the 5 farmers be a, b, c, d,e respectively. Therefore total no of apples are 7a, 9b, 11c, 13d and 14e respectively.

Given,

7a+1 = 9b+3 = 11c-1 = 13d+3 = 14e-6 = x

9b+3 = 13d+3

===> 9b = 13d

so take b = 13 and d = 9

9b+3 = 9*13+3 = 120

ie, x=120

substituting

7a+1 = 120

7a = 119

a = 17

11c-1 = 120

11c = 121

c=11

14e-6 = 120

14e = 126

e = 9

Yields per tree in the orchards of d 3rd & 4th farmers= 11,9

A) 29 min | B) 25 min |

C) 54 min | D) 57 min |

Explanation:

If virus is K in 1hr i.e 60 min

then in 57 min it was K/2 as it doubles every 3 minutes

=> In 54 min it was K/4.

At 54 minutes it was K/4.

A) -3 | B) -2 |

C) 0 | D) 1 |

Explanation:

We know that in A.P series

18th term = a + 17d

29th term = a + 28d

But given

a + 17d = 29..........(i)

a + 28d = 18......... (ii)

Solving equation (i) and (ii), we get

d = -1

put d = -1 in any of the above equations and we get,

a = 46

Now, we know 49th term can be written as, a + 48d

putting the value of a and d in the above equation,

a + 48d = 46 + 48(-1)

= 46 - 48

= -2

Hence, the 49th term is -2.

A) 8 hrs | B) 7 hrs 15 min |

C) 7 hrs 30 min | D) 8 hrs 20 min |

Explanation:

Total number of cards = 1500

total columns = 45

so, total punches=1500 x 45 = 67500

for 1 hour if we make 9000 punches,

we require 67500/9000 = 7.5

so 7hours:30mins.