MU-NLPC/Calc-aqua_rat huggingface dataset:
By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error Q that the carpenter can make in calculating the volume of the rectangular box? Choose the most appropriate option:
A) 1% B) 3% C) 10% D) 18% E) 22%

Solution: the dimensions are between 2-2.1, 1-1.1 and 2-2.1..   so MAX error in Volume=?..   IMPORTANT POINTS TO NOTE   1) Max ERROR would be when actuals and estimate are at the extreme ends..   2) BUT what about MAX % ERROR--   It will be when the base is the lowest...   so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..   SOLUTION   Actuals= 2*2*1=4..   Estimate=2.1*2.1*1.1=4.841..   Max % error Q=(4.841-4)/4 *100= 84.1/4 = 21.25%..   21.25% is closest to 22% in the choices..   ans 22%
Answer: E
A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $750? Choose the correct option.
A) $3,000  B) $3,150  C) $4,000  D) $4,150  E) $5,000

Solution: We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $750.   Since the salesperson receives a $150 salary, the remaining $600 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.   Let's TEST Answer C: $4,000   Since 15% of $1,000 = $150   15% of $4,000 = 4($150) = $600   this is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   $4,000
Answer: C
Y and Z start a business with Rs.8000 and Rs.12000 respectively. Hoe should they share their profits at the end of one year?
Choose the correct choice from the following choices
A) 1:2  B) 2:1  C) 3:1  D) 2:5  E) 2:3

Solution: Explanation:   They should share the profits in the ratio of their investments.   The ratio of the investments made by Y and Z =   8000 : 12000 => 2:3   Answer:2:3
Answer: E
Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 31.5 kg of zinc has been consumed in it?
Pick one:	A) 58 kg	B) 60 kg	C) 64 kg	D) 70 kg	E) None

Solution: Sol.   For 9 kg Zinc, mixture melted = (9+11) kg.   For 31.5 kg Zinc, mixture, melted = [20/9 x 31.5] kg   = 70 kg.   Answer 70 kg
Answer: D
In how many ways Chief Minister and Minister be elected from a team of 16 members?  Choose the correct answer.
A) 240 B) 210 C) 220 D) 200 E) 180

Solution: To do this, if captain is elected first, then we have 16 ways of doing this.   For election of vice-captain, we have only 15 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 16*15= 
16*15 = 240
240 ways.   240
Answer: A
Using all the letters of the word "SOME", how many words can be formed, which begin with S and end with E? Select.
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: There are four letters in the given word.   Consider 4 blanks ....   The first blank and last blank must be filled with S and E all the remaining two blanks can be filled with the remaining 2 letters in 2! ways.   The number of words = 2! = 2.   2NSWER:2
Answer: A
In 140 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: Choose the correct option: A) 20 m B) 28 m C) 22.5 m D) 9 m E) 12 m

Solution: Distance covered by B in 9 sec. =	140/45 x 9	m = 28 m.   A beats B by 28 metres.   Answer: Option 28 m
Answer: B
If the money was put in for the same duration of time by A,B and C, three business partners and four times A’s capital is equal to 6 times B’s capital is equal to 10 times C’s capital. Determine that out of a total profit of Rs 4650 what is C’s share?
Choose the correct choice from the following choices:
A) Rs 2250	B) Rs 1550	C) Rs 450	D) Rs 900	E) None of these

Solution: Explanation:   It is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.   Let A’s capital be x, B’s capital be y and C’s capital be z.   =>x+y+z = 4650   => 4x = 6y = 10z   =>C’s share is z so let us solve the question w.r.t. z   =>x = 5z/2   =>y = 5z/3   =>(5z/2)+(5z/3)+(z) = 4650   =>31z = 4650*6   =>z = 900   ANSWER Rs 900
Answer: D
If the quantity (p + 5) is 5 times the quantity (q + 5), then what is the relationship between p and q?	Choose the correct choice from the following choices
A) p = 5q + 30
B) p = 5q − 30
C) 5p = 5q + 20
D) p = 5q
E) p = 5q − 20

Solution: p+5= 
+5 = 5
5(q +5= 
 +5 = 5
5q+25   p=5q+20   option 5p = 5q + 20
Answer: C
A man spends 2/5 of his salary on house rent,3/10 of his salary on food and 1/8 of his salary on conveyance.if he has Rs.1400 left with him,find his expenditure on food and conveyance. Choose the correct option:	A) 1000	B) 2000	C) 3000	D) 4000	E) 5000

Solution: Part of salary left=1-(2/5+3/10+1/8)   Let the monthly salary be Rs.x   Then, 7/40 of x=1400   X=(1400*40/7)   =8600   Expenditure on food=Rs.(3/10*800)=Rs.2400   Expenditure on conveyence=Rs.(1/8*8000)=Rs.1000   1000nswer is 1000.
Answer: A
At a conference table, 8 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 8 employees? Select:	A) 5060	B) 5050	C) 5060	D) 5040	E) 5030

Solution: Head's sit is fixed. Now 7 people is left with 7 seats.   7 people can sit on 7 seats in 7! ways or 5040 ways.   Ans is 5040
Answer: D
A circular mat with diameter 7 inches is placed on a square tabletop, each of whose sides is 8 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Choose the correct choice from the following answers.
A) 6/7	B) 4/9	C) 5/2	D) 5/3	E) 1/7

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the 5/2loth = (pi)(r)^2 which is about (22/7)(7)(7)   Area of the Table = (8)(8)   So the quick way to estimate is looking at the fraction like this:154/64 nearest to 5/2   Answer: 5/2
Answer: C
In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?  Pick.
A) 8 1/3 B) 8 1/5 C) 8 1/6 D) 8 1/2 E) 8 1/7

Solution: (4000*3*R)/100 = (5000*5*4)/100   R = 8 1/3.8 1/3nswer: 8 1/3
Answer: A
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train? Pick one: A) 25 B) 24 C) 26 D) 27 7/9 E) 28

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.   Answer: Option 27 7/9
Answer: D
A train 500 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Choose the correct choice from the following choices:  A) 45 km/hr  B) 50 km/hr  C) 54 km/hr  D) 55 km/hr  E) 185 km/hr

Solution: Speed of the train relative to man = (500/10) m/sec = 50 m/sec. [50 * (18/5)] km/hr = 180 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 180 ==> x = 185 km/hr.   ANSW185 km/hrR: 185 km/hr
Answer: E
In a group of 100 adults, 50 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
Answers:
A) 48
B) 52
C) 54
D) 60
E) 76

Solution: 12 left-haded women compose   100-50= 
  100-50 = 50
50% (or 1/2) of all women, so there are total of   2*12= 
  2*12 = 24
24 women --> 100-24=76 men.   Answer: 76. --  100-24= 
 --  100-24 = 76
76 men.   Answer: 76.
Answer: E
Free notebooks were distributed in a class among all the students. Each student got notebooks which were 1/8th of the number of student. If number of student been half, then each child would have received 16notebooks in total. Find the total number of books distributed among students?  Options:
A) 430
B) 450
C) 460
D) 480
E) 512

Solution: Let suppose total number of students in class are X.   Then from the question we can conclude it that,   X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512   512
Answer: E
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 4 times?  Choose the correct choice from the following
A) 25/32	B) 13/4	C) 17/8	D) 57/64	E) 15/16

Solution: at least twice, but not more than 5 timesmeans exactly 2 times, 3 times, 4 times   The probability of getting exactly k results out of n flips is nCk/2^n   6C2/2^6+6C3/2^6+6C4/2^6=(20+15+15)/2^6=25/32   Option: 25/32
Answer: A
A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 1/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.  Choose one: A) 300 B) 200 C) 250 D) 150 E) 160

Solution: Basically, this question is asking you to figure out how many students are being double-counted.   A-Club has 200 members (1/2 of 400)   B-Club has 250 members (5/8 of 400)   C-Club has 300 members (3/4 of 400)   We can create an equation to solve this:   200+250+300 = n + x + 2y   where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.   The question provides y for us (50).   750 = 400 + x + 100   x =250   250
Answer: C
Worker A takes 5 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Select the correct option:
A) 15/4
B) 40/9
C) 50/9
D) 60/9
E) 80/9

Solution: one day work of 15/4 = 1/5   one day work of B = 1/15   so one day work of 15/4 and B together = 1/5 + 1/15 = 4/15   so total days required = 15/4   15/4NSWER:15/4
Answer: A
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference Z between the highest and the lowest incentive received by the 5 salesmen in the month?  Select
A) $4000	B) $5000	C) $9000	D) $11,000	E) $13,000

Solution: Break down the question in to steps:   Step #1: incentives received by 5 salesmen -->abcde   Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de   Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000   Step #4: What is the difference Z between the highest and the lowest incentive:   - The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.   - The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.   - Therefore the first two numbers( ab) must equal 4, 000   - There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b   if a = 1,000 b = 3,000 --> difference between the highest and the lowest incentive = 12,000 - 1,000 =11, 000   no other options for a or b to fit the criteria   Final List:1,0003,0007,00012,00012,000   Answer $11,000
Answer: D
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.	Choices
A) 30 m2	B) 40 m2	C) 60 m2	D) 80 m2	E) 90 m2

Solution: l = 10 m,   h = 8 m.   So, r = l2 - h2 = (10)2 - 82 = 6 m.   Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.   Answer: Option 60 m2
Answer: C
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
Options:  A) |k + 0.03| > 2.5  B) |k — 0.03| <= 2.5  C) |k — 2.5| > 0.03  D) |2k — 5| <= 0.06  E) |k — 2.5| >= 0.09

Solution: So, let's go through this step by step:   rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters.   In other words, any screw that is less than: 2.50 - 0.03= 
2.50 - 0.03 = 2.47
2.47or greater than 2.53 will be rejected.   If k represents the length of a screw   In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:   2.47 ≤ K ≤ 2.53   You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.   Let's look at (|2k — 5| <= 0.06): |2k — 5| <= 0.06 or dividing by 2   |k — 2.5| <= 0.03   For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53   For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47   2.47 ≤ k ≤ 2.53   (|2k — 5| <= 0.06)
Answer: D
A letter lock consists of three rings each marked with seven different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?	Choose the correct choice from the following answers
A) 177	B) 199	C) 342	D) 168	E) 167

Solution: Since each ring consists of seven different letters, the total number of attempts possible with the three rings is   = 7 * 7 * 7= 
7 * 7 * 7 = 343
343. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 343 - 1= 
343 - 1 = 342
342   Answer: 342
Answer: C
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year? Choose the correct option
A) 12	B) 14	C) 16	D) 18	E) 20

Solution: assume x is number of theft per year   24*100=120*1.1*x -> x = ~18   ANSWER:18
Answer: D
There has been successive increases of 25% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change? Select the correct option.
A) 23%	B) 27%	C) 31%	D) 35%	E) 39%

Solution: Let P be the original price per unit of gas.   Let x be the original gas consumption.   Let y be the reduced gas consumption.   y*1.1*1.25*P = x*P   y = x / (1.1*1.25) which is about 0.73x which is a decrease of about 27%.   The answer is 27%.
Answer: B
A vessel of capacity 2 litre has 35% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?  Choose the correct answer:
A) 31%. B) 71%. C) 49%. D) 29%. E) 37%.

Solution: 35% of 2 litres = 0.7 litres   50% of 6 litres = 3 litres   Therefore, total quantity of alcohol is 3.7 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37%   37%.
Answer: E
Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) – (3#3) is equal to  Options: A) -656 B) 82 C) 128 D) 512 E) 1522

Solution: -656nswer:   2^6 + 3^2 - 3^6 = -656   -656Ns -656
Answer: A
If x and y are positive integers and (5^x)−(5^y)=(2^y−1)∗(5^x−1), what is the value of xy? Choose the correct choice.
A) 48	B) 36	C) 24	D) 18	E) 12

Solution: x and y are positive integers which means we will have clean numbers. On the right hand side, you have a 2 as a factor while it is not there on the left hand side. Can a 2 be generated on the left hand side by the subtraction? Here I am thinking that if we take 5^y common on the left hand side, I might be able to get a 2.   56y(56^x−y −1)=2^y−1∗5^x−1   Now I want only 2s and 5s on the left hand side. If x-y is 1, then (5^x−y−1) becomes 4 which is 2^2. If instead x - y is 2 or more, I will get factors such as 3, 13 too. So let me try putting x - y = 1 to get   5^y(2^2)=2^y−1∗5^x−1   This gives me y - 1 = 2   y = 3   x = 4   Check to see that the equations is satisfied with these values. Hence xy = 12   Answer (12)
Answer: E
Find the invalid no.from the following series 15, 16, 34, 105, 424, 2123, 12756
Select the correct option
A) 16  B) 34  C) 105  D) 424  E) 2123

Solution: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1= 
15 *1 + 1 = 16
16.   3rd term= (2nd term) * 2 + 2 = 16 * 2 + 2= 
16 * 2 + 2 = 34
34   4th term= (3th term) *3 + 3 = 34 * 3 + 3= 
34 * 3 + 3 = 105
105   5th term= (4th term) * 4 + 4 = 105 * 4 + 4= 
105 * 4 + 4 = 424
424   6th term= (5th term) * 5 + 5 = 424 * 5 + 5= 
424 * 5 + 5 = 2_125
2125   6th term should 2125 instead of 2123.   2123
Answer: E
If the simple interest on a sum of money for 5 years at 18% per annum is Rs. 900, what is the compound interest on the same sum at the rate and for the same time?
Choose the correct choice:	A) Rs. 1287.76	B) Rs. 1284.76	C) Rs. 1587.76	D) Rs. 1266.76	E) Rs. 1283.76

Solution: Sum = (900 * 100) / (5 * 18) = Rs. 1,000.00   C.I. on Rs. Rs. 1,000.00 for 5 years at 18% = Rs. 2,287.76.   = Rs. 2,287.76 - 1,000.00 = Rs. 1287.76   Rs. 1287.76NSWER:Rs. 1287.76
Answer: A
What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?  Pick
A) 272	B) 120	C) 277	D) 2898	E) 212

Solution: When compounded annually, interest   = 12000[1 + 20/100]1 - 12000 = Rs.2400   When compounded semi-annually, interest   = 12000[1 + 10/100]2 - 12000 = Rs.2520   Required difference = 2520 - 2400 = Rs.120.Answer: 120
Answer: B
If grapes are 92% water and raisins are 20% water, then how many kilograms did a quantity of raisins, which currently weighs 5 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Answers:  A) 50  B) 54  C) 55  D) 56  E) 60

Solution: Let x be the original weight.   The weight of the grape pulp was 0.08x.   Since the grape pulp is 80% of the raisins, 0.08x = 0.8(5).   Then x = 50 kg.   The answer is 50.
Answer: A
In a vehicle's repair shed, 3 men and 8 boys can do a piece of work in 15 days; 4 men and 9 boys can do the same work in 12 days. Then, 5 men and 5 boys can do double the amount of this work in :  Pick one:	A) 20 days	B) 33 days	C) 24 days	D) 28 days	E) None of these

Solution: Explanation :   Solution: (3*15) men + (8*15) boys= (4*12) men + (9*12) boys   45 M + 120 B = 48 M+ 108 B <=> 3 M = 12 B => 1 M = 4 B.   .'. 3 M + 8 B = (3*4) B+ 8 B = 20 B.   5 M + 5 B (3*4)  + 8= 
(3*4)  + 8 = 20
20 B.   5 M + 5 B= (5*4) B + 5 B = 25 B.   Let the required number of days be x.   now, more boys, less days (IP)   more work, more days (DP)   boys 25 : 20   } : :15: x   work 1 : 2   .'. (25*1*x) = (20*2*15)   => x = 40*15/25= 
40*15/25 = 24
24.   Answer : 24 days
Answer: C
A bag contains 20 purple jellybeans, 18 green jellybeans, and 12 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?  Pick
A) 15%	B) 20%	C) 25%	D) 30%	E) 36%

Solution: Probability of green beans = 18 / (20 + 18 + 12) = 18/50 = 36%   Answer is 36%
Answer: E
consider a sequence of numbers is such that a1 = 11, a2 =16, and each subsequent an = an-2 + 9. Which of the following numbers is a member of the sequence? Choose the correct choice from the following choices
A) 216 B) 246 C) 289 D) 299 E) 368

Solution: each odd term(1st , 3rd, 5th,...) of the sequence is given by 11 + 9*(something)   each even term(2nd, 4th, 6th...) of the sequence is given by 16 + 9*(something)   So if you subtract the numbers by 11 or 16 then it should be divisible by 9   216-11(=205) or 216-16(=200) are not divisible by 9   246-11(=235) or 246-16(=240) are not divisible by 9   289-11(=278) or 289-16(=273) are not divisible by 9   299-11(=288) is divisible by 9ANSWER, 299-16(=283) are not divisible by 9   368-11(=357) or 368-16(=352) are not divisible by 9   So, Answer is 299
Answer: D
Mr. Yutaro’s class contains 10 boys and 6 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?  Choose the most appropriate option:
A) 9/48
B) 9/20
C) 11/24
D) 27/48
E) 1/2

Solution: Probability of a girl being chosen first, then a girl:   6/16 * 10/15   Probability of a boy being chosen first, then a boy:   10/16 * 6/15   Probability of a boy and a girl being chosen:   (6*10+6*10) / (15*16)   =1/2   Answer:1/2
Answer: E
A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?  Choose the correct choice from the following answers.
A) 76 days
B) 68 days
C) 24 days
D) 97 days
E) 17 days

Solution: B = 1/8 – 1/2 = 1/24   => 24 days   Answer: 24 days
Answer: C
The cost of an item was reduced from its usual selling price of $23.99 to $19.99. Which of the following is closest to the percent decrease in the price of the item? Answers.
A) 17%	B) 21%	C) 24%	D) 25%	E) 42%

Solution: The price decreased by 23.99 - 19.99= 
23.99 - 19.99 = 4
$4.   $4 is a bit more than 17% of original price of $24.   17%nswer: 17%.
Answer: A
In how many different number of ways 1 boy and 4 girls can sit on a bench? Select:
A) 120
B) 140
C) 160
D) 180
E) 200

Solution: npn = n!   5p5 = 5 × 4 × 3 × 2 × 1 = 120   120)
Answer: A
What is the difference between the local values of 6 in the number 56406?
Answers
A) 2992 B) 2997 C) 5994 D) 2077 E) 5211

Solution: Explanation:   6000 â€“ 6 = 5994   Answer:5994
Answer: C
A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is? Choose the correct choice
A) 5 5/9 % B) 5 5/6 % C) 5 8/9 % D) 1 5/9 % E) 5 3/9 %

Solution: Let sum = x. Then, amount   = 7x/6   S.I. = 7x/6 - x = x/6; Time   = 3 years.   Rate = (100 * x) / (x * 6 * 3)   = 5 5/9 %.   5 5/9 %nswer: 5 5/9 %
Answer: A
A bucket contains 2 mixtures A and B in the ratio 7:5. If 9 liters of the mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7:9. How much of the liquid A was there in the bucket?	Choose the correct choice from the following answers:
A) 15liters B) 21liters C) 12liters D) 18liters E) 25liters

Solution: 1st ratio = 7:5   2nd ratio = 7:9   Difference of cross products ratio = 7*9-7*5= 
7*9-7*5 = 28
28   common factor of the 1st ratio= (quantity replaced/sum of terms in 1st ratio) + (Quantity replaced*term A in 2nd ratio/Difference)   = (9/7+5) + (9*7/28) = 3   Quantity of A = 7*3= 
7*3 = 21
21liters   Answer is 21liters
Answer: B
A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
Choose the correct option
A) 15 1/3 days  B) 13 1/3 days  C) 19 1/3 days  D) 11 1/3 days  E) 12 1/3 days

Solution: 13 1/3 days   13 1/3 days   5/30 + 20/x = 1   x = 24   1/30 + 1/24 = 3/40   40/3 = 13 1/3 days
Answer: B
The largest number that exactly divides each number of the sequence
(15 - 1), (25 - 2), (35 - 3), ...., (n5 - n), ...... is	Choose the correct choice
A) 1	B) 15	C) 30	D) 120	E) None

Solution: Sol.   Required number = (25 - 2)   = (32 - 2)= 
(32 - 2) = 30
30.   Answer 30
Answer: C