MU-NLPC/Calc-aqua_rat huggingface dataset:
Running at the same constant rate, 6 identical machines can produce a total of 240 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?  Choose the correct choice from the following answers: A) 648 B) 1,800 C) 1,600 D) 10,800 E) 64,800

Solution: 6 machines produce 240 bottles per minute;   1 machine produces 240/6= 
240/6 = 40
40 bottles per minute;   10 machines produce 40*10= 
40*10 = 400
400 bottles per minute;   In 4 minutes 10 machines produce 400*4=1,600 bottles.   Answer: 1,600.
Answer: C
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Choose the correct choice from the following options:  A) 2996 sq m  B) 2897 sq m  C) 4312 sq m  D) 2768 sq m  E) 2786 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7)   = 4312 sq m   Answer:4312 sq m
Answer: C
Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?	Select the correct option
A) 182	B) 108	C) 162	D) 721	E) 105

Solution: Let the number be x. Then,   2/5 of 1/3 of 3/7 of   x = 15 => x = (15 * 5/3 * 3 * 5/2)   = 525/2   40% of 525/2 = (40/100 * 525/2)= 
(40/100 * 525/2) = 105
105   Answer:105
Answer: E
A city with a population of 218,000 is to be divided into 10 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?	Choose the correct answer:
A) 19,920 B) 19,940 C) 19,960 D) 19,980 E) 20,000

Solution: The minimum possible population occurs when all the other districts have a population that is 10% greater than the least populated district.   Let p be the population of the least populated district.   Then 218,000 = p + 9(1.1)p   10.9p=218,000   p = 20,000   The answer is 20,000.
Answer: E
A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Pick one:
A) 3 1/5 Km	B) 2 1/5 Km	C) 3 Km	D) 4 Km	E) 4 1/3 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km)
Answer: A
If p is a natural number and p! ends with q trailing zeros, then the number of zeros that (5p)! ends with will be Choose the most appropriate option.
A) a) (p+q) trailing zeros  B) b) (5p+y) trailing zeros  C) c) (5p+5y) trailing zeros  D) d) (p+5y) trailing zeros  E) e) none of them above

Solution: Let p = 1. p! = 1! = 1, which means q= 0   (5p)! = 5! = 120, trailing zeros = 1   1 = 1 + 0 = p + q   a) (p+q) trailing zerosnswer (a) (p+q) trailing zeros).
Answer: A
If a is an odd integer, which of the following must be an even integer? Choose the most appropriate option:
A) a^4−a+1 B) (a^4−a)(a+1/a) C) a^4−a^3+a^2+2a D) (a^3+a^2+a)^2 E) None of the above

Solution: Let assume a be 1..   A. 1-1+1..odd   B.(1-1)(2) = 0.. even   C.1-1+1+2..odd   D.1+1+1..odd   E.None   Ans: option (a^4−a)(a+1/a).
Answer: B
How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Choose the correct choice:
A) 23 sec  B) 30 sec  C) 27 sec  D) 48 sec  E) 49 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18   = 50/3 m/sec.   Time taken to pass the man = 800 * 3/50= 
800 * 3/50 = 48
48 sec.   Answer:48 sec
Answer: D
Let the function R(n) represent the product of the first n prime numbers, where n > 0. If x = R(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer Choose the most appropriate option:
A) ii only  B) iii only  C) i and ii only  D) i and iii only  E) ii and iii only

Solution: R(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of R(n). Thus, R(n) + 1 = even + 1 = odd. So, (i) is always true.   Now, use logic:   If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.   Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.   Answer: i and iii only.
Answer: D
Two sets of 3 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?	Choose the correct choice from the following answers:
A) 4	B) 7	C) 6	D) 12	E) it cannot be determined from the information given.

Solution: A=(2,3,4), sum of this=9   B=(4,5,6), sum of this=15,   The differenct between   15-9= 
  15-9 = 6
6   Hence,6 is the answer i.e.6
Answer: C
Find the least number must be subtracted from 568219 so that remaining no.is divisible by 5?
Choose the correct choice from the following choices.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: On dividing 568219 by 5 we get the remainder 4, so 4 should be subtracted   4
Answer: E
In how much time will a train of length 110 m, moving at 36 kmph cross an electric pole?	Choose one
A) sec  B) sec  C) sec  D) sec  E) sec

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 = 110/10= 
110/10 = 11
11 sec.   Answer:sec
Answer: D
A motorboat, whose speed in 15 km/hr in sƟll water goes 30 km downstream and comes back in a
total of 4 hours 30 minutes. The speed of the stream (in km/hr) is	Choose one:	A) 2 km/hr	B) 3 km/hr	C) 4 km/hr	D) 5 km/hr	E) None of these

Solution: Explanation:   Let the speed of the stream be x km/hr. Then,   Speed downstream = (15 + x) km/hr,   Speed upstream = (15 - x) km/hr   So we know from quesƟon that it took 4(1/2)hrs to travel back to same point.   So,   3015+x−3015−x=412=>900225−x2=92=>9x2=225=>x=5km/hr   Answer: 5 km/hr
Answer: D
If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
Choose the correct choice from the following answers
A) 1
B) 7
C) 3
D) 14
E) 16

Solution: Explanation:   Let, 1 spider make 1 web in x days.   More spiders, Less days (Indirect proportion)   More webs, more days (Direct proportion)   Hence we can write as   (spiders)7:1   (webs) 1:7}::x:7   ⇒7×1×7=1×7 × x   ⇒x=7   Answer: Option 7
Answer: B
Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent? Choose one
A) 5 15/19%  B) 3 15/19%  C) 4 15/19%  D) 6 15/19%  E) 9 15/19%

Solution: 950 --- 50   50 --- ? =>   =50/950 *100   = 5 15/19%   5 15/19%nswer: 5 15/19%
Answer: A
If x^3 = y^2 > z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z	Choose one.
A) I only
B) III only
C) I and II only
D) II and III only
E) I, II and III

Solution: Given : x^3 = y^2 > z   x^3 = y^2 is possible only when 9^3=27^2=729   I. x < y < z is true for x=9, y=27, z=30 i.e. Answers can only be Options A, C or E   II. x < z < y is true for x=9, y=27, z=10 i.e. Answers can only be Options C or E   III. y < x < z is not true for x=9, y=27   Answer: option I and II only
Answer: C
If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?	Pick:
A) -f(x)  B) 1/f(x)  C) 2/f(x)  D) 3/f(x)  E) f(x)

Solution: If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)   answer -f(x)
Answer: A
If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?	Choices
A) 1/2  B) 1  C) -1/2  D) -1  E) 0

Solution: When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.   Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p   => x = (p + q - r + p - q + r + q + r - p) / (r + q + p)   => x = (r + q + p) / (r + q + p) = 1   p + q + r is non-zero.   ANSWER:1
Answer: B
If 2 cards are selected (with replacement) at random from the deck of 52 cards then what is the probability that both of the selected cards will be a king, a queen, or a jack? A deck of cards has a total of 52 cards, consisting of 4 suits: spades (black), hearts (red), diamonds (red), and clubs (black). In each suit, there are 13 cards including 1 king, 1 queen, and 1 jack.  Choose the correct answer.
A) 1/16	B) 2/25	C) 3/64	D) 5/128	E) 9/169

Solution: P(both cards are king, queen, or jack) = 12/52*12/52 = 9/169   The answer is 9/169.
Answer: E
Income of A is 25% more than the income of B. What is the income of B in terms of income of A?  Select the correct option
A) 80% B) 75% C) 78.66% D) 71.25% E) None of these

Solution: Explanation:   One of the most basic questions.   Let income of B be 100. Income of 80% is 25% more than income of B which means Income of 80% becomes 125   Now income of B in terms of 80% = 100/125 *100= 
100/125 *100 = 80
80%   80%NSWER 80%
Answer: A
A sum of money at simple interest amounts to Rs. 1717 in 1 year and to Rs. 1734 in 2 years. The sum is:  Choose the correct choice from the following answers:	A) Rs. 1200	B) Rs. 1690	C) Rs. 1600	D) Rs. 1700	E) Rs. 1500

Solution: S.I. for 1 year = Rs. (1734 - 1717) = Rs. 17.   Principal = Rs. (1717 - 17) = Rs. 1700.   Answer: Option Rs. 1700
Answer: D
Two pipes A and B can fill a cistern in 12 and 24 minutes respectively, and a third pipe C can empty it in 36 minutes. How long will it take to fill the cistern if all the three are opened at the same time? Choose the correct choice from the following choices:	A) 10 2/7 min	B) 10 1/8 min	C) 11 1/7 min	D) 12 8/7 min	E) 11 3/7 min

Solution: 1/12 + 1/24 - 1/36   = 7/72   72/7 = 10 2/7   10 2/7 minnswer:10 2/7 min
Answer: A
The Guests at a football banquet consumed a total of 323 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet? Pick one.
A) 160 B) 161 C) 162 D) 163 E) 164

Solution: To minimize one quantity maximize other.   161*2 (max possible amount of food a guest could consume) = 322 pounds, so there must be more than 161 guests, next integer is 162.   Answer: 162.
Answer: C
If 20 % of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together.
Pick: A) 11 1/9 B) 10 1/9 C) 12 D) 15 E) Source: TIME material.

Solution: Use algebra :   0.2/11 1/9 + 0.8/B = 20   1/11 1/9 + 4/B = 100   0.8/11 1/9 + 0.2/B = 30   4/11 1/9+ 1/B = 150   15/B = 250   B = 3/50 work per day   11 1/9 = 3/100 work per day   Combined rate = 3/40 + 3/100 = 9/100   Time taken when working together = 100/9 = 11(1/9) days   11 1/9nswer (11 1/9)
Answer: A
Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share twice, no apples were left.How many apples were there? Choose the correct answer.
A) 62  B) 63  C) 64  D) 65  E) 66

Solution: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 6 times. So answer is (2^6)-1=63.   ANSWER:63
Answer: B
The percentage profit earned by selling an article for Rs. 1520 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?	Choose the correct option:
A) 3000
B) 1230
C) 1750
D) 5600
E) 3400

Solution: C.P. be Rs. x.   Then, (1520 - x)/x * 100 = (x - 1280)/x * 100   1520 - x = x - 1280   2x = 2800 => x = 1400   Required S.P. = 125 % of Rs. 1400 = 125/100 * 1400 = Rs. 1750.   ANSWER 1750
Answer: C
Jeremy bought 2Q steaks for P dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?	Options
A) 50RP/Q. B) 50QR/P. C) 25RQ/P. D) 25RP/Q. E) RP/(4Q).

Solution: Jeremy bought 2Q steaks for P dollars, so 1 steak = P/2Q   Jerome buys R steaks for a 50% discount: r* (P/4Q)   in cents the answer will be : r* (100 P/4Q)= 25 RP/ Q=25RP/Q.
Answer: D
There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?  Choose the correct answer
A) 80	B) 140	C) 120	D) 100	E) 150

Solution: Let the number of persons in building P = p   and the number of persons in building Q = q   If 15 persons are sent from P to Q,   then the number of persons in each building is the same   => p-15 = q+15   => p - q = 30 ----(Equation 1)   If 20 persons are sent from Q to P,   then the number of persons in P is double the number of persons in Q   => 2(q - 20) = (p + 20)   => 2q - 40 = p + 20   => 2q - p = 60 ----(Equation 2)   (Equation 1) + (Equation 2)=> q = 90   From Equation 1, p = 30 + q = 30 + 90= 
30 + 90 = 120
120   i.e., Building P has 120 persons   Answer : Option 120
Answer: C
There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 9 cans so that at least one red and at least one blue cans to remain the refrigerator.
Answers.
A) 460
B) 175
C) 493
D) 455
E) 445

Solution: Ways to pick 3 cans so that at least one red and at least one blue cans to remain the refrigerator =   total ways to pick 3 can out of 12 - ways to pick 3 red out of 7 red - ways to pick 3 blue out of 5 blue   12C3âˆ’7C3âˆ’5C3=220âˆ’35âˆ’10=175   ANSWER:175
Answer: B
In Country S, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
Choose the correct choice from the following choices.
A) 50% decrease	B) 30% decrease	C) 15% decrease	D) 30% increase	E) 55% increase

Solution: In Country S 1992 1996   No of construction workers 100 120   Unemployment Rate 16% 9%   Unemployed workers 16 11   % change in unemployed workers=(16-11)= 
(16-11) = 5
5/16=~33% decrease   Closest ans=30% decrease   Ans=30% decrease
Answer: B
What will be the compound interest on a sum of Rs. 26,000 after 3 years at the rate of 12% p.a.?	Choose the correct choice from the following answers:
A) s.10123.77	B) s.10123.21	C) s.10123.20	D) s.10123.28	E) s.10528.12

Solution: Amount = [26000 * (1 + 12/100)3]   = 26000 * 28/25 * 28/25 * 28/25   = Rs. 36528.12   C.I. = (36528.12 - 26000)   = Rs. 10528.12   Answer:s.10528.12
Answer: E
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 36 hours respectively. The ratio of their speeds is?	Choose the correct choice from the following answers:
A) 4:9
B) 4:3
C) 4:5
D) 3:1
E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (B's speed)   = √b : √a = √36 : √4   = 6:2 = 3:1   Answer:3:1
Answer: D
A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? Choose the correct choice from the following options.
A) A	B) B	C) C	D) all alike	E) None of these

Solution: Let B = 100   A = 50   C * (150/100) = 50   3C = 100   C = 33.3 then 'C' Cheapest   ANSWER:C
Answer: C
If three numbers are randomly selected from a set, what is the probability that sum will be greater than 18 if he given set is
{5,6,7,8,9,10}	Choose the correct choice from the following answers
A) 7/18
B) 5/13
C) 5/16
D) 5/19
E) 5/9

Solution: First problem is 6C3 = 18 .. Not 20..   Point 2, your sum should be greater than 18, so these are the following possibilities you have   ({5,7,8},{5,9,10},{6,7,8},{6,9,10},{8,9,10}) which leads to 5 combinations   So the probability is 5 on 18 or 5/18..   ANSWER:5/19
Answer: D
. Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is  Choose the most appropriate option.
A) 5/0
B) 5/9
C) 5/1
D) 5/3
E) 5/6

Solution: Explanation:   No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer:5/9
Answer: B
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
Choices:
A) Sunday
B) Friday
C) Saturday
D) Monday
E) NONE OF THESE

Solution: Explanation :   Given that 8th Feb, 2005 was Tuesday   Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)   366 days = 2 odd days   Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday. Sundaynswer : Option Sunday
Answer: A
A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?	Options
A) 3:3	B) 3:4	C) 3:8	D) 3:1	E) 3:2

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 3:4 =   6000 : 8000 => 3:4.Answer: 3:4
Answer: B
A customer purchased a package of ground beef at a cost of $1.76 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 36 percent less than the package of ground beef. What was the cost per pound of the steak?	Choices: A) $2.00 B) $2.25 C) $2.50 D) $2.75 E) $3.00

Solution: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.76.   Let x be the price per pound for the steak.   Then 0.64x = 176   x = 176/0.64 = $2.75   The answer is $2.75.
Answer: D
Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 1.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?	Choices
A) 1.065	B) 1.125	C) 1.225	D) 1.375	E) 1.425

Solution: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.   The total time is 4 + 2= 
4 + 2 = 6
6 hours   The average speed= total distance/total time taken = 2x/6 = x/3   The average speed of the complete journey is 1.5 km/hour   x/3 = 1.5   x = 4.5 km   The average speed while climbing = distance/time = 4.5/4= 
4.5/4 = 1.125
1.125 km/h   The answer is 1.125.
Answer: B
Griffin has a bag of marbles that contains 7 black marbles and 4 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?  Select.
A) 2/55 B) 3/85 C) 4/105 D) 4/165 E) 8/165

Solution: P(3 red marbles) = 4/11*3/10*2/9 = 4/165   The answer is 4/165.
Answer: D
The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?	Choose the correct choice from the following choices.
A) 26	B) 32	C) 87	D) 20	E) 23

Solution: A/8 = 8 * 8 => A = 8 * 8 * 8   x * 2x = 8 * 8 * 8   x = 16 => 2x = 32   Answer:32
Answer: B
A 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. Options:
A) 210m B) 220m C) 230m D) 240m E) 250m

Solution: Relative speeds=(120+80)km/hr   =200km/hr=(200*5/18)m/s=(500/9)m/s   let length of train be xm   x+280/9=500/9   x=220   Ans is 220m   ANSWER:220m
Answer: B
There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number? Choose the correct option:  A) A)5/4  B) B)5/8  C) C)6  D) D)6/7  E) E)7

Solution: Let the two numbers be x and y.   20/100 * x + y = 5/4y   => 1/5 x = 1/4 y => x/y = 5/4   5/4)
Answer: A
In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice:
A) 290 sec  B) 390 sec  C) 199 sec  D) 192 sec  E) 193 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/25= 
(1000 * 10)/25 = 400
400 sec.   Time taken by A= 400 - 10= 
400 - 10 = 390
390 sec.   Answer: 390 sec
Answer: B
Which of the following CANNOT be a value of 9/(x–9)?	Select the correct option
A) -1
B) -1/2
C) 0
D) 2
E) 9

Solution: The question doesn't ask for the value of x here, but for the possible results of the equation.   If 9/(x-9) = 0, then the numerator must be 0. But since the numerator is 9, the fraction can not be equal to 0.   The answer is 0.
Answer: C
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent H of the gasoline in the tank is brand Z? Choose the correct choice.
A) 50%	B) 40%	C) 37.5%	D) 331⁄3%	E) 25%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/2)*(3/4) H= 3/8 = 37.5%   Answer (37.5%)
Answer: C
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings? Pick:
A) 1:9
B) 1:8
C) 1:4
D) 1:1
E) 1:2

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings =1:1   Answer:1:1
Answer: D
A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of v when angle D is 140 degrees? Choose one.
A) 20
B) 40
C) 60
D) 80
E) 100

Solution: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.   An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.   angle D = 140 degrees   Thus,   arc ABC = 280 degrees   A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.   arc ADC = 360 - 280= 
360 - 280 = 80
80 degrees   The angle that intersects this arc, angle B, should have half this measure.   angle 40= v = 80/2= 
80/2 = 40
40 degrees   Answer=(40)
Answer: B
What is the next number: 2, 10, 82, __
Pick:	A) 630	B) 730	C) 830	D) 848	E) 900

Solution: 3^0 + 1 = 2   3^2 + 1 = 10   3^4 + 1 = 82   3^6 + 1 = 730   The answer is 730.
Answer: B
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?  Select the correct option
A) 1218  B) 2777  C) 1200  D) 2688  E) 1991

Solution: 1200P* (76/100) = 912   1200P1200 * (76/100)= 
1200 * (76/100) = 912
912   1200P= 12 * 100= 
12 * 100 = 1_200
> 1200P= 1200   Answer: 1200
Answer: C