MU-NLPC/Calc-aqua_rat huggingface dataset:
A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Choose the correct choice from the following choices:
A) 7:3	B) 4:9	C) 4:3	D) 2:3	E) 4:9

Solution: 12:9   = 4:3   Answer:4:3
Answer: C
A man pointing to a photo says "The lady in the photograph is my nephew’s maternal grandmother". How is the lady in the photograph related to the man’s sister who has no other sister ? Answers:
A) Cousin
B) Sister-in-law
C) Mother
D) Mother-in-law
E) None of these

Solution: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister.   ANSWER:Mother
Answer: C
Which of the following is a multiple of 4!+6?
Answers
A) 2!+3
B) 4!+12
C) 5!+6
D) 5!+30
E) 8!+12

Solution: considering prime factors:   4! + 6 = 4 * 3 * 2 + 6 = 6(4 + 1) = 6 * 5 = 2 * 3 * 5   So the correct answer is the one which is a multiple of 2, of 3 and of 5.   ANSWER:5!+30
Answer: D
Aden and Brad can do a piece of work in 18 days. Brad can Cody can do it in 24 days and Cody and Aden can do it in 36 days. If Aden, Brad, Cody work together, in how many days will they finish the work?	Choose the most appropriate option:
A) 10 days	B) 12 days	C) 14 days	D) 16 days	E) 17 days

Solution: (Aden + Brad)’s 1 day’s work = 1/18   (Brad + Cody)’s 1 day’s work = 1/24   (Cody + Aden)’s 1 day’s work = 1/36   Therefore, 2 (Aden + Brad + Cody)’s 1 day’s work = 1/18 + 1/24 + 1/36   = (4 + 3 + 2)/72   = 9/72   = 1/8   (Aden + Brad + Cody)’s 1 day’s work = 1/2 × 8 = 1/16   Therefore, Aden, Brad, Cody together will complete this work in 16 days. ANSWER : 16 days
Answer: D
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? Options:
A) 9 B) 8 C) 6 D) 4 E) 2

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer:8
Answer: B
The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Choose the correct choice from the following answers:
A) 35 years B) 45 years C) 51 years D) 52 years E) None of these

Solution: Explanation:   Age of the teacher = (38 * 15 - 37 * 14)= 
(38 * 15 - 37 * 14) = 52
52 years. Answer: 52 years
Answer: D
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?  Select the correct option
A) 257 m B) 632 m C) 245 m D) 737 m E) 243 m

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer:245 m
Answer: C
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 25000. What percentage of profit did he make?  Options:
A) 1.00%  B) 15.21%  C) 41.10%  D) 19.04%  E) 10.00%

Solution: The total CP = Rs. 16000 + Rs. 5000   = Rs. 21000 and SP = Rs. 25000   Profit(%) = (25000 - 21000)/21000* 100   = 19.04%   Answer: 19.04%
Answer: D
A father is now three times as old as his son. Seven years back, he was four times as old as his son. The age of the son (in years) is  Choose the correct choice from the following.
A) 12	B) 15	C) 18	D) 20	E) 21

Solution: If father's age is F and son's age is S, then   F=3S   and   F-7 = 4*(S-7)   3S-7 =4S-28   S=21   F=63 years   ANSW21R:21
Answer: E
If 'a' and 'b' are non-zero numbers such that their sum is five times the product, what is the value of 1/a + 1/b?  Choose the most appropriate option.
A) 4 B) 5 C) 6 D) 10 E) 15

Solution: a+b = 5ab   1/a + 1/b = (b + a)/(ab) = 5.   The answer is 5.
Answer: B
The G.C.D of 1.08, 0.36 and 0.9 is	Pick.
A) 0.13 B) 0.17 C) 0.18 D) 0.12 E) 0.11

Solution: Given numbers are 1.08, 0.36 and 0.90.   H.C.F of 108, 36 and 90 is 18.   H.0.18.F of a given numbers = 0.18   Answer:0.18
Answer: C
A shipment of 250 smartphones contains 76 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Select the correct option.
A) 1/250	B) 1/84	C) 1/11	D) 1/9	E) 1/3

Solution: Probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = (76/250)   Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 75(we already picked one) defective phones is = (75/249)   1/11ombined probability of series of events = product of the probabilities = (76/250)*(75/249)   76/250 is close to (7/23) and (75/249)= (25/83)   so answer is (7/23)*(25/83) = (1/11)   So, answer will be 1/11
Answer: C
Of the following values of n, the value of (-1/3 )^(-n) will be greatest for n =
Select the correct option:
A) 3  B) -3  C) 0  D) -2  E) 2

Solution: imo -2   (-1/3)^-2=   1/(1/9)= 
1/(1/9) = 9
9   oops i meant 2   2
Answer: E
The sum of four consecutive even numbers is 140. What would be the smallest number?
Choose the correct choice: A) 32 B) 88 C) 70 D) 123 E) 12

Solution: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 =140 => x = 18   Smallest number is: 2(x - 2) = 32   32nswer: 32
Answer: A
Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each?
Select the correct option.
A) 20
B) 27
C) 18
D) 23
E) 30

Solution: A1*P1=A2*P2   18*15=A2*10 => A2=27   Answer:27
Answer: B
In how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate?
Choose the correct choice from the following
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: number of ways = 2*2!*2! = 8   Answer is 82*2 *2= 
2*2 *2 = 8
8   Answer is 8
Answer: B
A goods train runs at the speed of 72 km/hr and crosses a 260 m long platform in 26 sec. What is the length of the goods train?  Select the correct option:  A) 278  B) 166  C) 151  D) 260  E) 109

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 260)/26 = 20   x = 260 m.   Answer:260
Answer: D
If '+' means ' ÷ ', '-' means '×', '' means '-'' means '+', then (280 + 1020) - 86 is -------.
Select
A) 70 B) 112 C) -392 D) 58 E) None

Solution: (280/1020)*86   14/51 * 86   1204/51   Getting a fraction...   So none...   ANSWNoneR:None
Answer: E
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1200 per sq.metre.	Choose the correct choice from the following answers:
A) Rs. 15,000
B) Rs. 24,750
C) Rs. 15,600
D) Rs. 16,500
E) None

Solution: Solution   Area of the floor	= (5.5 x 3.75)m²   = 20.635m ²   Cost of paying	= Rs. (1200 x 20.625)   = Rs.24,750.   Answer Rs. 24,750
Answer: B
When two different numbers are divided by a certain divisor the remainders are 147 and 192. When the sum of the two numbers is divided by the same divisor the remainder is 38: Find the divisor. Choose the correct option
A) 300	B) 301	C) 302	D) 303	E) 304

Solution: Let divisior be x.so 1st no.=a+147   2nd no=b+192.   After adding:(a+147+b+192)/x=>a+b+339/x   Remainder of above expression is 38(given).so rem[a+b+(301+38)]/x=>38 therefore x would be 301.   ANSWER:301
Answer: B
An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?  Pick one
A) 0.6976
B) 0.783
C) 0.986
D) 1.243
E) 1.3445

Solution: Required probability:   =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976=0.6976   Edit: Thank you Vaibhav for providing an alternative method.   0.6976lternate Method:   probability that the plane is hit when all the four shots are fired,   P=1−probability of not hitting the targetP=1−probability of not hitting the target   =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)   =1−0.3024=1−0.3024   =0.6976   0.6976
Answer: A
A carpenter worked alone for 1 day on a job that would take him 4 more days to finish. He and another carpenter completed the job in 2 more days. How many days would it have taken the second carpenter to do the complete job working alone? Choose the correct choice:
A) 5	B) 7	C) 9	D) 14	E) 24

Solution: A carpenter worked only 1 day on something that takes him 4 MORE days.   Means;   Carpenter finishes his work in 5 days.   Let his buddy finish the same task in x days.   Respective rates per day:   1/5 AND 1/x   To complete 1 work:   First guy worked for 3 days @ rate=1/5 per day.   Second one worked for 2 days @ rate=1/x per day   Expression:   Days*Rate=Work   3*1/5+2*1/x=1   3x+10=5x   2x=10   x=5 days.   5ns:5
Answer: A
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:	A) 7.16	B) 7.19	C) 7.13	D) 7.15	E) 7.11

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer:7.15
Answer: D
Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?	Choose the correct choice from the following options:
A) 30  B) 90  C) 120  D) 168  E) 188

Solution: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168   Using your analysis:   We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168= 
176 + 224 - 168 = 232
232   So, in the image we know that the number of students in the zone with the black boundary= 232   Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)   And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w   Since the total number of students = 400, we can write:   232 +b+w= 400   Or,b+w= 400 - 232= 
400 - 232 = 168
168   That is,b= 168 -w   So, the maximum value ofbwill happen forw= 0   This is how we get, the maximum value ofb= 168   168
Answer: D
If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB  Choose the correct choice from the following:  A) I only  B) II only  C) III only  D) I and II only  E) I and III only

Solution: I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;   II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;   III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).   I onlynswer: I only.
Answer: A
Three seventh of a number is 12 more than 40% of that number. What will be the 50% of that number?  Choose the correct choice from the following answers:
A) A)148
B) B)210
C) C)105
D) D)248
E) E)258

Solution: 3/7 x – 40/100 x = 12   x = 35 * 12   35 * 12 * 50/100= 
35 * 12 * 50/100 = 210
210/2= 
210/2 = 105
105   ANSWER:105
Answer: C
Tough and Tricky questions: Absolute Values.
If |a| = 1/4 and |b| = 1/2, which of the following CANNOT be the result of a + b?
Choose the correct choice from the following choices
A) -1	B) -1/4	C) 3/4	D) -3/4	E) 1/4

Solution: |a| = 1/4   -1bsolute value of 'a' can have two values = 1/4 and -(1/4)   |b| = 1/2   -1bsolute value of 'b' can have two values = 1/2 and -(1/2)   Now different combinations of a + b are as follows:   a + b = (1/4) + (1/2) = 3/4   - a - b = -(1/4) - (1/2) = -3/4   a - b = (1/4) - (1/2) = -(1/4)   -a + b = -(1/4) + (1/2) = 1/4   Cross verifying with the given options, left over option is -1.
Answer: A
In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?  Pick one
A) 2
B) 4
C) 12
D) 0
E) 13

Solution: E13This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next.
Answer: E
A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is  Select the correct option:
A) 280 meter B) 240 meter C) 210 meter D) 200 meter E) None of these

Solution: Explanation:   Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s   Length of the train = speed × time taken to cross the man = 15×20 = 300 m   Let the length of the platform = L   Time taken to cross the platform = (300+L)/15   => (300+L)/15 = 34   => 300+L = 15×34 = 510   => L = 510-300= 
510-300 = 210
210 meter   Answer: Option 210 meter
Answer: C
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? Select:
A) Rs.2389  B) Rs.2380  C) Rs.2317  D) Rs.2329  E) Rs.2318

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 6970 * 14/41 = Rs.2380.   Answer: Rs.2380
Answer: B
The least umber of five digits which is exactly
divisible by 12,15 and 18 is?  Choose the correct choice from the following answers
A) 10000 B) 10012 C) 10015 D) 10018 E) 10080

Solution: Least number of five digits is 10000   L.C.Mof 12,15,18 s 180.   On dividing 10000 by 180,the remainder is 100.   Therefore required number=10000+(180-100)= 
10000+(180-100) = 10_080
10080.   Option 10080
Answer: E
In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?  Choose the correct choice from the following options.
A) 52	B) 32	C) 62	D) 25	E) 20

Solution: Total = 100   T= 40 NT= 60   40*(60/100)= 
40*(60/100) = 24
24 60*(40/100)=24   24 + 24= 
24 + 24 = 48
48=> 100 - 48= 
100 - 48 = 52
52%   52NSWER 52
Answer: A
The product X of two prime numbers is between 17 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =
Choose the correct choice from the following options
A) 18  B) 29  C) 37  D) 44  E) 57

Solution: Option BC can be ruled out as they themselves are prime numbers   18 = 2*9 = 3*6 >> Ignore   44 = 2 * 22 = 4 * 11 >> Ignore   57 = 3*19= 
3*19 = 57
57
Answer: E
Which of the following is a pair of Co - Primes ?  Choose the most appropriate option:
A) 14,35	B) 18,25	C) 31,92	D) 32,62	E) 18,43

Solution: Co Primes - two numbers are said to be co prime if their HCF is 1.   18 and 25 are co prime numbers. ANSWER : 18,25
Answer: B
Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 3-cent stamps she could have bought ?
Choose the correct choice from the following.
A) 5 B) 10 C) 15 D) 20 E) 25

Solution: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.03y   => 2.65 = 0.30x + 0.20x + 0.03y   => 265 = 50x + 3y   So Max value of 50x < 265 = 250   Hence y = 5   5nswer - 5
Answer: A
A committee is reviewing a total of 40x black-and-white films and 10y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?	Pick:
A) 50/52
B) 55/52
C) 60/52
D) 40/52
E) 30/52

Solution: Say x=y=10. In this case we would have:   40x=400 black-and-white films;   10y=100 color films.   y/x%=10/10= 
10/10 = 1
1% of the black-and-white films, so 4 black-and-white films and all 100 color films, thus total of 104 films were selected.   Color films thus compose 100/104=50/52 of the selected films.   50/52nswer: 50/52
Answer: A
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(28)? Choose the correct option.
A) 2	B) 7	C) 11	D) 13	E) 17

Solution: f(28) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28   The greatest prime factor in this list is 13.   The answer is 13.
Answer: D
The average marks of a class of 30 students is 40 and that of another class of 50 students is 70. Find the average marks of all the students?
Answers.
A) 52.5 B) 52.9 C) 52.1 D) 58.75 E) 42.5

Solution: Sum of the marks for the class of 30 students = 30 * 40= 
30 * 40 = 1_200
1200   Sum of the marks for the class of 50 students= 50 * 70= 
50 * 70 = 3_500
3500   Sum of the marks for the class of 80 students=   1200 + 3500= 
1200 + 3500 = 4_700
4700   Average marks of all the students= 4700/80= 
4700/80 = 235/4 = around 58.75
58.75   Answer:58.75
Answer: D
In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?
Pick one: A) 11 B) 15 C) 22 D) 18 E) 25

Solution: Let the speed of motor boat instill water be X kmph   Then, speed in downstream = (X + 2) km   and. speed in upstream = (X - 2) kmph   Time taken to row 10km & back = (10/X+2,10/X-2)   10/X+2 + 10/X-2 = 55/60   11X2 - 240X - 44 = 0   (X - 22)(11x + 2) = 0   X = 22 or X = -2/11   Then X = 22 kmph   Answer is 22.
Answer: C
A can give B 100 meters start and C 120 meters start in a kilometer race. How much start can B give C in a kilometer race?
Choose the correct answer:	A) 10.22 meters	B) 11.22 meters	C) 22.22 meters	D) 33.22 meters	E) None of these

Solution: Explanation:   A runs 1000 meters while B runs 900 meters and C runs 880 meters.   Therefore, B runs 900 meters while C runs 880 meters.   So, the number of meters that 22.22 meters runs when B runs 1000 meters = (1000 x 880)/900 = 977.778 meters   Thus, B can give 22.22 meters (1000 - 977.77) = 22.22 meters start   Answer: 22.22 meters
Answer: C
In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 28160, how many purple chips were selected?
Answers
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 28160 = 1*5*8^3*11   The factors of 8 must come from the purple point value, so there are 3 purple chips.   The answer is 3.
Answer: C
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio T of students per class?
Choose the most appropriate option.
A) T=3	B) T=4	C) 6	D) 8	E) 12

Solution: Another way to look at the problem...   Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)   we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)   (ii)-(i)....   C=10R+10 = 10(R+1).......   so # of classes has to be multiple of 10   AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..   so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3   T=3
Answer: A
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 42 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? Choose the correct option:
A) 35  B) 36  C) 37  D) 38  E) 39

Solution: James worked for 41 hours hence he earned 40*x+2*2x=44x dollars;   We know that Harry also earned the same 44x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 14x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 14x/1.5x=9 additional hours, so Harry worked for total of 30+9= 
30+9 = 39
39 hours.   Answer: 39.
Answer: E
In a certain lottery, the probability that a number between 14 and 20, inclusive, is drawn is 1/6 . If the probability that a number 14 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn? Select
A) 1/18
B) 1/6
C) 1/2
D) 1/3
E) 5/6

Solution: You can simply use sets concept in this question. The formula   Total = n(A) + n(B) - n(A and B) is applicable here too.   Set 1: Number 14 or larger   Set 2: Number 20 or smaller   1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either14 or moreOR20 or lessOR both)   2/3 + P(Set 2) - 1/6 = 1   P(Set 2) = 1/2   Answer (1/2)
Answer: C
A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?	Choose the correct answer.
A) 1028 B) 1024 C) 1023 D) 1025 E) 1084

Solution: Explanation:   Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.   Hence, the required number of ways = 45 - 1.   = 210 - 1 = 1024 - 1= 
1024 - 1 = 1_023
1023   Answer:1023
Answer: C
A cube is divided into 729 identical cubelets. Each cut is made parallel to some surface of the cube . But before doing that the cube is coloured with green colour on one set of adjacent faces ,red on the other set of adjacent faces, blue on the third set. So, how many cubelets are there which are painted with exactly one colour?
Answers:	A) 293	B) 294	C) 295	D) 296	E) 298

Solution: total cubes created are 729   so a plane of big cube has 9*9 cubes   out of that(n-2)*(n-2)=7*7= 
7*7 = 49
49 are painted only one side   and a cube has six sides=6*49= 
6*49 = 294
294   ANSWER:294
Answer: B
What is the radius of a circle that has a circumference of 3.14 meters?	Answers: A) 0.1 B) 0.3 C) 0.5 D) 0.7 E) 0.9

Solution: Circumference of a circle = 2πr.   Given, circumference = 3.14 meters.   Therefore,   2πr = Circumference of a circle   or, 2πr = 3.14.   or, 2 * 3.14r = 3.14,[Putting the value of pi (π) = 3.14].   or, 6.28r = 3.14.   or, r = 3.14/6.28.   or, r = 0.5.   correct answer 0.5
Answer: C