MU-NLPC/Calc-aqua_rat huggingface dataset:
John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??  Choose the correct choice from the following answers:	A) 50000	B) 55000	C) 60000	D) 70000	E) 80804

Solution: A = P(1+r/n)^nt   A= total amount accrued   P = principal deposited   r = rate of interest in decimal form   n = number of times per year, interest compounded   t = time in number of years.   .   x(1+0.02/2)^2 - x = 40,000(1+0.04/4)^4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)   => x[(1.01)^2 - 1] = 40,000[(1.01)^4 - 1]   => x[(1.01)^2 - 1] = 40,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides   => x = 40,000(1.0201+1) =80804.   Hence answer is 80804.
Answer: E
B and C walk around a circular track. They start at 9 a.m from the same point in the opposite directions. B and C walk at a speed of 5 rounds per hour and 4 rounds per hour respectively. How many times shall they cross each other before 1 p.m  Choices
A) 34	B) 35	C) 36	D) 37	E) 38

Solution: Explanation:   Relative speed = (5+4)= 
(5+4) = 9
9 rounds per hour   So, they cross each other 9 times in an hour hence, they cross 36 times before 1 p.m   Answer: Option 36
Answer: C
On a certain bus, one-fourth of the children are boys that are wearing sneakers. One-third of the children on the bus are girls that are wearing sneakers, which of the following is a possible number of children on the bus? Choose the correct choice from the following answers.
A) 11 B) 16 C) 29 D) 30 E) 36

Solution: Let No. of Children = x   Boys wearing sneakers = x/4   Boys wearing sneakers = x/3   i.e. Total number of children must be divisible by 4 as well as by 3   i.e. Total number of children must be divisible by LCM of 4 & 3 i.e. 12   Only Option 36- 36 satisfies the requirement hence   ANSW36R:36
Answer: E
Sixteen men complete a work in 24 days while 48 children can do it in 16 days. Twelve men started the work, after 14 days 12 children joined them. In how Many days will all of them together complete the remaining work? Choices:
A) 12
B) 62
C) 27
D) 29
E) 17

Solution: Explanation:   Let man capacity = 2 units/day. Then total work = 16 × 2 × 24 = 768   Let the children capacity is k units/ days. So total work = 48 × k × 16   Equating above two equations we get k = 1. So children capacity = 1 unit / day.   Twelve men did 14 days of job. So they completed 12 × 2 ×14 = 336.   Remaining work = 768 - 336= 
768 - 336 = 432
432.   Now 12 children joined them. So per day capacity of entire team= 12 × 2 + 12 × 1 = 36.   So they complete the remaining work in 432/36= 
432/36 = 12
12 days.   12nswer:12
Answer: A
If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Choose the correct choice:
A) 1	B) 4	C) 5	D) 6	E) 7

Solution: Speed Ratio = 1:3/4 = 4:3   Time Ratio = 3:4   1 -------- 1/3   3 --------- ? è 1 hour   1nswer: 1
Answer: A
Rs.500 amounts to Rs.620 in 2 years at simple interest. If the interest is increased by 2%, it would amount to how much? Pick:
A) 120
B) 25
C) 614
D) 530
E) 210

Solution: (500*3*2)/100= 
(500*3*2)/100 = 30
30   500+ 30= 
500+ 30 = 530
530   Answer: 530
Answer: D
Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? Choose the correct choice from the following options:	A) 654	B) 655	C) 656	D) 588	E) 658

Solution: total cost 840   840*30/100= 
840*30/100 = 252
252   so the cut in amount is 252   the less amount to be spend is  840-252= 
 840-252 = 588
588   ANSWER:588
Answer: D
What is the sum of the integers from -190 to 191 inclusive? Choose the correct choice from the following options.
A) 0  B) 191  C) 375  D) 875  E) 965

Solution: sum/n= average.   sum=(average)(n)   average=a+b/2=190+191/2=0.5   number of items(n)=B-A+1=191-(-190)+1=195+191=382.   sum=average*n=0.5*382= 
0.5*382 = 191
191.   answer is 191
Answer: B
The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?	Choose one.
A) 6! * 7P6	B) 2(6!)	C) 6!)2	D) 6! * 7	E) 7! * 7

Solution: We can initially arrange the six boys in 6! ways.   Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.   Hence required number of ways   = 6! * 7P6   6! * 7P6nswer:6! * 7P6:
Answer: A
V is the volume of a cylinder; the radius of the cylinder is 3.5. The height of the cylinder is 650% more than the radius. Which of the following is true?
Choose the correct choice from the following options
A) 100 < V < 300  B) 300 < V < 500  C) 500 < V < 700  D) 700 < V < 900  E) 900 < V < 1100

Solution: As we see the answers are in form of range we can use approximation   Volume of cylinder is πr^2h   Given π= 22/7 and r = 3.5 so r^2 ~ 12 and h = 6.5 * 3.5 ~ 23   So 22/7 * 12 * 23 ~ 868   so answer should be   D. 700 < V < 900   Answer : 700 < V < 900
Answer: D
If there are 7 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?  Choose the correct choice from the following answers:  A) 32  B) 24  C) 56  D) 144  E) 280

Solution: Firstly, there are 7 ways to choose 3 groups from the 4 groups. Hence 7C3.   Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.   Hence, the total number of ways are 7C3 * (2^3) = 280   280
Answer: E
Rs 1000 is being charged at 50% per annum. what is the interest for 3rd year at compound interest? Choices: A) 3277 B) 2667 C) 1125 D) 2867 E) 9996

Solution: Explanation:   Total amount for two years = \inline 1000(1.5)^2=2250   Now , interest for third year = \inline \frac{2250\times 50\times 1}{100}=1125   Answer: 1125) 1125
Answer: C
The total weight of six nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?	Pick one
A) 0.18 oz.	B) 0.5 oz.	C) 1.8 oz.	D) 5 oz.	E) 18 oz

Solution: Average = Total/Number of items   = 3/6 = 0.5.   Hence, 0.5 oz.
Answer: B
A tourist purchased a total of $1,400 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?  Answers:  A) $1,430  B) $1,310  C) $1,290  D) $1,270  E) $1,170

Solution: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks   Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3   using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost   Therfore   1400 - 230= 
  1400 - 230 = 1_170
1170 hence answer is $1,170
Answer: E
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is? Choices
A) 1/26
B) 1/24
C) 1/20
D) 1/21
E) 1/21

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (1/26s E1 and E2 are independent)   = 1/2 * 1/13 = 1/26   1/26nswer:1/26
Answer: A
A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 800. How many workers were part of the latter production run?	Choose the correct choice
A) A)6 B) B)10 C) C)11 D) D)21 E) E)23.5

Solution: The daily average production is given by 5n + 20- given   In the first k days, 500 units are produced   = (5n+20)K =500   k = 500/5n+20...................................1   5 workers were added = 5(n+5)+20 = 5n +45   cumulative is 1250 .. thus for the current period = 800 -500= 
800 -500 = 300
300   (5n+45)K= 300   k = 300/5n+45........................................2   equate 1 and 2   500/5n+20 = 300 /5n+45   500(5n+45) = 300(5n+20)   2500n + 22500 = 1500n + 6000   1000n = -16500   n = 16   thus n+5 = 21   hence 21
Answer: D
an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -e and a*e=0, then e=?  Select the correct option: A) a) -a B) b) -1/a C) c) 1/a D) d)0 E) e)a

Solution: If a*e=0 and a=-e then a-e = o of a=e, so answer e)a
Answer: E
A searchlight on top of the watch-tower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?  Choose the correct choice from the following answers:
A) 1/4	B) 1/3	C) 1/2	D) 2/3	E) 5/6

Solution: 2 revolutions per minute = 1 revolution every 30 seconds   So no matter what anybody appearing at the tower cannot stay in the dark for more than 30 seconds. This will be our total number of possibilities i.e the denominator.   P(man in dark for at least 5 seconds) = 1 - P (man in dark for max of 5 seconds) = 1 - 5/30 = 1 - 1/6 = 5/6   or the other way would be:   P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 30 seconds because that is the max. In this approach it would be 25/30 seconds = 5/6.   Answer is 5/6
Answer: E
find four consecutive numbers such that the sum of the first three numbers is twelve more than the fourth number ?  Pick: A) 7,8,9,10 B) 3,4,5,6 C) 9,10,11,12 D) 6,7,8,9 E) None

Solution: Let   1st Integer = x   2nd Integer = x+1   3rd Integer = x+2   4th integer = x+3   =======================================   Given   x+x+1+x+2=(x+3)+12   3x+3=x+3+12   3x+3=x+15   3x=x+15-3   3x=x+12   3x-x=12   2x=12   x=12/2= 
12/2 = 6
6========================================   1st Integer = x = 6   2nd Integer = x+1 = 6+1= 
6+1 = 7
7   3rd Integer= x+2 =6+2= 
6+2 = 8
8   4th integer= x+3=6+3= 
6+3 = 9
9   Answer 6,7,8,9
Answer: D
By selling 16 pencils for a rupee a man loses 28%. How many for a rupee should he sell in order to gain 28%?  Select.
A) 8
B) 9
C) 7
D) 6
E) 4

Solution: 72% --- 16   128% --- ?     72/128 * 16= 
  72/128 * 16 = 9
9   Answer: 9
Answer: B
Find the simple interest on $10000 at 9% per annum for 12 months?
Choose the correct choice from the following choices
A) $410
B) $500
C) $650
D) $710
E) $900

Solution: P = $10000   R = 9%   T = 12/12= 
12/12 = 1
1 YEAR   S.I.= P*R*T/100 = 10000*9*1/100= 
10000*9*1/100 = 900
$900   Answer is $900
Answer: E
A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 200. How much did he have with him in the beginning?
Choices:
A) s 200 B) s 500 C) s 300 D) s 450 E) s 550

Solution: Suppose the amount in the beginning was Rs ’x’   Money spent on clothes = Rs 1x/3 s 500alance = Rs 2x/3   Money spent on food = 1/5 of 2x/3 = Rs 2x/15   s 500alance = 2x/3 - 2x/15 = Rs 8x/15   Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5   Therefore 2x/5 = 200 = 500   ANSWER:s 500
Answer: B
A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 40 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?	Options.
A) 3/40000 B) 1/3600 C) 1/20000 D) 1/60 E) 1/15

Solution: Let's see   Pick 40/1000 first   Then we can only pick 1 other pair from the 800   So total will be 40 / 800 *1000   Simplify and you get 1/20000   Answer is 1/20000
Answer: C
A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 8 : 1 ?  Choose the correct choice from the following choices:
A) 6 months B) 3 months C) 2 months D) 8 months E) 9 months

Solution: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 8. or x = (85000 * 12) / (42500 * 8)= 
(85000 * 12) / (42500 * 8) = 3
3.   So, B joined for 3 months.   Answer: 3 months
Answer: B
Dhoni weighs twice as much as Nameetha. Nameetha's weight is 55% of Bima's weight. Dravid weighs 35% of Leela's weight. Leela weighs 30% of Dhoni's weight. Who among these 5 persons weighs the least?	Select.
A) Dravid  B) Dhoni  C) Bima  D) Nameetha  E) Leela

Solution: if   Bima weight = x   we get   Nameetha's weight = 0.55x   Dhoni's weight = 1.1x   Leela's weight = 0.33x   and Dravid's weight = 0.1155x   Dravidnswer : Dravid
Answer: A
A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.  Pick
A) 3.5  B) 3.75  C) 4  D) 4.25  E) 4.5

Solution: (1000xtx3/100) + (1400xtx5/100) = 350 → t =3.5 answer 3.5
Answer: A
Find the length of the longest pole that can be placed in an indoor stadium 24 m long, 18 m wide and 16 m high  Pick one:
A) 31
B) 32
C) 33
D) 34
E) 35

Solution: sqrt(1156)=34   becoz max length is cuboid diagonal d=sqrt(L^2+B^2+H^2)   where L lenght   B breadth & H height   ANSWER:34
Answer: D
During a given week A programmer spends 1/4 of his time preparing flow chart, 3/8 of his time coding and the rest of the time in debugging the programs. If he works 48 hours during the week , how many hours did he spend debugging the program.  Pick one
A) 15 hrs B) 16 hrs C) 18 hrs D) 19 hrs E) 17 hrs

Solution: programmer takes 1/4*48= 
1/4*48 = 12
12 hrs a week to make flowchrt   same way.....18 hrs a week for codin...   so....for debugging=48-(12+18)= 
48-(12+18) = 18
18 hrs   ANSWER:18 hrs
Answer: C
Priya went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 2%. then what was the cost of the tax free items?  Select.
A) Rs. 175.50 B) Rs. 174.50 C) Rs. 174.00 D) Rs. 170.00 E) Rs. 173.50

Solution: Solution   Let the amount of taxable purchases be Rs.x.   Then, 2% of x	= 50/100   x ‹=› (50/100×100/2)   = 25   Cost of tax free items	= Rs.[200 - (25 + 0.50)]   = Rs. 174.50   Answer Rs. 174.50
Answer: B
8 friends are living in 8 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 8 parking spots. In how many ways can they park their cars so that exactly 6 people park their cars in the spots allotted to them?	Choices: A) 20 B) 28 C) 36 D) 44 E) 52

Solution: 8C6 = 28   The remaining 2 people in each case will be parked in each other's parking spots.   The answer is 28.
Answer: B
Find the value of 72519 x 9999 = m?  Select the correct option.
A) 709115678
B) 723417481
C) 710017481
D) 725117481
E) None

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?	Choose the most appropriate option:
A) 10
B) 26
C) 12
D) 24
E) 48

Solution: 1/8 + 1/24 = 1/6   6 * 2= 
6 * 2 = 12
12   Answer: 12
Answer: C
Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 12 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?	Choose the correct choice from the following answers:
A) 42	B) 42.5	C) 44	D) 50	E) 52.5

Solution: Total Time taken by jerry = (8/40)*60 Minutes + 12 Minutes + (20/60)*60 Minutes = 44 Minutes   42verage Speed = Total Distance / Total Time = (8+20) miles / (44/60)Hours = 28*60 / 44 = 42 Miles per hour   42nswer: option 42
Answer: A
In a class composed of x girls and y boys, What part of the class is composed of girls  Choose the correct choice from the following choices
A) y/(x + y)	B) x/xy	C) x/(x + y)	D) y/xy	E) 1/xy

Solution: X/(X+Y).... ANSWER:x/(x + y)
Answer: C
While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? Choices:	A) 1/2	B) 17/36	C) 91/216	D) 11/36	E) 25/216

Solution: Total outcomes possible: 36   Total outcomes possible with sum 7: 6   Probability to win when rolled once = 6/36   Probability not to win when rolled once = 30/36 = 5/6   Probability to win in three attempts= 1- Probability will not to win in all three attempts   = 1- (5/6* 5/6*5/6)   = 91/216   Answer is 91/216.
Answer: C
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. Choose the correct choice:  A) 240  B) 388  C) 379  D) 277  E) 122

Solution: Explanation:   (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630= 
8/21 * 630 = 240
240   240nswer: 240
Answer: A
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?	Choose the correct choice from the following.
A) 2	B) 2.2	C) 3	D) 3.5	E) 4

Solution: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3   All the three pipes together will fill the tank in 3 hours.   ANSWER:3
Answer: C
At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $2 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?  Choices:	A) 7	B) 8	C) 6	D) 10	E) 11

Solution: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/2<712.80- 0.5= 
12.80- 0.5 = 12.3
$12.30, which is enough for 12.3/2<7=~6.   Answer: 6.
Answer: C
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?	Choose the correct choice:
A) 228
B) 276
C) 199
D) 150
E) 882

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m. Answer:150
Answer: D
What values of x satisfy the equation x2/3 + x1/3 – 2 ≤ 0 ?	Choose the correct option:
A) – 8 ≤ x ≤ 1	B) – 1 ≤ x ≤ 8	C) 1 ≤ x ≤ 8	D) – 8 ≤ x ≤ 8	E) None of these

Solution: Explanation :   Let, x1/3 = y. The equation becomes y2 + y – 2 ≤ 0, or y2 + y ≤ 2.   Now, look at the upper limit. We know that y2 + y ≤ 2.   Among the positive numbers, 1 is the biggest number that satisfies the equation. No number greater than 1 can have y2 + y ≤ 2. So the upper limit is 1.   Maximum value of y is 1, hence maximum value of x1/3 is 1, and hence maximum value of x is 1.   This answer is there only for option 1. Hence that is the answer.   – 8 ≤ x ≤ 1nswer : – 8 ≤ x ≤ 1
Answer: A
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n?  Choose the correct choice from the following answers:
A) 37
B) 123
C) 41
D) 52
E) 87

Solution: 123 is 3 * 41, so n needs to be at least 41, so the answer is 41.
Answer: C
2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?
Answers
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: (2m + 4b)’s one day’s work = 1/4   (5m + 6b)’s one day’s work = 1/3   => (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work   => 7 men’s work = 2 boy’s work   So, we should be employ 5 more men to be completed the work.   ANSWER:5
Answer: C
Given that x = 2^b – (8^34 + 16^5), which of the following values for b yields the lowest value for |x|? Answers:
A) 101
B) 102
C) 103
D) 104
E) 122

Solution: 8^34 + 16^5 = 2^102 + 2^20   Compared to 2^102, the value of 2^20 is negligible.   2^102 - (2^102 +2^20) will minimize the value of |x|.   The answer is 102.
Answer: B
If the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?	Select: A) 6:1 B) 12:1 C) 24:1 D) 36:1 E) 72:1

Solution: Let x be the length of the small cube's side.   The total surface area of the small cube is 6x^2.   The total surface area of the large cube is 6(6x)^2=216x^2.   The ratio of surface areas is 36:1.   The answer is 36:1.
Answer: D
A number exceeds by 25 from its 3/8 part. Then the number is?  Select:
A) 32	B) 35	C) 39	D) 40	E) 45

Solution: Explanation:   x – 3/8 x = 25   x = 40   ANSWER IS 40
Answer: D
The sum of three consecutive even numbers is 42. Find the middle number of the three?
Choose the correct choice from the following.
A) 14
B) 16
C) 18
D) 22
E) 24

Solution: Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 42   6P = 42 => P = 7.   The middle number is: 2P = 14.   Option 14
Answer: A
CONVERT 1.6 hectares in ares Options: A) 130 ares. B) 160 ares. C) 180 ares. D) 230 ares. E) 250 ares.

Solution: 1.6 hectares in ares   1 hectare = 100 ares   Therefore, 1.6 hectares = 1.6 × 100 ares   = 160 ares.   ANSWER- 160 ares.
Answer: B
20 beavers, working together in a constant pace, can build a dam in 6 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam? Pick:
A) 10.
B) 4.
C) 5.
D) 6
E) 8.

Solution: Total Work = 20*6= 
20*6 = 120
120 Beaver hours   12 Beaver * x=120 Beaver hours   x=120/12= 
120/12 = 10
10   10.NSWER:10.
Answer: A
If both 2^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
Choose one
A) 6
B) 9
C) 12
D) 15
E) 18

Solution: The number a must include at least 3^2 = 9   The answer is 9.
Answer: B
Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly?	Choose the correct choice from the following:
A) 1 litre
B) 7 litre
C) 31 litre
D) 41 litre
E) None

Solution: Solution   Required measurement	= H.C.F of (496, 403, 713) litres   ‹=›31 litres.   Answer 31 litre
Answer: C
If both a and b belongs to the set {1,2,3,4 }, then the number of equations of the form ax2 + bx + 1 = 0 having real roots is  Options:
A) 10 B) 7 C) 6 D) 12 E) 15

Solution: Explanation :   ax2 + bx + 1 = 0 .   For real roots   => b2 -4ac ≥ 0 .   i.e b2 - 4a(1) ≥ 0 .   i.e b2 ≥ 4a.   For a = 1, 4a = 4, ∴ b = 2, 3, 4   a = 2, 4a = 8, ∴ b = 3, 4   a = 3, 4a = 12, ∴ b = 4   a = 4, 4a = 16, ∴ b = 4   ∴ Number of equations possible = 7.   Harsh Mishra a year ago   0 upvotes   Answer : 7
Answer: B
For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3y = –30, then y =  Choose the correct choice from the following options:	A) –15	B) –6	C) -3	D) 6	E) 15

Solution: (3+2)(y-3)=-30..   x-3=-6..   x=-3   -3
Answer: C
The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?  Choose the correct choice from the following answers:
A) Rs.3000 B) Rs.3300 C) Rs.3600 D) Rs.3900 E) Rs.3800

Solution: P = 144(100/5)2 => P = 3600   ANSWER:Rs.3600
Answer: C
The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
Pick one: A) 0.7% B) 8.3% C) 0.3% D) 0.39% E) 2.3%

Solution: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100   = 13.50 4500(R1 - R2)   = 1350   R1 - R2 = 0.3%   Answer: 0.3%
Answer: C