MU-NLPC/Calc-aqua_rat huggingface dataset:
Carina has 70 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have? Select the correct option.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Lets say 5 and 10 ounce packages be x and y respectively.   Given that, 5x+10y=70 and x=y+2. What is the value of y.   Substituting the x in first equation, 5y+10+10y=70 ->y=60/15.= 
60/15. = 4
4   4
Answer: C
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 2 hours, how many machines of type R were used?	Pick one.
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 2 hrs   So collective rate needed to finish the work in 2 hrs= 1/2   Let the no of machine be x   So, x/36 +x/18 =1/2   x3/36=1/2   x=36/6= 
36/6 = 6
6   So no of machine R is 6   Answer 6
Answer: C
Integers 3n+2 and 8n+1 are divisible by an integer p. If p is not equal to 1, then p equals to?	Choose the correct choice.
A) 2 B) 5 C) 7 D) 11 E) 13

Solution: If p divides 3n+2, then p divides 24n+16.   If p divides 8n+1, then p divides 24n+3.   Then p must equal 13.   The answer is 13.
Answer: E
A circular rim A having a diameter of 45 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 30 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation. Choose the correct choice from the following answers
A) 3x/2
B) 4x/5
C) 7x/5
D) 5x/7
E) 3x/4

Solution: t = S1/V1 = S2/V2   or, 45/x = 30/y   or, y = 45x/30 = 3x/2 (3x/2nswer 3x/2)
Answer: A
You buy a piece of land with an area of âˆš625, how long is one side of the land plot?  Choices:
A) 28
B) 29
C) 30
D) 31
E) 25

Solution: Try filling the numbers into the answer y x y =   Find the closest to 625.   Answer 25
Answer: E
A number a is squared and then multiplied by negative 1. The result of this operation is equal to 1 times the sum of 2times a and 1. What is one possible value of a ?
Pick one:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: -1*a^2=1(2a+1)   a= -1 or -1   a=-1=B   1NSWER:1
Answer: A
Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $12,000 higher than Store B's revenues. In the second month, Store A's revenues were $8,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $2,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? Choose the correct answer
A) $14,000 B) $15,000 C) $42,000 D) $46,000 E) $50,000

Solution: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +12 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +8 in favor of A. The average was +2 in favor of A. With these numbers, use the average formula to find the third month (T):   (12 + 8 + T)/3 = 2   20 + T = 6   T = -14   Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -14 represents a $14,000 advantage in favor of Store B. Choice ($14,000) is correct.
Answer: A
What was the day of the week on, 15th July, 1776?  Select:	A) Tuesday	B) Wednesday	C) Monday	D) Saturday	E) SUNDAY

Solution: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)   Counting of odd days :   1600 years have 0 odd day.   100 years have 5 odd days.   75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.   1775 years have (0 + 5 + 2)= 
(0 + 5 + 2) = 7
7 odd days= 0 odd day.   Jan Feb Mar Apr May Jun Jul   31 + 29 + 31 + 30 + 31 + 30 + 16= 
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198
198 days= (28 weeks + 1 days)   Total number of odd days = (0 + 1)= 
(0 + 1) = 1
1.   Required day was 'Monday'.   Answer:Monday
Answer: C
If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it?
Choose the correct choice from the following:  A) 76 hours  B) 66 hours  C) 57 hours  D) 90 hours  E) 18 hours

Solution: Explanation:   Let the required numbers of hours be X.   Less men, More hours (Indirect proportion)   Therefore, 10 : 36 :: 25 : X = (10 x X) = (36 x 25) = X = (36 x 25)/10 = 90.   Hence, 10 men can do it in 90 hours.   ANSWER: 90 hours
Answer: D
A boat can move upstream at 15 kmph and downstream at 75 kmph, then the speed of the current is?  Choose the correct choice from the following answers: A) 30 B) 20 C) 45 D) 10 E) 20

Solution: US = 15   DS = 75   M = (75- 15)/2= 
(75- 15)/2 = 30
30   30nswer:30
Answer: A
On a map, 1.5 inches represent 24 miles. How many miles approximately is the distance if you measured 49 centimeters assuming that 1-inch is 2.54 centimeters?
Choose the correct choice:  A) 174.2  B) 212  C) 288.1  D) 296  E) 308

Solution: 1.5 inch = 2.54*1.5 cm.   So, 2.54*1.5 represents 24 miles.   So for 49 cm.:   49/(2.54*1.5) = x / 24 ---> x = 24*49/(3.81) = 308   Answer will be 308.
Answer: E
Solve the number series by identifying the last number.
1 4 5 6 7 9 11 ?	Pick one:	A) 100	B) 120	C) 98	D) 89	E) 131

Solution: 100   100   Series of number that do not contain albhabet 'T'
Answer: A
If A^2 + B^2 = 15 and AB = 25, what is the value of the expression (A - B)^2 + (A + B)^2?
Choose the correct answer
A) 10  B) 20  C) 30  D) 60  E) 50

Solution: (a-b)^2 = a^2 + b^2 - 2ab = 15-25= -10   (a+b)^2 = a^2 + b^2 + 2ab = 15+25= 
15+25 = 40
40   so (a+b)^2 + (a-b)^2= 40 - 10 = 50   50
Answer: E
A student traveled 25 percent of the distance of the trip alone, continued another 20 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip? Pick:  A) 60  B) 80  C) 100  D) 120  E) 150

Solution: Let x be the total length of the trip.   0.25x + 20 miles + 0.5x = x   20 miles = 0.25x   x = 80 miles   The answer is 80.
Answer: B
M = {-6, -5, -4, -3, -2, -1}
T = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Choose the correct option:
A) 0	B) 1/3	C) 2/5	D) 1/2	E) 3/5

Solution: We will have a negative product only if 1, 2, 3, 4, or 5 are selected from set T.   P(negative product) = 5/10 = 1/2   The answer is 1/2.
Answer: D
Eight coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options
A) 2^9
B) 2^10
C) 3 * 2^8
D) 2^7
E) 3 * 2^10

Solution: Fix the third coin as H. The remaining 7 coins have 2^7 outcomes.   Ans:2^7
Answer: D
If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/e, which of the following statements could be false?
Options
A) n is a factor of both a and b B) (a*b)/n < ab C) ab is multiple of 2. D) (a*b)/n is a multiple of 2. E) e is a multiple of 4.

Solution: If we divide by e and get a multiple ofaand ofb, then e must be a common factor. Answer A must be true.   If a and b are even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.   If eitheraorbis even, thenabmust be even. Answer C must be true.   If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.   Ifbis 6 andais 2,nwould be 6, which is not 4. e is a multiple of 4. can be false.
Answer: E
A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 27m/h. what is the speedof the person while he was going to his office? Select:
A) 8km/h	B) 10km/h	C) 12km/h	D) 13km/h	E) 18km/h

Solution: u = k , v= 3k   \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=27   \inline \Rightarrow 1.5k = 27   \inline \Rightarrow k=18km/h   18km/h
Answer: E
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $198, how many hours overtime did he work?
Choose the correct choice from the following choices.
A) 8
B) 5
C) 9
D) 6
E) 13

Solution: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $198 - $120 = $78 Overtime rate (twice regular) 198 -  120= 
198 -  120 = 78
$78 Overtime rate (twice regular)= 2 x $3 = $6 per hour => number of overtime hours = $78/$6 = 13   Ans is 1378/ 6= 
78/ 6 = 13
13   Ans is 13
Answer: E
If X boxes of pineapple juice cost 342 cents, how much will Y boxes cost in dollars?	Pick
A) 342Y/X.
B) X/(342Y)
C) XY/(342).
D) 3.42X/Y
E) 3.42Y/X.

Solution: X boxes of pineapple juice cost 342 cents or 3.42 dollars.   cost of pineapple juice = 3.42/x   Cost of Y pineapple juices = Y*3.42/x   Hence, answer will be 3.42Y/X..
Answer: E
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price
remains constant, approximately what percentage of the selling price is the profit	Select
A) 70%  B) 80%  C) 90%  D) 100%  E) None of above

Solution: Explanation:   Let C.P.= Rs. 100.   Then, Profit = Rs. 320,   S.P. = Rs. 420.   New C.P. = 125% of Rs. 100 = Rs. 125   New S.P. = Rs. 420.   Profit = Rs. (420 - 125) = Rs. 295   Required percentage = (295/420) * 100   = 70%(approx)   70%nswer: 70%
Answer: A
A set of numbers has the property that for any number x in the set, x+1 is also in the set. If -1 is in the set, which of the following must also be in the set
1. 2
2. 0
3. -2
Select
A) 1 only  B) 2 only  C) 1 and 2 only  D) 2 and 3 only  E) 1,2 and 3

Solution: If X is in the set than X+ 1 is also in the set   If -1 in the set than    -1+1= 
 -1+1 = 0
0 is also in the set   Since + 1 is Present, 1 + 1= 2 Is also present in the set .   Therefore Ans 1 and 2 only
Answer: C
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(34)?  Choose the most appropriate option
A) 2	B) 7	C) 13	D) 17	E) 19

Solution: f(34) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28*30*32*34   The greatest prime factor in this list is 17.   The answer is 17.
Answer: D
A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?
Choose the correct choice from the following answers:  A) Rs.11.81  B) Rs.12  C) Rs.12.25  D) Rs.12.31  E) None

Solution: Solution   85 : 9 = 105 : x   x= (9×105/80)   = Rs.11.81   Hence, S.p per Kg	= Rs.11.81   Rs.11.81nswer Rs.11.81
Answer: A
4, 6, 12 , 14 , 28, 30, ?  Choose the correct choice.
A) 20	B) 40	C) no=60	D) 80	E) 100

Solution: C   60   The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32)= 
(28 + 32) = 60
60
Answer: C
In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.3, 9.0, 6.0, and 8.6, what was the point value of the dive?	Choose one:
A) 78.08 B) 73.6 C) 75.2 D) 76.8 E) 81.6

Solution: Degree of difficulty of dive = 3.2   Scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0   We can drop 6.0 and 9.0   Sum of the remaining scores = (7.5+8.3+8.6)= 24   Point of value of the dive = 24.4*3.2= 
24.4*3.2 = 78.08
78.08   78.08nswer 78.08
Answer: A
Find the middle one when the sum of 3 consecutive even numbers is 36?  Select the correct option.
A) 10
B) 12
C) 14
D) 16
E) 17

Solution: 3 consecutive numbers can be a - 1, a, a + 1   So sum of numbers = 3a = 36.   Hence a = 12.   12
Answer: B
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is  Select:
A) 600 B) 750 C) 1000 D) 1250 E) 1500

Solution: Explanation:   speed = (5x5/18)m/sec   = 25/18 m/sec.   Distance covered in 15 minutes = (25/18 x 15 x 60)m   = 1250 m.   ANSWER IS 1250
Answer: D
Difference between the compound interest and the simple interest accrued on an amount of Rs. 18000 in two year is Rs. 405. What was the rate of interest?
Choose one
A) 14%  B) 16%  C) 12.5%  D) 15%  E) 15.5%

Solution: C.I -S.I =P(R/100)^2   405=18000(R^2/10000)   (405*10000)/18000=R^2   R^2=225   Ans R=15%   ANSWER:15%
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?  Choices:
A) 5.78
B) 5.86
C) 5.76
D) 8.76
E) 5.46

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76
Answer: C
In baseball, the batting average is defined as the ratio of a player’s hits to at bats. If a player had anywhere from 4 to 6 at bats in a recent game and had anywhere from 1 to 2 hits in the same game, the player’s actual batting average for that game could fall anywhere between  Choose the correct choice from the following
A) 0.25 and 0.80  B) 0.25 and 0.75  C) 0.10 and 0.75  D) 0.30 and 0.75  E) 0.50 and 0.65

Solution: Average Range = Hits to Bats i.e 1/6 to 2/4 = 0.16 to 0.50   Answer: 0.10 and 0.75
Answer: C
6 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)  Choose the correct choice from the following answers
A) 4  B) 8  C) 10  D) 20  E) 40

Solution: lXbXh= 12000   h= 6000/50*30= 4 cm   '4' is the answer.
Answer: A
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?  Choose the correct option.
A) 120	B) 180	C) 270	D) 260	E) 230

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Smaller number = 270.   ANSWER: 270
Answer: C
Two taps can separately fill a cistern 7 minutes and 14 minutes respectively and when the waste pipe is open, they can together fill it in 8 minutes. The waste pipe can empty the full cistern in? Choose the correct choice from the following:
A) 6.2
B) 8.2
C) 11.2
D) 9.2
E) 7.2

Solution: 1/7 + 1/14 - 1/x = 1/8   x = 11.2   Answer:11.2
Answer: C
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 170 m. Then, A wins by: Choose the correct choice from the following choices:
A) 60 m B) 20m C) 43m D) 20m E) 23m

Solution: To reach the winning post A will have to cover a distance of (500 - 170)m, i.e., 330 m.   While A covers 3 m, B covers 4 m.   While A covers 330 m, B covers 4 x 330/3	m	= 440 m.   Thus, when A reaches the winning post, B covers 440 m and therefore remains 60 m behind.   A wins by 60 m.   60 mnswer:	60 m
Answer: A
Remainder of 2^47/47 ?  Pick.
A) 2  B) 3  C) 4  D) 5  E) 6

Solution: (2^(47/46))/47 = 2^1/47 = 2   2NSWER:2
Answer: A
Among 100 people, 50% like strawberry jam, 40% like apple jam, and 30% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam? Choices:
A) 40%  B) 30%  C) 25%  D) 50%  E) 40%

Solution: 50%+40%-30%=60% who like either Strawberry, Apple, or both.   That means 100%-60% 50 +40 -30= 
50 +40 -30 = 60
60% who like either Strawberry, Apple, or both.   That means 100%-60% = 40% do not like either Apple of Strawberry jam.   40% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   40%nswer is 40%  100 -60= 
  100 -60 = 40
40% do not like either Apple of Strawberry jam.   40% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   40%nswer is 40%
Answer: A
A committee of 3 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee? Select.
A) 1/28  B) 3/28  C) 1/14  D) 4/28  E) 3/14

Solution: 3/8*4/7*1/6*3! = 3/14. We are multiplying by 3! because we can choose secretary, economist, and accountant is several way: SEA, SAE, ESA, EAS, ASE, AES.   Answer: 3/14.
Answer: E
Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If five minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait? Select the correct option: A) 12 B) 24 C) 36 D) 60 E) 72

Solution: the difference of the speed is 1m per second so in five minute Sacha will be 300 m ahead of Bruno..   Bruno will cover this in  300/5= 
 300/5 = 60
60 secs..   60
Answer: D
The unit’s digit in the product (3127)^173 is:
Choose the correct choice.
A) 1
B) 3
C) 7
D) 9
E) 11

Solution: Unit digit in (3127)^173 = Unit digit in 7^173.   Now, 7^4 gives unit digit 1.   Therefore, 7^173= (74)^43 * 7^1. Thus, 7^173 gives unit digit 7.   ANSWER:7
Answer: C
A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?	Select the correct option
A) 4hr	B) 25 min	C) 45 min	D) 6 hr	E) 2 hr 30 min

Solution: 2 hr 30 minxplanation:   Speed upstream=2/2= 
2/2 = 1
1 kn/hr   Speed downstream=1/(20/60)= 
1/(20/60) = 3
3 km/hr   Speed in still water=1/2(3+1)=2 km/hr   Time taken to travel 5 km in still water=5/2=2 1/2 hours=2 hour 30 minutes   Answer:2 hr 30 min
Answer: E
Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
Choose the correct choice from the following.
A) $900 B) $300 C) $600 D) $700 E) $800

Solution: If Linda spent 3/4 of her savings on furnitute, the rest   4 / 4 - 3 / 4 = 1 / 4 on a TV   But the TV cost her $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800   correct answer $800
Answer: E
The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg. What is the weight of the new person?
Pick one:
A) 75 kg B) 85 kg C) 95 kg D) 65 kg E) 55 kg

Solution: The total weight increase = (8 x 2.5) kg = 20 kg   weight of new person = (45 + 20)= 
(45 + 20) = 65
65 kg   The answer is 65 kg.
Answer: D
As part of a game, five people each must secretly choose an integer between 1 and 5, inclusive. What is the approximate likelihood that all five people will choose different numbers?
Choose the correct choice from the following:
A) 4%  B) 12%  C) 16%  D) 20%  E) 25%

Solution: 4%ns:a)   1st person has option no's- (1,2,3,4,5) - there fore probability of getting a no = 5c1/5c1 = 1   2nd person has option no's any four ,   he has to choose a no from four no's - there fore probability of getting a no = 4c1/5c1 = 4/5   3rd person has option no's any three ,   he has to choose a no from three no's -there fore probability of getting a no = 3c1/5c1 = 3/5   4th person has option no's any two - there fore probability of getting a no = 2c1/5c1 = 2/5   4th person has option no's only one - there fore probability of getting a no = 1c1/5c1 = 1/5   =1*4/5*3/5*2/5*1/5 = 4%
Answer: A
The market price of an article was 40% more than its cost price. I was going to sell it at market price to a customer, but he showed me some defects in the article, due to which I gave him a discount of 28.57%. Next day he came again and showed me some more defects, hence I gave him another discount that was equal to 12.5% of the cost price. What was the approximate loss to me? Options
A) Loss of 10%  B) Loss of 12.5%  C) Loss of 15%  D) Loss of 25%  E) None of these

Solution: Let the cost price be Rs 100   Then, market price is Rs 140   Now, the first discount is of 28.57% (approx.) = 2/7 th of market price.   Hence, its selling price = 140 x 5/7 = Rs 100   Now since you are selling at cost price, any further discount will be equal to loss percentage.   ANSWER:Loss of 12.5%
Answer: B
Which of the following is equal to 1(1/2)%?	Choose the correct choice from the following choices
A) 0.012/100	B) 0.12/100	C) 1.5/100	D) 12/100	E) 12/10

Solution: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/2   How about adding a space:Which of the following is equal to (1 1/2)%   (1 1/2)% = 1.5% = 1.5/100   Answer:   1.5/100
Answer: C
A trader has 400 kg of rice, a part of which he sells at 36% profit and the rest at 24% loss. On the whole he losses 12%. What is the quantity sold at 24% loss?
Answers:
A) 80kg	B) 100kg	C) 175kg	D) 320 kg	E) 400 kg

Solution: Out of 400, some quantity gave 36% profit & remaining gave 24% loss   Now, 24% loss means -24% profit   From here, we got the 1st row of numbers i.e 36 & -24   The Resultant is again a loss of 12% , so profit of -12%; this will come up in the 2nd row   Using rules of alligation; -12 > -24; so subtracting:   - 12 - (-24) = -12 + 24= 
-12 + 24 = 12
12   36 > -12; again subtracting:     36 - (-12)= 
  36 - (-12) = 48
48   This gives the 3rd row i.e 12 & 48   So, the total   (12 + 48)= 
  (12 + 48) = 60
60, 48 have given a loss of 24%   So, calculation will be   48/(12+48)∗400=320 Answer = 175kg
Answer: C
Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen
Choose the correct choice from the following
A) 44/221
B) 55/221
C) 76/221
D) 45/221
E) 63/221

Solution: WE HAVE N(S)=52C2=(52*51)/(2*1)= 
(52*51)/(2*1) = 1_326
1326.   LET A=EVENT OF GETTING 55/221OTH 55/221LACK CARDS   55/221=EVENT OF GETTING 55/221OTH QUEENS   A55/221=EVENT OF GETTING QUEEN OF 55/221LACK CARDS   N(A)=26C2=(26*25)/(2*1)= 
(26*25)/(2*1) = 325
325,   N(55/221)=4C2=(4*3)/(2*1)= 
(4*3)/(2*1) = 6
6 AND   N(A55/221)=2C2=1   P(A)=N(A)/N(S)=325/1326;   P(55/221)=N(55/221)/N(S)=6/1326 AND   P(A55/221)=N(A55/221)/N(S)=1/1326   P(A55/221)=P(A)+P(55/221)-P(A55/221)=(325+6-1/1326)=330/1326=55/221   Option: 55/221
Answer: B
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 2520 interest only for the period. The principal amount borrowed by him was:	Pick one:  A) s. 2,000  B) s. 1,000  C) s. 5,000  D) s. 8,000  E) s. 7,000

Solution: Principal = Rs. (100 x 2520)/(12X3) = Rs. 7000. Answer: Option s. 7,000
Answer: E
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 12240, how much money did he borrow?  Choose the correct option.
A) 12000  B) 80288  C) 2668  D) 2600  E) 2781

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 12240   18x + 45x + 39x = (12240 * 100)   102x = 1224000 => x = 12000.   12000nswer:12000
Answer: A
A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability W that the 2 apples selected will include the spoiled one?  Choose the correct choice from the following options: A) a. 1/5 B) b. 3/10 C) c. 2/5 D) d. 1/2 E) e. 3/5

Solution: there can be two ways in which one can select a spoiled apple and a good apple.   1. you pick the spoiled one first and the good one later..   Prob of picking bad one = 1/5 (one bad apple)   Prob of picking a good one from the remaining 4 good apples (4/4 =1)   therefore the total prob for case 1 = i/5 * 1 = 1/5   Total prob W= porb1 + prob2 = 1/5+1/5 = 2/5.c. 2/5
Answer: C