MU-NLPC/Calc-aqua_rat huggingface dataset:
A container contains 1000 liters of milk, From this container 10 liters of milk was taken out and replaced by water. This process was repeated further 2 times. How much milk is now contained by the container?  Choose the correct choice:  A) 970.3liters  B) 1000.45liters  C) 879.65liters  D) 1020.56liters  E) 910.95liters

Solution: 970.3litersmount of milk left after 3 operations = 1000 (1 - 10/1000)^3 = 1000 * 99/100 * 99/100 * 99/100 = 970.3 liters   970.3litersnswer is 970.3liters
Answer: A
What is the two-digit number?
I. Sum of the digits is 7.
II. Difference between the number and the number obtained by interchanging the digits is 9.
III. Digit in the ten's place is bigger than the digit in the unit's place by 1.	Choices:
A) I and II only  B) II and III only  C) I and III only  D) All I, II and III  E) I and II as well as I and III

Solution: Let the tens and units digit be x and y respectively.   I. x + y = 7.   II. (10x + y) - (10y + x) = 9 x - y = 1.   III. x - y = 1.   Thus, I and II as well as I and III give the answer.   Answer: Option E   Explanation:   Let the tens and units digit be x and y respectively.   I. x + y = 7.   II. (10x + y) - (10y + x) = 9 x - y = 1.   III. x - y = 1.   Thus, I and II as well as I and III give the answer.   Correct answer is (E).   ANSWI and II as well as I and IIIR I and II as well as I and III I and II as well as I and III
Answer: E
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by two when k is any of the following values EXCEPT Choices
A) -1
B) -2
C) -1
D) 2
E) 5

Solution: We have the product of 3 integers: (x-1)x(x-k).   Note that the product of 3 integers is divisible by 2 if at least one multiple is divisible by 2. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 2 these numbers must have different remainders upon division by 2, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 2.   Next, if k=-1 then we'll have (x-1)x(x+1)=(x-1)x(x+1) --> which means that (x-1) and (x+1) will have the same remainder upon division by 2. Thus for k=-1 we won't be sure whether (x-1)x(x-k) is divisible by 2.   -1nswer: -1.
Answer: A
How many three digits number can be formed by using the digits 4,5,6,7,8,9 if the repetition of digits not allowed?	Choose the correct choice from the following choices
A) 80 B) 70 C) 60 D) 40 E) 30

Solution: For a number to be odd we must have 5,7 or 9 at the unit place. So there 3 ways of filling the unit place. Since the repetion of digits is not allowed, the tenths place can be filled with any of the remaining 5 digits in 5 ways. Now hundreds place can be filled in 4 ways by the remaining 4 numbers. So the required number of numbers is 3x5x4 =60 Answer : 60
Answer: C
Grace has 20 jellybeans in her pocket. She has 12 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Pick.
A) 4	B) 8	C) 12	D) 13	E) 17

Solution: The worst scenario is when she takes 12 red and 4 green, total of 16 jellybeans, and still doesn't have 3 distinct colors. But the next draw (17th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.   Answer: 17.
Answer: E
What will come in place of the x in the following Number series? 46080, ?, 384, 48, 8, 2, 1
Choose the correct answer: A) 1 B) 3840 C) 5 D) 7 E) 9

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   3840
Answer: B
A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?  Choose the correct choice from the following.
A) 10 days
B) 230 days
C) 50 days
D) 40 days
E) 20 days

Solution: B   30 days   Work done by A in 10 days=10/80=1/8   Remaining work=(1-(1/8))=7/8   Now, work will be done by B in 42 days.   Whole work will be done by 230 days in (42*8/7)= 
(42*8/7) = 48
48 days   Therefore, A's one day's work=1/80   230 days’s one day's work=1/48   (A+230 days)'s one day's work=1/80+1/48=8/240=1/30   Hence, both will finish the work in 30 days.
Answer: B
A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?	Pick
A) 15002 B) 15001 C) 15000 D) 15007 E) 15009

Solution: Principal = (100 * 5400) / (12 * 3) = Rs. 15000.Answer:15000
Answer: C
An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many T ways can the assembly line be arranged? Options
A) 120
B) 240
C) 360
D) 480
E) 720

Solution: C) 360   short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want T=6360!/2 -> 720/2 = 360
Answer: C
6x − 12 = 6y
5y + 5x = 5
Which of the following is the number of solutions to the system of equations shown above? Pick one:
A) More than three  B) Exactly three  C) Exactly two  D) Exactly one  E) None

Solution: 6x − 12 = 6y   => 6x - 6y = 12   => x- y =2 -- 1   5y + 5x = 5   =>x + y = 1 -- 2   From equation 1 and 2 , we get   2x = 3   => x=1.5   y=-0.5   Therefore , the given system will have Exactly one solution   Exactly one
Answer: D
A train starts full of passengers. At the first station, it drops one-third of the passengers and takes 280 more. At the second station, it drops one-half of the new total and takes 12 more. On arriving at the third station, it is found to have 248 passengers. Find the number of passengers in the beginning. Select.
A) 240  B) 248  C) 280  D) 288  E) 290

Solution: Let x be no. of passengers at beginning   At, 1st station is drops 1/3rd so remaining 2/3rd are in train only plus 280 i.e., 2x/3+280   at 2nd stop 1/2 of new total and 12 more i.e., (2x/3+280)/2 + 12 = 248   on solving above equation we get x as 288   ANSWER:288
Answer: D
A and B’s salaries together amount to Rs. 3,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?	Select: A) 2777 B) 2250 C) 2789 D) 2776 E) 2881

Solution: (5/100) A = (15/100) 2250   A = 32250   A + 2250 = 3000   42250 = 3000 => 2250 = 750   A = 2250   Answer 2250
Answer: B
A Man travelled a distance of 60 km in 8 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
Choose one
A) 16 km
B) 14 km
C) 12 km
D) 10 km
E) None of these

Solution: Explanation:   Let the time in which he travelled on foot = x hour   Time for travelling on bicycle = (9 - x) hr   Distance = Speed * Time, and Total distance = 60 km   So,   4x + 8(9-x) = 60   => 4x = 12   => x = 3   So distance traveled on foot = 4(3) = 12 km   Answer: Option 12 km
Answer: C
In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?	Choose the correct choice from the following.
A) 180
B) 200
C) 210
D) 230
E) 240

Solution: 7p3 = 7 × 6 × 5 = 210   210)
Answer: C
Worker A takes 6 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Choose the correct choice from the following answers.
A) 15/4 days B) 40/9 days C) 39/9 days D) 30/9 days E) 60/9 days

Solution: A's one hour work = 1/6.   B's one hour work = 1/10.   (A+B)'s one hour work = 1/6+1/10 = 8/30 = 4/15.   Both 15/4 days & B can finish the work in 15/4 days   15/4 days
Answer: A
Today is Monday. After 50 days, it will be :	Options.
A) Thursday B) Saturday C) Tuesday D) Sunday E) Wednesday

Solution: Each day of the week is repeated after 7 days.   So, after 49 days, it will be Monday.   After 50 days, it will be Tuesday   Answer is Tuesday
Answer: C
12 is 4% of a, and 4 is 12% of b. c equals b/a. What is the value of c?  Select the correct option
A) 1/2  B) 1/3  C) 1/6  D) 1/9  E) 1/12

Solution: 4a/100 = 12   a = 300   12b/100 = 4   b = 100/3   c = b/a = 100 / (3*300) = 1/9   The answer is 1/9.
Answer: D
By selling a bat for Rs.540/- a man loses 10% what is that bat cost price Pick:
A) s.600/-  B) s.630/-  C) s.700/-  D) s.780/-  E) s.800/-

Solution: 90 % ------> 540 (90 * 6 = 540)   100 % ------>600 (100 * 6 = 600)   Cost price = Rs.600/-   s.600/-)
Answer: A
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 7, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation: Select:  A) 5  B) 7  C) 9  D) 1  E) 11

Solution: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.   (2x + 2) + 2x + x = 7   5x = 5   x = 1.   Hence, B's age = 2x = 1 years.   Answer: Option 1
Answer: D
Find the probability that the number drawn is a factor of 50.  Choose the correct choice from the following:
A) 1/25 B) 1/50 C) 3/25 D) 3/50 E) 7/50

Solution: The factors of 50 are 1, 2, 5, 10, 25, 50   Therefore, required probability = 6/100 = 3/50.   ANSWER:3/50
Answer: D
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? Select:  A) 600  B) 887  C) 256  D) 654  E) 712

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer: 600
Answer: A
A circular road runs around a circular garden. If the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one-third of the outer circle, then the width of the road is :  Choose the correct option
A) 4 metres	B) 5 metres	C) 7 metres	D) 6 metres	E) 8 metres

Solution: let radius of inner circle=r1   radius of outer circle=r2   Also r1=1/3*r2   3*r1=r2   circumference of inner circle=2*pi*r1   circumference of outer circle=2*pi*r2   2*  * 1= 
2*  * 1 = 2
2*pi*r2=6*pi*r1 (since r2=3*r1)   2*pi*r1 + 6*pi*r1 =88 (as per question)   r1=3.5 m   r2=3*3.5= 
3*3.5 = 10.5
10.5 m   width of road=10.5 - 3.5= 
10.5 - 3.5 = 7
7 m Ans.   ANSWER:7 metres
Answer: C
The cost per pound of milk powder and coffee were the same in June. In July, the price of coffee shot up by 300% and that of milk powder dropped by 80%. If in July, a mixture containing equal quantities of milk powder and coffee costs $6.30 for 3lbs, how much did a pound of milk powder cost in July?	Choose the most appropriate option:
A) $4
B) $0.2
C) $1
D) $3
E) $1.65

Solution: Lets assume price of Coffee in June =100x   Price of milk powder in June =100x   Price of Coffee in July = 400x (because of 300% increase in price)   Price of milk powder in July = 20x (because of 80% Decrease in price)   Price of 1.5 pound of Coffee 1.5 pound of milk powder in July will be = 600x + 30x = 630x   As per question   630x600  + 30= 
600  + 30 = 630
630x   As per question   630x= 6.30$   x = 0.01S   So the Price of milk powder in July = 20x = 20 x 0.01 = 0.2$/pound   Answer $0.2
Answer: B
If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?	Choose the correct option.
A) 17.1	B) 17.3	C) 17.5	D) 17.7	E) 17.2

Solution: 29.94/ 1.45 = 299.4/14.5   = (2994/14.5) x 1/10) [ Here, Substitute 172 in the place of 2994/14.5 ]   = 172/10= 
172/10 = 86/5 = around 17.2
17.2   Answer is 17.2.
Answer: E
Two cars were driven by D and B. They were 580 miles apart when they started driving towards each other.D's car had traveled at a speed of 20 miles per hour, 4 hours per day for 5 days when it had met B's car. If B had driven 3 hours per day for 5 days, what was B's speed in miles per hour?	Select:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: 1. At 20mph for 4 hours a day, then driver D was traveling 80 miles per day. When D met with B, D had already traveled 400 miles.   2. This means that driver B had traveled 580-400= 
580-400 = 180
180 miles upon meeting up with D. B traveled a total of 3 x 5= 15 hours (3hrs/day for 5 days). 180 miles / 15 hours = 12mph   3. Answer 12!
Answer: E
Rahul went to a shop and bought things worth Rs. 25, out of which 54 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose one.
A) 19
B) 15.7
C) 19.9
D) 21.7
E) 22.8

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 54 Paise is given as tax   => Total tax incurred = 54 Paise = Rs.54/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 54/100   ⇒ 6(25 −0.3 −x) = 54   ⇒ (25 − 0.3 − x) = 9   ⇒ x = 25 − 0.3 − 9 = 15.7   15.7)
Answer: B
James celebrated his 23rd Birthday on 2016 but he was strangely born in 1950. How can this be possible? Choose one.
A) 1250	B) 1850	C) 1980	D) 1950	E) 1750

Solution: 1950   I was born in Hospital whose room number is 1950.
Answer: D
The average expenditure of a man for the first five months is Rs.240 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is : Choose the correct answer:
A) Rs.140  B) Rs.150  C) Rs.160  D) Rs.200  E) none

Solution: Explanation:   Total income = Rs.(240Ã—5+130Ã—7+290)=Rs.2400   Average monthly income   = Rs. (2400/12)=Rs.200   Correct Option: Rs.200
Answer: D
In the board game Yahtzee one way to get a lot of points is to roll a "Yahtzee", which is rolling the same number for all five six-sided dice. What is the probability that you will roll a Yahtzee on your first roll?	Pick:  A) Less than 0.1%  B) Between 0.1% and 0.5%  C) Between 0.5% and 1%  D) Between 1% and 2%  E) Greater than 2%

Solution: The acceptable rolls we need are any quad-tuple: 11111, 22222, 33333, 44444, 55555, and 66666. This makes 6 possibilities. The dice can fall in a combined 6*6*6*6*6 ways.   Hence the probability is 6/6^5 = 1/6^4 = 0.00077 = 0.077%   < 0.1%.   Less than 0.1%nswer: Less than 0.1%
Answer: A
A sum of Rs.4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. In the annual interest is Rs.352, the sum lent at 8% is  Choose the correct choice:
A) 2376  B) 3678  C) 3657  D) 2400  E) 2661

Solution: S.I = PNR/100   Answer with Explanation: Step (i) Given the total sum = Rs. 4000 Let the sum lent at 8% be Rs.x Let the sum lent at 10% be Rs. 4000 – x Ie) P = x , n=1, R = 8% P = 4000-x , n=1, R = 10%   100 81 XxX =   100 8x   100 1014000 XxX =   100 1040000 x    Given annual interest = Rs. 352   100 8x +   100 1040000 x  = 352 8x – 10x = 35200 – 40000 -2x = -4800   X =   2 4800 = Rs.2400/-   Answer:2400
Answer: D
The length of a rectangular garden is three times its width. If the area of the rectangular garden is 588 square meters, then what is the width of the rectangular garden?	Pick:
A) 12
B) 13
C) 14
D) 15
E) 16

Solution: Let x be the width of the garden.   3x^2 = 588   x^2 = 196   x = 14   The answer is 14.
Answer: C
A class consists of 4 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
Choose one.
A) 9
B) 32
C) 36
D) 60
E) 240

Solution: Easiest way is to treat it like an arrangements question in the following manner:   From the boys we need to select 2 to be clown and pet: This can be done in 3*4 ways   Similarly for the girls, we have 4*5 ways.   Thus total = 20+12= 
20+12 = 32
32 ways. Thus 32 is the correct answer.
Answer: B
a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12  Options:
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: add 44+12= 
44+12 = 56
56   now 56divided by 12 so we get 8 as reaminder   ANSWER:8
Answer: B
A,B and C started a business by investing Rs.2000/- , Rs.3000/- and Rs.4000/- respectively. Total profit is Rs.4500/-. Find the A’s share? Choose the most appropriate option:
A) Rs.1000/-	B) Rs.1500/-	C) Rs.2000/-	D) Rs.3000/-	E) Rs.3400/-

Solution: Rs.1000/- = Rs.2000/- , that is 2 parts   B = Rs.3000/- , that is 3 parts   C = Rs.4000/- , that is 4 parts   Total 9 parts -------> profit (4500/-)   ----->1 part -------->Rs.500/-   then Rs.1000/-'s share 2 parts -----> Rs.1000/-   Rs.1000/-
Answer: A
If x and y are positive integers, and x^3*y^4 = 3456, which of the following is the value of xy?  Choices:
A) 6
B) 10
C) 12
D) 14
E) 16

Solution: 3456 = 2^7*3^3 = 2^4*6^3   xy = 2*6= 
2*6 = 12
12   The answer is 12.
Answer: C
Suppose that the angle between the minute hand and hour hand of a
clock is 60o. If the minute hand is 16 inches long and the hour hand is
10 inches long, then what is the distance between the tip ends of the
hands in inches? Choose the correct answer:
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: This is a direct application of the Law of Cosines with two sides of a triangle   having lengths 10 inches and 16 inches and the angle between them being 60. If x denotes   the distance between the tips of the hands in inches, then   x2<-(square) = 102 +16-2<-(square)-2*10*16cos(60o)= 100 + 256-160= 
100 + 256-160 = 196
196   Hence, x= 14.   correct answer 14
Answer: E
If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?	Pick:
A) 63  B) 72  C) 144  D) 216  E) 400

Solution: 20 typists can type 48 letters, so 30 typists can type = 48*30/20   48*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 48*30*60/20*20= 216   216 is the answer
Answer: D
The ratio of number of boys and girls in a school is 3:5. If there are 320 students in the school, find the number of girls in the school?	Choose the correct answer:
A) 150
B) 250
C) 300
D) 200
E) 280

Solution: Let the number of boys and girls be 3x and 5x   Total students = 320   Number of girls in the school = 5*320/8= 
5*320/8 = 200
200   Answer is 200
Answer: D
If 1.5 a = 0.03 b, then the value of (b – a)/ (b + a) is	Choose the correct choice.
A) 490/51 B) 49/51 C) 4.9/51 D) 4.99/51 E) None of these

Solution: Explanation:   a/b = 0.03/1.5 = 3/150 = 1/50   (b – a)/(b + a)   = (1 – a/b)/((1 + a/b)   = (1 – 1/50)/ (1 + 1/50)   = 49/51   ANSWER 49/51
Answer: B
There is enough provisions for 600 men in an army camp for 25 days. If there were 250 men less, how long will the provision last? Choose the correct option:	A) 10days	B) 40days	C) 50days	D) 60days	E) 80days

Solution: Exp: We have, M1D1 = M2D2   600*25= 250* D2   D2 = 600*25/250= 
600*25/250 = 60
60 days.   Answer: 60days
Answer: D
The sale price sarees listed for Rs.495 after successive discount is 15% and 10% is?
Choose the correct choice from the following choices.
A) 288  B) 378  C) 342  D) 662  E) 262

Solution: 495*(85/100)*(90/100)   = 378   Answer: 378
Answer: B
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 28 revolutions, what will be the number of revolutions made by the larger wheel?  Choose one:
A) 15
B) 12
C) 21
D) 9
E) 22

Solution: Explanation:   Let the number of revolutions made by the larger wheel be x   More cogs, less revolutions (Indirect proportion)   Hence we can write as   (cogs) 6 : 14 :: x : 28   â‡’6Ã—28=14 Ã— x   â‡’x = 12   Answer: Option 12
Answer: B
(1.00001)(0.99999) - (1.00005)(0.99995) =  Choices:
A) 0	B) 10^-10	C) 3(10^-10)	D) 10^-5	E) 24(10^-10)

Solution: (1.00001*0.99999)-(1.00005*0.99995)   = (1+0.00001)(1-0.00001) - (1+0.00005)(1-0.00005)   = 1 - (0.00001)^2 - 1 + (0.00005)^2   = -(0.0000000001) + (0.0000000025)   = 0.00000000024=24(10^-10)   Answer 24(10^-10)
Answer: E
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.4, 2.4, 3.4, 4.4, ... What number should come next?	Pick one
A) 5.4	B) 3.6	C) 4.9	D) 5.0	E) 4.4

Solution: 5.4   In this simple addition series, each number increases by 1.0   5.4nswer : 5.4
Answer: A
4 dice are thrown simultaneously on the board. Find the probability show the same face? Choose the correct choice from the following:
A) 2/121	B) 2/227	C) 1/216	D) 1/219	E) 1/213

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/2, 1/4, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third? Choose the correct answer.
A) 1/16n
B) (n-1)/8n
C) 1/2n
D) (n+2)/2n
E) (3n-2)/2n

Solution: 1/2 * 1/4 * (1-1/n)   = 1/8 * (n-1)/n   = (n-1)/8n   Answer - (n-1)/8n
Answer: B
If 5 men can paint a wall 100 metres long in 10 days of a 8 hours each. In how many days of 6 hours each will 8 men paint a wall 30 metres long?  Choose one.
A) 1.5 DAY	B) 2 days	C) 2.5 days	D) 3 days	E) 3.5 days

Solution: Total hours in 10 days = 10 *8= 
10 *8 = 80
80 hours.   Total man-hours needed for paint 100m wall= 5 *8= 
5 *8 = 40
40 man-hours.   Man-hour needed for 1 meter wall painting= 400/100= 
400/100 = 4
4 man-hour.   Now,   30*4= 
30*4 = 120
120 m-h to do 30 meters.   120 m-h/8 men= 15 hours.   15 hr/6 hr/day = 2.5 days.   answer : 2.5 days
Answer: C
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  Choose the correct choice from the following options:	A) 369	B) 452	C) 145	D) 132	E) 209

Solution: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).   Required number   of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)   = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)   = (24 + 90 + 80 + 15)= 
(24 + 90 + 80 + 15) = 209
209.   Ans: 209
Answer: E
If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire?	Choose the correct option
A) 2 meters	B) 6 meters	C) 5 meters	D) 3 meters	E) 7 meters

Solution: 400 rev / minute = 400 * 60 rev / 60 minutes   = 24,000 rev / hour   24,000 * C = 144,000 m : C is the circumference   C = 6 meters   correct answer 6 meters
Answer: B
What is the area of a square field whose diagonal of length 20 m?  Choose the correct option.
A) 287	B) 269	C) 270	D) 200	E) 230

Solution: d2/2 = (20 * 20)/2= 
(20 * 20)/2 = 200
200   Answer:200
Answer: D
Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-2# = 2, what is the value of #2#?	Pick.
A) 5	B) 0	C) -4	D) -3	E) -5

Solution: #p# = ap^3 + bp - 1   #-2# = 2   putting p = -2 in above equation   -8a -(2b +1) = 2 or   #-2# = (8a+2b+1) = -2   therefore 8a+2b = -3 .....(1   now putting p =2   #2# = 8 a+2b - 1   using equation 1(8a+2b = -3)   #5# = -3-1 = -4   hence -4
Answer: C
Given a spinner with four sections of equal size labeled E, B, C, and D, what is the probability of NOT getting an E after spinning the spinner two times?	Choose the most appropriate option:	A) 15/16	B) 9/16	C) 1/2	D) 1/4	E) 1/8

Solution: The probability of NOT getting an E after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).   Answer: 9/16.
Answer: B