MU-NLPC/Calc-aqua_rat huggingface dataset:
P is three times as old as Q. In 7 years, P will be twice as old as Q. How old was P three years ago?
Choices:
A) 15  B) 18  C) 21  D) 24  E) 27

Solution: P = 3Q so Q = P/3   P+7 = 2(Q+7) = 2(P/3+7)   P/3 = 7   P = 21   Three years ago, P was 18.   The answer is 18.
Answer: B
Which of the following cannot be the sum of 4 different prime numbers?
Choose the most appropriate option.
A) 21 B) 17 C) 19 D) 32 E) 19

Solution: Option A: 21 = 2+3+5+11. Sum of 4 different prime numbers   Option B: 17 = 2+3+5+7. Sum of 4 different prime numbers   Option C: 19 = 2+3+5+9. This cannot be expressed as a sum of 4 different prime numbers   Option D: 32 = 5+3+11+13. Sum of 4 different prime numbers   Option E: 31 = 5+2+11+13. Sum of 4 different prime numbers   19orrect Option:19
Answer: C
9 people will pick a number between 1 and 9. What is the probability that exactly one person will pick a different number?
Pick:
A) 1/9	B) 1/9*9	C) 1/9!	D) 9!/9	E) 9!/9^9

Solution: Each person out of 9 has 9 options, hence total # of outcomes is 9^9;   Favorable outcomes will be 9!, which is # of ways to assign 9 different number to 9 people.   P=favorable/total=9!/9^9   Answer: 9!/9^9.
Answer: E
For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
Select the correct option:
A) 12%  B) 26%  C) 29%  D) 32%  E) 60%

Solution: In the first plot 30% of 300 seeds germinated, so 0.3 x 300 = 90 seeds germinated.   In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.   Since 90 + 70 = 260 seeds germinated out of a total of 300 + 200= 
300 + 200 = 500
500 seeds, the percent of seeds that germinated is (160/500) x 100%, or 32%.   Answer: 32%.
Answer: D
50 percent of the members of a study group are women, and 30 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer?	Select:	A) 0.16	B) 0.25	C) 0.45	D) 0.35	E) 0.15

Solution: Say there are 100 people in that group, then there would be 0.5*0.30*100= 
0.5*0.30*100 = 15
15 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=15/100.   Answer: 0.15
Answer: E
Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 3 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?	Choose one:
A) 16	B) 20	C) 15	D) 72/5	E) 24

Solution: x rate = k/3   y rate = k/2   k/3 + k/2 = 12k / T   solving T = 72/5   Answer 72/5
Answer: D
10 books are placed at random in a shelf. The probability that a pair of books will always be together i
Choose the correct choice from the following choices
A) 1/6  B) 1/0  C) 1/5  D) 1/2  E) 1/1

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
In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.	Choices
A) 10	B) 12	C) 14	D) 16	E) 19

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 24   => 2x = 24 => x = 12   12
Answer: B
Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than the speed of Kajol.
What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol?  Choose the correct choice from the following options
A) 32 B) 21 C) 27 D) None of these E) 18

Solution: Explanation:   Let t be the time after Kajol starts, when she meets Ajay, then   \inline t=\frac{300}{(x+y)}   This should be less than 2.5 or (x+y)>120   Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72   This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.   Answer: None of these
Answer: D
United Telephone charges a base rate of $8.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?  Select
A) 25 minutes B) 10 minutes C) 20 minutes D) 80 minutes E) 60 minutes

Solution: Lets take number of minutesx.   Given that, 8+0.25x=12+0.2x ->0.05x=2 -> x=80minutes   ANS 80 minutes
Answer: D
The average mark of the students of a class in a particular exam is 90. If 3 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam?	Choose the correct choice from the following:  A) 25  B) 35  C) 23  D) 22  E) 33

Solution: Let the number of students who wrote the exam be x.   Total marks of students = 90 x.   Total marks of (x - 3) students = 80(x - 3)   90x - (3 * 40) = 95(x - 3)   165 = 5x => x = 33   Answer: 33
Answer: E
Find the odd man out 3, 5, 7, 12, 13, 17, 19 Pick:
A) 3
B) 5
C) 7
D) 12
E) 13

Solution: 12 is an even number while the others are odd   ANSWER:12
Answer: D
From 6 positive numbers and 6 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?  Pick one:
A) 720
B) 625
C) 30
D) 960
E) 255

Solution: When will the product of 4 numbers be positive? It is positive when the number of negative numbers in the product is even i.e. when we have 0 negative numbers or 2 negative numbers or 4 negative numbers.   3 cases:   - 0 negative numbers - All numbers are positive - Selected in 6C4 = 15 ways   - 2 negative numbers - 2 are positive and 2 are negative - Selected in 6C2*6C2 = 15*15= 
15*15 = 225
225 ways   - 4 negative numbers - All numbers are negative - Selected in 6C4= 15 ways   Total number of ways = 15 + 225 + 15= 
15 + 225 + 15 = 255
255   Answer (255)
Answer: E
How many prime numbers W exist such that 90 < W < 106 and W is a factor of 99999919?  Choose the most appropriate option
A) 1. Zero  B) 2. One  C) 3. Two  D) 4. Three  E) 5. More than three

Solution: I found that considering the constraint..W is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.3. Two
Answer: C
If n is a natural number, then (6n2 + 6n) is always divisible by: Choices:  A) 6 only  B) 6 and 12 both  C) 12 only  D) by 18 only  E) None

Solution: EXPLANATION   (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.   Answer 6 and 12 both
Answer: B
If a and b are distinct positive integers. The units digit of a^2 is equal to the units digit of a, and the units digit of b^2 is equal to the units digit of b. If the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b? Choose the correct answer: A) 0 B) 1 C) 4 D) 5 E) 6

Solution: There are four digits which when squared give the same units digits: 0, 1, 5, 6   0^2 = 0   1^2 = 1   5^2 = 25   6^2 = 36   So a and b must take 2 of these values. They are positive integers so 0 is not possible.   If one of the digits is 1, when the other is multiplied by 1, you will get the same digit. 1*5 = 5   So 1 is out of the picture.   Then you have only two digits left 5 and 6. So out of a and b, one must be 5 and the other 6.   5*6= 
5*6 = 30
30 so units digit of their product= 0   0nswer (0)
Answer: A
A bag contains 6 black and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Choose the correct choice from the following answers.
A) 4
B) 4/3
C) 4/5
D) 4/9
E) 2/5

Solution: Let number of balls = (6 + 4)= 
(6 + 4) = 10
10.   Number of white balls= 4.   P (drawing a white ball) = 4/10 = 2/5   Hence Answer is 2/5
Answer: E
The total age of A and B is 16 years more than the total age of B and C. C is how many years younger than A ?	Options: A) 12 B) 16 C) 21 D) 18 E) 11

Solution: (A+B) - (B+C) = 16   A - C = 16.   C is younger than A by 16 years.   Answer: 16
Answer: B
In a recent election, Ms. Robbins received 7,200 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 60 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?	Pick one: A) 0.06N + 3,200 B) 0.1N + 7,200 C) 0.04N + 7,200 D) 0.1N + 8,000 E) 0.06N + 8,000

Solution: I will go with option C   According to question 60 percent of total votes (N) cas were cast by independent voters. This implies 40 percent of N are voters that belong to political party. And she received 7200 votes from independent voters and 10 percent from registered voters (i.e 0.1 * 0.4 * N = 0.04N). Hence total votes = 7200 + 0.04N ....option 0.04N + 7,200
Answer: C
Three friends neha, sabi and mahi divide $1100 amongs them in such a way that if $5, $8 and $4 are removed from the sums that neha, sabi and mahi received respectively, then the share of the sums that they got will be in the ratio of 2 : 8 : 6. How much did mahi receive?	Choose the most appropriate option.
A) $122
B) $152
C) $202
D) $107
E) $102

Solution: Explanatory Answer   Let the sums of money received by A, B and C be x, y and z respectively.   Then x - 5 : y - 8 : z -4 is 2a : 8a : 6a   When $5, $8 and $4 are removed, we are removing a total of $17 from $1100.   Therefore, 2a + 8a + 6a = 1100 - 17 = 1093   i.e., 16a = 1093   or a = 68.   We know that z - 6 = 16a = 6 * 16= 
6 * 16 = 96
96   Therefore, z= 96+6= 
96+6 = 102
$102   The correct choice is ($102)
Answer: E
The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 26
II. 70
III. 90	Select the correct option
A) I only B) III only C) I and II D) I​ and III E) II and III

Solution: m = 18k + 12 --> Values are 12, 30, 48, 66, 84   n = 24k + 14 --> Values are 14, 38, 62, 86   I. 26 --> 12 + 14 --> Possible   II. 70 --> Not possible   III. 90 --> Not possible   I onlynswer: I only
Answer: A
Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant? Options.
A) A)1/500  B) B)1/28  C) C)27/28  D) D)124/125  E) E)499/500

Solution: There are 5 consonants and 2 vowels in NOTHING .   probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)   Probability of both vowels = 227/282/727/282 = 1/21   So, Answer is 1 - 1/21 = 20/21 ------> 27/28.
Answer: C
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?	Answers:
A) 59028
B) 59010
C) 59190
D) 59000
E) 92700

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000   Answer:59000
Answer: D
If a large pizza has a radius that is 40% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza? Choose the correct choice from the following answers: A) 40% B) 80% C) 96% D) 112% E) 124%

Solution: Let the radius of medium pizza be r. Then the radius of large pizza is 1.4r.   The area of the medium pizza is pi*r^2   The area of the large pizza is pi*(1.4*r)^2 = 1.96*pi*r^2, an increase of 96%.   The answer is 96%.
Answer: C
In case O is the only individual sewing on committee B, which among the following shouldserve on committee A?  Choose one.
A) V and U  B) V and T  C) U and S  D) P and Q  E) T and U

Solution: P and Q should serve on A   ANSWER:P and Q
Answer: D
How many ONE letter words are formed using the letters of the word WALK?	Choose the correct option:
A) 1
B) 16
C) 7
D) 4
E) 2

Solution: The number of letters in the given word is 4.   The number of ONE letter words that can be formed using these four letters is 4P1=4*1= 
4*1 = 4
4   Answer:4
Answer: D
A can do a piece of work in 20 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in  Choose the correct choice from the following answers
A) 10days  B) 6days  C) 7.5days  D) 8.5days  E) 9days

Solution: Explanation:   B's 5 days work =   1/10∗5=1/2   Remaining work =1−1/2=1/2   10days can finish work =20∗1/2=10days   Option 10days
Answer: A
An unbiased die is tossed .find the probability of getting a multiple of 3	Answers.
A) 4/5 B) 1/3 C) 3/2 D) 4/3 E) 5/2

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(E)=n(E)/n(S)=2/6=1/3   Ans: 1/3
Answer: B
A car covers a distance of 624 km in 3 1/5 hours. Find its speed? Choose the correct choice from the following.
A) 104 kmph	B) 195 kmph	C) 109 kmph	D) 174 kmph	E) 101 kmph

Solution: 624/3 1/5   =195 kmph   Answer:195 kmph
Answer: B
The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average? Select the correct option.
A) 72 B) 55 C) 66 D) 11 E) 67

Solution: Sum of the marks for the 12 students = 12 * 36= 
12 * 36 = 432
432. The marks of each student are doubled, the sum also will be doubled.   The new sum= 432 * 2= 
432 * 2 = 864
864. So, the new average= 864/12 = 72.72nswer: 72
Answer: A
Mangala completes a piece of work in 12 days, Raju completes the same work in 34 days. If both of them work together, then the number of days required to complete the work is?	Choose the correct answer
A) 8 3/4 days
B) 10 1/4 days
C) 11 1/4 days
D) 12 2/3 days
E) 14 1/4 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 12× 34/46= 8 3/4 days   8 3/4 days)
Answer: A
Ella can fill K cans of water in 4 minutes. If there are T cans of water in one gallon, how many gallons can Ella fill in 36 minutes? Pick:
A) 4T/K
B) 4KT
C) 9T/K
D) 9K/T
E) 9KT

Solution: Ella can fill this number of cans in 36 minutes:  (36/4)= 
 (36/4) = 9
9K.   One can is 1/T gallons.   Ella can fill 9K*(1/T)= 9K/T gallons of water in 36 minutes.   The answer is 9K/T.
Answer: D
A box contains seven bulbs out of which 5 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good. Choose the correct choice from the following choices.
A) 125/167
B) 125/186
C) 125/126
D) 125/186
E) 20/21

Solution: Required probability   = 1 - 1/21   = 20/21   Answer: 20/21
Answer: E
A 240 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?  Choose the correct choice from the following options
A) 228
B) 144
C) 1266
D) 188
E) 211

Solution: S = 240/6 * 18/5= 
240/6 * 18/5 = 144
144 kmph   Answer: 144
Answer: B
Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm. Pick one.
A) 71 cm2	B) 121 cm2	C) 141 cm2	D) 171 cm2	E) 221 cm2

Solution: length = 17 cm, breadth = 13 cm   Perimeter of rectangle = 2 (length + breadth)   = 2 (17 + 13) cm   = 2 × 30 cm   = 60 cm   We know that the area of rectangle = length × breadth   = (17 × 13) cm22   = 221 cm2   ANSW221 cm2R : 221 cm2
Answer: E
An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?	Choose the correct choice from the following.
A) $115,000
B) $160,000
C) $215,000
D) $240,000
E) $365,000

Solution: Say the price of the house was $x, then 0.15*50,000+0.1*(x-50,000)=24,000 --> x=$215,000 (15% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).   Answer: $215,000
Answer: C
Felix earned 50% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?  Options
A) 25%
B) 9.09%
C) 14%
D) 22.73%
E) It cannot be determined from the information given.

Solution: This Q is all about taking the correct BASE for taking %s..   the very first step requires taking some numbers for each..   ONE should be 100...   it is easy to take 50 and 100 here..   but the BASE is 100 here, so the salary can be 100 and 150..   100 increases 10% =110..   150 decreases 10%=135..   so the increase is 25..   again the BASE is 110, so answer 25/110 * 100= 22.73% D   without calculations,   answer cannot be equal to or greater than 25, as 25 is on 110..   so 22.73% is the only one left
Answer: D
A box is in the shape of a semicircle with a radius of 12. What is the approximate perimeter of the semicircle?	Choices:
A) 54
B) 62
C) 25
D) 34
E) 60

Solution: perimeter of a circle =2pi*r   perimeter of a semicircle = pi*r + 2r   aprox perimiter = 3.14*12 + 2*12= 
3.14*12 + 2*12 = 61.68
61.68 approximately 62   answer 62
Answer: B
a and b are positive integers less than or equal to 7. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab? Choose the correct choice from the following answers:	A) 3	B) 4	C) 2	D) 6	E) none of the above

Solution: 686868 when divided by 2 gives the result 343434   CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2   SUm of the digits of No. which is divisible by 2 hence the Number 686868 will be divisible by 2
Answer: A
There are 50 students in a class. If 2 % are absent on a particular day, find the number of students present in the class. Choose the correct choice from the following options.
A) 43  B) 36  C) 28  D) 49  E) 11

Solution: Number of students absent on a particular day = 1 % of 50   i.e., 2/100 × 50 = 1   Therefore, the number of students present = 50 - 1= 
50 - 1 = 49
49 students.   Answer:49
Answer: D
A boat can move upstream at 22 kmph and downstream at 42 kmph, then the speed of the current is?
Choose one:
A) 15	B) 16	C) 18	D) 10	E) 12

Solution: US = 22   10S = 42   M = (42 - 22)/2= 
(42 - 22)/2 = 10
10 Answer:10
Answer: D
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?	Choose the correct choice from the following choices:
A) 10	B) 20	C) 24	D) 26	E) 29

Solution: 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   Short cut method:   a:b = 2:3   c:d = 3:4   1.Cross multiplication with both ratios   a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1   2. If 10 is added both the number means   10 * 3= 
  10 * 3 = 30
30 and   10 * 4= 
  10 * 4 = 40
40,   Then 30 ~ 40= 10   ===> 1 -----> 10   ===> 2 -----> 20   20
Answer: B
Mr. Yutaro’s class contains 11 boys and 5 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen? Choose the correct choice from the following answers.
A) 11/24
B) 9/20
C) 11/28
D) 27/48
E) 13/16

Solution: Probability of a girl being chosen first, then a girl:   5/16 * 11/15   Probability of a boy being chosen first, then a boy:   11/16 * 5/15   Probability of a boy and a girl being chosen:   (5*11+5*11) / (15*16)   =11+11/3*16   =22/48   =11/24,   11/24nswer:11/24
Answer: A
The average weight of a group of boys is 20 kg. After a boy of weight 31 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Select the correct option:
A) 12  B) 14  C) 18  D) 24  E) 10

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 20x   After the boy weighing 31 kg joins the group, total weight of boys = 20x + 31   So 20x + 31 = 21(x + 1) = > x = 10.   ANSW10R:10
Answer: E
On his drive to work, Leo listens to one of three radio stations A, B or X. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to X. If X is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?  Choose the correct choice from the following.
A) 0.027
B) 0.09
C) 0.417
D) 0.657
E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.3   Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3= 
0.7 * 0.3 = 0.21
0.21   Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to X and finally falls in love with the program= 0.7^2 * 0.3 = 0.147   Total = 0.657   Ans 0.657
Answer: D
The fourth proportional to 10, 15 and 18 is?  Pick.
A) 21	B) 27	C) 55	D) 88	E) 61

Solution: (15*18)/10= 
(15*18)/10 = 27
27   Answer:27
Answer: B
Today John is 3 times older than Mark. If in 14 years, John will be one year younger than twice the age of Mark on that day, how old is John today? Pick:
A) 13
B) 33
C) 36
D) 38
E) 39

Solution: Given after 14yrs john will be 1 year younger than twice mark's age   i.e 3M+14 = 2(M+14)-1   M=13   =>John's current age = 3M = 39   Answer is 39
Answer: E
Which is a better offer out of (i) a cash payment now of Rs.8100 or (ii) a credit of Rs.8250 after 6 months(6.5% S.I)	Choose the correct choice from the following choices
A) (i)  B) (ii)  C) both (i) and (ii)  D) only (i)  E) NONE OF THESE

Solution: Explanation:   PW=100*(i)mount / 100+(R+T)   (i)NSWER IS (i)
Answer: A
If f(x) = x^4/(x^4 - 1), what is f(1/x) in terms of f(x)?  Choose one:  A) f(x)  B) 1/-f(x)  C) -2/-f(x)  D) -3/-f(x)  E) -f(x)

Solution: If x = 2 then f(x) = 16/15 and f(1/x) = -16/15 which is equal to -f(x)   answer -f(x)
Answer: E
The number 0.5 is how much greater than 1/6 ?	Select the correct option: A) 1/3 B) 2/10 C) 1/50 D) 1/500 E) 2/500

Solution: let x be the difference   then   .5-1/3=x   5/10-1/3=x   x=1/3   ans 1/3
Answer: A
A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?  Pick:
A) 2 hr 30 min
B) 2 hr
C) 4 hr
D) 1 hr 15 min
E) 3 hr 15 min

Solution: Explanation:   Speed upstream =2/2= 
2/2 = 1
1km/hr   Speed downstream=1/(20/60)= 
1/(20/60) = 3
3km/hr   Speed in still water=1/2(3+1)=2km/hr   Time taken to travel 5 km in still water   =5/2=2(1/2)hours=2 hour 30mins   2 hr 30 minNSWER IS 2 hr 30 min
Answer: A