MU-NLPC/Calc-aqua_rat huggingface dataset:
Using all the letters of the word "THURSDAY", how many different words can be formed? Choose the correct choice from the following:
A) 9 B) 8! C) 2 D) 7 E) 5

Solution: Total number of letters = 8   Using these letters the number of 8 letters words formed is 8P8   = 8!.   Answer: 8!
Answer: B
If 10,000 microns = 1 decimeter, and 10,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?	Choose the correct choice from the following options:
A) 0.01
B) 1,000,000
C) 0.001
D) 1,000
E) 1.0e-05

Solution: Given that 10,000 microns = 1 decimeter =10,000,000,000 angstroms   So, 1 micron = 10,000,000,000/10,000   =1,000,000   Answer : 1,000,000
Answer: B
At a florist shop on a certain day, all corsages sold for either $20 or $30. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 35 percent. What was the store's actual revenue from corsages that day?
Choose the most appropriate option:  A) $320  B) $400  C) $600  D) $800  E) $1000

Solution: I am doing it elaborately, hope it will help you.   Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r   so, 20x+30y=r.........(1)   Now,   Given the situation, 20(x+8) + 30(y-8)= r-.25r   => 20x+160+30y-240 = .75r   => 20x+30y = .75r+80............(2)   so, r = .75r+80   => r = 320   The answer is $320.
Answer: A
A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate.If 70% of the males are literate, the number of literate females is : Choose the correct answer
A) 20,000 B) 24,000 C) 30,000 D) 34,000 E) 44,000

Solution: population - 3,00,000, males -1,80,000, females-1,20,000   50%of 3,00,000 literate - so 1,50,000 literate   70% of 1,80,000 literate -so 1,26,000 male literates , so rest s   1,50,000 - 1,26,000 = 24,000   ANSWER:24,000
Answer: B
50% of the population of a village is 23040. The total population of the village is ? Pick:
A) 32256
B) 24000
C) 44936
D) 46080
E) None

Solution: Answer   ∵ 50% of P = 23040   ∴ P = (23040 x 100) / 50 = 46080   Correct Option: 46080
Answer: D
If each side of a square is increased by 25%, find the percentage change in its area?	Pick
A) 65.25  B) 56.25  C) 65  D) 56  E) 46

Solution: Explanation:   let each side of the square be a , then area = a x a   New side = 125a / 100 = 5a / 4   New area =(5a x 5a) / (4 x 4) = (25a²/16)   increased area== (25a²/16) - a²   Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25% Answer: 56.25
Answer: B
Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 20 phone numbers by using the readable digits followed by 20 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
Answers:
A) 1/9 B) 10/243 C) 2/27 D) 10/271 E) 1/1000000

Solution: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).   If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).   P = 20/(9*9*3+9*3) = 2/27.   Answer: 2/27.
Answer: C
Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 9.9. The difference between the unit digit and hundreds digit of that number is :	Choose one
A) a) 4  B) b) 3  C) c) 2  D) d) 1  E) e) 0

Solution: Since the average increased by 9.9 and there were a total of 10 numbers, it means the incorrect number was 99 greater than the correct number.   Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)   Then the incorrect number was cba.   100c + 10b + a - (100a + 10b + c) = 99   99c - 99a = 99(c - a) = 99   99 = 99*1= 
99*1 = 99
99(c - a)   So c - a= 1   Answer (d) 1)
Answer: D
Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 16 years?
Answers:
A) 30
B) 35
C) 40
D) 36
E) 60

Solution: Explanation :   (A + B), five years ago = (15 * 2)= 
(15 * 2) = 30
30 years.   (A+B), now= (30+5*2)= 
(30+5*2) = 40
40 years.   (A + B + C), now= (20 x 3) years =60 years.   C, now = (60 - 40)= 
(60 - 40) = 20
20 years.   C, after 16 years= (20 + 16)= 
(20 + 16) = 36
36 years.   Answer : 36
Answer: D
Two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction. What time will they take to be 32 km apart?
Choose the most appropriate option.
A) 18	B) 16	C) 19	D) 15	E) 34

Solution: Explanation:   Relative speed = 7.5 - 5.5= 
7.5 - 5.5 = 2
2 kmph (because they walk in the same direction)   distance= 32 km   time = distance / speed=32/2= 
32/2 = 16
16 hr   Answer :16
Answer: B
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?	Select:  A) 6620  B) 2888  C) 2776  D) 2997  E) 2718

Solution: 6620 = 20000(11/10)3   = 26620   = 20000   ----------   6620.6620nswer: 6620
Answer: A
Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -10). What is the slope of line m ?	Select the correct option:
A) -3
B) 1
C) -1/3
D) 0
E) Undefined

Solution: Ans: B   Solution: line m goes through midpoint of (2, 4) and (6, -10). midpoint is (4,-3)   as we can see that the y axis of intercept point is (0,-2) means line m is parallel to x axis   slope M= 1   Ans: 1
Answer: B
A 140 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?	Select.
A) 35  B) 20  C) 47  D) 36  E) 40

Solution: 1: 2/5 = 5: 2   2/7 * 140= 
2/7 * 140 = 40
40   Answer:40
Answer: E
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score E for the exam?  Choose the correct option.
A) 74	B) 76	C) 78	D) 80	E) 82

Solution: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d   A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d   Solving above for Mean E= 74.   74nswer: 74.
Answer: A
A new savings account offers 5 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?	Choose the correct choice from the following answers.
A) $80.00  B) $84.40  C) $360.00  D) $6,303.75  E) $6,365.40

Solution: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.05) (1/2) = $150. (Note: the 6 months are “1/2” in the equation since 5% s a yearly rate, not a bi-yearly one).   Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,150. The interest earned during the final 6 months of the year is $6,150(.05)(1/2) = $153.75. Therefore, the total balance is the original amount ($6000) + $150 + $153.75= $6,303.75.   The correct answer is $6,365.40.
Answer: E
How many possible cases are there such that 2 stocks are selected at random from 10 stocks?	Select
A) 35	B) 40	C) 45	D) 50	E) 55

Solution: Number of possible cases = 10c2   =10!/(8!*2!)   =10*9/2= 
10*9/2 = 45
45   Answer 45
Answer: C
How many seconds will a 400 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the correct choice from the following answers:  A) 287  B) 288  C) 900  D) 277  E) 121

Solution: Let length of tunnel is x meter   Distance = 400+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   400+x = (65/3) * 60   400+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 400= 
1300 - 400 = 900
900 meters   Answer: 900
Answer: C
The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is :  Answers:
A) 20	B) 23	C) 169	D) 172	E) 198

Solution: Explanation:   Let the number be x and y . We know that,   (x+y)2=(x2+y2)+2xy=289+2×120   =289+240= 
289+240 = 529
529⇒x+y=√529=23   Correct Option: 23
Answer: B
What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x Select.
A) 23 B) 25 C) 29 D) 35 E) 39

Solution: (35)   The pattern is + 3, + 5, + 3, + 5, …………   So the missing term is = 30 + 5= 
30 + 5 = 35
35.
Answer: D
Out of 8 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
Pick.
A) 1/28
B) 10/28
C) 20/28
D) 11/28
E) 2/28

Solution: The number of exhaustive events = 8C2 = 28.   Let E be event of the 2 fruits being rotten. The number of favourable cases are   2C2 = 1 way.   Required probability = 1/28.   1/28NSWER:1/28
Answer: A
Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 7, while all other numbers remain the same, what is the new average of Set S? Choose one:	A) 6.6	B) 6.7	C) 6.8	D) 6.85	E) 6.9

Solution: Old set S - Total is avg * no of elements = 6.2*10= 
6.2*10 = 62
62   If one number is increased by 7 then total increased to  62+7= 
 62+7 = 69
69   New avg - 69/10= 6.9.   Hence answer is 6.9.
Answer: E
Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan? Choices.
A) 398 km  B) 892 km  C) 387 km  D) 300 km  E) 230 km

Solution: Let the distance travelled be x km.   Total time = (x/2)/30 + (x/2)/25   = 11 => x/60 + x/50 = 11 => (5x + 6x)/300   = 11 => x = 300 km   Answer: 300 km
Answer: D
A motorist travel to a place 150 km away at an average speed of 45 km/hr and returns at 30 km/hr.His average speed for the whole journey in km/hr is  Choose the correct choice from the following options:
A) 36 km/hr  B) 37.5 km/hr  C) 35.5 km/hr  D) 34.5 km/hr  E) None of these

Solution: Explanation:   36 km/hrverage speed will be   2xy/x+y km/hr   = {2(45)(30)}/{45+30} km/hr   = 36 km/hr   36 km/hrnswer: Option 36 km/hr
Answer: A
Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 10 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? Choose one: A) $506.00 B) $726.24 C) $900.00 D) $920.24 E) $926.24

Solution: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have   (2+3+4)= 
  (2+3+4) = 9
9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.   Interest earned after the first time interval: $10,000*2%=$200;   Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;   Interest earned after the third time interval: ($10,000+$200+$306)*4%300+ 6= 
300+ 6 = 306
$306;   Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;   Total: 200+306+(~420)400+ 8+(  12)= 
400+ 8+(  12) = 420
~$420;   Total: 200+306+(~420)=~$726.24.   Answer: $726.24.
Answer: B
If c and d are unique prime integers, which of the following must be even?
Pick:
A) c−d
B) 2c−2d
C) c−2d
D) 2c−d
E) cd^2

Solution: Any number multiplied by 2 has to be an even number   Answer 2c−2d
Answer: B
How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?	Choose the most appropriate option
A) 8
B) 11
C) 12
D) 13
E) None of these

Solution: Explanation:   Required numbers are 24, 30, 36, 42, ..., 96   This is an A.P. in which a = 24, d = 6 and l = 96   Let the number of terms in it be n.   Then tn = 96 a + (n - 1)d = 96   24 + (n - 1) x 6 = 96   (n - 1) x 6 = 72   (n - 1) = 12   n = 13   Required number of numbers = 13.   ANSWER IS 13
Answer: D
A meal cost $ 37.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be:
Select the correct option:	A) 41-43	B) 39-41	C) 38-40	D) 37-39	E) 36-37

Solution: 10%(37.5) = 3.75   15%(37.5) = 5.625   total amount could have been 37.5+3.75 and 37.5+5.625   => could have been between 41.25 and 43.125   => approximately between 41 and 43   41-43nswer is 41-43.
Answer: A
Alice and Paul have a plate with 37 cookies on it. They both eat cookies off of the plate every minute. Paul eats two cookies instead of one every third minute. Alice eats three cookies instead of one every fourth minute. How many minutes does it take them to eat all of the cookies?
Choose the correct answer.
A) 11 minutes	B) 12 minutes	C) 13 minutes	D) 14 minutes	E) 15 mintues

Solution: Alice eats 7 cookies every 4 minutes. Paul eats 4 cookies every 3 minutes. In 11 minutes, Alice eats 7*2 + 3= 
7*2 + 3 = 17
17 cookies, and Paul eats 4*3 + 2= 
4*3 + 2 = 14
14 cookies, for a total of  14+17= 
 14+17 = 31
31 cookies. In 12 minutes, Alice eats 7*3= 
7*3 = 21
21 cookies, and Paul eats 4*4= 
4*4 = 16
16 cookies, for a total of  21+16= 
 21+16 = 37
37 cookies. Thus, the answer is 12 minutes.
Answer: B
There are 193 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 25 are members of both sets A and B. How many of the members of set U are members of set A ?
Choose the correct choice from the following answers
A) 72 B) 85 C) 110 D) 98 E) 108

Solution: You had the answer almost right. The x = 85 refers to ONLY set A.   However what's being asked is how many members are part of set A. This will include:   1. Only Set A   2. Set A and Set B   So the answer is Set A = 85 + Set AB = 85+25= 
85+25 = 110
110   110
Answer: C
Aman started a business investing Rs. 40,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?	Choose the most appropriate option:
A) 12:105:118
B) 60:105:112
C) 12:105:110
D) 12:105:112
E) 60:105:111

Solution: Explanation:   Aman : Rakhi : Sagar = (40000 * 36) : (105000 * 30) : (140000 * 24)   = 60:105:112   Answer: 60:105:112
Answer: B
How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?	Options.
A) 11	B) 14	C) 55	D) 77	E) 12

Solution: T = (660 + 165)/54 * 18/5= 
(660 + 165)/54 * 18/5 = 55
55   Answer: 55
Answer: C
A dozen eggs and 5 pounds of oranges are currently at the same price. If the price of a dozen eggs rises by 3 percent and the price of oranges rises by 6 %. How much more will it cost to buy a dozen eggs and 10 pounds of oranges .  Choose the correct choice from the following answers:
A) 8%
B) 9%
C) 10%
D) 11%
E) 5%

Solution: Say currently both a dozen eggs and 5 pounds of oranges cost $100 (they are at the same price). So, to buy a dozen eggs and 5 pounds of oranges we need $100.   After the increase, the price of a dozen eggs will be $103 and the price of 5 pounds of oranges will be $106. So after the increase, to buy a dozen eggs and 5 pounds of oranges we'll need $209.   Increase = 9%.   Answer: 9%.
Answer: B
Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.	Choose the correct choice from the following:
A) 250 meters	B) 260 meters	C) 270 meters	D) 280 meters	E) 290 meters

Solution: Explanation:   First convert speed from km/hr to m/sec   So, Speed = 72*(5/18)= 
72*(5/18) = 20
20 m/sec   Time= 26 seconds   Let the length of the train be x meters.   We know, Distance = Speed*Time.   [you can remember this formula as remembering DUST = D*ST... Distance=Speed*Time]   x+250 = 20*26   => x = 270 meters   So length of the goods train is 270 meter   Option 270 meters
Answer: C
The total population of a country is 294000, out of which 150000 are males. Out of every 100 males, 98 can read and write, but only 53% of the total population can do so. Find the percentage of women who can read and write.  Pick one
A) 6.125 %  B) 5.125 %  C) 6.000 %  D) 4.125 %  E) None

Solution: Answer   Number of men who can read and write = 150000 × (98 ÷ 100) =147000   Number of men and women who can read and write =294000 × (53 ÷ 100) =155820   Number of women who can read and write 155820 - 147000= 
155820 - 147000 = 8_820
8820   Thus, out of 144000 women 8820 can read and write.   Required percentage= (8820 × 100) ⁄ 144000 %= 6.125   Correct Option: 6.125 %
Answer: A
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. What is the total distance traveled by the man?  Options.
A) 5.78  B) 5.71  C) 5.76  D) 5.73  E) 5.75

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer: 5.76
Answer: C
The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 50, then how long is the base of isosceles triangle?  Choices
A) 5
B) 10
C) 15
D) 20
E) 25

Solution: The base of the isosceles triangle is 50-20-20= 
50-20-20 = 10
10 units   The answer is 10.
Answer: B
A man can row upstream at 15kmph and downstream at 45kmph. Find the rate of current ?
Pick.
A) 15km/hr  B) 20km/hr  C) 10km/hr  D) 5km/hr  E) 25km/hr

Solution: Rate of current = 1/2 (45-15) = 15km/hr   15km/hrnswer is 15km/hr
Answer: A
There are 1000000 people in city X, out of these 70% people having voting rights and out of those 55% voters votes candidate A and out of them 20% voters are senior citizens.Then find out the number of senior citizens who votes candidate A having voting rights?	Choices.
A) 8300  B) 14500  C) 7700  D) 13000  E) 5900

Solution: Total number of people having voting rights = 100000; out of those 70% voters votes candidate A = 70000; out of them 55% voters votes candidate A = 38500; out of them 20% voters are senior citizens = 7700
Answer: C
The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 11000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is  Choose the correct choice:
A) Rs. 7000  B) Rs. 8000  C) Rs. 8500  D) Rs. 9000  E) None

Solution: Answer   Average salary   = 8000 + 5000 + 11000 + 7000 + 9000 / 5   = Rs. 8000   Correct Option: Rs. 8000
Answer: B
In certain code 'QUICK' is written as '178DI' and 'QUOTE' is written as '17953'. How is 'TOKE' written in that code?	Pick one
A) 183I  B) 5954  C) DI71  D) 3I89  E) 59I3

Solution: T = 5   O = 9   K = I   59I3 = 3   Answer: 59I3
Answer: E
A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1987 on her 32nd birthday first be eligible to retire under this provision?	Select the correct option
A) 2003  B) 2004  C) 2005  D) 2006  E) 2007

Solution: She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1987+19=2006.   Answer: 2006.
Answer: D
What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98 Choose the correct answer.
A) 80 B) 82 C) 92 D) 98 E) 100

Solution: Ordering the data from least to greatest, we get:   87, 88, 88, 90, 92, 93, 95, 96, 98   The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)   92
Answer: C
Three hoses work to fill a tub at at different rate. Hose W and B, working together, can fill the tub in 6/5 of an hour. Hoses W and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution	Choose the correct choice from the following answers: A) 3/10 B) 2/5 C) 1/2 D) 1 E) 6/5

Solution: Convert the given time to rate and you will be able to add it up.   Total Rate of W and B = Rate of W + Rate of B = 1/(6/5) = 5/6   Total Rate of W and C = Rate of W + Rate of C = 1/(3/2) = 2/3   Total Rate of B and C = Rate of B + Rate of C = 1/2   Adding all three,   2(Rate of W + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2= 
5/6 + 2/3 + 1/2 = 2
2   Rate of W + Rate of B + Rate of C= 1 tub/hour   Time taken by all three together to fill up the tub is 1 hour=1
Answer: D
Q(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point Q?	Pick one:
A) (1, 2).
B) (2, 0).
C) (0, -2).
D) (-2, 0).
E) (2, 2).

Solution: A quick glance at the options, Q(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=(-2, 0).
Answer: D
In a certain game, a player begins with a bag containing tiles numbered 1 through 12, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
Choose the correct choice
A) 5/18
B) 13/36
C) 3/8
D) 5/8
E) 23/36

Solution: player begins with containing tiles 1 to 10 and have equal probability of selecting means   Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.   Next , player draws one title , if number is even player stops or otherwise title is odd without replacement   player draws second title.   If second title is even , player stops or title is odd without replacement player draws third title.   in third title , without replacement of first and second title, player draws and stops it.   the sum of tilte probability is odd. here two conditions are possible.   1st condition is   1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.   Here are we are not selecting 1st condition as even stops because sum of tile is odd.   Here 5 odd numbers are there we can select 1out of 5 odd numbers.   without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.   here we are selecting one number out of remaining 9 numbers. so probability is 5/18.   we are selecting 1 even number out of 5.   2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.   Then probability is 5/10*4/9*3/8=1/12.   Finally sum of probability of two conditions is 5/18+1/12   =3/8.   so option 3/8 is correct.
Answer: C
A certain car averages 25 miles per gallon of gasoline when driven in the city and 45 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? Choose the correct option:
A) 28
B) 30
C) 33
D) 36
E) 40

Solution: 10*1/25 gpm+50*1/45 gpm=1.6=1.5 total gallons   60 total miles/1.5 total gallons=40 average mpg   E. 40
Answer: E