MU-NLPC/Calc-aqua_rat huggingface dataset:
Rajesh can finish 1/5 of his home work in 30 minutes. Seema can finish 3/7 of
her homework in one hour and Ramya can finish 3/4 of her homework in
two and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.00 PM for 30 minutes? Pick one.
A) 4:30pm B) 5:30pm C) 6:30pm D) 4:00pm E) 3:50pm

Solution: rajesh can finish his work in 2.5 hr,   ramya can finish her work in 2.4 hr   seema can finish in 3.3 hr   so 3:50 pm they can go to play   ANSW3:50pmR:3:50pm
Answer: E
The perimeter of a semi circle is 162 cm then the radius is?
Choose the correct choice:
A) 31.5	B) 28	C) 98	D) 37	E) 13

Solution: 36/7 r = 162   => r   = 31.5   31.5nswer: 31.5
Answer: A
A train covers a distance of 12 km in 10 minutes. If it takes 9 seconds to pass a telegraph post, then the length of the train is
Select the correct option.
A) 100m  B) 120m  C) 140m  D) 160m  E) 180cm

Solution: Explanation:   Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.   Length of the train = (Speed x Time) = (20 x 9) m = 180 m   Answer: Option 180cm
Answer: E
By selling 32 cucumber in a dollar, a man loses 40%. How many cucumber must he sell in a dollar to gain 20% profit?	Choose the correct answer.
A) 16	B) 18	C) 20	D) 25	E) 28

Solution: This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 cucumber for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many cucumber he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of cucumber in half to double our returns (from 60% to 120%), yielding  32/2= 
 32/2 = 16
16 cucumber, or answer choice 16.
Answer: A
One pump drains one-half of a pond in 5 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
Answers:	A) 1 hour	B) 1.2 hour	C) 3 hours	D) 5 hours	E) 1.1 hours

Solution: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.   We have the 1st pump working rate/hour = 1/2 : 5 = 1/10   Working rate of 2 pumps: 1/2 : 1/2 = 1.   Working rate of 2nd pump: 1 -1/10 = 9/10 --> Time taken for the 2nd pump to finish: 1 : 9/10 = 10/9 = 1.1 hours.   1.1 hours
Answer: E
V is the volume of a cylinder; the radius of the cylinder is 3.4. The height of the cylinder is 450% more than the radius. Which of the following is true?
Choose the correct answer.
A) 700 < V < 900  B) 300 < V < 500  C) 500 < V < 700  D) 100 < V < 300  E) 900 < V < 1100

Solution: As we see the answers are in form of range we can use approximation   Volume of cylinder is πr^2h   Given π= 22/7 and r = 3.4 so r^2 ~ 12 and h = 5.5 * 3.4 ~ 19   So 22/7 * 12 * 19 ~ 717   so answer should be   A. 700 < V < 900   700 < V < 900nswer : 700 < V < 900
Answer: A
Two pipes A and B can fill a tank in 8 hours and 16 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Choose the correct choice from the following:
A) 5 hours 20 min
B) 5 hours 49 min
C) 3 hours 50 min
D) 3 hours 22 min
E) 3 hours 42 min

Solution: Explanation:   Part filled by 5 hours 20 min in 1 hour = 1/8   Part filled by B in 1 hour = 1/16   Part filled by (5 hours 20 min + B) in 1 hour = ( 1/8 + 1/16) = (3/16)   Time taken to fill the tank is (16/3) = 16/3*60= 
16/3*60 = 320
320 mins= 5 hrs 20 mins   5 hours 20 minNSWER 5 hours 20 min
Answer: A
Cost is expressed by the formula tb^4. If b is doubled, the new cost W is what percent of the original cost?  Pick.
A) W=200
B) W=600
C) W=800
D) W=1600
E) W=50

Solution: Original Cost W, C1=t1*b1^4   New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1   C2=t2*(2b1) ^4   =16(t1*b1^4)   =16C1   16 times C1=>1600% of C1   Ans W=1600=1600
Answer: D
Bob invested $3000 in fund A and $1000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after bob made these investments. Bob's investment in fund A was worth how much more than his investment in fund B?	Choose the correct choice from the following answers:
A) 1. $1500 B) 2. $1550 C) 3. $1600 D) 4. $1670 E) 5. $1700

Solution: interest on fund A will be 360. rate of interest will be 6% per annum simple interest as 12% is for 2 year. this will make investment A 360 at the end of 2nd year.   interest on fund B will be 690 on 30% interest compounded annually. This will make investment B 1690 at the end of 2nd year.   4. $1670ifference in investment A and investment B=3360-1690= 
3360-1690 = 1_670
1670   answer is 4. $1670.
Answer: D
A number is increased by 70 % and then decreased by 70 %. Find the net increase or decrease per cent.
Choices:
A) 49%
B) 18%
C) 17%
D) 13%
E) 16%

Solution: Let the number be 100.   Increase in the number = 70 % = 70 % of 100   = (70/100 Ã— 100)   = 70   Therefore, increased number = 100 + 70= 
100 + 70 = 170
170   This number is decreased by 70 %   Therefore, decrease in number= 70 % of 170   = (70/100 Ã— 170)   = 11900/100= 
11900/100 = 119
119   Therefore, new number= 170 - 119= 
170 - 119 = 51
51   Thus, net decreases= 100 - 51= 
100 - 51 = 49
49   Hence, net percentage decrease= (49/100 Ã— 100) %   = (4900/100)= 
(4900/100) = 49
49 %   49%nswer:49%
Answer: A
Present age of a father is 3 years more than 3 times theage of his son. 3 years hence, father's age will be 10 years more than twice the age of the son. What is father's present age?
Choose the correct choice from the following options.
A) 28 B) 29 C) 33 D) 36 E) 39

Solution: Let the present age the son =x   Then, present age of the father =3x+3   Given that, three years hence, father's age will be 10 years more than twice the age of the son   ⇒(3x+3+3)=2(x+3)+10⇒x=10   Father's present age   =3x+3=3×10+3=33   33
Answer: C
If the average of 10,11,12,13,14,15,16,17,18 and x is 23, what is the value of x? Choose the correct answer:
A) 90
B) 89
C) 123
D) x=104
E) 110

Solution: Given (10+11+12+13+14+ 15+16+17+18+x)/10=23   126+x/10= 23   126+x=230   x=230-126= 
230-126 = 104
104   Answer is x=104
Answer: D
If log5 x = 2, what is √x?
Choose the correct answer.
A) 5  B) 3√2  C) 2√3  D) 5√3  E) 3√5

Solution: E. Plug the values into the distance formula:   DISTANC3√5=√(x2-xi)2*square*+(y2-y1)2*square*=√(1-(-2)2*square*+(-2-4)2*square*   Simplify:   =√32*sq*+62*sq*=√9+36= 
9+36 = 45
√45=3√5   correct answer 3√5)3√5
Answer: E
A box contains 12 apples, 11 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?	Select.
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: P(choosing a red apple 7 times in a row) = 11/12*10/11*9/10*8/9*7/8*6/7*5/6 = 5/12 < 0.5   The answer is 7.
Answer: E
If i equals the sum of the even integers from 2 to 224, inclusive, and k equals the sum of the even integers from 8 to 80, inclusive, what is the value of i - k?
Choose one:
A) 11028 B) 14172 C) 14284 D) 14015 E) 14397

Solution: Use following formulae for such problems:   Sum of evenly spaced integers = (# of integers)*(mean of integers)   # of integers = [(last - first)/2] + 1   Mean of integers = (last + first)/2   In above problem:   # of integers = [(224 - 2)/2] + 1= 112 and [(80-8)/2]+ 1 (224 - 2)/2  + 1= 
(224 - 2)/2  + 1 = 112
112 and [(80-8)/2]+ 1 = 37   Mean of integers (80-8)/2 + 1= 
(80-8)/2 + 1 = 37
37   Mean of integers= (224 + 2)/2= 
(224 + 2)/2 = 113
113 and   (80 + 8)/2= 
  (80 + 8)/2 = 44
44   Sum of integers= (112*113)= 
(112*113) = 12_656
12656 and   (37*44)= 
  (37*44) = 1_628
1628   Thus their difference (i - k)= 12656 - 1628= 
12656 - 1628 = 11_028
11028   11028NSWER:11028
Answer: A
A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400. Choose the correct choice:
A) 1909 B) 1900 C) 1908 D) 1901 E) 1902

Solution: 65 * 6 : 84 * 5 : 100 * 3   26:28:20   C share = 74000 * 95/100 = 7030 * 20/74= 
7030 * 20/74 = 1_900
> 1900   Answer: 1900
Answer: B
A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
Pick one.
A) 4 days B) 8 days C) 12 days D) 9 days E) 3 days

Solution: 2/5 + (2 + x)/10   = 1 => x   = 4 days   4 daysnswer: 4 days
Answer: A
A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?
Choose the correct choice from the following answers:
A) 720
B) 800
C) 890
D) 900
E) 950

Solution: 5 digit palindrome would look like this : abcba.abcba.   Thus, the first digit can be filled in 9 ways(1-9), the second digit can be filled in 10 ways (0-9) and the 3rd digit can again be filled in 10 ways. The last 2 digits would just mirror the already selected digit. Thus, the no of ways : 9*10*10*1*1= 
9*10*10*1*1 = 900
900.   ANSWER:900.
Answer: D
The side of a square is increased by 25% then how much % does its area increases?
Choose the correct choice from the following
A) 56.75 %
B) 56.25 %
C) 56.75 %
D) 57.25 %
E) 56.22 %

Solution: a = 100 a2 = 10000   a = 125 a2 = 15625   ----------------   10000 --------- 5625   100 -------? => 56.25 %   Answer:56.25 %
Answer: B
The cost of 3 kg of sugar is $15. What will the cost of 8 kg of sugar be?	Select the correct option
A) 20  B) 40  C) 80  D) 160  E) 180

Solution: 3 kg costs $15   1 kg costs $5   8 kg costs $40   The answer is 40.
Answer: B
In how many different number of ways 10 boys and 3 girls can sit on a shopa which can accommodate 3 persons?	Choose the correct option
A) 1800  B) 1716  C) 1617  D) 2000  E) None

Solution: Option '1716'   13p3 = 13x12x11= 1716
Answer: B
Tough and Tricky questions: Combinations.
Three contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
Select
A) 6 B) 9 C) 12 D) 16 E) 24

Solution: Four contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?   We have 2 slots to be filled using 3 contestants:3 options for slot1*3 option for slot2   = 3* 3= 
3* 3 = 9
9   Ans. 9) 9
Answer: B
Double of Quarter of 5 percent written as a decimal is :
Answers.
A) 0.003  B) 0.0005  C) 0.025  D) 0.005  E) None of these

Solution: Explanation :   Solution: (2)*(1/4)*5% = 0.025   Answer : 0.025
Answer: C
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 42, what is the remainder when k is divided by 7?
Choose the correct choice.
A) 5
B) 3
C) 6
D) 7
E) 10

Solution: Cant think of a straight approach but here is how I solved it:   K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)   so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 42)   Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5   so the possible value set for k = {5, 11, 17, 23, 29,35,41} (less than 42)   17 is the only common number in both the sets. Hence k = 17   Answer : 3
Answer: B
What number times (1⁄4)^2 will give the value of 4^3? Answers:
A) 4  B) 16  C) 64  D) 256  E) 1024

Solution: x*(1/4)^2 = 4^3   x = 4^2*4^3 = 4^5 = 1024   The answer is 1024.
Answer: E
A dishonest dealer professes to sell goods at the cost price but uses a weight of 990 grams per kg, what is his percent?	Choose the most appropriate option.
A) 1.01%
B) 25%
C) 22%
D) 29%
E) 45%

Solution: 990 --- 10   100 --- ? => 1.01%   1.01%nswer:1.01%
Answer: A
2/5 of the fish in an aquarium are red and 1/4 of the fish are brown. 1/2 of the red fish and 2/5 of the brown fish are male. If the rest of the fish in the aquarium are female, what is the probability that a fish randomly picked from the aquarium is male?
Choose the correct option:
A) 1/3  B) 2/5  C) 3/10  D) 3/20  E) 7/20

Solution: 1/2*2/5 + 2/5*1/4 = 3/10   The answer is 3/10.
Answer: C
Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be	Answers
A) 125 cm3	B) 625 cm3	C) 15525cm3	D) 1225cm3	E) None

Solution: Solution   The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm   ∴Volume = (25x5x5)cm3   ‹=›625cm3   Answer 625 cm3
Answer: B
7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?  Options.
A) 450  B) 500  C) 560  D) 650  E) 700

Solution: Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.   ∴ No. of books distributed in 1st day   = 7×5x+5×4x+8×2x=71x   No. of books distributed in 1Ind day   =7×5x+3×4x+5×2x=57x   And no. of books distributed in IIIrd day   =4×5x+5×4x+3×2x=46x   71x + 57x + 46x = 2000, x = 2000/174   57x=2000/174×57=650   650
Answer: D
What percent is 300 gm of 1 kg?  Choose the correct option:
A) 25%  B) 40%  C) 30%  D) 8%  E) 12%

Solution: 1 kg = 1000 gm   300/1000 Ã— 100 = 30000/1000= 
30000/1000 = 30
30 %   Answer is 30%
Answer: C
Pipe A can fill a tank in 5 hr, pipe B in 10hr and pipe C in 30hr. If all the pipes are open in how many hours will tank be filled?
Choose the correct choice from the following answers.
A) 1hr
B) 2hr
C) 3hr
D) 4hr
E) 5hr

Solution: Part filled by (A+B+3hr) in 1hour = 1/5 + 1/10 + 1/30 = 1/3   All the 3 pipes together will fill the tank in 3hours   Answer is 3hr
Answer: C
The average weight of a class of 24 students is 35 kg. if the weight of the teacher be included, the average rises by 400 g. the weight of the teacher is
Choices:
A) 45 kg
B) 50 kg
C) 53 kg
D) 55 kg
E) None of these

Solution: Solution   Weight of the teacher = (35.4 × 25 - 35 × 24) kg = 45 kg. 45 kgnswer 45 kg
Answer: A
There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?  Pick:
A) 18	B) 20	C) 21	D) 23	E) 26

Solution: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   Similarly, if 3 of the boxes have green balls, there will be 4 options.   If 4 boxes have green balls, there will be 3 options.   If 5 boxes have green balls, then there will be 2 options.   If all 6 boxes have green balls, then there will be just 1 options.   Total number of options = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21   21
Answer: C
F is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of F, and y is the minimum value of the sum of k distinct members of F, what is x + y?	Answers:
A) kn B) kn + k^2 C) kn + 2k^2 D) 2kn – k^2 E) 2kn

Solution: Probably the easiest way to solve this question would be to assume some values for n and k.   Say n=3, so F, the set of the first n positive odd numbers would be: F={1, 3, 5};   Say k=1, so X, the maximum value of the sum of K distinct members of F would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of F would simply be 1.   X+Y=5+1= 
5+1 = 6
6.   Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1= 
2*3*1 = 6
6.   Answer: 2kn.
Answer: E
Three candidates contested an election and received 1136, 7636 and 16628 votes respectively. What percentage of the total votes did the winning candidate got?	Select the correct option:
A) 65.4% B) 56% C) 57% D) 58% E) 59%

Solution: Total number of votes polled = (1136 + 7636 + 16628)= 
(1136 + 7636 + 16628) = 25_400
25400   So, Required percentage= 16628/25400 * 100 = 65.4%   65.4%NSWER : 65.4%
Answer: A
The average weight of 3 packets A, B and C is 84 kg. Another packet D added into the group and the average now becomes 80 kg. If another packet E, whose weight is 3 kg more than that of D, replaces A then the average weight of B, C, D and E becomes 79 kg. The weight of A is: Choices
A) 70 kg  B) 72 kg  C) 75 kg  D) 80 kg  E) None of these

Solution: Explanation :   A+B+C = (84x3) = 252kg, A+B+C+D=(80x4) = 320kg.   D = (320 - 252)= 
(320 - 252) = 68
68 , E= (68+3) =7l.   B+C+D+E = (79x4)=316.   (A+B+C+D) -(B+C+D+E)=(320 - 316)= 
(320 - 316) = 4
4kg.   A - E= 4 = A = (4+E)=75kg   Answer : 75 kg
Answer: C
The price of a T.V. set worth 20,000 is to paid in 20 instalments of 1000 each. If the rate of interest be 6% per annum, and the first instalment be paid at the time of purchase, then the value of the last instalment covering the interest as well will be :  Answers
A) 1050 B) 2050 C) 3000 D) None of these E) 2020

Solution: Money paid in cash = 1000.   Balance payment = (20000 – 1000) = 19000.   Answer None of these
Answer: D
if the ratio of two number is 6:7 and LCM of the number is 450 then what is the number.  Answers:
A) 11 B) 20 C) 25 D) 30 E) 35

Solution: product of two no = lcm *hcf   6x*7x=450*x   x=11   11NSWER:11
Answer: A
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.500, find the original price per kg?	Choose the most appropriate option:
A) s.12.7  B) s.12.4  C) s.12.5  D) s.12.1  E) s.12.9

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   500 --- 80   ? --- 2 => Rs.12.5   Answer:s.12.5
Answer: C
Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 3000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?	Select:
A) 100000
B) 100500
C) 63000
D) Data inadequate
E) None of these

Solution: Let the investment of X in 1995 be x.   ∴ Profit = x⁄5   ∴ Income = (x + x⁄5) = 6⁄5x   Investment of company X in 1996 would be (x – 3000) From the question,   (x - 3000) × 126⁄100 = 6⁄5x ⇒ x = 63000   Answer 63000
Answer: C
At a local gym there were 55 people working out at 4 p.m., of those people 29 did cardio-vascular exercises and 20 did weight training. If 13 did neither cardio-vascular exercises nor weight training, then how many people did both cardio-vascular exercises and weight training?  Choose the correct choice: A) 62 B) 49 C) 13 D) 12 E) 7

Solution: The total number =55   Cardio=29   Weight=20   Neither =13   N(CUW)= N(c) +N(w)-N(C intersection W)+N(neither C or W)   55=29+20-(Intersection)+13=7   Answer:7
Answer: E
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 32.49, the number of the member is the group is:
Select
A) 57 B) 67 C) 77 D) 87 E) 97

Solution: Explanation:   Money collected = (32.49 x 100) paise = 3249 paise.   ∴ Number of members = √(3249) = 57.   57nswer: 57
Answer: A
A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?	Choose the correct choice from the following options:
A) 1 days B) 12 days C) 52 days D) 60 days E) 10 2/3 days

Solution: 10 2/3 daysxplanation:   2/10 + 4/15 + x/20 = 1   x = 32/3 = 10 2/3 days   Answer: 10 2/3 days
Answer: E
A certain company employs 9 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible? Choose the correct choice from the following choices
A) 8
B) 24
C) 58
D) 336
E) 210

Solution: Number of ways to select 3 senior officers from 9 of them = 9C3 = 84 ways   Next we can determine the number of ways to select 1 junior officer.   number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways   Thus the number of ways to select 3 senior officers and 1 junior officer is 84 x 4 = 336 ways.   Answer: 336
Answer: D
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?  Choose one:	A) 287	B) 278	C) 698	D) 279	E) 275

Solution: S.I. for 1 year = (854 - 815)   = Rs. 39   S.I. for 3 years = 39 * 3   = Rs. 117   Principal = (815 - 117)   =Rs.698.   Answer: 698
Answer: C
A three digit number divisible by 7 becomes divisible by 3 when 16 is subtracted from it. The largest such number is :
Pick one: A) 994 B) 981 C) 963 D) 951 E) 942

Solution: Out of all the 5 options, only 994 is NOT divisible by 3. 994ll others are divisible   So 994nswer = 994 (No further calculation required)   994ddition of any two non-divisible numbers by 3 gives the resultant divisible by 3   16 is non-divisible by 3; we are subtracting a number from that so that the resultant becomes divisible by 3   994pplying the above rule,It means that the number which we are going to add should be non-divisible by 3   So comes the answer = 994   994nswer : 994
Answer: A
John has 6 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 12 shoes, what is the probability that she will select 2 shoes of the same color? Answers
A) 2/5	B) 1/5	C) 1/9	D) 1/8	E) 1/11

Solution: Can be tackled in this way as well: Probability of selecting any 1 out of 12 shoes = 12/12= 
12/12 = 1
1   Probability of selecting the next shoe (out of 12 available) having the same color= 1/9 (as after selecting the 1st one, there is only 1 another shoe left with the same color).   Thus the total probability = 1*1/11=1/11.   1/11 is the correct answer.
Answer: E
The average weight of 9 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person? Choose the correct answer: A) 76 kg B) 77 kg C) 78.5 kg D) Data inadequate E) None of these

Solution: total weight increases = 9 × 1.5 = 13.5 kg   so the weight of new person = 65 + 13.5= 
65 + 13.5 = 78.5
78.5 kg   Answer 78.5 kg
Answer: C
Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 350 shoppers liked exactly 2 juices, and 100 shoppers liked all three juices, how many shoppers took the taste test?	Choose the correct choice from the following answers.
A) 1,300  B) 1,000  C) 900  D) 700  E) 450

Solution: Given: Atleast 1 juice was liked by the participants. --> Neither = 0   Assume, I -->No overlap between the sets   II --> Overlap between 2 sets   III --> Overlap between 3 sets   I + 2*(II) + 3*(III) = 100 + 200 + 700   I   + 2*(350) + 3*(100)= 
  + 2*(350) + 3*(100) = 1_000
1000   I= 0   Total number of shoppers who took the taste test = I + II + III = 0 + 350 +100= 
0 + 350 +100 = 450
450   Answer: 450
Answer: E