CAT Practice Test: August 25 - CAT MCQ

Total distance travelled = 285 km
Total time taken = 6 hours
Average speed of journey = 285/6 km/h
By alligation method,

Therefore, the ratio of time spent travelling at 40 km/h to that travelling at 55 km/h =
Total time of journey = 6 hours
Therefore,
Time of travel at 55 km/h = 3 hours
Therefore, distance travelled at this speed = 55 × 3 = 165 km
This is our required solution.

Applying the rule of alligation,

Gold : Copper = 6 : 4 = 3 : 2

Gold in the first alloy = 20%
Gold in the second alloy = 40%
By alligation:

Ratio of the two alloys = 2 : 3
Quantity of the second alloy = 100 × 3/2 = 150 gm

Cost price of the mixture = (10 × 40 + 30 × 20) = 1000
Selling price of the mixture = Cost price + (Cost price × 15%)
Selling price of the mixture = 1000 + 
Per kg selling price = = = 28.75

Total amount of milk = 40 litres
Amount of milk replaced by water = 10 litres
Now, ratio of milk to the total mixture = 
Water content in the mixture = 64 - 27 = 37
Hence, ratio of milk to water = 27 : 37

Cost price = ₹ 1000, selling price = 0.9 of 1200 = 1080.

On a marked price of  ₹ 250, a discount of 20% would mean a selling price of ₹ 200. Since this represents a 25% profit we get:
1.25 xCP = 200 → CP = 160.

For ₹ 96, we can buy a dozen pair of gloves. Hence, for  ₹16 we can buy 2 pairs of gloves.

As there is 1 odd day in 1900 years
In 49 years from 1900 to 1949, there are 49 ÷ 4 = 12 leap years and 37 ordinary years. There are (12 × 2 = 24) + 37 = 61 odd days or 5 odd days
From 1st January, 1950 till 26th January, 1950, there are 5 odd days
So, in total there are 0 + 1 + 5 + 5 = 11 odd days or 4 odd days
Hence, From 1st January, 1600 till 26th January, 1950, there are 4 odd days
So 26th January 1950 is Thursday.

The angle between the two hour hands after some time is 90°.
As they both start at 12 o'clock, the hour hand of clock A makes 45° and the hour hand of clock B makes 45° from their initial position.
The hour hand of clock A moved 45° from its initial position. Therefore, number of minutes the hour hand makes is 45 × 2 = 90 minutes
In 90 minutes, the minute hand makes an angle of 90 × 6° = 540°
360° is a complete revolution ⇒ 540° = 360° + 180° from its initial position.
As both hands move 180° in either direction, the minute hands of two clocks coincide i.e. the angle between them is zero degree.

Hour hand:
1 day = 36 hours and the hour hand covers the dial twice every day
So, the dial covers 36/2 = 18 hours in one complete round
One complete angle in the clock dial is 360°.
So, in 1 hour, hour hand moves 360/18 = 20°
So, for 12 hours, hand moves 12 × 20 = 240°
Also, 1 hour = 90 minutes
Now, for 1 minute, hour hand moves (20/90)°
Thus, for 18 minutes, it moves 20/90 × 18 = 4°
So, for 12:18 am, hour hand moves = 240 + 4 = 244°
Minute hand:
Now, minute hand moves 90 minutes to complete one hour.
Thus, for 1 minute, it moves 360/90 = 4°
For 18 minutes, it moves 4 × 18 = 72°
So, the angle between hour hand and minute hand at 12.18 am is 244 - 72 = 172°

As 320th day of the Nth year and 206th day of the N + 1th year are same days i.e. Thursday, there must be 0 odd days between these 2 days (The number of days between these 2 days must be divisible by 7).
If Nth year is a non-leap year, the number of days between 2 days = (365 - 320) + 206 = 251 days
Here, number of odd days in 251 days is 6.
So, we can say that it is not an ordinary year.
If Nth year is a leap year, then number of days between 2 days
⇒ (366 - 320) + 206 = 252 days
Number of odd days in 252 days is 0.
So, we can say that Nth year is a leap year.
To find the 168th day of the year N - 1, we have to find the number of odd days between 320th day of Nth year and 168th day of N - 1th year.
⇒ (365 - 168) + 320
⇒ 517 days
The number of odd days in 517 ⇒ 6 odd days
The 168th day of N - 1 year is a Thursday - 6 = Friday

 Please note that the more relevant thing in this case is not the number of strikes, but the number of time intervals. In other words, if a clock has to strike 4, there are three time intervals between the 4 strikes (this is so taken because the first strike happens at the 0th second). So in 7 seconds, the pendulum elapses three time intervals. To strike 11, there has to be 10 time intervals, which will take = 23.33 seconds.

From 3:00 p.m. today to 9:00 p.m. the next day, there are a total of 30 hours of faster clock.
In a day (i.e. in 24 × 60 = 1440 minutes), the slow watch will show 1437 minutes and the faster will show 1444 minutes.
The faster is showing 1444 minutes and the slower will show 1437 minutes.
If the faster is showing 30 hours, the slower will show 
Thus, the slow clock will show = 8 

Draw a figure as per given instruction in the question. We can see that according to graph he is facing East.

Draw a figure as per given instruction in the question. We can see that according to graph It is clear from the diagram that the man is towards south from the starting point.

Draw a figure as per given instruction in the question. We can see that according to graph It is clear from the diagram that Ashok was in South direction from the starting point.

Draw a figure as per given instruction in the question. We can see that according to graph he is now in north direction.

Draw a figure as per given instruction in the question. We can see that according to graph It is clear from the diagram that now they are going towards North–East.

The word Accrue (Verb) means: to increase over a period of time; to allow a sum of money or debts to grow over a period of time. Therefore grow in the correct mearest word.

The word Vindictive (Adjective) means : trying to harm or upset somebody or showing that you want to, because you think that they have harmed you; spiteful; revengeful. Option (c) spiteful is the correct synonym as it means-having or showing a desire to harm, anger or defeat someone.

The word Barren (Adjective) means: not good enough for plants to grow on it; infertile unproductive.

The word Ostracise (Verb) means: to refuse to let somebody; a member of a social group: refuse, shun. Hence the words banish and ostracise are synonymous.

The word Trite (Adjective) means: dull and boring because it has been expressed so many times before; not original; banal; very ordinary and containing nothing that is interesting or important. Hence, the words trite and commonplace are synonymous.

Endow is to provide with something desirable.

Incisive is sharp or quick to understand.

Engender is to cause or create.

Obviate is to make something unnecessary, hence include is the closest antonym.

As we know that ,
Penchant is a natural inclination towards something, lone means only, alone, single.
Therefore , Disinclination is opposite of Penchant word .