MU-NLPC/Calc-aqua_rat huggingface dataset:
How many three letter words are formed using the letters of the word TIME?
Choose the correct option:
A) 22
B) 28
C) 27
D) 24
E) 91

Solution: Explanation:   The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is â´Pâ‚ƒ = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   Answer: 24
Answer: D
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?	Choose the correct choice from the following answers:
A) 3/4
B) 1/4
C) 7/4
D) 1/2
E) None of these

Solution: Explanation:   Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases= [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27   So Probability = 27/36 = 3/4   Option 3/4
Answer: A
A carpenter makes 4 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers? Options: A) 3. B) 4. C) 5. D) 6. E) 7.

Solution: I believe it is C because if 1C makes 3 beds in 1 day then:   1C's rate = 3/1   So 5c's = 3/1 * 5= 
3/1 * 5 = 15
15/1= 
15/1 = 15
15 beds in a day.   Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed.   Time= Amount / Rate   Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 4.7   So, in order for the carpenters to be able to finish they need 5 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day.   5.
Answer: C
In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 82% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? Choose the correct choice from the following:
A) 63.
B) 73.
C) 81
D) 91
E) 108

Solution: Total students = 420   Boys = 312, Girls = 108   Total playing soccer = 250   82%of 250 = 205 are boys who play soccer.   Girls who play soccer = 45.   Total girls who do not play soccer = 108 - 45= 
108 - 45 = 63
63.   Correct option: 63.
Answer: A
A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?	Answers.
A) 271  B) 266  C) 350  D) 277  E) 232

Solution: D = 72 * 5/18 = 25 = 500 – 150   = 350   Answer:350
Answer: C
For one cake, a recipe calls for 3 cups of milk, 2 cups of sugar, and 2 cups of flour. Sally wants to bake as many cakes as possible and has 27 cups of milk and 18 cups of flour. How many cups of sugar does she need?	Choose the correct choice from the following answers
A) 27
B) 18
C) 9
D) 36
E) 2

Solution: First, we need to figure out how many cakes Sally can make with her milk and flour.   Both the amount of milk and flour she has is 9 times the amount needed for one cake, so she can make 9 cakes.   Since she needs sugar for 9 cakes, she needs 9 times 2 cups of sugar = 18 cups   Answer: 18)
Answer: B
A man sold 18 toys for Rs. 27300, gaining thereby the cost price of 3 toy find the cost price of a toy Choose the correct choice from the following choices
A) s. 600 B) s. 800 C) s.500 D) s.900 E) s. 1300

Solution: Let the cost of one toy = X.   Then, cost of 18 toys = 18X.   Gain = 3X.   SP of 18 toys = Rs. 27300.   Gain = SP â€“ CP   3X = 27300 â€“ 18X   21X = 27300   X = Rs. 1300.   ANSWs. 1300R : OPTION s. 1300
Answer: E
Mangala completes a piece of work in 20 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is Choose the correct option
A) 4 days	B) 6 days	C) 8 days	D) 10 days	E) 12 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 20 × 30/50 = 12 days.   Answer : 12 days
Answer: E
27 is a perfect cube. When x is perfect cube which is added to the prime factor of 27, the result is not a prime number. What is the square root of x? Choose the correct choice.
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: 27 is 3*3*3   2*2= 
2*2 = 4
4, 3+4=7   4*4= 
4*4 = 16
16, 3+16=17   6*6= 
6*6 = 36
36, 3+36=39   8*8= 
8*8 = 64
64, 3+64=67   10*10= 
10*10 = 100
100, 3+100=103   here C is the only addition that is not a prime number.   so the answer is 6
Answer: C
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?	Choose the correct choice.
A) 675, Rs.1350 B) 575, Rs.1350 C) 1350, Rs.675 D) 1450, Rs.775 E) 1550, Rs.875

Solution: 675, Rs.1350rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 2 = Rs.1350   675, Rs.1350NSWER:675, Rs.1350
Answer: A
From the integer n, if n*n*n is odd, then what is true from below options?
Choose the correct choice from the following answers:
A) n is odd
B) n*n is even
C) n is odd and n*n is even
D) n is even
E) None

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: C
In how many different ways can the letters of the word ‘I’ be arranged?
Choose one
A) 7  B) 2  C) 3  D) 1  E) 5

Solution: D   1   The word SMART has 1 distinct letters.   Number of arrangements = 1!   = 1 x 1 = 1   Answer is 1
Answer: D
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?  Choose the correct choice from the following answers:
A) 0	B) 5	C) 8	D) 9	E) 4

Solution: Explanation:   Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.   x = 5k + 3   x^2 = (5k + 3)^2   = (25k^2 + 30k + 9)   = 5(5k^2 + 6k + 1) + 4   On dividing x2 by 5, we get 4 as remainder.   4)
Answer: E
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 44 years. What will be the age of the B ten years hence?  Pick one.
A) 22  B) 88  C) 26  D) 96  E) 51

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 44 => b + c = 88 --- (2)   From (1) and (2), we cannot find b.   Answer: 88
Answer: B
Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:	Choices:
A) 36	B) 45	C) 48	D) 49	E) 50

Solution: Relative speed=60+90= 
60+90 = 150
150*5/18=(125/3)m/s   Total Distance covered=(1.10+0.9)= 
(1.10+0.9) = 2
2 km= 2000m   Required time = (2000*3/125)= 
(2000*3/125) = 48
48sec   ANSWER:48
Answer: C
A woman goes shopping during a door buster sale at JcPenney's. You are given a ticket with a random number on it when you arrive at the store. The number on the ticket is the pecent you get to take off of your total bill. The woman bought a shirt for $9.99, a pair of jeans for 19.99 and a jacket for $36.00. Her total was 65.98 before her secret door buster discount. If she paid 59.38 after her discount, What number did the woman have on her ticket? Select the correct option
A) 10  B) 5  C) 15  D) 20  E) 25

Solution: 65.98-59.38= 6.50 = amount of money saved   65.98÷6.50=9.999 = percent of the total bill   9.99 is rounded up to 10.   The answer is 10
Answer: A
Which of the following number is divisible by 4 and 9?	Answers:
A) 2368 B) 2736 C) 3954 D) 3814 E) None of these

Solution: For a number to be divisible by 4, the number formed by the last two digits of that number must be divisible by 4.   For a number to be divisible by 9, the sum of its digits must be divisible by 9.   Among the choices, choices (a) and (b) are divisible by 4 but of the first two choices, only choice (b) is divisible by 9.   Hence choice (b) is divisible by both 4 and 9.   ANSWER:2736
Answer: B
A girl is organizing her jellybean collection in which each color has its own row. In each row, there are as many jellybeans as the number of jellybean colors. Her little brother chops each jellybean into the same number of peices as the number of jellybean colors. If the final number of jellybean pieces is m, then:	Choose the correct choice from the following answers.
A) m is a perfect square B) m is an odd number C) m is an even number D) m is a perfect cube. E) None

Solution: For example, if there were 4 jellybean colors, the girl would have made a 4x4 arrangement. The boy chopped up each jellybean into 4, the number of pieces would be  (4*4)*4= 
 (4*4)*4 = 64
64 pieces, which is a cube of 4.   Answer: m is a perfect cube.
Answer: D
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 16km? Select
A) 3	B) 6	C) 8	D) 9	E) 7

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 16   T = 16/2= 
16/2 = 8
8   Answer:8
Answer: C
A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
Pick.
A) 987
B) 271
C) 108
D) 27
E) 28

Solution: Length = Speed * time   Speed = L/T   S = 600/20= 
600/20 = 30
30M/Sec   Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 108 Kmph   Answer:108
Answer: C
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.3 years. The ration of the number of boys to the number of girls in the class is? Select
A) 5:6  B) 2:3  C) 2:5  D) 2:1  E) 2:4

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.3 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.3)   = k = 0.5/0.6 = 5/6   Required ratio = 5/6 : 1 = 5:6.   5:6nswer:5:6
Answer: A
Line J has a y-intercept of 11 and passes through point (a,b). What is the slope of Line J in terms of a and b?  Answers:	A) (a−6)/b	B) (a−b)/6	C) (6−a)/b	D) (6−b)/a	E) (b-11)/a

Solution: You know that the line goes through point (a,b) and the y-intercept of 11 tells you that the line also goes through point (0,11).   slope m = (y-y1)/(x-x1) = (b-11)/(a-0)= (b-11)/a   (b-11)/a
Answer: E
The sum of three consecutive integers is 102. Find the lowest of the three?
Choose the correct choice from the following answers
A) 40 B) 53 C) 29 D) 33 E) 35

Solution: Explanation:   Three consecutive numbers can be taken as (P - 1), P, (P + 1).   So, (P - 1) + P + (P + 1) = 102   3P = 102 => P = 34.   The lowest of the three = (P - 1) = 34 - 1= 
34 - 1 = 33
33.   ANSWER IS 33
Answer: D
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?	Choices:	A) 25%	B) 20%	C) 18%	D) 30%	E) 40%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   25%NSWER 25%
Answer: A
A ribbon is cut into three smaller strips in the ratio 2:3:5. If the shortest of the three strips is 30 inches in length, what was the length, in inches, of the ribbon before it was cut?	Pick one.
A) 60
B) 75
C) 90
D) 150
E) 170

Solution: Given 2x = 30 so x =15   Have to find 2x+3x+5x = 30+45+75= 
30+45+75 = 150
150   Ans 150
Answer: D
The average daily wages of A, B and C is Rs 120. If B earns Rs 40 more than C per day and ,A earns double of what C earns per day, the wage of A per day is?  Select the correct option
A) Rs 80  B) Rs 120  C) Rs 160  D) Rs 100  E) Rs 140

Solution: Let daily wages of C = X   Then, daily wages of A = 2X   and daily wages of B = X + 40   Hence, average daily wages of A, B and C   = (X + 2X + X + 40) / 3 = (4X + 40)/3   Thus, (4X + 40)/3 =120   =>4X + 40 = 360   =>4X = 320   X = 80.   Therefore, Wages of A per day = 2 x 80 = Rs 160.   ANSWER:Rs 160
Answer: C
A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the greatest possible number of contributors at the dinner?	Choices.
A) 33
B) 34
C) 35
D) 36
E) 37

Solution: Nearest to 1749≈1750   175/50=35 (Caution: Collection is   1750 - 1= 
  1750 - 1 = 1_749
1749)   Counting 1 less= 50*34= 
50*34 = 1_700
1700 >> 49 remains which will be adjusted with the 34 members     51* 34= 
  51* 34 = 1_734
1734 >> 15 remains which will be adjusted with 15 members   52 * 15 + 51 * 19= 780 + 969= 
780 + 969 = 1_749
1749   Answer= 34
Answer: B
The age of Somu is one-third his father's. 7 years back he was one-fifth of his father's age. What is his persent age ?	Choose the correct choice from the following answers:
A) 11	B) 13	C) 14	D) 12	E) 10

Solution: Explanation :   Let Somu's age be x and that of his father be 3x.   So, x - 7 = 3x - 7/5 = x = 14   Answer : Option 14
Answer: C
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:  Choose one:
A) 200m	B) 225m	C) 245m	D) 250m	E) 300m

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.   ANSWER 245m
Answer: C
The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 800?
Choose the correct option:
A) 13 B) 10 C) 9 D) 7 E) 6

Solution: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^9 = 512 < 800, then the greatest possible length of integer z is 9.   The answer is 9.
Answer: C
The rate of failure in an examination is 39.25%. Find the least number of total candidates appeared in the examination.  Choose the correct choice from the following answers.
A) 100  B) 200  C) 300  D) 400  E) 500

Solution: if 100 student appear then failure=39.25 ......... which is not possible because number of student can not be fraction,like wise in 200 student,failure=78.5, so we have to make the failure percentage into a unit digit failure not fraction...so min no of student =400 so that no of failure=157..........so least no of student appeared in the exam= 400.   ANSWER:400
Answer: D
In the word CONTRACTUAL, the positions of the first and the eleventh letters are interchanged. Similarly, the positions of the second and the tenth letters are interchanged, and so on, up to the positions of fifth and seventh letters are interchanged, keeping the position of sixth letter unchanged. Which letter will be the third to the right of the sixth letter from the left end?  Select: A) U B) N C) T D) A E) None of these

Solution: New word will be LAUTCARTNOC   6th letter from the left end is A,and and 3rd to the righ of thet letter is N.   ANSWER:N
Answer: B
In an examination, 35% of students failed in quants and 42% of students failed in verbal while 14% failed in both the topics. If 222 students passed in both the topics, how many students appeared to write the examination?  Pick
A) 500	B) 600	C) 700	D) 800	E) 900

Solution: DETAILED SOLUTION   Percent of students failing quants = 35   Percent of students failing verbal = 42   Sum = 35 + 42= 
35 + 42 = 77
77   Percent of students failing both= 14   = ) Percent of students failing either one = 77 – 14 = 63. Thus, 37% students passed in both the topics   = ) 37% of x = 222 = ) x = 600   Correct Answer: 600
Answer: B
Three coins are tossed. What is the probability of getting at most two tails?  Choose the correct choice.
A) 7/8 B) 1/8 C) 1/2 D) 1/7 E) 1/3

Solution: Total number of outcomes possible when a coin is tossed = 2 (âˆµ Head or Tail)   Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 Ã— 2 Ã— 2 = 8   (âˆµ i.e., S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})   E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}   Hence, n(E) = 7   P(E) = n(E)/n(S)=7/8   7/8nswer:7/8
Answer: A
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Choose the correct choice from the following answers
A) 7 years.	B) 8 years.	C) 9 years.	D) 10 years.	E) 11 years.

Solution: EXPLANATION   Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25   x = 5.   Hence, B’s age = 2x = 10 years.   Answer 10 years.
Answer: D
A can do a work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Select the correct option:
A) 15/2  B) 10  C) 7/2  D) 12  E) 6

Solution: Ratio of times taken by 15/2 and B = 160:100 = 8:5   suppose B alone to take x days to do the work   then, 8:5::12:x   8x= 5*12   x=15/2 days   correct option is 15/2
Answer: A
In a 1000 m race, A beats B by 200 meters or 24 seconds. Find the speed of B? Choose the correct choice from the following:
A) 6	B) 8.3	C) 7	D) 5	E) 2

Solution: Since A beats B by 200 m or 24 seconds, i   t implies that B covers 200 m in 24 seconds.   Hence speed of B = 200/24 = 8.3 m/s.   Answer: 8.3
Answer: B
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?  Choose the correct choice.
A) 6 B) 7 C) 8 D) 65 E) 4

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   6nswer: 6
Answer: A
In a recent head-to-head run-off election, 12,000 absentee ballets were cast. 1/6 of the absentee ballets were thrown out and 3/5 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?  Choose the correct choice from the following choices
A) 2,000
B) 3,000
C) 4,000
D) 8,000
E) 9,000

Solution: 5/6 * 2/5 (total absentee votes) = 1/3 (total votes)=1/3*12000= 
1/3*12000 = 4_000
4000   Answer is 4,000
Answer: C
The average height of 15 girls out of a class of 30 is 152 cm. and that of the remaining girls is 156 cm. The average height of the whole class is :  Choose the correct choice:
A) 150 cms
B) 151 cms
C) 152 cms
D) 154 cms
E) 156 cms

Solution: Explanation:   Average height of the whole class =(15×152+15×156/30)=154 cms   Answer 154 cms
Answer: D
10^25 - 360 is divisible by all of the following except: Choose the correct choice from the following choices
A) A.7	B) B.8	C) C.5	D) D.4	E) E.2

Solution: The last three digits ( 1000 - 360 ) 640   640 is divisible by 2,4,8,5   640 is not evenly divisible by 7 so the answer is A.7) 7
Answer: A
Present ages of Kiran and Syam are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Syam's present age in years?  Choose the most appropriate option
A) 21	B) 22	C) 23	D) 25	E) 24

Solution: Ratio of the present age of Kiran and Syam =5:4   Let present age of Kiran =5x   Present age of Syam =4x   After 3 years, ratio of their ages =11:9   ⇒(5x+3):(4x+3)=11:9⇒9(5x+3)=11(4x+3)⇒45x+27=44x+33⇒x=33−27=6   Syam's present age =4x=4×6=24   Answer is 24.
Answer: E
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?  Pick one: A) 150 B) 250 C) 270 D) 280 E) 290

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   Answer 270)270.
Answer: C
A, B and C started a shop by investing Rs. 10,000, Rs. 20,000 and Rs. 30,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 9,000, then the total profit was : Choose the correct option:
A) 30,000 B) 60,000 C) 18,000 D) 120,000 E) None

Solution: Sol.   A : B : C = 10000 :20000 : 30000 = 1: 2 : 3. so, Câ€™s share : Total Profit = 3 : 6   Let the total profit be Rs. x. Then, 3/6 = 9000/x   x = 9000 * 6 / 3= 
9000 * 6 / 3 = 18_000
18000.   Answer 18,000
Answer: C
If the area of circle is 1520 sq cm then its circumference?
Pick.
A) 221
B) 138
C) 166
D) 116
E) 112

Solution: 22/7 r2 = 1520 => r = 22   2 * 22/7 * 22 = 138   Answer: 138
Answer: B
In how many ways can the letters of word EMULATION be arranged such that NO two vowels appear together?  Choose the correct choice from the following.
A) 9!
B) 5!*4!
C) 4!*5!
D) 5!*4!*2!
E) 6!*4!

Solution: No 2 vowels together = the only arrangement possible will be V C V C V C V C V (with V=vowel, C=consonant). This is true as we have 5 vowels and 4 consonants and any other combination will force us to pair 2 vowels together.   Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 5!*4! ----> 4!*5! is the correct answer.
Answer: C
Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
Choose the most appropriate option.
A) 65, 15
B) 64, 16
C) 62, 18
D) 60, 20
E) 61, 30

Solution: Explanation:   x + y = 80   x – 4y = 5   x = 65 y = 15   65, 15NSWER IS 65, 15
Answer: A
How many prime numbers are between 78/14 and 55/4?	Pick
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: 78/14= 39/7 = 6-   55/4 = 14-   Prime numbers between 6 and 14 are 7, 11 and 13   - sign signifies that the number is marginally less .   Answer 3
Answer: B
5 pears and 2 apples cost $16. 3 pears and 3 apples cost $15. How much does one apple cost? Choose the correct choice from the following.
A) 3.5
B) 3.25
C) 3
D) 2.5
E) 2

Solution: Let cost of 1 pear = x, let cost of 1 apple = y   5x + 2y = 16   y = (16 - 5x)/2   Again,   3x + 3y = 15   3x + 3((16 - 5x)/2) = 15   3x + 24 - 7.5x = 15   3x + 24 = 15 + 7.5x   9 = 4.5x   x = 2   Now plug this value into one of the initial equations:   5x + 2y = 16   5(2) + 2y = 16   10 + 2y = 16   2y = 6   y = 3   Answer: 3   ANSWER:3
Answer: C
Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?
Pick one:
A) 2140
B) 2520
C) 2980
D) 3260
E) 3680

Solution: The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5.   The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520   The answer is 2520.
Answer: B
A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number L of imported lamps stocked at the store?
Choose one: A) 3 B) 10 C) 13 D) 20 E) 23

Solution: We want to minimize not maximize the expression,.   L=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.   But i'm guessing 123-5x/20 can be written as 123- x/4   if x has to be the greatest multiple of 4 less then 410, then it would be 408.   Hence 123-408/4 --> 123-102 -->21   Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.23
Answer: E
If a coin is tossed three times, what is the probability that on the first toss the coin lands on tails and then lands on heads the next two tosses?  Choose the correct choice from the following answers
A) 1/8
B) 1/3
C) 1/4
D) 1/2
E) 1

Solution: P(THH) = 1/2*1/2*1/2=1/8   The answer is 1/8.
Answer: A
By selling 99 pens, a trader gains the cost of 9 pens. Find his gain percentage?
Answers:  A) 9 1/3%  B) 9 7/3%  C) 9 1/8%  D) 9 1/3%  E) 9 1/11%

Solution: Let the CP of each pen be Rs. 1.   CP of 99 pens = Rs. 99   Profit = Cost of 9 pens   = Rs. 9   Profit% = 9/99 * 100   = 9 1/11%   Answer: 9 1/11%
Answer: E
About the number of pairs which have 16 as their HCF and 121 as their LCM, the conclusion can be Choose the correct choice from the following answers
A) only one such pair exists  B) only two such pairs exist  C) many such pairs exist  D) many such pairs exist  E) such pair did not exists

Solution: Explanation:   HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.   Correct Option: such pair did not exists
Answer: E