MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?  Select
A) 5/8 B) 5/9 C) 5/2 D) 5/1 E) 5/0

Solution: Explanation:   Two balls can be picked from nine balls in ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ways.   The required probability = (5 * 4)= 
(5 * 4) = 20
20/36= 5/9   Answer:5/9
Answer: B
A water tank is one-third full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?	Choose the correct answer:
A) 6 min.to empty
B) 9 min.to empty
C) 5 min.to empty
D) 4 min.to empty
E) 7 min.to empty

Solution: Explanation:   Clearly,pipe B is faster than pipe A and so,the tank will be emptied.   part to be emptied = 1/3   part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15   so, the tank will be emptied in 5 min   Answer: 5 min.to empty
Answer: C
Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?	Choose the correct option.
A) 11 1/5%	B) 11 8/9%	C) 11 1/9%	D) 13 1/9%	E) 11 4/9%

Solution: 900 --- 100   100 --- ? => 11 1/9%   Answer:11 1/9%
Answer: C
If an apple orchard has 10,000 apples on its trees, and every day half of the apples on the trees are harvested, how many will still be on the trees after 4 days?	Choose the correct choice from the following answers.
A) 500 apples
B) 625 apples
C) 1000 apples
D) 1250 apples
E) 1500 apples

Solution: 10000/(2^4)=10000/16= 
10000/16 = 625
625   The answer is 625 apples.
Answer: B
A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?	Pick.
A) 1:2 B) 1:5 C) 1:4 D) 1:1 E) 1:8

Solution: T = 192/32= 
192/32 = 6
6 h   T= 6 - 3= 
6 - 3 = 3
3   Time Ratio= 6:3 = 2:1   Speed Ratio = 1:2   1:2nswer: 1:2
Answer: A
Dacid obtained 96, 95, 82, 87 and 92 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Select: A) 67 B) 26 C) 87 D) 26 E) 90

Solution: Average   = (96+95+82+87+92)/5   = 452/5 = 90.   Answer: 90
Answer: E
The sum of ages of Aswin ,Sachin and Sumesh is 93 years.10 years ago ratio of their age was 2:3:4.what is the present age of sachin. Choose the correct choice from the following options
A) 19
B) 21
C) 31
D) 41
E) 51

Solution: Solution:Sum of the present ages of Aswin ,Sachin and Sumesh=93   Sum of the ages of Aswin ,Sachin and Sumesh 10 years ago=93- 10*3= 
93- 10*3 = 63
63   Age of sachin 10 years ago=(3/(2+3+4)) * 63= 
(3/(2+3+4)) * 63 = 21
21.   Present age of Sachin=21+10= 
21+10 = 31
31   Answer 31
Answer: C
After giving a discount of rs.50 the shopkeeper still gets a profit of 20%,if the cost price is rs.180.find the markup %?
Choices.
A) 0.5
B) 0.6
C) 0.48
D) 0.65
E) 0.45

Solution: cost price=180   s.p=180*120/100= 
180*120/100 = 216
216   disc=50   so...mark price=216+50=266......   mark up%=266-180/180=86/180=.48 or 48%   ANSWER:0.48
Answer: C
Rocky is 22 and his brother Ronnie is 25 years old. How many years ago was the ratio of their ages 2:5 ?
Answers
A) 20 years
B) 2 years
C) 10 years
D) 22 years
E) 24 years

Solution: let be x years ago....   so, (22-x)/(25-x)=2/5........solve it.   x=20years   20 yearsNSWER:20 years
Answer: A
If the operation # is defined for all a and b by the equation a@b =(a*b)-1, then 2#(3#1) = Select the correct option
A) 4 B) 2 C) 3 D) 1 E) 5

Solution: work within the parenthesis first so solve (3#1) first   (3#1)=(3*1)-1= 
(3*1)-1 = 2
2   now take 2 plug back into equation and solve the rest   (2#2)=(2*2)-1= 
(2*2)-1 = 3
3   so 3 is the answer....this question is merely testing order of operations   remember PEMDAS   Option 3 is answer
Answer: C
A ballet instructor has decided to divide her next class into equal groups. Unfortunately, the number of students doesn't divide equally by the group size that she wanted. It turns out that in order for the groups to be equal, she must increase her group size by one and cut three children from the roster. Which of the following can describe the initial number of students in the class and the instructor's initial group size (in the order Students; group size)? Choices
A) 82; 5.	B) 54; 9.	C) 27; 4.	D) 15; 6.	E) 35; 7.

Solution: Option E) Initially 35 students then reduced to 32 students; and Initially a group size of 7 increased to a group size of 8 fits the requirement.   32 / 8= 
32 / 8 = 4
4 groups of students
Answer: E
Evaluate 25% of 450 + 45% of 250  Choose the correct choice.
A) 225	B) 242	C) 252	D) 262	E) 272

Solution: Explanation:   = (25/100) * 450 + (45/100) * 250= 
(25/100) * 450 + (45/100) * 250 = 225
225   Option 225
Answer: A
xy=1 then what is (7^(x+y)^2) / (7^(x-y)^2)  Choose the correct answer.
A) 2401  B) 4  C) 8  D) 16  E) 32

Solution: (x+y)^2 - (x-y)^2   (x+y+x-y)(x+y-x+y)   (2x)(2y)   4xy   4   7^4 = 2401   2401nswer 2401
Answer: A
A fruit salad mixture consists of apples, peaches, and grapes. There are 2 times as many pounds of apples as grapes and 3 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 9 pounds per fruit, how many more pounds of apples than grapes does the mixture have?	Choose the correct answer.
A) 15
B) 12
C) 9
D) 6
E) 3

Solution: A+P+G= 9*2   A=2G   P=3G   3G+2G+G= 9*2   G= 9*2/6= 
9*2/6 = 3
3   A= 3*2= 
3*2 = 6
6   Difference= 6-3= 
6-3 = 3
3   '3' is the answer
Answer: E
If an amount of Rs.142136 is distributed equally amongst 163 persons, how much amount would each person get?	Select:
A) Rs.862  B) Rs.872  C) Rs.882  D) Rs.892  E) None of these

Solution: Explanation:   Amount each person would get = Rs.142136/163 = Rs.872   Answer: Option Rs.872
Answer: B
There are 12 teachers in a school. If the average age of the teachers is 36, what will be the new average age if a 30 year old teacher joins the school?
Choose the correct choice from the following:
A) 35.54
B) 34.52
C) 32.3
D) 35
E) 34.44

Solution: (sum of the 12 ages)/12 = 36   sum of the 12 ages = 432   new sum = 432+30= 
432+30 = 462
462   new average= 462/13 = 35.54   ans: 35.54
Answer: A
How many numbers from 10 to 100000 are exactly divisible by 9? Choose the correct choice from the following.
A) 900
B) 11110
C) 1100
D) 1200
E) 1400

Solution: 10/9 = 1 and 100000/9 =11111 ==> 11111 - 1= 
11111 - 1 = 11_110
11110.   Answer : 11110
Answer: B
A student committee that must consists of 3 members is to be formed from a pool of 9 candidates. How many different committees are possible	Pick one
A) 5
B) 8
C) 40
D) 56
E) 84

Solution: Out of 9 people, any 3 can be selected for a committee. So 9c3=84 is the answer.   84
Answer: E
2 men and 4 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
Choose the correct choice from the following options
A) 12	B) 15	C) 18	D) 21	E) 48

Solution: The list should be WMWMW. Hence, from women 4! And men 2!, we get (4!)(2!)=48. Therefore, the correct answer is 48.
Answer: E
The average of all odd numbers up to 200 is	Choose the correct option: A) 50 B) 100 C) 120 D) 75 E) 80

Solution: The numbers are 1,3,5,7,--------,197,199   Average = (199-1)/2 + 1= 
(199-1)/2 + 1 = 100
100   Answer is 100
Answer: B
A rectangular swimming pool is 10 feet by 12 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 360 square feet. What is the width of the deck? Choose the correct choice from the following:
A) 7	B) 2	C) 3	D) 4	E) 6

Solution: Let the width =W   Total Area of the pool and deck= (2W+10)(2W+12)   We can Test the answer choices along with unit digit method   A) 2 feet ...........14*16 has unit digit 4..........Eliminate   B) 2.5 feet.........15*17 has unit digit 5..........Eliminate   C) 3 feet............16*18 has unit digit 8...........eliminate   4) 4 feet............18*20 has unit digit 0...........hold   E) 5 feet............20*22 has unit digit 0...........Eliminate ( bigger size)   Answer:4 w=4
Answer: D
A day-trader plans to invest a total of $23,400 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
Choose the correct choice from the following answers: A) $2,200 B) $3,000 C) $3,500 D) $3,800 E) $3,900

Solution: We can also just keep track of theHUNDREDS DIGITS(since the hundreds digit is different for each answer choice).   Total of 14 minimized investments = (14)(1400) = $???600   The 15th investment + $???600 = $23,400   So, theHUN$3,800RE$3,800S $3,800IGITSof the 15th investment must be 8   Answer: $3,800
Answer: D
16, 23, 19, 19, 22, 15, 25, ?
What number should replace the question mark?
Pick one: A) 13 B) 11 C) 16 D) 18 E) 19

Solution: 11   11   There are two alternate sequences: +3 and â€“4;
Answer: B
The sum of two consecutive number is 49. Which is the larger number? Select the correct option: A) 42 B) 43 C) 25 D) 45 E) 46

Solution: Let consecutive number be x, x+1   Therefore sum of the consecutive number is x + x+1=49   2x+1=49   2x=48   x=24   Therefore larger number is x+1=25   ANSWER:25
Answer: C
If 0 < a < b and k = (4a + 3b)/b , which of the following must be true?	Choose the correct choice from the following choices
A) k < 2 B) k < 7 C) k > 19 D) k > 9 E) k > 11

Solution: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.   As for your question, it is very simple and straightforward with number plug in.   Assume a=1 and b=2 as a < b, you get k = (4+6)/2= 
(4+6)/2 = 5
5. This eliminates all but option k < 7 , making it the correct answer.
Answer: B
the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0
Choose the correct choice from the following choices:
A) 11th  B) 12th  C) 13th  D) 14th  E) 15th

Solution: t2 + t19 = t8 + t15 + t12   => a+d + a+18d = a+7d + a+14d + a+11d   => a + 13d = 0   => t14 = 0 i.e. 14th term is zero.   ANSWER:14th
Answer: D
How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?  Choose the correct choice from the following answers:
A) 52 B) 55 C) 57 D) 60 E) 63

Solution: Selling Price(SP) of 1 kg mixture= Rs. 9.24   Profit = 10%   Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP   =100(100+10)×9.24=100110×9.24=92.411= Rs.8.4   By rule of alligation,   CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind   Rs. 9 Rs. 7   Mean Price   Rs.8.4   8.4 - 7= 
8.4 - 7 = 1.4
1.4 9 - 8.4= 0.6   i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3   Suppose x   kg of kind1 sugar is mixed with 27 kg of kind2 sugar.   then x : 27 = 7 : 3   ⇒3x=27×7⇒x=9×7=63   63
Answer: E
A chair is bought for Rs.600/- and sold at a loss of 5% find its selling price
Answers
A) s.570/-
B) s.550/-
C) s.560/-
D) s.590/-
E) s.580/-

Solution: 100 % ------> 600 (100 * 6 = 600)   95 % ------> 540 (95 * 6 = 570)   Selling price = Rs.540/-   s.570/-)
Answer: A
A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?	Options:
A) 7 1/2 days  B) 8 days  C) 5 days  D) 9 days  E) None of them

Solution: Ratio of times taken by A and B = 160 : 100 = 8 : 5.   Suppose B alone takes x days to do the job.   Then, 8 : 5 :: 12 : x = 8x = 5 x 12 =x = 7 1/2 days.   7 1/2 daysnswer is 7 1/2 days.
Answer: A
At a constant Rate of flow, it takes 120 minutes to fill a swimming pool if a large hose is used and 180 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?  Choose the most appropriate option
A) 52  B) 54  C) 56  D) 58  E) 72

Solution: time taken to fill the pool by Large Hose =120 minutes =L or 1/L=1/120 similarly 1/S=1/180   simultaneously it will take 1/L+1/S=1/120+1/180=5/360=72 minutes   Answer : 72
Answer: E
In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are strategy majors? Answers:
A) 3  B) 5  C) 8  D) 11  E) 13

Solution: pqrs = 1365 = 3 * 5 * 7 * 13   Since 1< p < q < r < s, the number of students who are strategy majors is s = 13.   The answer is 13.
Answer: E
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Pick one:
A) Rs. 3(2/9) B) Rs. 2(2/9) C) Rs. 2(1/9) D) Rs. 2(2/7) E) Rs. 2(3/7)

Solution: Here r = 10 % ,x = 100 and A = 5 kg   Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)   Rs. 2(2/9)
Answer: B
Sudhir started a business with Rs.60,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
Choose one.
A) 3:1	B) 2:3	C) 4:3	D) 3:4	E) 3:5

Solution: 60000*12:60000*(12-8)   =720000 :240000   =3:1   3:1NSWER:3:1
Answer: A
If A> 0 and A is divisible by the product of the first nine positive integers, all of the following must be factors of A except  Choose the most appropriate option.
A) 35
B) 40
C) 63
D) 315
E) 704

Solution: A is divisible by 9!,which is 1*2*3*4*5*6*7*8*9   A=(9!) * some number   A. 35 = 5*7 so will divide A   B. 40 =5*8 so will divide A   C. 63 =9*7 so will divide A   D. 315 =5*7*9 so will divide A   E. 704 =8*8*11 This will not divide A   Ans 704
Answer: E
How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr
Choose the correct option:	A) 115min	B) 215min	C) 315min	D) 415min	E) None of these

Solution: ExplanaƟon:   We know that,   Time=DistanceSpeedSpeed=20 km/hr=20   ∗   518m/sec=509m/sec Time =(400   ∗   950)=72sec=115min   115minnswer: OpƟon 115min
Answer: A
A train has a length of 150 metres. It is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.  Choose the correct answer:
A) 152 km/hr B) 178 km/hr C) 182 km/hr D) 172 km/hr E) 142 km/hr

Solution: Length of the train = 150 m   Speed of the man =2 km/hr   Relative speed = 153/3=50 m/s   =50Ã—18/5=180 km/hr   Relative speed = Speed of train - Speed of the man (as both are moving in the same direction).   Therefore,Speed of the train = Relative speed + Speed of the man=180+2= 
180+2 = 182
182 km/hr   ANSWER:182 km/hr
Answer: C
A certain stock exchange designates each stock with a two-letter or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes without using the letters A, B, or C? Select
A) 10,494	B) 11,585	C) 12,696	D) 13,787	E) 14,898

Solution: The number of two-letter codes is  23*23= 
 23*23 = 529
529.   The number of three-letter codes is 23*23*23=12,167.   The total number of codes is 529+12,167=12,696.   The answer is 12,696.
Answer: C
If ‘HYDERABAD’ is coded as ‘FWBCPYZYB’, then ‘MUMBAI’ is coded as
Answers:	A) KSKZYG	B) EDYHGG	C) GYTHNK	D) RTFGBKJ	E) TGFRbH

Solution: H= 8 = 8-2= 
8-2 = 6
6= F   Y = 25 = 25-2= 
25-2 = 23
23= W   SIMILKSKZYGRLY,   M=13= 13-2= 
13-2 = 11
11=K   U = 21 = 21-2= 
21-2 = 19
19=S   B = 2 =28 -2= 
28 -2 = 26
26= Z   KSKZYG = 1 = 27 -2= 
27 -2 = 25
25= Y   I = 9 = 9-2= 
9-2 = 7
7= G   SO KSKZYGNS IS   KSKZYG
Answer: A
In a game of 60 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 22?  Choose one.
A) can give C 1 points B) can give C 4 points C) can give C 2 points D) can give C 6 points E) can give C 8 points

Solution: A: B = 60 : 55, A : C = 60 : 45.   B/C = ( B/ A * A/C) = (55 / 60 * 60 / 45) = 11/9 = 22 /18   Therefore ,In a game of 22, B can give C 4 points.   Answer is can give C 4 points.
Answer: B
A train crosses a platform 100 m long in 60 seconds at a speed of 45 km/hr. The time taken by the train to cross an electric pole is :
Choose the correct choice from the following
A) 8 sec
B) 52 sec
C) 1 minute
D) Data inadequate
E) None of these

Solution: Explanation:   Speed = (45 *5/18)m/sec =25/2m/sec   Let the length of the train be x metres.   Then,x+100 / 25/2 =60 or x=650m   Time, taken by the train to cross an electric pole = (650 *2/25)= 
(650 *2/25) = 52
52 sec.   ANSWER IS 52 sec
Answer: B
Find a two digit number, given that the sum of the digits is 12 and the difference of the digits is 6.?  Pick.
A) 41 B) 46 C) 42 D) 46 E) 47

Solution: Using elimination method find which of the options fit the description of the number   ... from the option only 41 meets this description   sum of digits---4+1 = 5   difference of digits ---4-1 = 3   41nswer 41.
Answer: A
Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
Choose the correct choice from the following answers:  A) 5000  B) 4500  C) 5400  D) 5600  E) 6000

Solution: Let the investment 9% stock rs x   then investment in 10% stock = rs(9800-x)   9/75 xx = 10/80 *(9800-x)   3x/25 = 9800 - x   x=5000   5000NSWER 5000
Answer: A
A family pays $850 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total. Select
A) $1,000 B) $1,250 C) $1,400 D) $1,800 E) $2,200

Solution: Upfront payment for insurance plan = 850$   Family needs to pay 20 % of first 1000 $ in expense = 200$   Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 850 + 200= 
850 + 200 = 1_050
1050 $   Total amount paid by insurance plan for first 1000 $= 850 $   Total amount paid by family will equal amount paid by plan when medical expense = 1250 $   (Since insurance plan will pay 100% of amount that exceeds 1050$ )   Answer $1,250
Answer: B
Find the greatest number which leaves the same remainder when it divides 16, 46 and 82.	Choose the correct choice from the following options:
A) 18
B) 8
C) 12
D) 16
E) None of these

Solution: 82 - 46= 
82 - 46 = 36
36   46 - 16= 20   82 - 16= 
82 - 16 = 66
66   The H.C.F of 20, 36 and 66 is 2.   ANSWNone of theseR:None of these
Answer: E
How many different ways can you select a pilot and a co pilot if you have 60 people to choose from?
Pick one.
A) 199	B) 200	C) 398	D) 4950	E) 3540

Solution: You are not just choosing two from 60. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.   So the answer is in a sense (60C2) x 2 = 3540=3540
Answer: E
When positive integer x is divided by positive integer y, the remainder is 3. If x/y = 96.15, what is the value of y?
Choose the correct choice from the following answers.
A) 96  B) 75  C) 48  D) 25  E) 20

Solution: by the definition of a remainder, the remainder here is equal to 3/y. the remainder in decimal form is given as .15   therefore, 3/y = .15   solve for y and get 20.   20
Answer: E
The square root of (7 + 3âˆš5) (7 - 3âˆš5) is  Choose the most appropriate option:
A) âˆš5  B) 2  C) 4  D) 3âˆš5  E) 5

Solution: Explanation:   âˆš(7 + 3âˆš5)(7 - 3âˆš5)	=	âˆš(7)2 - (3âˆš5)2 = âˆš49 - 45= 
49 - 45 = 4
âˆš4= 2.   ANSWER IS 2
Answer: B
The diagonals of a rhombus are 12 cm and 20 cm. Find its area?
Options.
A) 329  B) 288  C) 120  D) 238  E) 31

Solution: 1/2 * 12 * 20= 
1/2 * 12 * 20 = 120
120   Answer: 120
Answer: C
If X = the product of six distinct prime numbers, how many factors does X have besides 1 and itself? Select.
A) 50	B) 56	C) 62	D) 68	E) 74

Solution: Since X has 6 distinct prime factors, X has a total of 2^6 = 64 factors.   Besides 1 and itself, X has 62 factors.   The answer is 62.
Answer: C
180 college students were asked in a survey if they preferred Windows or Mac brand computers. 50 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 60 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?	Choices
A) 25  B) 70  C) 50  D) 60  E) 75

Solution: 180 = 50(Mac) + x(Window) + 60(both) => x=70   ANSWER:70
Answer: B
An article is bought for Rs.750 and sold for Rs.700, find the loss percent? Select the correct option:	A) 6 2/5%	B) 6 2/9%	C) 6 5/3%	D) 6 3/3%	E) 6 2/3%

Solution: 750 ---- 50   50 ---- ? => 6 2/3%   Answer: 6 2/3%
Answer: E
Two integers x and y are chosen without replacement out of the set {1, 2, 3,......, 10}. Then the probability that x^y is a single digit number.
Select.
A) 11/90	B) 13/90	C) 17/90	D) 19/90	E) 23/90

Solution: it can take 9 values when x=1..   it can take another 8 values when y=1..   when x=2, y=3 as other values already considered..   when x=3, y=2 as other values already considered.. total-19 values so prob=19/90   ANSWER:19/90
Answer: D
A box contains Six bulbs out of which five are defective. If five bulbs are chosen at random, find the probability that all the four bulbs are defective?  Select the correct option
A) 1/127
B) 1/129
C) 1/12
D) 1/8
E) 1/6

Solution: Out of six, one are good and five are defective. Required probability   = 5C5/6C5   = 1/6   Answer: 1/6
Answer: E
There are 3 black cards, 2 white cards, and 7 green cards, in a box. What is the least number of cards that you have to pull out to make sure that you will have a matching pair? Choose the most appropriate option:  A) 8  B) 4  C) 5  D) 12  E) 11

Solution: Since there are 3 colors, if you take 3 cards, you could still have 1 card per color and not have a match.   Therefore, upon taking the 4th card, you will definitely have a match since the 4th card will form at least a pair with the 1st 3   So 3+1= 
3+1 = 4
4   Answer is 4
Answer: B
A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $18 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item?	Choose the correct choice:
A) $25  B) $26  C) $27  D) $28  E) $29

Solution: Let x be the price that buyers see online.   The distributor wants to receive 1.2(original price) which should be 80% of x.   1.2(18) = 0.8x   x = 1.2(18) / 0.8 = 1.5(18) = $27   The answer is $27.
Answer: C
If a - b = 3 and a^2 + b^2 = 29, find the value of ab.
Select
A) 5
B) 10
C) 12
D) 14
E) 15

Solution: 2ab = (a^2 + b^2) - (a - b)^2   = 29 - 9= 
29 - 9 = 20
20   ab= 10.   10)
Answer: B
An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 50 miles per hour, then 60 miles per hour, then 80 miles per hour. If the test took 30 hours to complete, how many miles was the car driven during the entire test?  Select:
A) 1500
B) 1830
C) 1645
D) 1562
E) 1600

Solution: let x be the distance..   so time taken by three cars is x/50,x/60,x/80... total time taken= x/50+x/60+x/80=x*59/1200 =30(given)   x=610... total =3x=1830   Answer is 1830
Answer: B
The ratio of the money with Rita and Sita is 7:15 and that with Sita and Kavita is 7:16. If Rita has $490, how much money does Kavita have?  Choose the correct choice from the following options:
A) $1500
B) $1800
C) $2000
D) $2400
E) $2600

Solution: Rita : Sita : Kavita   7 : 15   7 : 16   49 : 105 : 240   The ratio of money with Rita, Sita and Kavita is 49:105:240   We see that 49 = $490   Then 240 = $ 2400   Answer is $2400
Answer: D