MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Choose the correct answer
A) 76 sec  B) 89 sec  C) 87 sec  D) 15 sec  E) 16 sec

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:89 sec
Answer: B
In how many ways can a committee of 6 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls? Choose the most appropriate option
A) 67
B) 64
C) 65
D) 66
E) None of these

Solution: There are 2 options: the selected groups have no girls or one girls.   -First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10= 
6*10 = 60
60   -Second case: 4 boys: 5C4= 5   So there are 60 + 5 = 67 ways in total.   67
Answer: A
If the radius of a circle decreased by 50% its area is decreased by:	Choose the correct choice from the following.
A) 75 B) 79 C) 72 D) 70 E) 80

Solution: Original area = πr(power)2   New area = π(r/2)(power)2 = (πr(power)2)/4   Reduction in area = [(πr(power)2 - (πr(power)2)/4]2 = (3πr(power)2)/4   Reduction percent = ((3πr(power)2)/4 × 1/(πr(power)2 × 100) % = 75%   75nswer is 75.
Answer: A
A certain psychologist charges $25 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $250, what is the total charge to a patient who receives only 2 hours of therapy ?  Select
A) $115 B) $135 C) $150 D) $165 E) $192

Solution: Let the charge for first hour = x+25   then charge for each additional hour = x   x+25 + 4x = 250   => 5x = 225   => x = 45   Total charge for patient for 3 hours of therapy = x+25 + x = 2x+25   = 115 $   $115nswer $115
Answer: A
A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost W for a course at the gym's highest level?	Pick:
A) $175  B) $245  C) $425  D) $675  E) $725

Solution: Let the cost of a course in level 1 = x   => Cost of level 2 = x-(50*1)... and so on   => cost of level 11 = x-(50*10) = x-500   => Total cost W of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)   = 11x -50 (1+2+....+10)   = 11x - (50*55)   => 11x-2750 = 4675   11x = 7425   x= 675   x-500=175   $175nswer $175
Answer: A
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H  Answers: A) 153 B) 150 C) 137 D) 126 E) 89

Solution: let the number be x, now x is halved => x/2..the question asks what is x?   x(number) + x/2 (half of that number) = something   => 3x/2 = something   => x = 2 (something) / 3   so the answer choice must be divisible by 3   eliminate C, E right away   check the rest   D satisfies   3x/ 2 = 126   => x = 84   Verify. 84+ 42 = 126   Answer is 126
Answer: D
A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Choose the correct choice from the following choices:
A) 1750
B) 2789
C) 2500
D) 1550
E) 2000

Solution: Total production of salt by the company in that year = 1000+ 1100+ 1200+ .... + 2100= 18600.   Average monthly production of salt for that year = 18600/12= 
18600/12 = 1_550
1550.   Answer: 1550
Answer: D
A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 4:2:3, respectively, but he wanted to make more money, so he shifted the ratio to 2:2:5, respectively. How many more acres of land were planted with tobacco under the new system?	Select
A) 90 B) 150 C) 270 D) 300 E) 450

Solution: Originally (3/9)*1350= 
(3/9)*1350 = 450
450 acres were planted with tobacco.   In the new system (5/9)*1350= 
(5/9)*1350 = 750
750 acres were planted with tobacco.   Thus   750-450= 
  750-450 = 300
300 more acres were planted with tobacco.   The answer is 300.
Answer: D
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :	Pick one
A) 117.8  B) 118  C) 124.75  D) 149  E) 187

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   124.75
Answer: C
A invested $300 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?
Pick.
A) $100  B) $75  C) $20  D) $120  E) $50

Solution: A:$75 = 300*12:200*6   A:$75 = 3:1   A's share = 100*3/4= 
100*3/4 = 75
$75   Answer is $75
Answer: B
Find the least number of complete years in which a sum of money put out at 13% compound interest will be more than double of itself?  Choose the correct choice from the following
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: 6 years   Answer: 6
Answer: B
0.07 x 0.00112 is equal to:  Choose the correct answer.
A) 6.48 x 10(power -5)	B) 6.84 x 10(power -4)	C) 4.68 x 10(power -4)	D) 7.84 x 10(power -5)	E) None of them

Solution: 7 x 112 = 784. Sum of decimal places = 7   So, 0.07 x 0.00112 = 0.0000784 = 7.84 x 10(power -5)   Answer is 7.84 x 10(power -5)
Answer: D
If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? Select the correct option:
A) a.66000  B) b.67000  C) c.68000  D) d.69000  E) e.70000

Solution: 1% is quite small and hence the answer is a.66000)
Answer: A
For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6?	Choose the correct answer:
A) None
B) One
C) Two
D) Three
E) Four

Solution: The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there.   2^6=64   2^5*3=96   Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it.   Answer is 2 (Two).
Answer: C
Three small cruise ships, each carrying 8 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?  Pick:
A) 9,832 B) 10,752 C) 11,364 D) 12,548 E) 13,786

Solution: The number of ways for the ships to go to the ports is 3! = 6.   At Port A, the number of ways to choose two winners is 8C2 = 28.   At Port B, the number of ways to choose one winner is 8.   At Port C, the number of ways to choose one winner is 8.   The total number of ways to give out gift certificates is 6*28*8*8 = 10,752   The answer is 10,752.
Answer: B
If I walk at 8 km/h, I miss the bus by 14 minutes. If I walk at 9 km/h, I reach 16 minutes before the arrival of the bus. How far I walk to reach the bus stand ? Pick one.
A) 3.4 km
B) 2.9 km
C) 2.4 km
D) 2.6 km
E) 2.8 km

Solution: d = product of speed difference of time /difference of speed   d = 8 X 9/60[14âˆ’(âˆ’16)/9-8]   [Here, â€“ve sign indicates before the schedule time]   â‡’ d = 2.4 km   Answer 2.4 km
Answer: C
A shopkeeper sells one radio for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. What is his total gain or loss percentage?
Choose the correct choice: A) 6 15/17% B) 5 15/17% C) 3 15/17% D) 4 15/17% E) 5 15/18%

Solution: selling price of first radio=840   gain =20%   cost price of first radio=840×100/120=700   selling price of second radio =960   loss =4%   cost price of second radio =960×100/96=1000   total cost price =700+1000= 
700+1000 = 1_700
1700   total selling price=840+960= 
840+960 = 1_800
1800   total gain=1800−1700=100   total gain percentage =100*100/1700=100/17%=5 15/17%   Answer : 5 15/17%
Answer: B
On a certain Monday, Carlos drove to work at an average speed of 10 miles per hour and home from work along exactly the same route at an average speed of 20 miles per hour. Which of the following is closest to his average speed for both trips combined?	Choices:  A) 17  B) 16  C) 15  D) 14  E) 13.33

Solution: To solve the average speed questions, we need to know the total distance and the total time.   Let us assume that the distance from work = D   This will also be the distance from work to home   Hence total distance travelled = 2D   Time in going to work = D/10,   Time in coming back from work = D/20   Hence average speed of both the trips = 2D/ (D/10 + D/20)   = 2*20/3 = 13.33   13.33
Answer: E
J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?  Choose the correct option
A) 93.5  B) 90  C) 6.75  D) 6.25  E) 2

Solution: Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.   Let, P = 400   then J = (75/100)*400= 
(75/100)*400 = 300
300   also J= (80/100)*T   i.e. T = 300*100/80= 
300*100/80 = 375
375   and T= [1-(r/100)]*P   i.e. 100-r = 100*T/P = 100*375/400= 
100*375/400 = 375/4 = around 93.75
93.75   i.e. r= 6.25   Answer: Option 6.25
Answer: D
Jennifer had $120 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? Choose the correct option.
A) $16	B) $14	C) $5	D) $15	E) $0

Solution: 1/5 x $120 = $24 for sandwich   1/6 x $120 = $20 for museum   1/2 x $120 = $60 for book   $24 + $20 + $60 = $104 spent   $120 - $104  24 +  20 +  60= 
 24 +  20 +  60 = 104
$104 spent   $120 - $104 = $16 left over   correct answer $16 120 -  104= 
 120 -  104 = 16
$16 left over   correct answer $16
Answer: A
In Football game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?  Choose the correct choice from the following answers:
A) 1/3	B) 4/9	C) 5/9	D) 2/3	E) 3/4

Solution: In Football game,Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:   P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.   Answer: 5/9.
Answer: C
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?  Choose the correct choice:  A) 16  B) 18  C) 22  D) 23  E) 24

Solution: == 3:5:7   Total parts = 15   = The largest number value is 42   = The largest number is = 7   = Then 7 parts -----> 42 ( 7 * 6 = 42 )   = smallest number = 3 & Largest number = 7   = Difference between smallest number & largest number is = 7 - 3= 
7 - 3 = 4
4= Then 4 parts -----> 24 (4 * 6 = 24)   24
Answer: E
What is the number of integers from 11 to 1010 (inclusive) that are divisible by neither 12 nor by 15?
Choose the most appropriate option:
A) 565 B) 856 C) 783 D) 590 E) 300

Solution: In 1000 consecutive numbers, number of multiples of 12 = 1000/12 = 83 (Ignore decimals)   In 1000 consecutive numbers, number of multiples of 15 = 1000/15 = 66   Number of multiples of 12*15 i.e. 180 = 1000/180 = 5   Number of integers from 11 to 1010 that are divisible by neither 12 nor by 15 = 1000 - (83 + 66 - 5) {Using the concept of sets here) = 856   Answer is 856
Answer: B
A man has some hens and cows. If the number of heads be 44 and the number of feet equals 140, then the number of hens will be: Choose the correct choice:
A) 22 B) 23 C) 18 D) 26 E) 28

Solution: let hens be x and cows be y   now,   feet: x*2+y*4=140   heads: x*1+y*1=44   implies, 2x+4y=140 and x+y=44   solving these two equations, we get x=18 and y=26   Therefore, hens are 26.   ANSWER:18
Answer: C
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is -. Options:
A) 1/6
B) 2/18
C) 3/2
D) 25/42
E) 4/7

Solution: Explanation:   Total fruits = 9   Since there must be at least two apples,   (âµCâ‚‚ * â´Câ‚)/â¹Câ‚ƒ + âµCâ‚ƒ/â¹Câ‚ƒ = 25/42.   25/42
Answer: D
In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 107800. How many times did he participate in the competition?	Answers
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: 107800 = 2*2*2*5*5*7*7*11   John participated 8 times.   The answer is 8.
Answer: E
In a School, 50 percent of the students are choose apples and the remaining are Mango. In a vote of choosing fruits, if 65 percent of the students who are apples and 25 percent of the students who are Bananas are expected to vote for Candidate A, what percent of the students are expected to vote for Candidate A ?
Choose the correct choice from the following answers:
A) 63%  B) 45%  C) 50%  D) 71  E) 57%

Solution: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.   50*0.65= 
50*0.65 = 32.5
32.5 Democrats are expected to vote for Candidate A;   50*0.25= 
50*0.25 = 12.5
12.5 Republicans are expected to vote for Candidate A.   Thus total of   32.5+12.5= 
  32.5+12.5 = 45
45 students are expected to vote for Candidate A, which is 45% of the total number of students   Answer: 45%.
Answer: B
Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
Select:
A) Rs.19
B) Rs.18
C) Rs.16
D) Rs.5
E) Rs.3

Solution: Average price per book   = (1150 + 920) / (65 + 50) = 2070 / 115 = Rs.18   Answer:Rs.18
Answer: B
A boy has 9 trousers and 13 shirts. In how many different ways can he select a trouser and a shirt?	Choose the correct answer
A) 100  B) 102  C) 117  D) 108  E) 110

Solution: The boy can select one trouser in nine ways.   The boy can select one shirt in 13 ways.   The number of ways in which he can select one trouser and one shirt is 9 * 1 = 117 ways.   117
Answer: C
A certain car uses one gallon of gasoline every 34 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
Choose the correct option
A) 15% B) 20% C) 22.5% D) 35% E) 50%

Solution: 4 miles on the highway = 4/34 gallons;   4 miles in the city = 4/20 gallons;   Total = 4/34 + 4/20 = 27/85 gallons.   8 miles on the highway = 4/17 gallons .   The % change = (27/85 - 4/17)/(4/17) = 0.35.   Answer: 35%.
Answer: D
A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?  Pick one:
A) 7000  B) 7029  C) 2778  D) 2800  E) 2791

Solution: Let the sum be Rs. x.   (x * 18 * 2)/100 - (x * 12 * 2)/100 = 840 => 36x/100 - 24x/100 =840   => 12x/100 = 840 => x = 7000.7000nswer:7000
Answer: A
The sum of the first eight terms of a geometric series is 10,001 times the sum of its four terms . Find the common ratio of these series Choose the correct choice from the following answers
A) 1000  B) 1  C) 10  D) 100  E) 0.1

Solution: a (r^ 8 - 1)/(r - 1 ) = 10001 a (r^ 4 –1)/(r – 1)   r ^4 +1 = 10001, r =10   ANSWER:10
Answer: C
If A ^B means A raised to the power of B, in which of the following choices must P be greater than Q	Choose the correct answer.
A) 7  B) 1  C) 2  D) 3  E) 4

Solution: Option A is wrong as P = Q   Option 1 is wrong as PQ=Log0.92Log0.9=0.79139PQ=Log0.92Log0.9=0.79139   Option C is also wrong as aP>aQaP>aQ then P>Q if a > 1   Answer:1
Answer: B
A committee of three people is to be chosen from 4 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?  Choices
A) 16
B) 24
C) 26
D) 30
E) 32

Solution: Total no of ways of choosing a committee = 8C3 = 56   No of ways to choose first couple = 4C1 = 4   No of ways to choose 1 person from remaining 6 = 6C1 = 6   Total number of ways of choosing a married couple to be in the same committee = 4*6= 
4*6 = 24
24   So, no of ways not choosing a married couple= 56-24= 
56-24 = 32
32   ANS:E. 32
Answer: E
Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?  Select.
A) 297
B) 268
C) 300
D) 179
E) 172

Solution: 1/2:1/3:1/4 = 6:4:3   3/13*1300= 
3/13*1300 = 300
300   Answer: 300
Answer: C
In a certain kindergarten, half of the children are allergic to peanuts, 10 children are not allergic to cashew nuts, 10 children are allergic to both peanuts and cashew nuts, and 18 children are allergic to cashew nuts. How many of the kindergarten's children are NOT allergic to peanuts and are NOT allergic to cashew nuts?	Choose the correct choice from the following answers
A) 14  B) 10  C) 8  D) 6  E) 4

Solution: We are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10, so total =10+18=28...   Children allergic to both are 10...   18 are allergic to cashew nuts, so and half or  28/2= 
 28/2 = 14
14 are allergic to peanuts..   So children allergic to at least one of the TWO are 18+14-10=22..   Therefore children NOT allergic to any of the TWO are 28-22= 
28-22 = 6
6   ANSWER:6
Answer: D
The average temperature for Tuesday, Wednesday and Thursday was 45°C. The average temperature for Wednesday, Thursday and Friday was 50°C. If the temperature on Friday be 53°C, what was the Temperature on Tuesday?	Select:
A) 39°C  B) 44°C  C) 37°C  D) 42°C  E) 38c

Solution: 38cxplanation:   T + W + T = 45 × 3 = 135°C   W+ T+ F = 50 × 3 = 150°C   Also, temperature on Friday = 53°C   Temperature on Tuesday = 135 +53 - 150= 
135 +53 - 150 = 38
38°C   Answer: Option 38c
Answer: E
If a man walks at a rate of 10kmph, he misses a train by 14minutes. However, if he walks at the rate of 12kmph, he reaches the station 10minutes before the arrival of the train. Find the distance covered by him to reach the station.	Options:
A) 6	B) 15	C) 12	D) 4	E) 8

Solution: Let the required distance x km   difference in the times taken at two speeds = 12min = 1/5 hr   (x/10)-(x/12) = 1/10   x = 6   the required distance is 6 km   6nswer is 6
Answer: A
One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)? Options.
A) 1/13  B) 3/13  C) 5/13  D) 4/13  E) 2/13

Solution: Clearly, there are 52 cards, out of which there are 12 face cards.   P (getting a face card) = 12/52   = 3/13   Answer should be 3/13
Answer: B
If S is the least common multiple of 90,196, and 300, which of the following is NOT a factor of S?  Choose one:
A) 600 B) 700 C) 900 D) 2,100 E) 4,900

Solution: IF S is the least common multiple of 90,196 and 300, which of the following is NOT a factor of S?   600- 600   B- 700   C- 900   D- 2100   E- 4900   90 = 2 * 3 * 3 * 5   196 = 2 * 2 * 7 * 7   300 = 2 * 2 * 3 * 5 * 5   LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7   (TWO 2, TWO 3, TWO 5, TWO 7)   600 = 2 * 2 * 2 * 3 * 5 * 5   700 = 2 * 2 * 5 * 5 * 7   900 = 2 * 2 * 3 * 3 * 5 * 5   2100 = 2 * 2 * 3 * 5 * 5 * 7   4900 = 2 * 2 * 5 * 5 * 7 * 7=600
Answer: A
The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after 5 seconds an object is falling at a speed of 50 miles per hour, how fast will it be falling after 12 seconds?  Choose one.
A) 18 miles per hour	B) 120 miles per hour	C) 216 miles per hour	D) 1080 miles per hour	E) 5400 miles per hour

Solution: Since Velocity is proportional to Time   Velocity =k*Timewhere k is the constant of proportionality   Time= 5 seconds   Velocity = 5k = 50 miles per Hour   i.e. k = 10   i.e. The relation between Velocity and Time becomes   Velocity =10*Time   Time= 12 seconds   Velocity = 10*12= 
10*12 = 120
120 miles per hour   Answer: Option 120 miles per hour
Answer: B
Two sides of a triangle have lengths x and r and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to r ?  Choose the correct choice from the following answers:
A) a) 2 : 3  B) b) 3 : 4  C) c) 4 : 3  D) d) 3 : 2  E) e) 2 : 1

Solution: Ahhhh....my bad. Thank you, you're correct. 8x = 6r --> x/r = 3/4.   Actually b) 3 : 4 is the right answer.
Answer: B
If (10^40) – 34 is written as an integer in base 10 notation, what is the sum of the digits in that integer?  Choose the correct choice from the following answers:
A) 354
B) 254
C) 344
D) 364
E) 324

Solution: We know that (10^40) is ending 00, so (10^40) – 34=9....9966   total number of digits in (10^40) – 34 is 40, or 38 digits of 9 and two digits 6 and 6.   answer choice is   38*9+12= 
  38*9+12 = 354
354   354nswer is 354 354
Answer: A
There are 24 students in a class. In how many different ways can a committee of 3 students be formed?  Choose the correct choice from the following options:
A) 1250	B) 1800	C) 2024	D) 3256	E) 2864

Solution: 2420243 = 24*23*22 / 6= 
24*23*22 / 6 = 2_024
2024   The answer is 2024.
Answer: C
How many pages the book have, if total 297 digits are used to form the page numbers? Pick.
A) 135 pages B) 136 pages C) 137 pages D) 138 pages E) 139 pages

Solution: First 9 pages .. 9 digits   next 90 pages .. 180 digits   next 36 pages ... 108 digits   ----------------------   Total ...135 pages ...297 digits   135 pagesNSWER:135 pages
Answer: A
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 80 sq. feet, how many feet of fencing will be required? Choose the correct choice from the following
A) 28  B) 40  C) 68  D) 88  E) 78

Solution: We have: l = 20 ft and lb = 80 sq. ft.   So, b = 4 ft.   Length of fencing = (l + 2b) = (20 + 8)= 
(20 + 8) = 28
28 ft.   28NSWER:28
Answer: A
X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit? Select the correct option:
A) 14400	B) 13400	C) 11500	D) 12500	E) 13000

Solution: Ratio of the investment   =21000:17500=210:175 =42:35=6:5   Share of X in the profit   =26400×6/11=2400×6=14400   14400nswer is 14400.
Answer: A
In a graduating class, 40 percent of the students are male. In this class, 50 percent of the male students and 30 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?	Select the correct option: A) 0.56 B) 0.62 C) 0.68 D) 0.74 E) 0.8

Solution: Let x be the total number of students.   The number students who are younger than 25 is 0.5*0.4x+0.7*0.6x = 0.62x   The answer is 0.62. 0.5*0.4 +0.7*0.6= 
 0.5*0.4 +0.7*0.6 = 0.62
0.62x   The answer is 0.62.
Answer: B
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?  Pick:  A) 5/21  B) 5/25  C) 5/29  D) 5/26  E) 5/22

Solution: Number of ways of (selecting at least two couples among five people selected)   As remaining person can be any one among three couples left.   Required probability   = (10 * 6)/252 = 5/21   5/21nswer: 5/21
Answer: A