MU-NLPC/Calc-aqua_rat huggingface dataset:
In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are accounting majors?	Select the correct option:
A) 3	B) 5	C) 8	D) 11	E) 17

Solution: pqrs = 1365 = 3* 5 *7 * 13   Since 1< p < q < r < s, the number of students who are accounting majors is p = 3.   The answer is 3.
Answer: A
If the manufacture gains 10%, the wholesale dealers 15% and the retailer 25% then find the cost of production of a table, the retail price of which is $1265 ?	Pick one:
A) $650  B) $800  C) $1200  D) $950  E) $1050

Solution: Let the cost of production of the table be $x   Then, 125% of 115% of 110% of x = 1265   125/100 * 115/100 * 110/100 * x = 1265   253/160 * x = 1265   x = 1265*160/253= 
1265*160/253 = 800
$800   Answer is $800
Answer: B
If a, b, c and d are positive integers less than 4, and 4^a+3^b+2^c+1^d=78 then what is the value of b/c?
Choose the correct option.
A) 3	B) 2	C) 1	D) 1/2	E) 1/3

Solution: Since a, b and c are positive integers less than 4 we have the following possibilities:   4^a=4,16,or 64   3^b=3,9,or 27   2^c=2,4,or 8   Trial and error gives us quite quick the solution of   4^a=64   3^b=9   2^c=4   64+9+4= 
64+9+4 = 77
77   i.e. c=2 and b=2 ----> b/c=1/1= 
1/1 = 1
1   The correct answer is 1
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? Answers.
A) 12/457 B) 12/855 C) 12/455 D) 12/456 E) 12/451

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.Answer: 12/455
Answer: C
A cube of edge 10cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
Select the correct option:
A) 6cm
B) 8.25cm
C) 11.25cm
D) 15.12cm
E) 3.33cm

Solution: Increase in volume = volume of the cube = 10*10*10 cm^3   Rise in water level = volume / area = 10*10*10/20*15 = 3.33cm   Answer is 3.33cm
Answer: E
Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 11 from the product of their ages a year from today. What is their age today?  Pick one
A) 2.  B) 4.  C) 5.  D) 7.  E) 9.

Solution: ad = (a+1) (d+1) -11   0= a+d-10   a+d = 10   a=d (as they are twin brothers)   a=d=5   5. is the answer
Answer: C
What is the remainder when 1201 × 1202 ×1203 × 1207 is divided by 6?	Choose the correct choice:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: The remainders when dividing each number by six are: 1, 2, 3, and 1.   The product is 1*2*3*1= 
1*2*3*1 = 6
6   The remainder when dividing 6 by 6 is 0.   The answer is 0.
Answer: A
If f(x) = 7 x +12, what is f-1(x) (the inverse function)?  Select the correct option: A) (x-12)/7 B) (x-12)/6 C) (x-12)/5 D) (x-12)/4 E) (x-12)/3

Solution: f(x) = 7 x + 12   take both side f-1(x)   f(f-1(x))= 7 f-1(x) + 12   x= 7(f-1(x)) +12   f-1(x) = (x-12)/7   (x-12)/7NSWER:(x-12)/7
Answer: A
In certain code 'TWICE' is written as '34$5δ' and 'WEARS' is written as '4δ29%'. How is 'SEAT' written in that code?	Answers:
A) 22 B) 23 C) 697 D) 66P E) 82

Solution: Answer: Option 23
Answer: B
The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 40%. What is the mark up on the cost price?  Options:	A) 40%	B) 8%	C) 25%	D) 16.66%	E) 26%

Solution: The most natural way to deal with 'weights' questions is by assuming values.   Say the trader's balance shows 100 gms. It is actually 90 gms because it weighs 10% less. Say, the cost price is $90 ($1/gm). Since he gets a profit of 40%, the selling price must be 90+(40/100)*90= 
90+(40/100)*90 = 126
$126   Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $126, the mark up is simply 26%.   Ans : 26%
Answer: E
A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 60% more recliners. What is the percentage increase of the gross?
Choose the most appropriate option:
A) 10%
B) 15%
C) 20%
D) 28%
E) 50%

Solution: Say a recliner is actually worth $100   If she sells 100 recliners then she earns $10000   After the discount of 20%, she will earn $80 per recliner and she sells 60% more ie.,160 recliners   Hence her sales tields 160*80= 
160*80 = 12_800
$12800   Increase in sales=12800-10000= 
12800-10000 = 2_800
$2800   So% increase= 2800*100/10000= 
2800*100/10000 = 28
28%   28% is the answer
Answer: D
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 178 votes. Find the total number of valid votes?
Choose the correct option:
A) 445
B) 570
C) 480
D) 520
E) 550

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10 = 178 => 4x/10 = 178   => 4x = 1780 => x = 445.   445NSWER:445
Answer: A
If Jack walked 6 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?	Select the correct option:	A) 4	B) 4.8	C) 6	D) 6.25	E) 15

Solution: Distance walked in 1 hour and 15 mins = 6 miles   Speed per hour = Distance/Time = 6/(5/4)= 
6/(5/4) = 24/5 = around 4.8
4.8 miles per hour   Answer 4.8
Answer: B
A man has some hens and cows. If the number of heads be 100 and the number of feet equals 180, then the number of hens will be:	Select the correct option:  A) 22  B) 23  C) 80  D) 90  E) 28

Solution: Explanation:   Let the number of hens be x and the number of cows be y.   Then, x + y = 100 .... (i)   and 2x + 4y = 220 x + 2y = 110 .... (ii)   Solving (i) and (ii) we get: x = 90, y = 10.   The required answer = 90.   Answer: 90
Answer: D
A clock loses 10 minutes each hour.
If the clock is set correctly at noon,what time is it when it reads 3 PM ?  Answers:
A) 3:36 PM  B) 3:47 PM  C) 3:45 PM  D) 2:36 PM  E) 3:30 PM

Solution: A   3:36 PM.   The clock loses 10 minutes each hour,   so it loses 5 minutes every half-hour,   and it loses 1 minute very 6 minutes.   It is 12:50 PM at 1:00 o'clock.   It is 1:40 PM at 2:00 o'clock.   It is 2:30 PM at 3:00 o'clock.   It is 2:55 PM at 3:30 o'clock.   It is 3:00 PM at 3:36 o'clock.
Answer: A
The present age of Suraj is 6 times Vijay’s age. The present age of Vijay’s 20 years less than Suraj’s present age. What is the present age of Suraj?	Pick:
A) 20 years
B) 22 years
C) 18 years
D) 16 years
E) None of these

Solution: S=6V, V=S-20   S=6(S-20)   5S=120   S=24   ANSWNone of theseR:None of these
Answer: E
A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?  Choose the correct choice from the following answers
A) 22 days
B) 4 days
C) 13 days
D) 6 days
E) 9 days

Solution: (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).   B's 1 day's work =((1/4)-(1/12))=(1/6)   Hence, B alone can complete the work in 6 days.   Answer is 6 days.
Answer: D
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when a boy gets any no. of prizes?  Choose one: A) 55 B) 58 C) 343 D) 354 E) 200

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (7 x 7 x 7) ways = 73 ways = 343 ways Or nr ways = 73 ways = 343 ways
Answer: C
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/11	Pick one:
A) None  B) I only  C) III only  D) II and III only  E) I, II, and III

Solution: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.   On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.   We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us I only as the only possible answer.
Answer: B
Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 16 times smaller, from source B alone?  Pick one
A) 6 hours and 40 minutes
B) 15 minutes
C) 12 minutes
D) 10 minutes
E) 25 minutes

Solution: Let the movie size be 400 u.   Given,A+C=4 hrs.   A+C=100 u/hr   And A+B+C=2.5 hrs or   400/2.5= 
  400/2.5 = 160
160 u/hr   B alone=160-100= 
160-100 = 60
60 u/hr   Trailer=40 times smaller or  400/16= 
  400/16 = 25
25 u   B will take 25/60 hrs or 25 minutes.   Ans 25 minutes
Answer: E
Eight carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if seven of the carpenters work together at their respective rates ?	Choose the correct choice
A) 11/15	B) 3/5	C) 11/30	D) 329/480	E) 5/9

Solution: Farmer A, B, C, and D   A's rate: 1/3 job/hour   B's rate: 1/4 job/hour   C's rate: 1/5 job/hour   D's rate: 1/7 job/hour   By intuition we know that the three fastest farmers are A B and C.   As such   (1/3 + 1/4 + 1/5)*(7/8) = ?   47/80 or (329/480)
Answer: D
One pipe can fill a pool three times faster than a second pipe. When both pipes are opened, they fill the pool in seven hours. How long would it take to fill the pool if only the faster pipe is used?	Choose the correct choice.
A) 3.6 hr
B) 4.7 hr
C) 5.1 hr
D) 9.3 hr
E) 9.7 hr

Solution: fast pipe + slow pipe = together   One pipe fills the pool three times faster than the other pipe so,   hourly fill rates:   1/x + 1/3x = 1/7   Let x = number of hours it would take the fast pipe to fill the pool thus,   x=9.3 hours   Answer: 9.3 hr
Answer: D
Of a certain group of 100 people, 40 graduated from High School M, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School M, did not graduate from College Y, and do not live in City Z ? Choose the correct choice from the following answers
A) 5 B) 15 C) 35 D) 65 E) 85

Solution: 1. m+y+z+my+yz+mz+myz+ none=100. Fornoneto be maximum others have to be minimum   2. We know the underlined portions sum to 65 and that is the minimum value of others   3. Maximumnone= 100-65= 
100-65 = 35
35=35
Answer: C
After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 5650 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ? Choose the correct choice:  A) 2160  B) 2350  C) 2000  D) 2300  E) None of these

Solution: Explanation :   Total Exp = 5000+1500+4500+2500+2000+5650= 
5000+1500+4500+2500+2000+5650 = 21_150
21150   Exp in %= 100-10= 
100-10 = 90
90%, 21150= 90%   Saving = 10 % = 21150 X 10/90 = Rs. 2350   Answer : 2350
Answer: B
1,1,3,2,1,5,3,4,10,4,2,?  Answers:
A) 10	B) 11	C) 12	D) 13	E) 14

Solution: 1+1+1= 
1+1+1 = 3
3   2+1+2= 
2+1+2 = 5
5   3+4+3= 
3+4+3 = 10
10   4+2+4= 
4+2+4 = 10
10   10NSWER:10
Answer: A
Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 7200 different outfits, then for how many garments does Dave have exactly five choices?
Select:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: 7200 = 72*100 = 72*5^2*2^2   Dave has exactly 5 choices for two garments.   The answer is 2.
Answer: C
What is the least common multiple of 12, 18, and 24?  Pick one:
A) 72
B) 120
C) 240
D) 360
E) 720

Solution: Let us first write the numbers in the form of prime factors:   12 = 2^2 * 3^1   18 = 2^1 * 3^2   24 = 2 * 17^1   The LCM would be the largest powers of the prime numbers from all these three numbers.   Hence LCM = 72   Option 72
Answer: A
The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N. Pick one:
A) 797
B) 197
C) 597
D) 997
E) 297

Solution: According to the division process of whole numbers, N can be written, using multiplication, as follows   N = quotient *divisor + remainder = 15* 13 + 2= 
15* 13 + 2 = 197
197 correc answer 197
Answer: B
P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together? Choose one:	A) 4(3/4)	B) 7	C) 4	D) 5	E) 4(1/2)

Solution: Option E   Explanation:   Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.   Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9 of the total   They would take 9/2 days = 4 (1/2) days to complete the work working together.
Answer: E
How many positive factors of 42 are not factors of 56?  Pick.
A) 1  B) 2  C) 3  D) four  E) 5

Solution: 42=2*3*7.   So, total number of factors for 42 = 2*2 *2= 
2*2 *2 = 8
8   factors for 42= 1,2,3,6,7,14,21 and 42   56=2*2*2*7   So, total number of factors for 56 = 4*2= 
4*2 = 8
8   factors of 56= 1,2,4,7,8,14,28 and 56.   Factors same in 42 and 56 are 1,2,7 and 14.   Hence, answer will be four.
Answer: D
A dog takes 5 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 5 leaps of the hare, the ratio of the speed of the dog to that of the hare is : Select the correct option.
A) 25 : 10	B) 25 : 8	C) 25 : 9	D) 8 : 25	E) 24 : 8

Solution: Explanation:   Dog : Hare = (5*5) leaps of hare : 8 leaps of hare = 25 : 8   Answer: 25 : 8
Answer: B
If integer k is equal to the sum of all even multiples of 15 between 390 and 615, what is the greatest prime factor of k?  Answers:	A) 5	B) 7	C) 8	D) 13	E) 17

Solution: if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600.   using arithmetic progression to find n : 600 = 390 + (n - 1) 30   210+ 30 = 30n   240 = 3n => n = 8   the sum would be: 8* mean   mean = [600 + 390] / 2 = 495   8*495   8
Answer: C
A certain list of 100 data has an average (arithmetic mean) of 8 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 106 data with standard deviation less than d?	Choices
A) -8 and 0	B) 0 and 0	C) 0 and 8	D) 0 and 16	E) 8 and 8

Solution: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 8 and 8 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.   Answer: 8 and 8.
Answer: E
If 6 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?  Choose the correct choice from the following options.
A) 3:2	B) 2:2	C) 3:4	D) 1:2	E) 6:1

Solution: 2:2   2:2   6M + 22:2 = 4(1M + 12:2)   6M + 22:2 = 4M + 42:2   2M = 22:2   The required ratio of work done by a man and a boy = 2:2
Answer: B
How long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250m in length?	Options:
A) 28.8 sec	B) 16.8 sec	C) 15.2 sec	D) 25.4 sec	E) 16.2 sec

Solution: D = 150 + 250= 
150 + 250 = 400
400 m   S= 50 * 5/18 = 125/9   T = 400 * 125/9 = 28.8 sec   28.8 secNSWER:28.8 sec
Answer: A
In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 7th Rd and 8th Ave in the shortest possible time, how many different routes could he take?	Answers:
A) 156	B) 180	C) 225	D) 252	E) 281

Solution: Bills needs to walk 5 blocks north and 5 blocks east.   One possible solution is NNNNNEEEEE.   There are 10C5 = 252 possible solutions.   The answer is 252.
Answer: D
How many integers are divisible by 5 between 10! and 10! + 20 inclusive?  Pick one:
A) 5 B) 7 C) 8 D) 9 E) 10

Solution: A - 7   10! is divisible by 5   There are 4 numbers between 10! and 10!+20 that are divisible by 5.   Hence 5
Answer: A
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio F of men to women? Choose one:
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 3:1

Solution: (5:2)F= 184 x 5 + 170 x 2 = 1260.5:2
Answer: A
40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 35 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?  Pick:
A) 1/4 B) 21/26 C) 2/3 D) 7/8 E) 8/7

Solution: Say total male = 40   Total female =60   Required ratio =( .35/40)/ (.65/60) = 21/26 21/26 is the answer
Answer: B
The average of first 17 even numbers is?  Answers
A) 10
B) 11
C) 18
D) 20
E) 24

Solution: Sum of 17 even numbers = 17 * 18= 
17 * 18 = 306
306   Average= 306/17= 
306/17 = 18
18   ANSWER:18
Answer: C
Which of the following equivalent to (1/216)^2?  Pick
A) (0.01)^3
B) (0.02)^3
C) (0.03)^3
D) (0.04)^3
E) (0.05)^3

Solution: (1/36)^2 = (1/6^3)^2 = (1/6)^6 = (1/36)^3 = (0.02)^3   Answer: Option (0.02)^3
Answer: B
On the coordinate plane , points P and U are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?	Choose the correct choice from the following choices:  A) (1.5,1)  B) (2,-5)  C) (0,0)  D) (1,1.5)  E) (2,2)

Solution: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.   One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).   Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PU is the diameter of the circle.   There can be a case when PU is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.   If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y COR(1,1.5)INATE and mark the ans=(1,1.5)
Answer: D
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 180 sandwiches were made, how many bologna sandwiches
were made? Choices: A) 63 B) 30 C) 38 D) 42 E) 48

Solution: For deciding such task we should calculate all parts 5 + 7 + 8= 
5 + 7 + 8 = 20
20 parts   and we should calculate how many sandwiches holds 1 part:   180 / 20= 
180 / 20 = 9
9 sandwiches in one part   For bologna we have 7 parts so:    7 * 9= 
 7 * 9 = 63
63   63nswer is 63
Answer: A
Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Choose the correct choice from the following:  A) 100  B) 150  C) 120  D) 130  E) 140

Solution: 4x 5x 6x   100 50 25   400x + 350x + 150x = 16000   x = 20   6x = 120   ANSWER 120
Answer: C
At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 10'o clock.  Select
A) 60sec B) 62sec C) 66sec D) 64sec E) 54sec

Solution: At 6'0 clock, clock ticks 6 times.   So, there must be 5 intervals between clock ticks.   Time Between first and last ticks = 30sec   So, 1 interval = 30/5= 
30/5 = 6
6sec   So 6'o clock 5 *6= 
5 *6 = 30
30sec   7'o clock 6 *6= 
6 *6 = 36
36sec   .   .   9'o clock 8 *6= 
8 *6 = 48
48sec   10'o clock 9 *6= 
9 *6 = 54
54sec   So, 54sec at 10'o clock.   ANSW54secR:54sec
Answer: E
If one length of a square is tripled, and the original parameter is 4y. What is the new length of one of the sides?	Pick one
A) 12y/3
B) 2y/2
C) 6y/3
D) 12y/4
E) 4y/3

Solution: If the original parameter is 4y, each length of the square is 4y/4. If the parameter is tripled, then each length becomes 3(4y)/4. This is 12y/4. Answer option 12y/4.
Answer: D
The number 94 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers? Pick one:
A) 9 B) 14 C) 15 D) 18 E) 20

Solution: The only possible sum for 4 different squares of an integer with total sum number is 95 are :   48 + 36 + 9 + 1 = 95 which are the square from numbers :8, 6, 3, 1 (total sum number is 16)   or   80 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 14)   hence the answer is (14)
Answer: B
A man spends Rs. 1800 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Choose the correct choice from the following:
A) 2050	B) 2150	C) 2250	D) 2350	E) 2450

Solution: Explanation:   Total expenditure for the first 3 months = 3 Ã— 1800 = 5400   Total expenditure for 4 months = 4 Ã— 1550 = 6200   Total expenditure for 5 months = 5 Ã— 1800 = 9000   Total expenditure and saving (which is income for one year)   = 5400 + 6200 + 9000 + 5200 = Rs. 25800   So, Average monthly income = 25800/12 = Rs. 2150   Answer 2150
Answer: B
If a fair coin is flipped three times in a row, what is the probability that there will be at least one head and one tail?	Choose the correct choice:	A) 3/4	B) 11/12	C) 15/16	D) 31/32	E) 63/64

Solution: The number of possible outcomes is 2^3 = 8   There is one way to get no heads and one way to get no tails.   Thus there are 6 outcomes with at least one head and one tail.   P(at least one head and one tail) = 6/8 = 3/4   The answer is 3/4.
Answer: A
A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ? Options.
A) 6 and 1 kmph B) 8 and 2 kmph C) 8 and 1 kmph D) 9 and 1 kmph E) 2 and 1 kmph

Solution: Explanation:   Downstream speed = 72km/8hrs = 9 kmph   upstream speed 72  /8= 
72  /8 = 9
9 kmph   upstream speed= 84km/12hrs = 7 kmph   speed of boat 84  /12= 
84  /12 = 7
7 kmph   speed of boat= avg of downstream and upstream speeds   speed of boat = (9+7)/2= 
(9+7)/2 = 8
8 kmph.   current speed= half of the difference of downstream and upstream speeds   currend speed = (9-7)/2= 
(9-7)/2 = 1
1 kmph   Answer: 8 and 1 kmph
Answer: C