MU-NLPC/Calc-aqua_rat huggingface dataset:
If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? Pick one:
A) 24/91
B) 45/91
C) 2/3
D) 67/91
E) 84/91

Solution: We have a pool of 10 men and 5 women   We need a jury of 12 people   What is the probability that the jury will comprise at least 2/3 men?   2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.   15C12 = 455 ways to select a jury of 12 from a pool of 15   5C5 = 1 way to select all 5 women   10C7 = 120 ways to select 7 men from a pool of 10   1*120= 
1*120 = 120
120 ways to select a jury with fewer than 8 men   (455-120)/455= 335/455 = 67/91   Answer 67/91
Answer: D
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 1 hours, how many machines of type R were used? Select.
A) 3  B) 4  C) 6  D) 9  E) 12

Solution: Rate of machine R =1/36   Rate of machine S =1/18   since same no of machines used for R and S to do the same work in 1 hrs   So collective rate needed to finish the work in 1 hrs= 1/1   Let the no of machine be x   So, x/36 +x/18 =1/1   x3/36=1/1   x=12   So no of machine R is 12   Answer 12
Answer: E
A company produces 60000 bottles of water everyday. If a case can hold 5 bottles of water .How many cases are required by the company to hold its one day production	Choose the correct answer.
A) 12000	B) 4500	C) 5000	D) 8000	E) 9000

Solution: Number of bottles that can be held in a case = 5   Number of cases required to hold 60000 bottles = 60000/5= 
60000/5 = 12_000
12000 cases.   So the answer is 12000=12000
Answer: A
What is the average (arithmetic mean) of all the multiples of ten from 10 to 160 inclusive?
Choose the correct choice from the following options.
A) 90 B) 95 C) 70 D) 105 E) 110

Solution: 10 and 190 inclusive would mean there are 15 terms.   No need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10, 20, 30........160   The middle term is the average which is the tenth term = 70   70 is the answer.
Answer: C
Vijay's salary is Rs. 21,600 per month. In the first month of the year, he spends 30% of his income on clothing, 20% of the remaining on entertainment and some percentage of the remaining on food. He saves of the amount he spends. Find the percentage of spending on food as a percentage of saving.	Choose the correct choice from the following answers:  A) 180%  B) 124%  C) 160%  D) 154%  E) 140%

Solution: Let monthly income be = x on clothing =.3x on entertainment = .2(.7x) =.14x on food = (.16x)k saving =( .3x .14x .16xk)*13 solving we get k =.31.16 putting the value and we get ...... on the food =.31x ,and saving =.25x %on food / %on saving = .06x/.25x =24%   correct answer - 124%
Answer: B
The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?	Choose one: A) 2 years B) 6 years C) 7 years D) 9 years E) 4 years

Solution: Amount = (30000 + 4347) = Rs. 34347   Let the time be n years. Then,   30000(1 + 7/100)n = 34347   = (107/100)n = 34347/30000 = (107/100)2   n = 2 years.   2 yearsnswer: 2 years:
Answer: A
5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Answers.
A) 3238  B) 2667  C) 4400  D) 2977  E) 2712

Solution: X * (95/100) * (85/100) = 3553   X = 4400   Answer: 4400
Answer: C
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Choose the correct answer.
A) 24029 B) 24000 C) 24028 D) 24014 E) 24012

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of B = 6/13 (52000) = Rs. 24000   Answer:24000
Answer: B
A cistern has a leak which empty it in 8 hrs, A tap is turned on which admits 6 liters a minute into the cistern, and it is now emptied in 12 hours, How many liters does the cistern hold ? Choose the correct choice from the following answers.
A) 8640	B) 8740	C) 8840	D) 8540	E) 8940

Solution: Inflow of water in 12hrs with rate 6 lit/min= 6*60*12= 
6*60*12 = 4_320
4320   But, the same volume is emptied in 12 hrs, so the total capacity= total inflow + total outflow= 4320+4320= 
4320+4320 = 8_640
8640   8640NSWER:8640
Answer: A
In a contest, a bowl contains 20 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize? Answers:  A) 2/39  B) 3/40  C) 1/40  D) 1/20  E) 1/10

Solution: P(not winning) = 19/20*18/19 = 9/10   P(winning) = 1 - 9/10 = 1/10   The answer is 1/10.
Answer: E
60% of a number is added to 180, the result is the same number. Find the number? Choose the correct choice from the following answers.
A) 300  B) 277  C) 266  D) 99  E) 450

Solution: :   (60/100) * X + 180 = X   2X = 900   X = 450   Answer: 450
Answer: E
Kanul spent $5000 in buying raw materials, $200 in buying machinery and 30% of the total amount he had as cash with him. What was the total amount?	Choose the correct choice
A) $7456.00	B) $7500.55	C) $7428.57	D) $7852.56	E) $7864.00

Solution: Let the total amount be x   then, (100-20)% of x = 5000+200   70% of x = 5200   70x/100 = 5200   x = $52000/7   x = $7428.57   Answer is $7428.57
Answer: C
There are n cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?	Options:  A) n(n-1)  B) n(n+1)  C) n(n-1)/2  D) n(n+1)/2  E) n2

Solution: the Q basically asks to choose two cities out of n and since the DIRECTION is important, we are looking at Permutations or combinations with Order..   nP2=nC2∗2!=n(n−1)2∗2=n(n−1)   n(n-1)NSWER:n(n-1)
Answer: A
A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 16 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?  Choose the most appropriate option:
A) 1/10 B) 13/50 C) 1/2 D) 7/10 E) 9/10

Solution: C+M+B-CM-MB-CB-2CMB = 100   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-16-2CMB = 100   B-CB-MB-2CMB =26   hence the probability = 26/100 = 13/50.   13/50
Answer: B
A jeep takes 8 hours to cover a distance of 280 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Select
A) 28 Kmph	B) 52 Kmph	C) 20 Kmph	D) 23 Kmph	E) 65 Kmph

Solution: Time = 8   23 Kmphistance = 280   3/2 of 8 hours = 8 * 3/2= 
8 * 3/2 = 12
12 Hours   Required speed= 280/12= 23 Kmph   23 Kmph)
Answer: D
If Scott has earned x dollars by working 3 days a week at a constant daily rate for w weeks, which of the following represents his daily wage?  Pick one:
A) 3xw B) 3w/x C) w/(3x) D) xw/3 E) x/(3w)

Solution: In 1 week -- Scott works 3 days   In 'w' weeks---Scott works 3w days   3w day's wage -- x $   1 day's wage --- x/3w $   Answer : x/(3w)
Answer: E
If k is an integer and 0.00010101 x 10^k is greater than 10, what is the least possible value of k? Choose one: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: 0.00010101 * 10^k > 10   We need to move the decimal point to the right 5 places to get 10.101   This is equivalent to multiplying by 10^5.   The answer is 5.
Answer: C
The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product
(n − 1)(n − 2)...3.2.1 is not divisible by n is
Choose one:	A) 5	B) 7	C) 13	D) 14	E) 16

Solution: Explanation :   (n-1)! is always divisible by n unless and untill n is a prime number   e.g.(5-1)!=4! which is not divisible by 5 bcuz 5 is a prime number   Therefore, find all prime numbers in the range of 12 to 40 i.e   13, 17, 19, 23, 29, 31 and 37   Hence, the number of positive integers n is 7.   Answer : 7
Answer: B
The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?  Choose the correct choice from the following answers:  A) 48 years  B) 52 years  C) 56 years  D) Cannot be determined  E) None of these

Solution: Let the present ages of P and Q be 5x and 7x years respectively.   Then, 7x - (5x + 6) = 2   2x = 8 => x = 4   Required sum = 5x + 7x = 12x 5  + 7= 
5  + 7 = 12
12x= 48 years.   48 yearsNSWER:48 years
Answer: A
If n = 7p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ? Pick one.
A) Two	B) Three	C) Four	D) Six	E) Eight

Solution: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:   n = 4 x 3   n = 12   Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.   1, 12, 6, 2, 4, 3   From this we see that we have 4 even divisors: 12, 6, 2, and 4.   If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so   n = 4 x 5   n = 20   The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.   No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.   The answer is Eight
Answer: E
What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 60%? Answers.
A) 150% B) 160% C) 156% D) 158% E) 162%

Solution: The question is very easy. My logic is the following:   A surface = 6*a^2   After 60% increase A surface = 6* ((1.6a)^2) = 6*2.56*a^2   The increase in the surface area = (6*2.56*a^2 - 6*a^2)/6*a^2 = (6*a^2(2.56-1))/(6*a^2) = 2.56-1= 
2.56-1 = 1.56
1.56= 156%   Answer :156%
Answer: C
Usha took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 375 as interest at the end of the loan period, what was the rate of interest?	Pick one:
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Let rate = R% and time = R years.   Then, (1500 * R * R) / 100 = 375   15R2 = 375   R2 = 25 => R = 5   Answer:5
Answer: B
If q is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of q ?  Choose one:	A) 10	B) 12	C) 14	D) 16	E) 18

Solution: Answer is C.   numbers in format of 3^k in the series from 1 to 30 inclusive q are: 3*1, 3*2, 3*3, 3*4, 3*5, 3*3*2, 3*7, 3*8, 3*3*3, 3*10. Total number of 3 = 13. So k=14.
Answer: C
What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/6  Choose the correct choice from the following.
A) 2/5
B) 3/5
C) 1/6
D) 1/7
E) None of these

Solution: Explanation:   2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/6 = .833   So biggest is 5/6 and smallest is 2/3   Their difference is 5/6 - 2/3 = 1/6   Option 1/6
Answer: C
A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart. What is the length of the side of his property and how many posts did he buy? Choose the correct choice from the following.
A) 100 m, 15
B) 100 m, 16
C) 120 m, 15
D) 120 m, 16
E) None

Solution: Explanation :   Let ,the length of the side of the property be 'x' and 'y' be the number of posts bought.   When the space between polls is 8 m, the number of poles is (x/8)+1.   =>(x/8)+1 =y. --------------(i)   When space between poles is 6m, the number of poles is (x/6)+1 and 5 more are required.   =(x/6)+1 =y+5 --------------(ii)   On solving both of the equations, we get :-   x=120 and y=16.   Answer : 120 m, 16
Answer: D
A, B and C have Rs.600 between them, A and C together have Rs.250 and B and C Rs.450. How much does C have? Select:
A) 70
B) 90
C) 120
D) 100
E) 140

Solution: A+B+C = 600   A+C = 250   B+C = 450   --------------   A+B+2C = 700   A+B+C = 600   ----------------   C = 100   ANSWER:100
Answer: D
P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is R's share?  Choose the correct choice from the following
A) 108 B) 120 C) 134 D) 144 E) None of these

Solution: Explanation :   The ratio of their initial investment = 1/2 : 1/3 : 1/4   = 6 : 4: 3   Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively   A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12   = (12+30) : 4*12 : 3*12   =(4+10) : 4*4 : 12   = 14 : 16 : 12   = 7 : 8 : 6   R's share = 378 * (6/21)= 
378 * (6/21) = 108
108. 108nswer : Option 108
Answer: A
In a shop certain saree was marked down 10% the first week and another 10% the next week. What percent of the regular price was the final cost of the saree after the two markdowns?	Pick one
A) 30%  B) 36%  C) 40%  D) 60%  E) 81%

Solution: If the price of the saree is 100, and it is marked down by 10% twice or charged 90% of the price first and 90% of the price of reduced price, the final price is :-   100*90*90/10000= 
100*90*90/10000 = 81
81   81% is the final price of old price.   81% is the answer
Answer: E
If x is an integer and 2.134 × 10^x is less than 220,000, what is the greatest possible value for x?  Choose the correct option
A) 7  B) 6  C) 5  D) 4  E) 3

Solution: x is an integer and 2.134 × 10x is less than 220,000, what is the greatest possible value for x?   for 2.134 × 10x is less than 220,000 to remain true, the greatest number is 213,400, which makes x=5   C. 5
Answer: C
A circle in the coordinate plane passes through points (-3, -2) and (-1, 4). What is the smallest possible area of that circle? Choose the correct choice from the following options
A) 13π
B) 26π
C) 10π
D) 52π
E) 64π

Solution: The distance between the two points is sqrt(40).   radius = sqrt(40)/2   Area= pi*(sqrt(40)/2)^2   10π.10π
Answer: C
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Choose one
A) 40 m  B) 60 m  C) 70 m  D) 80 m  E) 90 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was Choose one
A) 344  B) 218  C) 200  D) 388  E) 211

Solution: Explanation:   Let original 200ost price is x   Its Selling price = (105/100) * x = 21x/20   New 200ost price = (95/100) * x = 19x/20   New Selling price = (110/100 )* (19x/20 )= 209x/200   [(21x/20) - (209x/200)] = 1   => x = 200   Answer: 200) Rs 200
Answer: C
Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?  Choices
A) 22 sec	B) 77 sec	C) 76 sec	D) 20 sec	E) 66 sec

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 sec.   Answer:20 sec
Answer: D
The mean of set A does not exceed mean of any subset of set A. Which of the following must be true about set A?
I. Set A contains only one element
II. All elements in set A are equal
III. The median of set A equals the mean of set A Answers
A) of the three qualities is necessary  B) II only  C) III only  D) II and III only  E) I, II, and III

Solution: The only necessary condition seems to be II.   If all nos are equal.... them mean of any subset is the same.   I is obviously ruled out ( e.g. A = {1,1,1} )   But III, what about 3?   It is not necessary in itself, rather, is automatically implied by II.   All sets that satsify II satisfy III=II and III only
Answer: D
Given two sets X = {1,1,4,4,3,3} and Y = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number  Choose the correct choice from the following choices.
A) 1/2	B) 1/6	C) 1/5	D) 1/7	E) 1/8

Solution: One way to look at it:   The number from set X can be ANYTHING.   The number selected from set Y will determine whether the sum is odd or even.   For example, if a 4 is selected from set X, we need a 0 from set Y to get an even sum.   If a 3 is selected from set X, we need a 1 from set Y to get an even sum.   And so on.   So, P(sum is even) = P(select 1/2NY number from set X 1/2NDselect the number from set Y that makes the sum even)   = P(select 1/2NY number from set X)xP(select the number from set Y that makes the sum even)   = 1x1/2   = 1/2   = 1/2
Answer: A
If m+n gives remainder as 8 and m-n gives remainder as 6 when both are divide by 12, what is the remainder when m*n is divided by 6? Choose one:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: let   m+n=12a+8   m-n=12b+6   m*n=(6*(a+b)+7)(6*(a-b)+1))   7%6=2   ans = 1   1NSWER:1
Answer: A
Mary works in a restaurant a maximum of 80 hours. For the first 20 hours, she is paid $8 per hour. For each overtime hour, she is paid at a rate which is 25% higher than her regular rate. How much Mary can earn in a week? Pick one:
A) 600
B) 720
C) 760
D) 620
E) 700

Solution: Mary receives $8(20)=$160 for the first 20 hours.   For the 60 overtime hours, she receives $8(0.25) +$8 = $10 per hour, that is $10(60)=$600.   The total amount is $160+$600 = $760   Answer 760 360.160+ 600= 
160+ 600 = 760
$760   Answer 760 360.
Answer: C
Rick deposited $850 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?  Select.
A) 5
B) 25
C) 50
D) 55
E) 65

Solution: 5x+15y=850 --1   x+y=60 ---2   multiply eq 2 with 5 and subtract from eq 1   5x+15y=850   5x+5y=300   10y= 550   y=55 and x = 5   therefore $15 bills = 15   ANSWER:55
Answer: D
How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 850 meters in length?
Choose the correct option
A) 28	B) 27	C) 55	D) 18	E) 67.7

Solution: T = (850 + 165)/54 * 18/5   T = 67.7   Answer: 67.7
Answer: E
If q is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
Pick one.
A) 1 B) 2 C) 3 D) 6 E) 12

Solution: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey q=4n, if it really wanted to convey so.   From other questions that I have seen, proper wordings could be:   If q is three times as large as n   OR simply,   If q is three times n=3
Answer: C
A cricket bat is sold for $850, making a profit of $225. The profit percentage would be	Select
A) 24%
B) 25%
C) 30%
D) 36%
E) 40%

Solution: 225/(850 - 225) = 225/625 = 9/25 bit more than 33%.   Answer: 36%
Answer: D
What is the 8th term in this sequence?
2,3,5,16,27,43,76 Choose the correct option
A) 127  B) 125  C) 178  D) 124  E) 121

Solution: 2+3= 
2+3 = 5
5 +0= 
5 +0 = 5
5   5+3=10+6= 
10+6 = 16
16   16+5= 
16+5 = 21
21+6= 
21+6 = 27
27   27+16= 
27+16 = 43
43+0= 
43+0 = 43
43   43+27= 
43+27 = 70
70+6= 
70+6 = 76
76   76+43= 
76+43 = 119
119+6= 
119+6 = 125
125   so 8th term is 125   ANSWER:125
Answer: B
Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is  Select the correct option:	A) 37	B) 29	C) 27	D) 48	E) 22

Solution: Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 60 or x = (60 * 4) / 5= 
(60 * 4) / 5 = 48
48.   Answer: 48
Answer: D
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?  Select
A) 3	B) 4	C) 6	D) 8	E) 9

Solution: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3   3
Answer: A
A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?	Answers
A) 23% B) 10% C) 32% D) 98% E) 31%

Solution: 2420 --- 242   100 --- ? => 10%   Answer: 10%
Answer: B
Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes 7 hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car? Choose the correct choice from the following answers.
A) 7/4	B) 4/3	C) 15/4	D) 10/3	E) 64/21

Solution: Rate(1)=1/6   Rate(2)=1/7   Combined = 13/42   Work done in 2 days=13/21   Work left = 8/21   Rate * Time = Work left   1/8 * Time = 8/21   Time=64/21   64/21
Answer: E
If 'a' and 'b' are non-zero numbers such that their sum is six times the product, what is the value of 1/a + 1/b?	Choose the most appropriate option
A) 5 B) 6 C) 7 D) 8 E) 12

Solution: a+b = 6ab   1/a + 1/b = (b + a)/(ab) = 6.   The answer is 6.
Answer: B
In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 270, then the least and greatest integer on the card would be
Choose the correct answer: A) 3 and 15 B) 3 and 20 C) 4 and 13 D) 4 and 16 E) 5 and 14

Solution: Given: 15<x(x+1)<270.   Now, it's better to test the answer choices here rather than to solve:   If x=4 then x(x+1)=20>15 --> so, the least value is 4. Test for the largest value: if x=16 then   x(x+1)=16*17= 
16*17 = 272
272>270   Answer: 4 and 16.
Answer: D
The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed two times, what is the probability that the coin turns up tails on at least one of the tosses?
Answers:
A) 1/4	B) 3/4	C) 3/8	D) 5/8	E) 7/8

Solution: P(2 heads)= 1/2*1/2=1/4.   P(at least one tail)=1-1/4=3/4.   The answer is 3/4.
Answer: B
How many times thekeys of a writter have to bepressed in order to write first 400 counting no's?  Pick one.
A) 900	B) 980	C) 1000	D) 1092	E) 1200

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   1092
Answer: D
Lakshmi went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 20%. then what was the cost of the tax free items?	Options:	A) Rs. 197	B) Rs. 190	C) Rs. 187	D) Rs. 167	E) Rs. 191

Solution: Solution   Let the amount of taxable purchases be Rs.x.   Then, 20% of x	= 50/100   x ‹=› (50/100×100/20)   = 2.50   Cost of tax free items	= Rs.[200 - (2.50 + 0.50)]   = Rs. 197   Rs. 197nswer Rs. 197
Answer: A