- Question
70% of the students in a school play football, 75% play cricket, 80% play basketball and 85% play carrom. The minimum percentage of students who play all four games is:
a)10
b)20
c)66.66
d)15
e)33.33
Explanation
SOLUTION[ A ] 10
Let ‘100x’ be the number of students who joined XCRI last year.
Let ‘a’, ‘b’, ‘c’ and d be the number of students who play 1 game, 2 games, 3 games and 4 games respectively.
Therefore,
a + b + c + d = 100x 1)
a + 2b + 3c + 4d = 70x + 75x + 80x + 85x
a + 2b + 3c + 4d = 310x 2)
By equation (2) – (1)
b + 2c + 3d = 210x
We have to minimize ‘d’ for that we have to maximize c. But c < 100x
At Cmax = 90x, dmin = 10x
Therefore, we can say that the minimum percentage of students who play all four games = 10%.
Question-2
If India celebrated its Republic Day on a Thursday in the year 1989, then on which day of the week, would the Indians be celebrating their Independence Day in the year 1993?
a)Tuesday
b)Friday
c)Monday
d)Sunday
e)Thursday
Explanation
SOLUTION[D] -SUNDAY
Question-3
At any point of time, let x be the smaller of the two angles made by the hour hand with the minute hand on an analogue clock (in degrees). During the time interval from 2:30 p.m. to 3:00 p.m. Determine, what is the minimum possible value of x in the given case ?
a)90
b)300
c)45
d)180
e)75
Explanation
SOLUTION[A] 90
The difference between the hour and minute hand of a clock is given by |30H – 5.5m| Here H is the current hour and m represents the number of completed minutes in the current hour.
In the given time frame of 2: 30 to 3: 00 pm.
At 2:30 pm the angle = |30 * 2 – 5.5 * 30| = 105 degrees
At 3: 00 pm the angle = |30 * 3 – 5.5 * 0| = 90 degrees
The function of 30H5.5m = constantly increases as the value of m increases from 31, 32. 59.
Because of the modulus function, the net value of the function remains positive
Between 2: 30 to 2: 59 the angle is constantly increasing. The minimum value is 2: 30 which is equal to 105 degrees which is greater than the 90 degrees when the time is 3: 00.
Hence 90 degrees is the minimum angle
Question-4
Two tanks of similar volume are full of a mixture of oil and water. In the first, the ratio of oil and water is 5:8 and in the second, it is
7:19. If both these tanks are poured in a larger tank, what would be the resultant ratio of oil and water?
a)17:53
b)17:35
c)151:304
d)17:52
e)1:3
Explanation
SOLUTION [B] -17:35
Tank I-
Oil/total volume = 5/13 = 10/26
Tank II- Oil/total volume = 7/26
resultant ratio of oil to the total volume = x / 26
x = (10 + 7)/2 = 8.5 We can mark answer here, Numerator must be multiple of 17 and denominator must not be multiple of 13, C)
resultant ratio of oil to the total volume = 8.5/26 = 17/52
the resultant ratio of oil and water = 17 / (52 – 17) = 17/35
Question-5
Two normal dice are thrown on a game board, the face of the two dice show the numbers 3 and 2 respectively. What shall be the total of faces that lie exactly opposite to the face of the dice ?
a)9
b)12
c)6
d)7
e)10
Explanation
SOLUTION[A]9
In a standard six-sided die, the sum of the opposite faces always equals 7. So, if one die shows a 3, then the face opposite to it would be a 4 (since 3 + 4 = 7). Similarly, if the other die shows a 2, then the face opposite to it would be a 5 (since 2 + 5 = 7). Therefore, the total of the faces opposite to the faces showing 3 and 2 would be 4 + 5 = 9.
Question-6
In the country of Four, there are four cities, A, B, C and D.
B is to the East of A, C is to the South of B,
D is to the West of C, and
A is to the North of D.
The Government of Four is planning to connect these four cities by road such that it is possible for a person to go from a city to any of the other three cities. At the same time, the Government wants to ensure that the total road length is minimum.
The distances between A to B, B to C, C to D and D to A are all equal to 10 km.
What should be the total length of the road in kilometres ?
a)30.30
b)28.30
c)29.50
d)25.50
e)26.30
Explanation
SOLUTION[B] 28.30
For the minimum length of the government should be diagonal roads. The length of the road will be the same as the length of a diagonal of a square whose side length is 10 km.
Length of one diagonal= sqrt(2) * 10 = 1.414 * 10 = 14.14 km.
Therefore, the total length of both roads = 2 * 14.14 = 28.30km
