MU-NLPC/Calc-aqua_rat huggingface dataset:
On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000?
Choose the correct option:
A) 15  B) 16  C) 18  D) 20  E) 24

Solution: 5,000(1 + x)^10 = 20,000   (1+x)^10 = 4 = 2^2   (1+x)^10 = ((1+x)^5)^2 = 2^2   Therefore, (1+x)^5 = 2   5000(1 + x)^n = 40,000   (1+x)^n = 8   (1+x)^n = 2^3   (1+x)^n = ((1+x)^5)^3 = (1+x)^15   Therefore, n = 15.   The answer is 15.
Answer: A
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire
rest of the car, then the share of each of the remaining persons increased by ?  Choose the correct choice from the following answers.
A) 1/9 B) 1/8 C) 1/7 D) 7/8 E) 8/7

Solution: When there are eight people, the share of each person is 1/8th the total cost   ANSWER:1/8
Answer: B
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is	Choose one
A) 2/2  B) 1/2  C) 7/2  D) 8/2  E) 6/2

Solution: Explanation:   The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer:1/2
Answer: B
Departments A, B, and C have 4 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?	Choose the correct choice from the following choices
A) 12,610  B) 40,000  C) 100,000  D) 190,000  E) 400,000

Solution: 4c1 * 4c1* 4c1*20c2 = 10*10*10*190=12,610. Hence 12,610 is the correct answer.
Answer: A
A father is Quadrice as old as his daughter today. After 20 years, he would be only two times as old. At the time of daughter’s birth, how much old the father be? Choose the most appropriate option
A) 30
B) 10
C) 40
D) 20
E) 60

Solution: A   30   If the ages of daughter and father today by ‘A’ and ‘4A’ years correspondingly.   4A + 20 = 2 (A+20)   A = 10 years => 4A = 40 years.   30t the time of daughter’s birth, father’s 30ge   40 – 10 = 30 years old
Answer: A
The unit digit in the product (784 x 618 x 917 x 463) is:  Choose the correct option: A) 5 B) 9 C) 16 D) 2 E) 42

Solution: Explanation:   Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2   2
Answer: D
Find the average of all the numbers between 16 and 34 which are divisible by 5?	Select the correct option:
A) 10
B) 20
C) 28
D) 30
E) 15

Solution: Average = (20+25+30) 3 = 85/3 = 28   Answer is 28
Answer: C
How much time will take for an amount of Rs. 100 to yield Rs. 81 as interest at 4.5% per annum of simple interest? Choices.
A) 7	B) 4	C) 18	D) 10	E) 15

Solution: Time = (100 * 81) / (100 * 4.5) = 4 years'   Answer:18
Answer: C
A fill pipe can fill 1/3 of cistern in 20 minutes in how many minutes, it can fill 3/4 of the cistern?	Options:	A) 15 min	B) 45 min	C) 25 min	D) 40 min	E) 50 min

Solution: 1/3 of the cistern can fill in 20 min   3/4 of the cistern can fill in = 20*3*3/4= 
20*3*3/4 = 45
45min   Answer is 45 min
Answer: B
There are 4 copies of 5 different textbooks. In how many ways can they be arranged on a shelf?	Choose the most appropriate option:
A) 20!/4!  B) 20!/5(4!)  C) 20!/(4!)^5  D) 20!  E) 5!

Solution: There are 4 copies of 5 different textbooks.20!/((4!)^5)   Answer - 20!/(4!)^5
Answer: C
We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value Q of the ratio A/B? Choose one:	A) 1/2	B) 1/3	C) 2/3	D) 1/4	E) 1/5

Solution: Q-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.   Therefore, the answer is 1/2.
Answer: A
In a bag, there are 10 discs, numbered 1 to 10 (no duplicates). If we randomly choose 4 of the discs, what is the probability that the range of the numbers chosen is 7?
Choose the correct choice from the following
A) 1 / 14	B) 1 / 7	C) 3 / 14	D) 9 / 28	E) 4 / 7

Solution: Probability (A) = No of suitable outcomes where A happens/Total no of outcomes   We use combinations to get "No of suitable outcomes where A happens" and "Total no of outcomes" and then calculate the required probability. So for the time being, just forget that you have to find some probability.   Focus on two things: "No of suitable outcomes where A happens" and "Total no of outcomes"   It is easy to find total number of outcomes. 10C4. e.g. (2, 3, 4, 6), (4, 1, 9, 5) etc etc etc   In how many combinations is range 7? (This is the "No of suitable outcomes where A happens")   (3, 10, a, b), (2, 9, c, d) and (1, 8, e, f)   a and b are numbers between 3 and 10 (so that range doesn't exceed 7)   c and d are numbers between 2 and 9   e and f are numbers between 1 and 8   In how many ways can you choose a and b? 6C2 (Any 2 out of 6 numbers between 3 and 10). So how many 4 number combinations are there which look like this: (3, 10, 4, 6), (3, 10, 7, 5) etc?   I hope you agree it is 6C2.   Similarly, you get 6C2 combinations of the type (2, 9, c, d) and 6C2 of the type (1, 8, e, f).   No of suitable combinations = 63 / 142 + 63 / 142 + 63 / 142   Now, the required probability = No of suitable combinations where A happens/Total no of outcomes   = (3*63 / 142)/103 / 144 =3/14   3 / 14orrect answer is 3 / 14
Answer: C
If 0.25 : x : : 2 : 6, then x is equal to
Choose the correct choice:
A) 0.65 B) 0.25 C) 0.75 D) 0.85 E) None

Solution: Sol.   (x×2) = (0.25×6) ⇒ x = 1.5/2 = 0.75.   Answer 0.75
Answer: C
Ravi can do a piece of work in 26 days while Prakash can do it in 40 days. In how many days will they finish it together?	Options:  A) 15 25/33 days  B) 16 1/33 days  C) 17 1/33 days  D) 17 25/33 days  E) 18 1/33 days

Solution: 1/26 + 1/40 = 33/520   520/33   = 15 25/33 days   15 25/33 daysnswer: 15 25/33 days
Answer: A
Find the invalid no.from the following series 12, 19, 24, 31, 36, 39	Choose the correct choice
A) 13  B) 18  C) 40  D) 39  E) 25

Solution: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 39 is wrong.   Answer : 39
Answer: D
For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(101) + h(100)?
Choose the most appropriate option:  A) 0  B) 100  C) 102  D) 99  E) 105

Solution: h(101) = 1*3*5*7*9*...*99*101   h(100) = 1*3*5*7*9*...*99   h(101) +h(100) = 1*3*5*7*9*...*99 + 1*3*5*7*9*...*97 = 1*3*5*7*9*...*99*(101 + 1) = 1*3*5*7*9*...*99*102   hence:102
Answer: C
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? Select: A) 19 B) 70 C) 27 D) 29 E) 20

Solution: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%.Answer: 70
Answer: B
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 65 kilometers, Maxwell's walking speed is 2 km/h, and Brad's running speed is 3 km/h. What is the distance traveled by Maxwell when they meet in the middle?	Choose the correct option.
A) 25  B) 23  C) 22  D) 24  E) 26

Solution: Consider Max starts from Point A and Brad Starts from Point B and move towards each other.   Assume they shall meet at point O after Time 'T'. The question asks us to find OA.   From the question stem we can make out :- Distance OA = 50km - Distance OB   => 2xT = 65 - 3xT (i.e distance =Speed x Time)   => 5T = 65   Hence T = 13   OA = 2x 13 = 26 Km   Answer : 26
Answer: E
How many 1/3 pound paperback books together weigh 25 pounds? Answers
A) 35	B) 50	C) 60	D) 75	E) 80

Solution: Explanation:   If each book weighs 1/3 pound, then 1 pound = 3 books. We can set up a proportion to solve: 1 pound / 3 books = 25 pounds / x books. Now cross-multiply:   (1)(x) = (3)(25)   X = 75   Answer :(75)
Answer: D
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)?  Choose the correct choice from the following:	A) 3/13	B) 3/12	C) 3/11	D) 3/12	E) 3/18

Solution: Explanation:   Clearly, there are 52 cards, out of which there are 12 face cards.   P (getting a face card) = 12/52=3/13.   3/13nswer: 3/13
Answer: A
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 11:00 a.m., at what time was it one-eighth full?	Choose one:
A) 10:00 a.m. B) 7:00 a.m. C) 6:00 a.m. D) 4:00 a.m. E) 2:00 a.m.

Solution: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 11:00 a.m -1 hour = 10:00 a.m.   10:00 a.m.nswer: 10:00 a.m..
Answer: A
A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
Choose the correct choice from the following answers:
A) 1 hour 30 minutes
B) 1 hour 23 minutes
C) 1 hour 20 minutes
D) 1 hour 28 minutes
E) 1 hour 26 minutes

Solution: Let the distance and original speed be d km and k kmph respectively.   d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3   => (5d - 4d)/4k = 1/3 => d = 4/3 k   Time taken to cover the distance at original speed   = d/k = 4/3 hours = 1 hour 20 minutes.   Answer:1 hour 20 minutes
Answer: C
Which of the following are divisible by both 2 and 3?
I. 234,124,422
II. 88,865,544,274
III. 5,555,554,673	Select.
A) I​ only  B) I and II​  C) II and III  D) II Only  E) I​ and III

Solution: III. is not divisible by 2 since the last digit is odd so we eliminate option C and E, we are left with option A, B and D   Among option I and II lets check the divisibility of 3   I. is divisible by 3 since sum of the digits is 24 , which is divisible by 3   II. is not divisible by 3 since sum of the digits is not divisible by 3   Thus among the given options only (A) holds true.   I​ onlynswer: I​ only
Answer: A
Three numbers are in the ratio 3:5:8. The largest number value is 152. Find difference between Smallest & largest number is?
Choices:
A) 16  B) 90  C) 38  D) 95  E) 78

Solution: Explanation:   == 3:5:8   Total parts = 16   = The largest number value is 152   = The largest number is = 8   = Then 8 parts -----> 152 ( 8 * 19 = 152 )   = smallest number = 3 & Largest number = 8   = 95ifference between smallest number & largest number is = 8 - 3= 
8 - 3 = 5
5= Then 5 parts -----> 95 (5 * 19 = 95)   Answer: Option 95
Answer: D
Andrew grossed $530 one week by working 49 hours. His manager pays him time-and-a-half for all hours worked in excess of 35 hours. What is Andrew's regular hourly wage?
Select the correct option
A) $10 per hour
B) $15 per hour
C) $5 per hour
D) $12 per hour
E) $20 per hour

Solution: Denote by x the regular hourly wage.   Then 1.5x is the hourly overtime wage.   For 35 hours, Andrew received a salary of 35x.   For 49-35=12 hours, he received 12(1.5x)=18x   Total salary: 35x+18x=53x which equals $530.   53x35 +18= 
35 +18 = 53
53x which equals $530.   53x=530 implies x=10 ($10 per hourndrew receives $10 per hour)   $10 per hournswer $10 per hour 10.
Answer: A
4, 12, 48, 240, 1440,10080,80640 (...)	Options:
A) 7620 B) 10080 C) 6200 D) 10020 E) 725760

Solution: 725760xplanation :   Go on multiplying the given numbers by 3, 4, 5, 6, 7,8,9   Answer : Option 725760
Answer: E
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum E of all possible 2-digit remainders for x/y? Choose the correct choice from the following:
A) 560	B) 616	C) 672	D) 728	E) 784

Solution: ans B 616...   remainders = .32=32/100=8/25=16/50 and so on..   so two digit remainders are 16+24+32+....+96..   E=8(2+3+4....+12)=616.616
Answer: B
If Albert’s monthly earnings rise by 27%, he would earn $567. If, instead, his earnings rise by only 26%, how much (in $) would he earn this month?	Pick one:
A) 643
B) 652
C) 562
D) 578
E) 693

Solution: =567/1.27∗1.26   =562=562   Answer is 562
Answer: C
If cement, gravel and sand are to be mixed in 7:10:13 and 9 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.  Choose the correct choice from the following options.
A) 38 7/8
B) 36
C) 38 4/7
D) 34 5/7
E) 34 6/7

Solution: Cement:Gravel:Sand = 7:10:13 --> total of   7+10+13= 
  7+10+13 = 30
30 parts.   If we use 9 tons of cement, then we'll get 9/7*30= 38 4/7 tons of mixture.   Answer: 38 4/7.
Answer: C
The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 4 seconds? Pick one.
A) 4 B) 9 C) 39 D) 48 E) 63

Solution: Given: z=s^2+2s for 0≤s≤7   z(4) = 4^2 + 2*4 = 24   z(7) = 7^2 + 2*7 = 63   Therefore z(7) - z(3) = 63 - 24= 
63 - 24 = 39
39 km/hr   Option 39
Answer: C
The ratio of male to female in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class?  Choose one:
A) a)160 degree
B) b) 168 degree
C) c)191 degree
D) d)72 degree
E) e)204 degree

Solution: let the common ratio be x.. so M=2x and F=3x and Total=5x   1 of M= 2x and 1 of F= 3x..   Total preferring that carrer =5x   Now 5x= 360, so x=360/5=72..   so x*8/3= 72*8/3= 
72*8/3 = 192
192   d)72 degree
Answer: D
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Select
A) 160	B) 175	C) 180	D) 195	E) 205

Solution: Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 * 8 * 4)= 
(5 * 8 * 4) = 160
160.   Therefore, 160 * 2.40 + x * 3.20= 432   => 3.20x = 432 - 384= 
432 - 384 = 48
48=> x = 15.   Hence, total hours of work = (160 + 15)= 
(160 + 15) = 175
175.   ANSWER:175
Answer: B
A certain airline's fleet consisted of 70 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?  Choose the correct choice from the following.
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: Let x be the number of years.   4x > 70 - 3x   7x > 70   x > 10   The answer is 11.
Answer: E
Calculate Rebecca's average score in an exam if she obtained the following marks 70, 57, 69, 89 and 85 out of 100 in different subjects.
Select:
A) 74
B) 94
C) 54
D) 84
E) 64

Solution: Explanation:   (70+57+69+89+85)/5= 
(70+57+69+89+85)/5 = 74
74   74nswer: Option 74
Answer: A
In a simultaneous throw of 2 dice, what is the probability of getting a total of 8? Choose the correct choice from the following answers
A) 3/17
B) 7/36
C) 1/36
D) 5/36
E) 7/17

Solution: n(S) = 6*6= 
6*6 = 36
36   E= event of getting a total of 8 = {(2,6),(3,5),(4,4),(5,3),(6,2)}   probability = 5/36   Answer is 5/36
Answer: D
In how many different ways can the letters of the word 'DETAIL' be arranged such that the consonants must occupy only the even positions?	Choose the correct choice from the following options:  A) None of these  B) 64  C) 120  D) 36  E) 360

Solution: D   3 consonants DTL can be arranged in 3!=6 ways. Similarly 3 vowels can be arranged on odd places in 3!=6 ways.   Total = 6*6= 
6*6 = 36
36.   Answer: 36.
Answer: D
A lemonade stand sold only small and large cups of lemonade on Tuesday. 4/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? Choose the correct choice from the following answers
A) (a) 7/16  B) (b) 7/15  C) (c) 10/21  D) (d) 7/31  E) (e) 1/2

Solution: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 4 are small and 1 is large. Now let the small ones cost $6. so the large ones would cost $7.   So,   4*6= 
4*6 = 24
24 and   1*7= 
  1*7 = 7
7.   Total revenue was 24+7= 
24+7 = 31
31   and Large cup sales as found above is 7   Therefore answer is 7/31   (d) 7/31
Answer: D
What is the greatest of 3 consecutive integers whose sum is 36?	Pick
A) 12  B) 13  C) 14  D) 15  E) 16

Solution: 36 / 3= 
36 / 3 = 12
12   The three numbers are 11, 12, and 13.   The answer is 13.
Answer: B
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Choose the correct choice from the following choices:
A) 22.04%
B) 16.12%
C) 8%
D) 18.25%
E) 10.5%

Solution: Per quarter, interest = 2.5% So for a year, interest = 10% Due to quarter cumulation, effective yield (YTM) would be slight higher than 10% Answer = 10.5% =ANSW10.5%R:10.5%
Answer: E
The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 15,000? Choose the correct choice from the following options:	A) 50,000	B) 750,000	C) 850,000	D) 7,500,000	E) 750,000,000

Solution: number of cars sold = x=800000-50y   y=15000   x=800000-750000= 
800000-750000 = 50_000
50000   revenue from 50000 cars=15000*50000= 
15000*50000 = 750_000_000
750000000   ANSW750,000,000R:750,000,000
Answer: E
240 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?  Choose the correct choice
A) 1~10 B) 10~20 C) 20~30 D) 55~65 E) 65~75

Solution: 240 = 2^4*3*5   There are factors in each range except for 65~75   The answer is 65~75.
Answer: E
The average weight of 9 person's increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg. What might be the weight of the new person?  Choose the most appropriate option
A) 72 kg	B) 77.5 kg	C) 135.5 kg	D) Data inadequate	E) None of these

Solution: Total weight increased = (9 x 5.5) kg = 49.5 kg.   Weight of new person = (86 + 49.5)= 
(86 + 49.5) = 135.5
135.5 kg.   Answer: Option 135.5 kg
Answer: C
The radius of a circle is increased by 1%. Find how much % does its area increases?	Choose the correct choice from the following answers:  A) 2.06  B) 2.09  C) 2.03  D) 2.01  E) 2.02

Solution: r = 100 r = 101   r2 = 10000 r2 = 10201   10000 ---- 201   100 ---- ? => 2.01%   Answer:2.01
Answer: D
A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 12 multiples of 14, how many multiples of 7 are there in Q?
Choose the most appropriate option
A) 20  B) 21  C) 22  D) 23  E) 24

Solution: Halfway between the multiples of 14, there will be another multiple of 7.   The total number of multiples of 7 is  12+11= 
 12+11 = 23
23.   The answer is 23.
Answer: D
what is the remainder when 89001 is divided by 18  Answers:  A) 3  B) 8  C) 9  D) 4  E) 6

Solution: 89001 / 18   89001 / 9*2   9889 / 2 => rem = 1   we have cancelled it by 9   reqd remainder = 9*1= 
9*1 = 9
9   ANSWER:8
Answer: B
Arrange the given words in the sequence in which they occur in the dictionary and choose the correct sequence. Pick one
A) 3, 5, 2, 1, 4 B) 3, 5, 2, 1, 8 C) 3, 5, 2, 1, 2 D) 3, 5, 2, 1, 5 E) 3, 5, 2, 5, 5

Solution: Explanation:   The correct alphabetical order is   Each, Eager, Earlier, Economic, Edition   3, 5, 2, 1, 4NSWER: 3, 5, 2, 1, 4
Answer: A
What will be the day of the week 15th August, 2010?
Choose the correct choice from the following answers:
A) Thursday B) Sunday C) Monday D) Saturday E) Friday

Solution: Explanation:   15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)   We know that number of odd days in 400 years = 0   Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)   Number of odd days in the period 2001-2009   = 7 normal years + 2 leap year   = 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day   Days from 1-Jan-2010 to 15-Aug-2010   = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)   = 227   227 days = 32 weeks  + 3= 
 + 3 = 3
3 odd day   Total number of odd days= (0 + 4 + 3)= 
(0 + 4 + 3) = 7
7 odd days= 0 odd day   0 odd day = Sunday   Hence 15th August, 2010 is Sunday.   Answer: Option Sunday
Answer: B
A man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph. What is then time taken to row a distance of 90 km down the stream ?	Options
A) 8hrs  B) 5 hrs  C) 15 hrs  D) 15 hrs  E) 20 hrs

Solution: Speed in down stream = 10 +8= 
10 +8 = 18
18   Time taken to cover 90 km down stream= 90/18= 
90/18 = 5
5 hrs.   ANSWER:5 hrs
Answer: B
The angles of a triangle are in the ratio 1:9:8. Find the measurement of the largest of three angles of triangle.  Pick one:
A) 90° B) 100° C) 120° D) 140° E) 160°

Solution: If the ratio of the three angles is 1:9:8, then the measures of these angles can be written as x, 9x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   x + 9x + 8x = 180   Solve for x   18x = 180   x = 10   The measures of the three angles are   x = 10°   9x = 9 × 10 = 90°   8x = 8 × 10 = 80°   90°
Answer: A
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 1/7 and that of Ravi is 1/5. Find the probability that both of them are selected. Select the correct option.
A) 1/35 B) 2/3 C) 7/35 D) 5/7 E) 7/5

Solution: Let A be the event that Ram is selected and B is the event that Ravi is selected.   P(A) = 1/7   P(B) = 1/5   Let C be the event that both are selected.   P(C) = P(1/35) x P(B) as 1/35 and B are independent events:   = 1/7 x 1/5 = 1/35   1/35NSWER:1/35
Answer: A
Person X joins a job at 20 yrs. First 3 years salary = 10,000 p.a. Afterwards every year increment of 2,000 per year for 10 years. Then salary becomes constant till retirement. At retirement average salary is 25,000. (throughout career). At what age he retires? Choose the most appropriate option:	A) 50	B) 60	C) 40	D) 70	E) 80

Solution: Let age of retirement = x   so according to the given condition 25000*(x-20)   =10000*3+12000+14000+16000+18000+20000+22000+24000+26000+28000+30000+30000(x-33)   = 30000+210000+30000x-990000   = 30000x-750000   or 25000x-500000=30000x-750000   or 5000x = 250000   or x = 50   50NSWER:50
Answer: A
If 25% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class? Choose the most appropriate option:	A) 500	B) 600	C) 620	D) 640	E) 660

Solution: We know 25 % people study biology,therefore the no of people not studying = 100 - 25= 
100 - 25 = 75
75%   > Therefore the people not studying biology out of a total 880 people are= 75 % of 880   >   (75/100)*880= 
  (75/100)*880 = 660
660 people   660
Answer: E