MU-NLPC/Calc-aqua_rat huggingface dataset:
There are two positive numbers in the ratio 5 : 8. If the larger number exceeds the smaller by 15, then find the smaller number?
Choose the correct choice from the following options:
A) 25
B) 24
C) 28
D) 88
E) 99

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 15 => 3x = 15 => x = 5.   Smaller number = 5x = 25.   25nswer:25
Answer: A
Insert the missing number.
7, 26, 63, 124, 215, 342, (....)
Choose the correct choice
A) 222
B) 737
C) 388
D) 511
E) 200

Solution: Numbers are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1) etc.   So, the next number is (83 - 1) = (512 - 1)= 
(512 - 1) = 511
511.   Answer:511
Answer: D
A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 7 minutes less than they can row it in still water. How long would they take to row down with the stream Choose the correct option.
A) 45 or 23 minutes	B) 73 or 12 minutes	C) 77 minutes	D) 19 minutes	E) 25 minutes

Solution: A method has been discussed here to nullify the calculations though.   All I can input here is,   speed of a crew in still water = 1/2 ( speed upstream + speed downstream)   approximating this for time,   t = 1/2(84+ (t-7))   giving t = 77   77 minutes
Answer: C
A big container is 30% full with water. If 54 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?	Pick one.
A) 36 liters	B) 40 liters	C) 45 liters	D) 54 liters	E) 120 liters

Solution: A big container is 30% full with water and after 54 liters of water is added, the container becomes 75% full. Hence these 54 liters account for 45% of the container, which means that the capacity of it is  54/0.45= 
 54/0.45 = 120
120 liters.   OR: if the capacity of the container is x liters then: 0.3x+54=0.75x --> x=120 liters.   Answer: 120 liters
Answer: E
A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of Y square inches. Which of the following equations must be true?	Choose the correct choice from the following answers
A) 2W^2 + PW + 2Y = 0  B) W^2 − PW + 2Y = 0  C) 2W^2 − PW − 2Y = 0  D) W^2 + PW + Y = 0  E) 2W^2 − PW + 2Y = 0

Solution: P = 2(L+W)-----------------1)   Y= LW------------------------2)   option A is not possible why ?? because all the terms are positive.   lets try option B , put value of P and A from 1 and 2 we have,   2W^2-2(L+W)W + 2(LW)   2W^2 - 2LW - 2W^2 + 2LW=0.   hence answer is W^2 − PW + 2Y = 0.
Answer: B
Kyle received a bag of 82 marbles for his birthday. If he shares his marbles equally with his 5 best friends (including himself) how many more marbles will he have than his friends?
Select the correct option:
A) 1 marble	B) 2 marbles	C) 3 marbles	D) 4 marbles	E) 5 marbles

Solution: In order to divide the marbles into 6 parts, the amount must be divisible by 6.   Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3   Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3   We need to make subtract an even this number even in order for it to be divisible by 2.   sum of digits of 82 = 10 and 6 is divisible by 3. Subtracting 4 yeilds an even number.   Hence we need to subtract 4 for the number to be divisible by 6.   Correct Option: 4 marbles
Answer: D
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Choose the most appropriate option:  A) 76 cm2  B) 56 cm2  C) 18 cm2  D) 98 cm2  E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle   = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   Answer:35 cm2
Answer: E
There are 6 positive and 8 negative numbers. Four numbers are choosen at random and multiplied.the probability that the product is positive is:  Choose the correct choice from the following answers.
A) 500/1001  B) 503/1001  C) 303/1001  D) 301/1001  E) 505/1001

Solution: 6c4/14c4 + (6c2*8c2)/14c4 + 8c4/14c4 =505/1001   case1: only 4 positive no.   case2: 2 positive and 2 negative no.   case3: 4 negative no.   ANSW505/1001R:505/1001
Answer: E
If a=(10^10)-47, what is the sum of all the digit of a?  Choose the correct answer:
A) 40 B) 45 C) 50 D) 55 E) 80

Solution: Start small and check for any pattern:   10^2 - 47 = 53 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits   10^3 - 47 = 953 -> number of digits = power of 10; number of 9s = (power of 10) - 2; 53 is the last 2 digits   ...extrapolate   10^10 - 47 -> number of digits = 10; number of 9s = 8; 53 will be the last 2 digits   Sum,a = 9*8 + 5 + 3= 
9*8 + 5 + 3 = 80
80.   Answer (80).
Answer: E
In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 10 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?  Options:
A) 62% B) 68% C) 72% D) 76% E) 80%

Solution: Let in May Lee family's total income =100   in May Mrs Lee's income =60   in May rest of the family's income = 40   In june Mrs Lees income = 60*110/100= 
60*110/100 = 66
66   In june Total income= 66+ 40= 
66+ 40 = 106
106   % of Mrs Lee's income= 66/106 =62.26   (62%)
Answer: A
One half of a two digit number exceeds its one third by 9. What is the sum of the digits of the number?
Choose the correct choice from the following.
A) A)3	B) B)5	C) C)7	D) D)9	E) E)11

Solution: x/2 – x/3 = 9 => x =54   5 + 4= 
5 + 4 = 9
9   ANSWER:9
Answer: D
A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did B get in a profit of Rs.2400 ?	Choices:
A) s. 532 B) s. 600 C) s. 822 D) s. 812 E) s. 810

Solution: Let the total amount in the partnership be 'x'.   Then A's share = x/3   B's share = x/4   C's share = x/5   D's share = x - (x/3 + x/4 +x/5) = 13x/60   A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13   B's share in the profit of Rs. 2400 = 15 (2400/60) = Rs. 600.   Answer: s. 600
Answer: B
A and B can do a piece of work in 4 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?	Options.
A) 4.05 days	B) 5.05 days	C) 14.76 days	D) 8.05 days	E) 15.05 days

Solution: A + 5.05 days = 1/4   5.05 days + C = 1/12   C + A = 1/16   -------------------------------   2(A + 5.05 days +C) = 1/4 + 1/12 + 1/16 = 19/48   A + 5.05 days +C = 19/96   96/19 = 5.05 days   ANSWER:5.05 days
Answer: B
In a street, there are certain number of houses. People in that street are decided to paint their houses with certain colours. If four houses are painted with each colour, then one house will be left without any colour. If five houses are painted with each colour, then one colour will remain. Find the number of houses in that street?	Choices.
A) 6
B) 36
C) 25
D) 7
E) 9

Solution: on the basis of question   x = 4y+1   x = 5(y-1)   on solving these 2 equations x 4 +1= 
4 +1 = 5
5(y-1)   on solving these 2 equations x= 25   ANSWER:25
Answer: C
There are 5 bags three of which each contains 4 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a black ball has been drawn, find the chance that it came from first group.	Choose one
A) 2/7	B) 6/35	C) 8/25	D) 5/13	E) 3/5

Solution: Please go through my solution and suggest any mistake.   Chances of selecting a black ball from group 1: 1/3----------------------Chances of selecting a black ball from group 2: 4/5   Thus combined probability of section of black ball from group 1:   3/5 x 1/3 = 1/5   Thus combined probability of section of black ball from group 2:   2/5 x 4/5 = 8/25   Out of these chances, chance of occurrence of first case : (1/5) / (1/5 + 8/25) = 5/13   5/13
Answer: D
The total of the ages of Amar, Akbar and Anthony is 56 years. What was the total of their ages three years ago ?  Choose the correct choice from the following options:  A) 71  B) 47  C) 66  D) 16  E) 18

Solution: Explanation:   Required sum = (56 - 3 x 3) years = (56 - 9)= 
(56 - 9) = 47
47 years.   Answer: 47
Answer: B
Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs? Select the correct option:
A) 60
B) 70
C) 80
D) 100
E) 45

Solution: let x be the number of 25 ounce cans. Therefore (x+30) is the number of 15 ounce cans.   Total volume is same, therefore   25x=15(x+30)   10x=450   x=45   Ans - 45
Answer: E
A man can row upstream at 10kmph and downstream at 20kmph. Find the rate of current ? Choose the correct choice from the following choices:  A) 10km/hr  B) 15km/hr  C) 20km/hr  D) 5km/hr  E) 3km/hr

Solution: Rate of current = 1/2 (20-10) = 5km/hr   Answer is 5km/hr
Answer: D
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 24%. What quantity of whisky is replaced ?
Choose one
A) 1/3
B) 2/3
C) 2/5
D) 3/5
E) 16/21

Solution: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.   Let x ml be the amount removed ---> total alcohol left = 4-0.4x   New quantity of whiskey added = x ml out of which 0.19 is the alcohol.   Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.24 ---> x = 160/21 ml.   Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (160/21)/10 = 16/21.   Hence, 16/21 is the correct answer.
Answer: E
12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 7.  Pick one
A) 150 B) 152 C) 154 D) 158 E) 160

Solution: D = d * Q + R   D = 17 * 9 + 7   D = 153 + 7= 
153 + 7 = 160
160   ANSW160R 160
Answer: E
The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?  Choose the correct choice from the following answers:
A) -4% B) -2% C) +4% D) +2% E) None of these

Solution: Explanation :   Let initial price of Maruti car be Rs. 100.   As price increases 30%, the price of car become 100 + 30% of 100 = Rs. 130.   Due to increase in price, sales is down by 20 %.   It means, it is going to make 20% less revenue as expected after increment of price.   So, new revenue = 130 - 20 % of 130 = Rs 104.   The initial revenue was Rs 100 which becomess Rs 104 at the end.   It means there is 4% increment in the total revenue.   Answer : +4%
Answer: C
total dinning bill of 6 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .  Answers
A) 21.84
B) 22.84
C) 23.84
D) 24.84
E) 25.48

Solution: dinner bill of 6 person = 139 + 10% tip   so,   10% of 139 = (139*10)/100= 
(139*10)/100 = 139/10 = around 13.9
13.9   So, the actual total amount= 139+13.9= 
139+13.9 = 152.9
$ 152.9   so per head bill= 152.9/6 = $ 25.48   ANSW25.48R:25.48
Answer: E
A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?	Choices:
A) 37  B) 26  C) 48  D) 21  E) 92

Solution: Speed on return trip = 150% of 40 = 60 km/hr.   Average speed = (2 * 40 * 60)/(40 + 60)= 
(2 * 40 * 60)/(40 + 60) = 48
48 km/hr.   Answer:48
Answer: C
If you roll 2 dice, what is the probability of rolling a 7? Options
A) 1/2	B) 1/3	C) 2/13	D) 3/14	E) 1/6

Solution: Counting how many times the sum of the two numbers equals 7, you will find that 6/36 times, there is a 7 as a sum, thus Answer: 1/6
Answer: E
A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is?  Choose the correct answer.
A) 17 B) 98 C) 88 D) 85 E) 83

Solution: Let the number of wickets taken till the last match be x. Then,   (12.4x + 26)/(x + 5) = 12   = 12.4x + 26 = 12x + 60   = 0.4x = 34   = x = 340/4= 
340/4 = 85
85.   Answer: 85
Answer: D
If two balls are randomly selected from a green urn containing 9 black and 9 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
Options
A) A.2/9 B) B.4/9 C) C.4/17 D) D.1/3 E) E.1/9

Solution: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.   Probability (first ball is white) = 9/18   Probability(second ball is white) = 8/17   Probability (both balls are white) = (9/18)*(8/17) = 4/17   Answer C.4/17
Answer: C
-24x29+36=? Choose one
A) 2436  B) 2801  C) -2801  D) -660  E) None of them

Solution: Given exp.=-24x(30-1)+36   =-(24x30)+24+36   =-720+60   =-660   Answer is -660
Answer: D
Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $2, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?	Choose the correct choice from the following
A) $22	B) $24	C) $30	D) $36	E) $48

Solution: E its is.   Let price = X   (x-2)8 = 6X   X= 8   hence total money = 6*8= 
6*8 = 48
48
Answer: E
The ratio of the present ages of Sunita and Vinita is 4:5. Six years hence the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence?	Answers
A) 3  B) 4  C) 5  D) 1  E) 7

Solution: Explanation:   Present age sunita : vinita = 4 : 5   Let their age is 4x and 5x respectively..   After 6 yrs their age ratio will be 14 : 17   Therefore 4x+65x+6=14174x+65x+6=1417   ⇒ x = 9   Therefore their present ages are 36,45 respectively.   After 12 yrs their ages will be 48, 57 respectively.   ⇒ Ratio after 12 years will be 48: 57 = 16: 19 = 16 : 19   3nswer: 3
Answer: A
Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what is ratio of male to female students on honor roll? Options: A) 5/9 B) 8/15 C) 23/30 D) 43/60 E) 53/90

Solution: let the total students be 30   given 3/5 of the students are females = 18   then males = 2/5 = 12   5/6 of the females are on honor roll = 15   males on the honor roll = 2/3= 8   ratio of M:F students on honor roll = 8/15   8/15
Answer: B
If 7 men and 2 boys working together, can do six times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? Choose the most appropriate option:
A) 2:5
B) 2:3
C) 1:8
D) 4:1
E) 3:2

Solution: 7M + 2B = 6(1M + 1B)   7M + 2B = 6M + 6B   1M = 4B   The required ratio of work done by a man and a boy = 4:1   Answer:4:1
Answer: D
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? Choose the most appropriate option:  A) 40/9 days  B) 20/9 days  C) 30/9 days  D) 60/9 days  E) 10/9 days

Solution: A's one hour work = 1/8.   B's one hour work = 1/10.   (A+B)'s one hour work = 1/8+1/10 = 9/40.   Both 40/9 days & B can finish the work in 40/9 days   40/9 daysnswer : 40/9 days
Answer: A
The compound interest on $2000 at 10% per annum is $662. The period(in years) is?
Pick one: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: A = P(1 + R/100)^T   2662 = 2000(1 + 10/100)^T   (11/10)^T = 2662/2000   (11/10)^T = (11/10)^3   T = 3 years   Answer is 3
Answer: B
45 men can complete a work in 19 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
Choose the correct option:
A) 6.2
B) 10
C) 15
D) 7.8
E) 8

Solution: 45*19 men can complete the work in 1 day   1 man's 1 day work = 1/855   45 men 6days work = 6*1/19 =6/19   remaining work = 1-6/19 = 13/19   75 men's 1 day's work = 75/855 = 5/57   13/19 work is done by them in  57/5 * 13/19= 
 57/5 * 13/19 = 39/5 = around 7.8
7.8days   Answer is 7.8
Answer: D
A,B and C are employed to do apiece of work for Rs.529. A and C are supposed to finish 19/23 of the work together. How much shall be paid to B?
Pick one
A) 10
B) 11
C) 12
D) 14
E) 16

Solution: C   12   12 men can complete a work in 18 days. Six days after they started working, 4 more men joined them. How many days will all of them together complete the remaining work?
Answer: C
A 40-liter solution of alcohol and water is 5 percent alcohol. If 4.5 liters of alcohol and 5.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Choose the correct choice from the following.
A) 7%  B) 10%  C) 13%  D) 16%  E) 19%

Solution: The percent of alcohol in the solution is (0.05(40) + 4.5) / 50 = 6.5/50 = 13%   The answer is 13%.
Answer: C
A Bus 125 m long passes a man, running at 5 km/hr in the same direction in which the bus is going, in 10 seconds. The speed of the bus is:  Pick one
A) 100 km/hr	B) 50 km/hr	C) 55 km/hr	D) 60 km/hr	E) 35 km/hr

Solution: speed = 125/10=25/2   ==>25/2*18/5   ==>45 km/hr   speed of bus x km/hr   x-5 km/hr ==> 45   x = 50 km/hr   ANSWER 50 km/hr
Answer: B
Jim walks 3.3 mph and wants to walk to Dales house that's 3.5 miles away. How long will it take him to get there? Choose the correct choice from the following answers:
A) 78 minutes approx  B) 61 minutes approx  C) 34 minutes approx  D) 1 hr 6 m approx  E) 1 hr 33 min approx

Solution: 3.5/3.3= 1 hr 6 mins approx   Correct answer 1 hr 6 m approx
Answer: D
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? Choose the correct option
A) 12.8 kmph
B) 32.5 kmph
C) 18.5 kmph
D) 12.5 kmph
E) 12.4 kmph

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7   Solving the equation, the speed of man in still water is 12.5 kmph.   Answer:12.5 kmph
Answer: D
A class of students appeared in two different tests of quantitative ability both of which were scored out of 100. The scores of each student in each test could be expressed as a product of two distinct prime numbers. If a student’s scores in the two tests did not have any common prime factors, what is the maximum possible difference between his two scores?  Choose one.
A) 79  B) 83  C) 88  D) 89  E) 91

Solution: I started by listing out the primes   2,3,5,7,11,13,17,19,23,29,31,37   Then I tried to maximize the score--we know the minimum score will be 6 as the product has to be between two distinct primes.   Our max score is 100 so lets try to get as close to 100 as possible. 19*5=95   95-6= 
95-6 = 89
89   ANSWER:89
Answer: D
5 coins are tossed together. What is the probability of getting exactly 2 heads? Choose the correct choice:
A) 10	B) 5/16	C) 3/16	D) 7/16	E) 8/16

Solution: Since 5 coins are tossed, sample space = 20/2= 
20/2 = 10
10   Getting exactly 2 heads=32   p(E) = 20/32=5/16   ANSWER:5/16
Answer: B
A sum of money at simple interest amounts to Rs. 820 in 3 years and to Rs. 854 in 4 years. The sum is: Pick
A) 500
B) 718
C) 780
D) 910
E) None

Solution: Sol.   S.I. for 1 year = Rs. (854 - 820) = Rs. 34.   S.I. for 3 years = Rs. (34 * 3) = Rs. 102.   âˆ´ Principal = Rs. (820 - 102) = Rs. 718   Answer 718
Answer: B
If x + y + z = 0 then,
x^2 + y^2 + z^2/(x-y)^2 + (y-z)^2 + (z-x)^2 = ?  Choose the most appropriate option:
A) 0	B) 1	C) xyz	D) x+y+z	E) None

Solution: =>(x + y + z)² = x² + y² + z² + 2xy + 2xz + 2yz   => x + y + z = 0 given   =>So, x² + y² + z² = - 2(xy + xz + yz) .....(1)   (x² + y² + z²)   ------------------- = ?   (x-y)²+(y-z)²+(z-x)²   (x² + y² + z²)   ------------------------------------   2(x² + y² + z²)- 2(xy + xz + yz)   (x² + y² + z²)   ------------------------------- [:: from (1)]   2(x² + y² + z²) + x² + y² + z²   (x² + y² + z²)   ------------------ .........[::if x,y,z != 0, excluding the trivial case]   3(x² + y² + z²)   => ans 1/3   ANSWNoneR:None
Answer: E
Rs.525 among A, B and C such that B may get 2/3 of A and C together get. Find the share of C?  Choices:
A) 228	B) 150	C) 992	D) 277	E) 232

Solution: A+150+C = 590   5A = 6150 = 8C = x   A:150:C = 1/5:1/6:1/8   = 24:20:15   15/59 * 590 = Rs.150   Answer: 150
Answer: B
The average score of a cricketer in 2 matches is 60 and in other 3 matches is 50. Then find the average score in all the 5 matches?
Choose the correct choice:  A) 54  B) 27  C) 30  D) 35  E) 42

Solution: 54verage in 5 matches = (2*60 + 3*50)/2+3 = 120+150/ 5 = 270/5= 
270/5 = 54
54   54nswer is 54
Answer: A
In how many ways can the letters of wordELECTRICALbe arranged such that all the Consonants always appear together?  Choose the most appropriate option:
A) 9!	B) 5!*4!	C) 5!*6!	D) 5!*4!*2!	E) 6!*4!

Solution: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (10 letters, 4 vowels E, E, I, A and 6 consonant L, C, T, R, C, L)   For all consonants together, consider them as 1 group {L, C, T, R, C, L} E E I A --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways   Thus total arrangements with all consonants together = 5!*6! --> 5!*6! is the correct answer.
Answer: C
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 21. The corrected new mean is :	Options
A) 36.54
B) 36.58
C) 36.23
D) 36.14
E) 36.81

Solution: Explanation:   Correct Sum = (36 * 50 + 48 - 21)= 
(36 * 50 + 48 - 21) = 1_827
1827.   Correct mean= = 1827/50= 
1827/50 = 1_827/50 = around 36.54
36.54   36.54nswer: 36.54) 36.54
Answer: A
A Cuban cigar would cost 6 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?	Choose the correct choice:  A) 12.7$.  B) 23$.  C) 25.5$.  D) 35$.  E) 11.7$.

Solution: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.   From the given data we know French cigar < Cuban cigar < Arabic cigar   and each is more expensive 1.5 times. Therefore eliminate options C,D,A straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.   Therefore 11.7$. is the answer.
Answer: E
23 people are there, they are shaking hands together, How many hand shakes possible, if they are in pair of cyclic sequence ? Choose the correct choice from the following choices.
A) 20
B) 77
C) 66
D) 88
E) 11

Solution: 20nswer:20
Answer: A
The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams R?	Choose the correct answer:	A) 16	B) R=32	C) R=64	D) 128	E) 512

Solution: Weight directly proportional to 4 pi r^2   Now, 4pi is constant, so, weight is directly proportional to r^2.   When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;   (0.15)^2 * 4 proportional to 8*4, solving further   (0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (R=32)
Answer: B
A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 60 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?
Select the correct option:	A) −5%	B) 5%	C) 12%	D) 20%	E) 80%

Solution: The actual answer is obtained by multiplying 160% by 70% and subtracting 100% from this total. That is: 160% × 70% = 112%; 112% − 100% = 12%.   Answer: 12%
Answer: C