MU-NLPC/Calc-aqua_rat huggingface dataset:
A bottle company produces 100 glass bottles per day. One-fifth of the bottles produced are defective and one-quarter of all bottles produced are rejected by quality control technician. If one-tenth of the nondefective bottles are rejected by mistake, and if all the bottles not rejected are sold, then what percent of the bottles sold by the company are defective?
Choose one.
A) 16%	B) 8%	C) 4%	D) 2%	E) 1%

Solution: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. 4%orrect Answer is 4%
Answer: C
Three years ago the average age of a class of six members was 20 years. A boy have been added, the average age of the class is the same today. What is the age of the boy? Choose the correct choice from the following: A) A)1 B) B)2 C) C)3 D) D)4 E) E)5

Solution: 6 * 23= 
6 * 23 = 138
138   7 * 20= 
7 * 20 = 140
140   `2   2
Answer: B
What is the minimum number of years upon which SI on Rs 2600 at 6.67% interest rate will be in whole number?  Choices:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Explanation:   Simple Interest =Principal * Rate * Time   Principal = 2600 Rs   Interest Rate = 6.67%   => SI = 2600 * (20/3)*Time   SI of the number will be a whole number for the first time when time is three as denominator of rate is 3.   Hence time should be set to 3 years.   3NSWER: 3
Answer: A
there is 16 question. when u attempted paper you get 20 marks. for correct answer u get 5 marks and wrong answer you get 0 marks . if you dot attempt question you get 2 marks. which is not attainable marks.  Choose the correct choice.
A) 97 B) 95 C) 96 D) ALL E) NONE

Solution: there are 16 questions each of 5, so totally 80 marks+20 marks for attempting   95: it can be attained if 15 answers are answered and last one was a wrong atempt   97: it can be attained if 16 are attempted and in which one was wrong   "96" was the answer which cannot be attained in any manner   ANSWER:96
Answer: C
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?  Choose the correct option:  A) 83.37%  B) 83.23%  C) 83.39%  D) 82.33%  E) 83.33%

Solution: Percentage of milk in the mixture formed   = [80/100 (180) + 36] / (180 + 36) * 100%   = (144 + 36)/216 * 100%   = 5/6 * 100%   = 83.33%   Answer: 83.33%
Answer: E
If the simple interest on a certain sum of money for 8 years is one–fifth of the sum, then the rate of interest per annum is
Select:
A) 4.1%
B) 7%
C) 2.5%
D) 2.8%
E) 3%

Solution: Explanation:   Let the Principal(P) be x   Then, Simple Interest(SI) = x/5   Time(T) = 8 years   Rate of interest per annum(R) = (100×SI)/PT   = (100 × (x/5)/(x × 8) = 20/8= 
20/8 = 5/2 = around 2.5
2.5%   Answer: Option 2.5%
Answer: C
A can do a piece of work in 4 days. B can do it in 7 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it? Answers:
A) 22 days
B) 28/3 days
C) 67 days
D) 17/5 days
E) 18 days

Solution: C = 1/2 - 1/4 - 1/7 =3/28   => 28/3 days   Answer:28/3 days
Answer: B
Jackson has $313,197 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?	Choose the correct choice from the following options:
A) $6	B) $2	C) $3	D) $4	E) $5

Solution: In order to divide the sum in 9 parts, the amount must also be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 313,197 = 24 and 18 is divisible by 9.   Hence we need to subtract 6 to this number for it to be divisible by 9   Correct Option: $6
Answer: A
If −2≤w≤0 and n > 19, which of the following CANNOT be the value of wn?	Choose the correct choice from the following: A) -48 B) -38 C) -20 D) 0 E) 19

Solution: value of wn not equal to -19=19 -19....Rest all are achievable
Answer: E
Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days?
Choose the correct choice:
A) 5 B) 3 C) 4 D) 6 E) 1

Solution: Rate of one machine = 1 job / (20*4) days   let X = number of machines needed to complete the job in 10 days   1/(4*20) * 10 * X = 1 job   X = 8   8-4= 
8-4 = 4
4   ANSWER: 4
Answer: C
There are 4 more women than men on Centerville's board of education. If there are 6 members on the board, how many are women?  Pick:  A) 3  B) 5  C) 6  D) 7  E) 8

Solution: Given: M=W-4 so, W+(W-4)=6 --> W=5.   Answer: 5.
Answer: B
Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 60 mph. What is his average speed of travel for the entire journey?	Select the correct option
A) 53.33 mph B) 56.67 mph C) 52 mph D) 64 mph E) 66.67 mph

Solution: Average Speed = Total distance/ Total time = (40 * 2 + 60 * 3)/(2 + 3) = 260/5= 
260/5 = 52
52   Answer: 52 mph
Answer: C
If David bought TV for Rs.20000 and He luckily bought with 50% due to his lottery. What was the price if David didn't select for a lottery.  Choose the correct choice from the following answers: A) 30000 B) 35000 C) 40000 D) 45000 E) 50000

Solution: 40000P* (50/100) = 20000   40000P40000 * (50/100)= 
40000 * (50/100) = 20_000
20000   40000P= 400 * 100= 
400 * 100 = 40_000
> 40000P= 40000   Answer:40000
Answer: C
A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 36, what is the total amount?
Select
A) 115 B) 116 C) 117 D) 118 E) 156

Solution: x:y:z = 100:45:50   20:9:10   9 --- 36   39 --- ? => 156   ANSW156R:156
Answer: E
Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 5 times as much as Mork did, what was their combined tax rate?	Choose the most appropriate option:
A) 32.5%	B) 34%	C) 35%	D) 31.67%	E) 37.5%

Solution: Say Morks income is - 100   So tax paid will be 40   Say Mindys income is 5*100= 
5*100 = 500
500   So tax paid is 30% * 500= 150   Total tax paid = 40+150= 
40+150 = 190
190.   Combined tax % will be 190/100+500= 31.67%
Answer: D
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 40? Select the correct option
A) 1/16
B) 5/42
C) 1/8
D) 3/16
E) 1/4

Solution: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);   42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;   So, the probability is 2/16=1/16.   1/16nswer: 1/16
Answer: A
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 3? Choose the correct choice from the following choices
A) 76.66 kmph
B) 69.66 kmph
C) 48 kmph
D) 66.66 kmph
E) 56.66 kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (x)/40 + (3x)/60 = (3x + 6x)/120 = 9x/120 = 3x/40 Average speed = (2x + 3x)/(3x/40)   = 200/3 kmph.   =66.66 kmph   ANSWER:66.66 kmph
Answer: D
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?
Choose the correct choice from the following answers:
A) 10 min  B) 12 min  C) 20 min  D) 19 min  E) 24 min

Solution: Let the distance be x km. Then,   ( Time taken to walk x km) + (time taken to ride x km) =37 min.   ( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min.   But, the time taken to walk 2x km = 55 min.   Time taken to ride 2x km = (74-55)= 
(74-55) = 19
19 min.   ANSWER 19 min
Answer: D
The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144,
find the other number  Pick:
A) 400 B) 256 C) 120 D) 420 E) 560

Solution: Explanation:   Solve this question by using below formula.   Product of 2 numbers = product of their HCF and LCM   144 * x = 12 * 5040   x = (12*5040)/144= 
(12*5040)/144 = 420
420   Answer: Option 420
Answer: D
Two trains leaving from two station 50 miles away from each other with constant speed of 60 miles per hour, approaches towards each other on different tracks. if length of each train is 1/6 mile. when they meet How much time they need to pass each other totally ?	Choose the correct answer:	A) 277	B) 87	C) 27	D) 10	E) 72

Solution: Explanation:   The trains are coming towards each other so their relative speed is 60 + 60= 
60 + 60 = 120
120 mph   In this case the distance would be addition of lengths of trains.i.e 1/6 + 1/6= 1/3 m   T = dsds = 1/3 1/120 3/120 = 1/1360 h   Answer: 10
Answer: D
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 22. Which of the following integers is the higher of the remaining two integers? Select.
A) 83	B) 86	C) 44	D) 22	E) 55

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 22   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   B + B -22= 144   B = (144 + 22)/2= 
(144 + 22)/2 = 83
83   83nswer:Option 83
Answer: A
What is the last digit in the product (3^65 x 6^59 x 7^71)	Choose the correct choice from the following options: A) 5 B) 6 C) 4 D) 8 E) 9

Solution: Explanation:   Unit digit in 34 = 1 Unit digit in (34)16 = 1   Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3   Unit digit in 659 = 6   Unit digit in 74 Unit digit in (74)17 is 1.   Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3   Required digit = Unit digit in (3 x 6 x 3) = 4.   Answer is 4
Answer: C
Jim bought edging to go around a circular garden with a radius of 7 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
Choose one
A) 43.96' additional edging
B) 48.84' additional edging
C) 38.84' additional edging
D) 18.84' additional edging
E) 58.84' additional edging

Solution: circumference of small garden = 2 x 3.14 x 7 = 43.96'   double of the circumference of small garden = 2 x 43.96' = 87.92'   More feet to be buy =87.92 - 43.96= 
87.92 - 43.96 = 43.96
43.96   43.96' additional edgingnswer :43.96' additional edging
Answer: A
Can you find the last term in the sequence that is given below ?
2, 12, 36, 80, 150, ? Pick one:
A) 252 B) 199 C) 416 D) 312 E) 521

Solution: C   252   Explanation:   A unique pattern has been made into use in this series.   All numbers are (n^3 + n^2) where n is 1, 2, 3 and so on.   In first number, n = 1   1^3 + 1^2 = 1 + 1= 
1 + 1 = 2
2   In second number, n= 2   2^3 + 2^2 = 8 + 4= 
8 + 4 = 12
12   In third number, n= 3   3^3 + 3^2 = 27 + 9= 
27 + 9 = 36
36   In fourth number, n= 4   4^3 + 4^2 = 64 + 16= 
64 + 16 = 80
80   In fifth number, n= 5   5^3 + 5^2 = 125 + 25= 
125 + 25 = 150
150   Similarly for the sixth number, n= 6   6^3 + 6^2 = 216 + 36= 
216 + 36 = 252
252.
Answer: A
A parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week?
Pick one.
A) $140 B) $100 C) $220 D) $240 E) $260

Solution: 10$ per week!   An year has 52 weeks.   Annual charges per year = 52* 10= 
52* 10 = 520
520$   30$ per month!   An year has 12 months.   Annual charges per year= 12 * 35= 
12 * 35 = 420
420$    520 - 420= 
 520 - 420 = 100
100   Ans $100
Answer: B
Out of 400 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?  Choose the correct choice from the following answers:
A) 120
B) 150
C) 100
D) 180
E) 220

Solution: n(A)=325,n(B)=175,n(AuB)=400-50= 
400-50 = 350
350.   Required number= n(AnB)=n (A)+n (B)-n(AuB)=325+175-350= 
325+175-350 = 150
150.   Answer is 150
Answer: B
SHOW TIMER STATISTICS
To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she have to provide the photos for the magazine?
Choose the correct choice from the following.
A) 5  B) 10  C) 12  D) 15  E) 50

Solution: Veronica can choose 3 photos in 5C3 = 10 ways   She can choose 4 photos in 5C4 = 5 ways   Total number of ways = 10 + 5= 
10 + 5 = 15
15   Answer: 15
Answer: D
The sale price sarees listed for Rs.390 after successive discount is 14% and 15% is?  Select the correct option.
A) 285  B) 277  C) 290  D) 662  E) 262

Solution: 390*(86/100)*(85/100)   = 285   285nswer: 285
Answer: A
Which of the following is closer to (26!+25!)/(26!-25!)?  Pick one.
A) 1 B) 36 C) 25 D) 16 E) 49

Solution: Notice that 26! = (26)(25!), so we can factor out 25! from top and bottom.   (26!+25!)/(26!-25!)=[25!(26+1)]/[25!(26-1)]   = (26+1)/(25-1)   = 27/25   ≈ 1   1nswer: 1
Answer: A
If a certain computer is capable of printing 4900 monthly credit card bills per hour, while a new model is capable of printing at a rate of 6600 per hour, the old model will take approximately how much longer than the new model to print 10000 bills?	Choose the most appropriate option:	A) 31	B) 76	C) 88	D) 26	E) 81

Solution: Explanation:   Old model is capable of printing at a rate of 4900 per hour   New model is capable of printing at a rate of 6600 per hour   Old model time taken to print 10000 cards = 10000/4900 = 100/49   New model time taken to print 10000 cards = 10000/6600 = 100/66   Old model – new model: 100/49 - 100/66 = 1700 /(49 × 66) = 850/(49 × 33) = 0.525 hrs => 31 mins   Therefore, the old model will take approximately 31 mins longer than the new model to print 10000 bills   31nswer: 31
Answer: A
In how many different ways can the letters of the word ‘LOVE’ be arranged ?	Choose one
A) 24
B) 120
C) 720
D) 40320
E) 6

Solution: 24   24   Required number of arrangements = 4! = 24
Answer: A
Robert borrows a certain amount at 15% p.a. simple interest. How many years will it take for the amount to become twice the principal?
Select:
A) 4 years 4 months B) 5 years 2 months 3 days C) 6 years 5 months D) 3 years E) 8 years

Solution: Solution: simple interest question   B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate   after putting the values 15   2= [1+(15t/100)]   t= 4/3 which is (4+1)/3= 4 + 1/3 means 4 years and   (12*1)/3= 
  (12*1)/3 = 4
4 months.   Total time is 4 years 4 months   4 years 4 monthsnswer is 4 years 4 months
Answer: A
Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(3a) if a is even. Then (4#3) + (3#4) – (3#3) is equal to
Choose the correct choice from the following.
A) 64  B) 82  C) 128  D) 512  E) 4096

Solution: Answer:   4^6 + 3^6 - 3^6 = 4^6=4096   ANs 4096
Answer: E
In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 27 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students play only cricket ?
Choose the correct answer:
A) 36
B) 38
C) 39
D) 40
E) 37

Solution: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)+N(C∩T)-2(N(B∩T∩C))   =75-30+27-(2*16)= 
75-30+27-(2*16) = 40
40   ANSWER:40
Answer: D
A is twice as good a workman as B and they took 6 days together to do the work B alone can do it in?  Select:
A) 25 days
B) 18 days
C) 21 days
D) 11 days
E) 13 days

Solution: WC = 2:1   2x + x = 1/6   x = 1/18 => 18 days   Answer: 18 days
Answer: B
A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Choose the correct choice from the following answers
A) 12	B) 6	C) 7	D) 8	E) 9

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 220 * 3/55= 
220 * 3/55 = 12
12 sec.   12nswer: Option 12
Answer: A
The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
Choose the most appropriate option.
A) 8:3
B) 7:5
C) 4:3
D) 2:3
E) 3:1

Solution: Explanation:   Milk in 1-liter mixture of A = 4/7 liter.   Milk in 1-liter mixture of B = 2/5 liter.   Milk in 1-liter mixture of C = 1/2 liter.   By rule of allegation we have required ratio X: Y.   X : Y   4/7 2/5   So Required ratio = X: Y = 1/10: 1/14 = 7: 5.   ANSWER IS 7:5
Answer: B
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?	Choices:
A) 10 sec  B) 32 sec  C) 82 sec  D) 20 sec  E) 89 sec

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 sec.   Answer:20 sec
Answer: D
Two trains 110 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?  Choose the correct choice from the following choices.
A) 10.9	B) 10.7	C) 10.3	D) 10.8	E) 9.72

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 110 + 160= 
110 + 160 = 270
270 m.   Required time= 270 * 9/250 = 243/25= 
243/25 = 243/25 = around 9.72
9.72 sec.   'Answer: 9.72
Answer: E
In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 4P pots?  Choose the correct option:
A) M/15
B) 15M
C) 15/M
D) 4M/15
E) 15/4M

Solution: The time it takes to wash 4P pots is 4M minutes which is 4M / 60 = M/15 hours.   The answer is M/15.
Answer: A
A division of a company consists of five men and seven women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?	Pick one
A) 5/22
B) 7/22
C) 5/33
D) 7/33
E) 5/66

Solution: The total number of ways to choose two representatives is 12C2=66.   The number of ways to choose two females is 7C2=21.   P(choosing two female representatives)=21/66=7/22   The answer is 7/22.
Answer: B
On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 35 percent of the sales representatives prefer to stay at Hotel XYZ and 65 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?  Choose the correct choice: A) 33 B) 36 C) 39 D) 42 E) 45

Solution: 18 people stay in XYZ and 42 people stay in ABC.   21 people prefer XYZ and 39 people prefer ABC.   Let's put all 21 people who prefer XYZ in hotel ABC.   Then 18 people who prefer ABC will stay in XYZ.   The highest possible number who are not given their preference is 21+18= 
21+18 = 39
39.   The answer is 39.
Answer: C
Jane makes toy bears. When she works with an assistant, she makes 71 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
Choose the most appropriate option:
A) 20%
B) 80%
C) 90%
D) 180%
E) 200%

Solution: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 68.4 bears per 36 hours a week or 1.9 bears/hr ([40 bears * 1.71] / [40 hrs * .90]).   [(1.9 - 1)/1] * 100% = 90%   ANSWER:90% (1.9 - 1)/1  * 100= 
 (1.9 - 1)/1  * 100 = 90
90%   ANSWER:90%
Answer: C
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 28 years later?
Pick one.
A) $ 160,000	B) $ 320,000	C) $ 360,000	D) $ 450,000	E) $ 540,000

Solution: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?   The investment gets doubled in 70/p years. Therefore, the investment gets doubled in   70/5= 
  70/5 = 14
every 14 years. After 28 years, the investment will get doubled 28/14= 
28/14 = 2
2 times.   So the amount invested will get doubled thrice.   So, 40000 *2= 80000   80000*2= 
80000*2 = 160_000
160000   Hence, the answer is $ 160,000.
Answer: A
What percent of 5 letter combinations that can be made from the letters of the word HERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
Choose the correct choice from the following options.
A) 20% B) 23.8% C) 25% D) 30.2% E) 35%

Solution: a) noof combinations when all 5 letters are different = 7*6*5*4*3   b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3   b/a = 5/21= 0.238   23.8%
Answer: B
A car travels from point A to point B. The average speed of the car is 60 km/hr and it travels the first half of the trip at a speed of 45 km/hr. What is the speed of the car in the second half of the trip? Choose the correct choice from the following answers.
A) 75	B) 80	C) 90	D) 95	E) 100

Solution: Let D be the distance and let V be the speed in the second half.   The total time = T1 + T2   D/60 = D/90 + (D/2) / V   D/180 = D/2V and so V = 90 km/hr   The answer is 90.
Answer: C
If A^2 + B^2 = 30 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2?
Choose the correct choice from the following:
A) 10  B) 20  C) 30  D) 60  E) 70

Solution: (a-b)^2 = a^2 + b^2 - 2ab = 30-20= 
30-20 = 10
10   (a+b)^2= a^2 + b^2 + 2ab = 30+20= 
30+20 = 50
50   so (a+b)^2 + (a-b)^2= 50 +10= 
50 +10 = 60
60   60
Answer: D
The probability that a number selected at random from the first 50 natural numbers is a composite number is? Select the correct option:  A) 17/26  B) 17/25  C) 17/29  D) 17/24  E) 17/21

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   Answer:17/25
Answer: B
A group of 10 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?  Select:
A) E/(12 - n) B) (12 - n)/E C) nE / [10(10-n)] D) E/[12(12-n)] E) (12-n)E/(12n)

Solution: total cost =E   no of people willing to participate initially =10   initial cost for each =E/10   when n people decided not to participate   nE / [10(10-n)]ost for each =E/10-n   nE / [10(10-n)]
Answer: C
In a division, divident is 729, divisior is 38 and quotient is 19. Find the remainder.
Choose the correct choice:
A) A)4
B) B)3
C) C)2
D) D)5
E) E)7

Solution: 7xplanation:   729 = 38 x 19 + r   729 = 722 + r   r = 729 - 722= 
729 - 722 = 7
7   Answer: Option 7
Answer: E