MU-NLPC/Calc-aqua_rat huggingface dataset:
The temperatures in degrees Celsius recorded at a certain specific point in the evening in various parts of a country were 10°, 5°, -2°, -1°, -5°, 15°. What is the median of these temperatures?  Options: A) -2°C B) -1°C C) 2°C D) 3°C E) 5°C

Solution: Explanation:   To get the median first we need to sort the temperatures in ascending order:   -5°, -2°, -1°, 5°, 10°, 15°   When the number of values in a list is even, the median is the average of the middle two values in the list in this case -1 and 5, i.e. 2.   Answer: Option 2°C
Answer: C
10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
Select:
A) 1/8	B) 1/2	C) 1/5	D) 1/5	E) 1/3

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer:1/5
Answer: C
what is the sum of the first 18 odd natural numbers Choose the correct choice from the following: A) 300 B) 400 C) 500 D) 324 E) 700

Solution: sum of first n odd natural nuber is = n^2   so sum of the first 18 odd natural numbers=(18)^2=324   ans 324   ANSWER:324
Answer: D
A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely as the case may be? . Select
A) Emptied; 16 mins B) Filled; 8 mins C) Emptied; 12 mins D) Filled; 12 mins E) None of These

Solution: if A and B open together   since B can empty faster than A so tank will empty not fill.   the whole tank will empty in   16*8/(16-8)= 
  16*8/(16-8) = 16
16 min   since tank is half so it will take only 8 min to empty.   ANSWNone of TheseR:None of These
Answer: E
A person want to give his money of $4500 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?	Choose the correct choice from the following answers: A) $2000 B) $1500 C) $2500 D) $1800 E) $1600

Solution: $1500's share = 4500*3/9= 
4500*3/9 = 1_500
$1500   Answer is $1500
Answer: B
Scott's average (arithmetic mean) golf score on his first four rounds was 38.What score does he need on his fifth round to drop his average score by 2 points?  Choose the correct choice from the following answers
A) 68 B) 28 C) 78 D) 88 E) 312

Solution: Average score for first 4 rounds = 38   Average score after 5 rounds = 36   Score Scott needs on his 5th round to drop average score by 2 points =38 - (2*5)= 
38 - (2*5) = 28
28   Answer 28
Answer: B
Without stoppages a train travels a certain distance with an average speed of 80 km/h and with stoppages with an average speed speed of 60 km/h. How many minutes per hour does the train stops ?	Choose one:
A) 25 min  B) 10 min  C) 18 min  D) 15 min  E) 20 min

Solution: let us assume the distance is x km.   if the train travels 80km/h without stopages then it takes (x/80) hour to rech.   and with stopage it takes (x/60) hour.   let the train stops t min per hour.   then according to the question   (x/80)=(x/60)+(t/60)*(x/60)   then t=15 min.   ANSWER:15 min
Answer: D
4,25,121,289,? Options
A) 345  B) 445  C) 515  D) 529  E) 645

Solution: Prime numbers- 2,3,5,7,11,13,17,19,23.....   Series - 2^2,5^2,11^2,17^2,23^2   Series- 4, 25, 121, 289, 529.   So next term in series is- 529.   ANSWER:529
Answer: D
Half of 7 percent written as decimal is Choose the most appropriate option
A) 5	B) 0.5	C) 0.025	D) 0.035	E) None of these

Solution: Explanation:   It will be 1/2(7%) = 1/2(7/100) = 7/200= 
7/200 = 7/200 = around 0.035
0.035   Option 0.035
Answer: D
There are 6 red balls and 4 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that all 3 balls selected are blue balls? Pick:
A) 1/18
B) 1/24
C) 1/30
D) 1/36
E) 1/48

Solution: The number of ways of choosing 3 balls from the jar is 10C3 = 120.   The number of ways of choosing 3 blue balls is 4C3 = 4.   P(3 blue balls) = 4/120=1/30.   The answer is 1/30.
Answer: C
The sum of money will be double itself in 20years and simple interest find rate of interest? Choose the most appropriate option
A) 10%  B) 5%  C) 15%  D) 20%  E) 25%

Solution: T = 20 years   P= principle amount = x   A = total amount = 2x   SI = simple interest = A-P = 2x-x = x   R = 100SI/PT = 100x/20x =5%   Answer is 5%100 /20= 
100 /20 = 5
5%   Answer is 5%
Answer: B
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? Select the correct option.
A) 2.98 B) 2.88 C) 2.82 D) 2.86 E) 2.81

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer: 2.88
Answer: B
P, Q and R have Rs.4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Select.
A) Rs.3000	B) Rs.1600	C) Rs.2400	D) Rs.4000	E) None of these

Solution: Let the amount with R be Rs.r   r = 2/3 (total amount with P and Q)   r = 2/3(4000 - r) => 3r = 8000 - 2r   => 5r = 8000 => r = 1600.   ANSWER:Rs.1600
Answer: B
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.9, what is the probability that Malachi will return home at the end of the day on the following Monday? Choose the correct choice:
A) 0.009
B) 0.128
C) 0.488
D) 0.512
E) 0.64

Solution: Re-phrasing the question:   What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain   Probablity of rain = 0.9   Therefore, probability of no rain = 0.1   0.1*0.1*0.9= 
0.1*0.1*0.9 = 0.009
0.009   Hence 0.009
Answer: A
What is the value of 3x^2 − 1.6x + 0.3 for x = 0.8?	Choose the most appropriate option
A) −0.3	B) 0	C) 0.3	D) 0.94	E) 2.46

Solution: 3x^2-1.6x+0.3 for x=0.6   =3(0.8*0.8)-2*0.8*(0.8)+0.3   =0.8*0.8+0.3= 
0.8*0.8+0.3 = 0.94
0.94   Correct Option : 0.94
Answer: D
A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?  Choose the correct choice from the following answers:  A) 1/20  B) 1/6  C) 1/11  D) 4/21  E) 5/21

Solution: series : a1, a2....a20,n   sum of a1+a2+...+a20 = 20*x (x = average)   so, n = 2*x   Hence, a1+a2+..+a20+n = 22x   So, the fraction asked = 2x/22x = 1/11   Answer 1/11
Answer: C
A = {2, 3, 5, 7, 19}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Choose the correct choice from the following choices:
A) 32  B) 16  C) 19  D) 20  E) 36

Solution: Step 1: Find out the number of products you get.   5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4= 
5*4 = 20
20   Step 2: Remove the products that appear more than once.   Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.   2, 3   2, 4, 6   The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.   Answer= 20 - 1 = 32   Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.   32
Answer: A
A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 700 . He sold both the items together for Rs. 3500. What percentage of profit did he make? Pick one:
A) 20.12%
B) 96.21%
C) 52.17%
D) 75.01%
E) 23.00%

Solution: The total CP = Rs. 1600 + Rs. 700   = Rs. 2300 and SP = Rs. 3500   Profit(%)   = (3500 - 2300)/2300 * 100   = 52.17%   Answer: 52.17%
Answer: C
Find three consecutive odd integers so that the sum of twice the first, the second
and three times the third is 152.
Choose one
A) 20,23,25	B) 23,25,27	C) 25,28,31	D) 30,33,35	E) 29,31,35

Solution: First x Make the first x   Second x+2 Odd numbers sowe add 2(same as even!)   Third x+4 Add 2more (4 total) to get the third   2F +S +3T =152 Twicethefirstgives2F andthree times thethirdgives3T   2(x)+(x+2)+3(x+4)=152 Replace F , S, and T withwhatwe labled them   2x+x+2+3x+12=152 Distirbute through parenthesis   6x+14=152 Combine like terms 2x+x+3x and 2+14   −14 −14 Subtract 14 fromboth sides   6x=138 Variable ismultiplied by 6   6 6 Divide both sides by 6   x=23 Our solution for x   First 23 Replace xwith 23 in the original list   Second  (23)+2= 
 (23)+2 = 25
25 The numbers are 23, 25, and 27   Third (23)+4= 
(23)+4 = 27
27   correct answer 23,25,27
Answer: B
A girl borrows 65000 for 5 years at 5% p.a. simple interest. she immediately lends it to another person at 9 % p.a. for 5 years. Find her gain in the transaction per year. Choose the correct choice from the following options.
A) 2600 B) 2500 C) 2550 D) 2650 E) 3600

Solution: Gain in 5 years   = [(65000Ã—9Ã—5/100)âˆ’(65000Ã—5Ã—5/100)]   = (29250 â€“ 16250) = 13000.   âˆ´ Gain in 1 year = (13000â„5) = 2600   2600nswer 2600
Answer: A
A man walks from B to C, a distance of x miles, at 15 miles per hour and returns at 12 miles per hour. What is his average speed?
Choose the correct choice from the following options:
A) 10 mph
B) 13 mph
C) 12 mph
D) 13.3 mph
E) 14 mph

Solution: Total distance covered = 2x   Time taken12miles / hour = x/12 hrs   Time taken @ 15 miles / hour = x/10 hrs   Avg speed = 2x / (x/15 + x/12) = 13.3 mph   Ans is 13.3 mph
Answer: D
The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds? Pick one.
A) 4
B) 9
C) 15
D) 48
E) 33

Solution: Given: z=s^2+2s for 0≤s≤7   z(3) = 3^2 + 2*3 = 15   z(6) = 6^2 + 2*6 = 48   Therefore z(7) - z(3) = 48 - 15= 
48 - 15 = 33
33 km/hr   Option 33
Answer: E
Johnny borrows $30,000 from Tony at 2% daily interest compounded daily. How much does Johnny owe Tony after 8 weeks? Pick.
A) 30000*0.02^56	B) 30000*1.12	C) 30000*2.12	D) 30000*1.02^56	E) (30000*1.02)^56

Solution: A=A= P(1+r100)^n   So, A=30000(1+2/100)^7∗8   So, A=A= 30000(1.02)^56   Hence answer will be (30000*1.02^56)
Answer: D
A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ? Options
A) 150 m
B) 200 m
C) 125 m
D) 115 m
E) None

Solution: 150 mnswer   ∵ 8 m shadow means original height = 12 m   ∴ 1 m shadow means original height = 12/8 m   ∴ 100 m shadow means original height = (12/8) x 100 m   = (6/4) x 100 = 6 x 25 = 150 m   Correct Option: 150 m
Answer: A
At what rate percent per annum will a sum of money double in 16years?
Choices:
A) 10.6%	B) 3.65%	C) 6.25%	D) 8.32%	E) 11%

Solution: Let principle = P   S.I. = P   T = 16yrs   Rate = 100*P/P*16 = 25/4= 
25/4 = 25/4 = around 6.25
6.25%   Answer is 6.25%
Answer: C
The organizers of a week-long fair have hired exactly six security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?  Choose the correct option
A) 7	B) 6	C) 5	D) 3	E) 2

Solution: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 4 guards.   To choose 2 out of 4, we will have 4C2 = 6 different pairs.   The answer is 6.
Answer: B
The sum of even numbers between 1 and 31 is:  Choose the correct choice from the following
A) 240
B) 789
C) 520
D) 879
E) 456

Solution: Explanation:   Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30   Let the number of terms be n. Then   a + (n - 1)d = 30   =>2 + (n - 1) x 2 = 30   n = 15.   Sn =	n/2(a + l)=15/2	x(2 + 30) = (15 x 16) = 240.   240NSWER:240
Answer: A
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length W of a cube whose surface area is equal to 6z?	Choose the correct choice from the following options.
A) W=16  B) W=8√2  C) W=8  D) W=2√2  E) (√2)/3

Solution: 800 score Official Solution:   The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.   The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (W=2√2).
Answer: D
In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?	Choose the correct option
A) 1/20  B) 1/10  C) 1/5  D) 2/5  E) 3/4

Solution: In this corporation, there are 400 total employees. There are 100 women. Of the 300 men, 20% have advanced degrees —-10% of 300 must be 30, so 20% of 300 must be 60. Add the women and the men with advanced degrees:   100 + 60= 
  100 + 60 = 160
160. This is the OR region, full set of individuals that satisfy the condition “has an advanced degree or is female.” Of the 400 employees, what’s the probability of picking one of the 160 in this particular group?   P= 160/400 = 16/40 = 4/10 = 2/5   Answer = 2/5
Answer: D
The ratio between the speeds of two trains is 5: 7. If the second train runs 840 kms in 6 hours, then the speed of the first train is ?  Pick one: A) 90 km/hr B) 120 km/hr C) 100 km/hr D) 110 km/hr E) None of these

Solution: Explanation:   Let the speeds of two trains be 5X and 7X km/hr.   7/X=840/6=>X=20Km/hr   So speed of first train is   20*5= 
  20*5 = 100
100 km/hr   Option 100 km/hr
Answer: C
A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
Choices.
A) 100 B) 114 C) 126 D) 154 E) 157

Solution: There are 8 students and the maximum capacity of the cars together is 9.   We may divide the 8 students as follows   Case I: 5 students in the first car and 3 in the second   Or Case II: 4 students in the first car and 4 in the second   Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.   Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.   Therefore, the total number of ways in which 8 students can travel is:   \inline {\color{Blue}8126_{3}+8126_{4}}=56 + 70= 
56 + 70 = 126
126   126
Answer: C
Excluding the stoppages, the speed of a bus is 32 km/hr and including the stoppages the speed of the bus is 16 km/hr. For how many minutes does the bus stop per hour? Choose the correct option:  A) 15 min  B) 10 min  C) 12 min  D) 30 min  E) 18 min

Solution: Speed of the bus without stoppage=32 km/hr   Speed of the bus with stoppage=16km/hr   30 minifference in speed=16 km/hr   so,the time taken in the stoppages = time taken to cover 16 km=(16/32)hr = 1/2 hr =30 min   ANSWER:30 min
Answer: D
From the given equation find the value of c: cÂ²-3c-10
Select: A) 1 B) 3 C) 5 D) 2 E) -5

Solution: (c - 5)(c + 2)   5 = -2 or 5   Answer is 5
Answer: C
Walking at 5/6th of its usual speed a cab is 5mnts late. Find its usual time to cover the journey? Choose the most appropriate option:
A) 25m
B) 45m
C) 32m
D) 50m
E) 62m

Solution: New speed = 5/6th of usual speed   New time = 6/5th of usual time   6/5 UT - UT = 5m   UT/5 = 5m   UT = 25m   25mnswer is 25m
Answer: A
A fair coin is tossed repeatedly. If heads appears on first 6 tosses what is the probability that tail appears on the next two tosses?  Choices.
A) 1/6 B) 1/5 C) 1/3 D) 1/4 E) 1/6

Solution: Explanation :   Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.   1/2 * 1/2 = 1/4   Answer : 1/4
Answer: D
A and B go around a circular track of length 600 m on a cycle at speeds of 18 kmph and 48 kmph. After how much time will they meet for the first time at the starting point?
Choose the correct choice from the following answers
A) 120 sec  B) 176 sec  C) 360 sec  D) 187 sec  E) 189 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 600/ (18 * 5/18) , 600/ (48 * 5 /18) }   = 360 sec.   Answer: 360 sec
Answer: C
If 6 and 8 are factors of 60n, what is the minimum value of n?  Pick one
A) 2
B) 4
C) 7
D) 14
E) 56

Solution: 60n/6*8 should be integer => 2*2*3*5*n/2*3*2*2*2 = 5*n/4 must be an integer   for this to be true n must multiple of 4, thus min of n = 4   hence 4
Answer: B
How many 3-digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number?  Choose the correct option
A) 16 B) 120 C) 160 D) 180 E) 240

Solution: prime digits 2,3,5 and 7.   three digit numbers _ _ _   1st place can be filled in 4 ways   2nd place can be filled in 10 ways   3rd place can be filled in 3 ways   Total=4*10*3= 
4*10*3 = 120
120   Ans : 120
Answer: B
There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'S', then how many triangles can be determined with the 15 points that contain the point S?  Choose the correct answer
A) 91  B) 105  C) 182  D) 210  E) 455

Solution: Fist point is S which is fixed so can be selected in 1 way   Second point can be selected in 14 ways   Third point can be selected in 13 ways   so total ways = 1x14x13 = 182   but answer is 91 which is 182/2=182
Answer: C
If a:b=5:6 and b:c=2:3 find a:b:c?
Choices:
A) 6:5:9
B) 5:9:3
C) 9:5:6
D) 5:9:6
E) 5:6:9

Solution: a:b = 5:6, b:c = 2:3   5:6   2:3   (a = a × b, b = b × b and c = b × c)   a:b:c = 5:6:9   5:6:9
Answer: E
A train running at the speed of 50 km/hr crosses a post in 4 seconds. What is the length of the train? Select the correct option
A) 90 B) 120 C) 60 D) 95 E) 75

Solution: Speed=(54x5/18)=15 m/sec.   Length of the train=(Speed x Time).   Length of the train=15x4m=60m.   Answer: 60
Answer: C
A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?	Choose the most appropriate option.
A) 8 days B) 10 days C) 15 days D) 11 3/7 days E) None of these

Solution: Explanation:   (x â€“ 5)/15 + x/20 = 1   x = 11 3/7 days   ANSWER IS 11 3/7 days
Answer: D
If log 2 = 0.30103, the number of digits in 520 is  Choose the correct choice from the following answers:
A) 14 B) 16 C) 18 D) 25 E) 26

Solution: Solution   Log 520	=20 log 5   =20 ×[log(10/2)]   =20 (log 10 - log 2)   =20 (1 - 0.3010)   =20×0.6990   =13.9800.   Characteristics	= 13.   Hence, the number of digits in Log 5(20) is 14.   14nswer 14
Answer: A
60 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? Choose the correct choice from the following choices:
A) 80 litres  B) 90 litres  C) 120 litres  D) 170 litres  E) None of these

Solution: Explanatory Answer   To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*60= 
800/600*60 = 80
80 litres.   However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.   i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.   Therefore, with a 1200 cc engine, quantity of diesel required= 1200/800*80= 
1200/800*80 = 120
120 litres.   Answer 120 litres
Answer: C
What should be the least number to be added to the 3198 number to make it divisible by 8?	Choose the correct option
A) 12 B) 17 C) 2 D) 77 E) 26

Solution: Answer : 2   Option : 2
Answer: C
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 292 runs?	Choose the correct choice:
A) 6.5  B) 6.22  C) 6.29  D) 6.39  E) 6.13

Solution: Required run rate   = [292 - (3.2 * 10)]/40   = 260/40= 
260/40 = 13/2 = around 6.5
6.5   6.5nswer: 6.5
Answer: A
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: Choose the correct choice from the following answers
A) Rs. 650	B) Rs. 690	C) Rs. 698	D) Rs. 700	E) Rs. 740

Solution: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.   S.I. for 3 years = Rs.(39 x 3) = Rs. 117.   Principal = Rs. (815 - 117) = Rs. 698.   Answer: Option Rs. 698
Answer: C
In how many years will a sum of money doubles itself at 25% per annum on simple interest?
Choose the correct choice from the following options:
A) 4%  B) 8%  C) 10%  D) 12%  E) 15%

Solution: P = (P*25*R)/100   R = 4%   4%nswer:4%
Answer: A
Entry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is :  Choose the correct option.
A) 33 B) 37 C) 60 D) 28 E) 27

Solution: Explanation:   Let the total original sale be Rs. 100. Then, original number of visitors = 100.   New number of visitors = 120/0.75= 
120/0.75 = 160
160.   Increase %= 60 %.   Answer: 60) 60 %
Answer: C
If 8 persons can do 8 times of a particular work in 8 days, then, 9 persons can do 9 times of that work in?	Options
A) 3 days
B) 4 days
C) 6 days
D) 7 days
E) 8 days

Solution: That is, 1 person can do one time of the work in 8 days.   Therefore, 9 persons can do 9 times work in the same 8 days itself   8 days)
Answer: E
Consider two statements
Statement 1 => If R is an integer and R=2p+1 where p is not an integer.
Statement 2 => If S is an integer and S=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of R and S respectively
Select: A) 1) Odd,Even B) 2) Odd,Odd C) 3) Even,Odd D) 4) Even,Even E) 5) Cannot be determined

Solution: answer will be 5) Cannot be determined   R = integer   R = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out   if n were even R would odd   if n odd R would be even   ANSW5) Cannot be determinedR IS 5) Cannot be determined
Answer: E
A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?	Pick one
A) 1/4
B) 1/5
C) 2/5
D) 3/5
E) 3/7

Solution: Let E be the event that ‘number 4 appears at least once’ and F be   the event   that ‘the sum of the numbers appearing is 6’.   Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),   (5,4), (6,4)}   and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}   We have P(E) = 11/36   and P (F) = 5/36   Also EnF = {(2,4), (4,2)}   Therefore P(EnF) = 2/36   the required probability   P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.   2/5)
Answer: C
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -  Pick:
A) 8/13 B) 6/13 C) 3/13 D) 4/13 E) 1/13

Solution: Explanation:   P(Sá´œK) = P(S) + P(K) - P(Sâˆ©K), where S denotes spade and K denotes king.   P(Sá´œK) = 13/52 + 4/52 - 1/52 = 4/13   Answer: 4/13
Answer: D