MU-NLPC/Calc-aqua_rat huggingface dataset:
A can do a piece of work in 6 hours; B and C together can do it in 5 hours, while A and C together can do it in 3 hours. How long will B alone take to do it? Choose the correct choice:
A) 3 6/8 hours	B) 4 6/8 hours	C) 2 6/8 hours	D) 5 5/8 hours	E) none of the above

Solution: A's 1 hour's work = 1/6 ;   (B + C)'s 1 hour's work = 1/5 ;   (B + C)'s 1 hour's work = 1/3   (A + B + C)'s 1 hour's work = (1/6 + 1/5) = 11/30   B's 1 hour's work = (11/30 - 1/3) = 8/30   B alone will take 30/8 hours to do the work.   =3 6/8   3 6/8 hoursnswer = 3 6/8 hours
Answer: A
At a certain conference, 78% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance? Answers.
A) 18.0%  B) 62.0%  C) 79.2%  D) 86.67%  E) 82.0%

Solution: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.   78% regestered at least 2 weeks and paid full fee.   10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.   90% *X=78% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER 86.67%)
Answer: D
1. X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?	Choose the correct choice:
A) Rs.14400	B) Rs.26400	C) Rs.12000	D) Rs.12500	E) Rs.13000

Solution: Explanation:   Ratio of the investment   =21000:17500=210:175=21000:17500=210:175 =42:35=6:5=42:35=6:5   Share of X in the profit   =26400Ã—611=2400Ã—6=14400   Rs.14400NSWER IS Rs.14400
Answer: A
1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?
Choose the correct answer.
A) 20.12.91	B) 22.12.91	C) 24.12.91	D) 25.12.91	E) 26.12.91

Solution: Explanation:   Given that 1.12.91 is the first Sunday   Hence we can assume that 3.12.91 is the first Tuesday   If we add 7 days to 3.12.91, we will get second Tuesday   If we add 14 days to 3.12.91, we will get third Tuesday   If we add 21 days to 3.12.91, we will get fourth Tuesday   => fourth Tuesday = (3.12.91 + 21 days) = 24.12.91   Answer: Option 24.12.91
Answer: C
In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 3 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?  Pick one.
A) 27/343
B) 3/7
C) 27/125
D) 279/343
E) 9/125

Solution: Let us take 7*5= 
7*5 = 35
35 as the total number of customers. So  7*3= 
 7*3 = 21
21 customers bought a bagel and 5*5= 
5*5 = 25
25 customers bought a coffee.   chances that at least 1 customer bought a coffee and a bagel= 1 - chances that no customer bought a coffee and a bagel   chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33=12*23*2/35*17*3=552/1785   chances that at least 1 customer bought a coffee and a bagel= 1 - 552/1785 = 1233/1785 = 279/343   Answer 279/343.
Answer: D
Out of 7 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
Choose the correct choice from the following answers:	A) 19/20	B) 24/25	C) 29/30	D) 34/35	E) 39/40

Solution: P(no graduates) = 3C3 / 7C3 = 1/35   P(at least one graduate) = 1- 1/35 = 34/35   The answer is 34/35.
Answer: D
If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 4m + n?
Pick
A) 11	B) 18	C) 55	D) 25	E) 33

Solution: k^4=5400∗mn   k^4=3^3.2^3.5^2.mn   In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2   mn=3.2.5^2   mn = 150 = 10 * 15 (Least possible)   Answer = 4*10 + 15= 
4*10 + 15 = 55
55   ANSWER:55
Answer: C
If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 15000 sheets of xerox paper? Select:
A) $1250  B) $700  C) $1350  D) $900  E) $1000

Solution: 30 sec approach - solve it using approximation   15000 sheet at full price, 5 cent = 750   15000 sheet at max discount price, 4 cent = 600   Your ans got to be between these two.   Ans $700 it is.
Answer: B
A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half. Choose the correct answer:
A) 15 mins
B) 20 mins
C) 25 mins
D) 30 mins
E) 35 mins

Solution: Explanation:   Let the total time be x mins.   Part filled in first half means in x/2 = 1/40   Part filled in second half means in x/2 =1/60 +1/40 =1/24   Total =X/2 X 1/40 + X/2 X 1/24 =1   x=30mins   ANSWER IS 30 mins
Answer: D
How many five-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?	Choose the correct choice from the following answers:
A) 33
B) 66
C) 0
D) 99
E) 132

Solution: A number ending with 3 can never be a perfect square.   Answer: 0
Answer: C
A total of 24 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?	Options:
A) 32.2	B) 31.5	C) 32	D) 32.5	E) 33

Solution: Let 32.2w = average age of women   32.2verage = (Number of men X average age of men + Number of women X average age of women)/total number of people   35 * 50 = 24 * 38 + 26 * 32.2w   =>1750 = 912 + 26 32.2w   => 26 32.2w = 838   =>32.2w = 32.2   32.2nswer 32.2
Answer: A
How many different values of positive integer x, for which |x+7|<x, are there?  Select the correct option:
A) 0  B) 2  C) 3  D) 8  E) 16

Solution: Answer A   I opted to put the random value option.   i used 0 , 7 , -7 and the the extreme of 30 and -30..   i was able to solve it in 1:09   2
Answer: B
The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years Q in which the population would be doubled assuming there is no emigration or immigration is  Choose the correct choice from the following answers.
A) Q=20
B) Q=25
C) Q=30
D) Q=35
E) 40

Solution: Suppose the population of the country in current year is 1000.   So annual increase is  1000 + 39.4 - 19.4= 
 1000 + 39.4 - 19.4 = 1_020
1020   Hence every year there is an increase of 2%.   2000=1000(1+(2/100))^n   n=35 Answer is Q=35
Answer: D
What is the greatest power that 2 can be raised to so that the resulting number is a factor of 20!? Choose the most appropriate option.
A) 4
B) 8
C) 10
D) 20
E) 15

Solution: the number of 2s in 20!= 20/2=10..   ans 10
Answer: C
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit? Choose the correct choice from the following answers.
A) 10000  B) 20000  C) 22000  D) 24000  E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000   30000
Answer: E
Q-1: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 5?
Choose one:
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: 6   Two digit numbers divisible by 5 must end in either 0 or 5. Since there is no 0, all correct answers are a combination of the other digits and 5. There are six other numbers plus the 5 so there are 6 correct answers.   Correct answer is 6.
Answer: D
225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees Options:
A) 10
B) 12
C) 14
D) 16
E) 17

Solution: 26 trees have 25 gaps between them,   Required distance (225/25) = 10   10
Answer: A
The original price of a suit is $160. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?  Choose the correct choice from the following choices
A) $140
B) $145
C) $150
D) $155
E) $160

Solution: 0.75*(1.25*160)= 
0.75*(1.25*160) = 150
$150   The answer is $150.
Answer: C
There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?  Select the correct option
A) 320
B) 345
C) 375
D) 380
E) 400

Solution: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence   3x + 5x = 600   Solve for x   8x = 600   x = 75   Number of boys   3x = 3 × 75 = 225   Number of girls   5x = 5 × 75 = 375   375
Answer: C
A fortune teller has a unique way of predicting his customer’s prognosis. He has three parrots kept in three different cages. Each cage has three cards with a one digit non-zero number inscribed on every card. No two cards have the same number and no cage contains two cards with the number totaling ten. Further the total of numbers on the three cards in the first cage is greater by two than that in the second and by four than that in the third. When a customer asks for his prognosis, the fortune teller lets out the three parrots, which randomly pick one card out of their respective cages. Before the prognosis is made, the fortune teller totals the numbers on the three cards picked out by the parrots and charges the customer the same number of rupees as the total of the numbers on the cards. One day a customer paid seven rupees for his prognosis.
Which of the following combinations of cards may be picked for prognosis?	Pick one.
A) 5, 7, 8  B) 7, 9, 4  C) 2, 6, 3  D) 1, 3, 8  E) None of these

Solution: considering the cages named as A B and C   according to the given conditon A=2B and A=4C   the customer paid the amount as the sum of three cards ,i,e card A,card B and card C=7   A+B+C=7 so, A+(A/2)+(A/4)=7   Solving, we get A=4   therefore a,b,c=4,2,1   ANSWNone of theseR:None of these
Answer: E
How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol? Select:	A) 100/7	B) 5	C) 20/3	D) 8	E) 39/4

Solution: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.   If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.   100/7ccording to the statement;   20+x = 30% of (100+x)   OR   20+x=(100+x)3/10   200+10x=300+3x   7x=100   x=100/7   100/7ns:100/7
Answer: A
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Choose the correct choice from the following answers
A) 4 years  B) 8 years  C) 2 years  D) 4 years  E) 6 years

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   ANSW6 yearsR 6 years
Answer: E
A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ?
Choose the most appropriate option:
A) 1000
B) 800
C) 1400
D) 1200
E) None of them

Solution: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x   A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.   Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.   Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000.   1000nswer is 1000
Answer: A
When two dice are rolled, what is the probability that the difference between the two numbers is 3?  Choose the correct choice from the following options
A) 1/9
B) 2/9
C) 1/3
D) 2/3
E) None of the above

Solution: We have 6 outcomes that satisfy the question:   1-4   2-5   3-6   4-1   5-2   6-3   the probability is (1/6*1/6)*6= 1/6.   I think the answer is None of the above
Answer: E
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 3360, then what is the smallest possible value of n?	Choose the correct choice from the following
A) 6	B) 7	C) 8	D) 9	E) 10

Solution: 3360=2^5*3*5*7   2^5 means that n must be at least 8. That is, We need 2, 4, 6, and 8.   The answer is 8.
Answer: C
Amy's sells kale at x dollar per pound for the first 30 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal? Pick:
A) 24  B) 25  C) 26  D) 27  E) 46

Solution: For Amy's deal to be better, the cost has to be less or equal to Lucia's   Assuming 'n' is the number of pounds of kale, the equation is   30x + (n-30) (0.8x) <= 14x + (n-14)(0.9x)   Resolve it:   ==> 30x + 0.8nx - 24x <= 14x + 0.9nx - 12.6x   ==> 4.6x <=0.1nx   ==> 46x < =nx   ==> x (n-46) > = 0   as x cannot be 0,   ==> n - 46 >=0   ==> n > = 46   so the minimum value is 46   '46' would be the correct answer
Answer: E
When m is divided by 9, the remainder is 3. When m is divided by 13, the remainder is 9. If 1 < m < 200, what is the greatest possible value of m?  Choose the correct choice from the following options.
A) 47 B) 65 C) 103 D) 117 E) 165

Solution: Looking at the choices, options BD can be eliminated as they are divisible by 13   Starting from the highest number 164;   165 = 162 + 3 (162 divisible by 9)   165 = 156 + 9 (156 divisible by 13)   it fits the result   Answer = 165
Answer: E
Indu gave Bindu Rs.1250 on compound interest for 2 years at 8% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Choose the correct choice from the following choices
A) 1 B) 2 C) 8 D) 4 E) 5

Solution: 1250 = D(100/4)8   D = 8   Answer: 8
Answer: C
Bill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!! Pick one.
A) 0  B) Profit of $87.5  C) Loss of $25  D) Profit of $80  E) Profit of $85

Solution: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.   50 packets was sold at a 20% profit --> gives profit of 10*0.2*50= 
10*0.2*50 = 100
$100.   25 packets was sold at a 5% loss --> gives loss of 10*0.05*25= $12.5.   The overall Profit is $100 - $12.5 = $87.5.   Answer: Profit of $87.5.
Answer: B
When E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?
Choose one.
A) 13	B) 31	C) 49	D) 57	E) 67

Solution: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....   by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed E in the form of 9x+4   In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition   Correct Answer - 57
Answer: D
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Select:
A) 10  B) 28  C) 26  D) 11  E) 12

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.   10nswer:10
Answer: A
A policeman noticed a criminal from a distance of 265 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ?
Pick one
A) 100 m  B) 120 m  C) 130 m  D) 150 m  E) None of these

Solution: Explanation :   Solution: Relative speed = (9 - 8)= 
(9 - 8) = 1
1 km/hr.   Distance covered in 3 minutes= (1 * 3/60) km = 1/20 km = 50 m.   .'. Distance between the criminal and policeman = (265 - 50)= 
(265 - 50) = 215
215 m.   Answer : None of these
Answer: E
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number? Choose the correct choice:
A) 29  B) 84  C) 42  D) 28  E) 64

Solution: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is = 28   ANSWER: 28
Answer: D
P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
Choose the correct choice from the following answers:
A) 10
B) 11
C) 13
D) 12
E) 15

Solution: Work done by P in 1 day = 1/15   Work done by Q in 1 day = 1/10   Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6   Work done by P and Q in 2 days = 2 × (1/6) = 1/3   Remaining work = 1 – 1/3 = 2/3   Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15)= 
(2/3) / (1/15) = 10
10 days   Total time taken= 2 + 10= 
2 + 10 = 12
12 days   Answer is 12.
Answer: D
A man sells 4000 common shares of a Company x (each of par value Rs. 10), which pays a dividend of 40% at Rs. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Rs. 25) that pays a dividend of 15%. If the market value of Company Y is Rs. 15, find the number of shares of Company Y purchased by the man  Choose the correct choice from the following options
A) 4000  B) 8000  C) 3000  D) 6000  E) 5000

Solution: Just too much information is given in the question to confuse. This is a straight and simple question   Market Value of Company X (his selling price) = Rs.30   Total shares sold = 4000   Amount he gets = Rs.(4000 × 30)   He invests this amount in ordinary shares of Company Y   Market Value of Company Y(His purchasing price) = 15   Number of shares of company Y which he purchases = 4000×30/15=8000   Answer is 8000.
Answer: B
The sum of two positive integers multiplied by the larger number is 204. The difference multiplied by the smaller number is 35. The larger number is  Choose the correct option
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: let a and b be the 2 no.s , and a being the smaller   (a+b)*b=204   (b-a)*a=35   on solving   we get   b^2+a^2 = 169=13^2   remembering the pythagorean triplets of 5,12,13.   We get the values of a=5 and b=12   ANSW12R:12
Answer: E
Of all the homes on Gotham Street, 2/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Pick one:
A) a) 7/15 B) b) 3/15 C) c) 4/15 D) d) 2/5 E) e)1/5

Solution: let total homes be 15   termite ridden= 2/3(15)= 10   termite ridden and collapsing = 3/5(10)=6   thus homes that are termite ridden, but not collapsing = 10-6= 
10-6 = 4
4   thus required ratio= 4/15   Answer c) 4/15
Answer: C
How many positive factors do 120 and 96 have in common?
Choose one.
A) 8
B) 12
C) 16
D) 18
E) 24

Solution: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)   HCF of 120 and 96 is 24   Number of factors of 24 = 8   8nswer :8
Answer: A
Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?	Choose the correct choice from the following answers:
A) Rs.5000  B) Rs.6000  C) Rs.7000  D) Rs.7500  E) Rs.6500

Solution: Suppose Arun invested Rs.x. Then, Kiran : Arun = (30000 * 6) : (x * 12)   Therefore, 180000/ 12x = 6000/3000   or x = 18000/24   = 7500.   ANSWER:Rs.7500
Answer: D
In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 19 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
Choose the correct choice
A) 33 years
B) 44 years
C) 35 years
D) 36 years
E) 37 years

Solution: Explanation :   Let the age of youngest player be x.   Then, age of the captain = (x + 11).   => 3*19 + 3*28 + 3*30 + x + x + 11= 
+ 11 = 11
11*28.=> 57+84+90+2x+11=308   so 2x = 66   so x = 33.   Age of the captain = (x+11)   = 44 years.   Answer : 44 years
Answer: B
A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)	Choose the correct choice from the following answers.
A) 880mx/P  B) 440P/mx  C) 352mx/P  D) 1760mx/P  E) 5P/352mx

Solution: 1 square foot needs 2/5P gallons of paint.   The width of each stripe is x/12 feet.   The length of each stripe is 5280m feet.   The area of each stripe is (5280m)(x/12) = 440mx square feet.   For two stripes, the total area is 880mx square feet.   The number of gallons needed is (880mx)*(2/5P) = 352mx/P gallons.   The answer is 352mx/P.  (880  )*(2/5 )= 
  (880  )*(2/5 ) = 352
352mx/P gallons.   The answer is 352mx/P.
Answer: C
If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ?  Choose the correct choice from the following choices.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: If 2^98= 256L + N and 0<=N<=4, what is the value of N?   To solve this, note that 2^8 = 256, so 2^98 = 2^[(8*12)+2]=4*[256*256*......12 times]   As this is a multiple of 256, N can only be 0.   0NSWER:0
Answer: A
If p and r are integers, and p^2 = 36r, then r must be divisible by which of the following?
Answers: A) 2 B) 4 C) 9 D) 7 E) 14

Solution: Ans: D   Solution: for p to be an int 36 r must be whole square of a number.   36r= 9*2*2*r   to make it whole square we need 9   so r can must be divisible by 9y where y is itself a whole square.   so 9 is the ans
Answer: C
99^n is such a number begin with 8, least value of n? Choose the correct option.
A) 96157627 B) 96157601 C) 26779287 D) 26876297 E) 269181122

Solution: Answer:   Explanation:   In a more traditional way, this problem can be solved like below.   99(100 - 1) = 9900-99= 
9900-99 = 9_801
9801   9801(100 - 1)= 980100-9801= 971299   971299(100 - 1) = 97129900 - 971299 = 96157601   Answer:96157601
Answer: B
44 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be : Choose the correct choice from the following
A) 56 m B) 88 m C) 120 m D) 137 m E) None

Solution: Sol.   Let the length of the wire b h.   Radius = 1/2 mm = 1/20 cm. Then,   22/7 * 1/20 * 1/20 * h = 44 ⇔ = [44 * 20 * 20 * 7 / 22= 
44 * 20 * 20 * 7 / 22 = 5_600
5600cm= 56 m.   56 mnswer 56 m
Answer: A
A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?	Choose one
A) 21 days  B) 51 days  C) 35 days  D) 31 days  E) 24 days

Solution: 21 days   21 days   WC = 2:1   2x + x = 1/14 => x = 1/42   2x = 1/21   21 days can do the work in 21 days.
Answer: A
In how many ways can a cricket eleven be chosen out of a batch
of 15 players  Options:
A) 1255 B) 1355 C) 1340 D) 1365 E) 1300

Solution: Required number of ways   = 15C 11 = 15C (15-11)   = 15 C 4   15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1   = 1365   ANSWER 1365 1365
Answer: D