MU-NLPC/Calc-aqua_rat huggingface dataset:
Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money R would he earn per month?  Choose the correct choice from the following
A) $700  B) $754  C) $770  D) $782  E) $893

Solution: OFFICIAL SOLUTION:   (C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:   $812 = 1.16S, where S is his current salary.   Then S = $812/1.16= 
812/1.16 = 700
$700.   Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:   R=$700 + $70 = $770.   The correct answer is choice ($770).700 +  70= 
700 +  70 = 770
$770.   The correct answer is choice ($770).
Answer: C
Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 36 seconds. The length of each train is: Choose the most appropriate option:
A) 82m
B) 50m
C) 72m
D) 80m
E) None of these

Solution: Explanation:   The relative speed of train is 46-36= 
46-36 = 10
10 Km/hr= (10 X 5) / 18 = 25/9 m/s10×518=259m/s   In 36 secs the total distance travelled is 36x25/9 = 100 m.   Therefore the length of each train is = 100/2= 
100/2 = 50
50 m.   Answer 50m
Answer: B
The cost per unit of electricity during a 4 year period is as follows:
Year 1, $0.75 per unit;
Year 2, $1.50 per unit;
Year 3, $2.25 per unit;
Year 4, $3 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?  Choose the correct choice:
A) $1.55
B) $1.44
C) $1.66
D) $1.77
E) $1.88

Solution: Let money spent each year = $225   Units bought first year = 300   Units bought second year = 150   Units bought third year = 100   Units bought fourth year = 75   Total number of units = 625   Total money spent = 225*4= 
225*4 = 900
900   Average= 900/625= 
900/625 = 36/25 = around 1.44
1.44   Answer : $1.44
Answer: B
A motorist knows six different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?  Pick
A) 4
B) 8
C) 12
D) 24
E) 36

Solution: Explanation:   Total number of routes from Bristol to Carlisle = (6 x 3 x 2) = 36.   Answer: 36
Answer: E
In a room with 8 people, 5 people have exactly 1 friend in the room and 4 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
Options.
A) 5/21  B) 3/7  C) 4/7  D) 5/7  E) 25/28

Solution: (5/8)(6/7) + (4/8)(5/7) if you choose one of the 5 with one other friend, then you have a 6/7 chance of not picking their friend 2nd. If you choose one of the 4 with 2 friends, you have a 5/7 chance of not picking one of their friends second. Add them up.   30/56 + 20/56   50/56=25/28 E. 25/28
Answer: E
At 6′o a clock ticks 6 times. The time between first and last ticks is 25 seconds. How long does it tick at 12′o clock
Options:
A) 47	B) 55	C) 28	D) 66	E) 11

Solution: Explanation:   For ticking 6 times, there are 5 intervals.   Each interval has time duration of   25/5= 
  25/5 = 5
5 secs   At 12 o'clock, there are 11 intervals,   So total time for 11 intervals= 11 × 5 = 55 secs.   Answer: 55
Answer: B
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12% while buying and by 20% while selling. What is his percentage profit?	Choose the correct answer.
A) 10.22%  B) 20.22%  C) 21.22%  D) 40%  E) Can't be calculated

Solution: The owner buys 100 kg but actually gets 112kg;   The owner sells 100 kg but actually gives 80kg;   Profit:   (112-80)/80*100= 
  (112-80)/80*100 = 40
~40%   Answer: 40%.
Answer: D
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Pick one:
A) 4/9	B) 5/8	C) 4/7	D) 4/11	E) 5/9

Solution: 2/3 ---- 12   ? ----- 8 ==> 4/9   4/9NSWER 4/9
Answer: A
In how many different ways can 5 people be seated in a room with 7 chairs?  Choose the correct option.
A) 2,520
B) 181,440
C) 403,200
D) 1,814,400
E) 3,628,800

Solution: Order doesn't matter   With 7 chairs and only 5 to seat   5!- Number of ways the 5 can seat on the chair   7C2 - Number of ways the 2 empty sits can be vary with the 5 seated   5! * 7C2 = 2,520 2,520nswer - 2,520
Answer: A
Using all the letters of the word "NOKIAS", how many words can be formed, which begin with N and end with A?  Choose the correct choice from the following.
A) 8	B) 24	C) 9	D) 3	E) 1

Solution: There are five letters in the given word.   Consider 6 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 4! ways.   The number of words = 4! = 24.   Answer:24
Answer: B
Chris mixed 5 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?	Pick one:
A) 5/17
B) 1/5
C) 1/4
D) 1/3
E) 3/7

Solution: 1 lbs of raisin = $1   5 lbs of raisin = $5   1 lbs of nuts = $3   4 lbs of nuts = $12   Total value of mixture = 12+5= 
12+5 = 17
17   Fraction of the value of raisin= 5/17 = 1/5   5/17ns:5/17
Answer: A
How many prime numbers between 1 and 100 are factors of 7,150 ?
Choose the correct choice from the following answers
A) One	B) Two	C) Three	D) Four	E) Five

Solution: Make prime factorization of 7,150 --> 7,150=2∗5^2∗11∗13 So, 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150.   Answer: Four.
Answer: D
Five coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Choose the correct answer:	A) 2^4	B) 2^10	C) 3 * 2^8	D) 3 * 2^9	E) 3 * 2^10

Solution: Fix the third coin as H. The remaining 4 coins have 2^4 outcomes.   2^4
Answer: A
What is the next number of the following sequence
1,3,4,5,6,1,9,16,25,... Choices:
A) 14
B) 15
C) 36
D) 17
E) 18

Solution: (1, 3 ,4,5, 6) (1, 9, 16, 25,x)   square of 1st group gives 2nd group   1^2 = 1   3^2 = 9   4^2 = 16   5^2 =25   6^2 =36   ANSWER:36
Answer: C
One vessel contains a mixture of 6 parts pure wine and 4 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine. Select the correct option:
A) 35;36  B) 7 : 8  C) 7 : 4  D) 42 : 45  E) None of these

Solution: 6/10 : 9/14   LCM of 5,14 = 70   (6/10)*70 : (9/14)*70   42:45   Answer is 42 : 45.
Answer: D
Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.14000 at the end of the year, B's share is
Choose the most appropriate option:	A) Rs.4000	B) Rs.5040	C) Rs.7500	D) Rs.6600	E) None

Solution: Solution   Let C = x.   Then, B = 4x and 2A = 3x4x = 12x or A = 6x.   âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.   So B's capital	= Rs(14000 x 4 / 11)   = Rs.5040.   Answer Rs.5040
Answer: B
Which of the following is not a prime number ?
Select the correct option:  A) 21  B) 23  C) 27  D) 29  E) 31

Solution: 21 is not a prime number. Choice 21 is the correct answer.
Answer: A
A reduction of 35% in the price of apples would enable a man to obtain 42 more for Rs.20, what is reduced price per dozen?
Choose the correct choice from the following.
A) 1.7  B) 3.5  C) 6.3  D) 7.1  E) 10.4

Solution: 1.7   20*(35/100) = 6 --- 42   ? --- 12 => Rs.1.7
Answer: A
A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money? Choose the most appropriate option
A) 288
B) 262
C) 72
D) 205
E) 267

Solution: A:B:C = 100:65:40   = 20:13:8   8 ---- 40   41 ---- ? => Rs.205   Answer: 205
Answer: D
If 15 ≤ x ≤ 25, and 0.2 ≤ y ≤ 0.6, what is the greatest possible value of 3/(x·y)? Choose the correct answer:
A) 1/3	B) 0.6	C) 0.9	D) 1	E) 3

Solution: or greatest possible value of 3/(x·y), x and y should be made minimum   minimum value of x is 15 and minimum value of y is 0.2   so greatest possible value of 3/(15*0.2)= 
3/(15*0.2) = 1
1   ANSWER:1
Answer: D
In a diving competition, each diver has a 35% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)	Pick one:
A) 1/5	B) 1/15	C) 4/25	D) 80/541	E) 61/125

Solution: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)   Given:Probability of Perfect dive = 0.35 = 35/100 = 1/3   i.e. Probability of Non-Perfect dive = 0.65 = 65/100 = 2/3   The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect   Method-1:   i.e. Probability of First two being Imperfect and Third being Perfect dive = (2/3)*(2/3)*(1/3) =80/541   80/541
Answer: D
A beekeeper has 1200,000 bees living in 13 beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?  Choose the correct answer.
A) 24345
B) 113207
C) 454646
D) 4645646
E) 456677656

Solution: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+12*(0.8)*x = 1200,000 => 10.6x = 1200,000 => x = 113207.   113207 is the answer.
Answer: B
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?	Options.
A) 22 B) 18 C) 12 D) 88 E) 66

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12   Answer: 12
Answer: C
John is traveling to a meeting that is 22 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? Choose the correct choice from the following options
A) 25 mph  B) 44 mph  C) 41 mph  D) 49 mph  E) 56 mph

Solution: Well 44mph. B. Time*rate=distance --> 0.5*rate=22 --> rate=44
Answer: B
Which of the following cannot be the range of a set consisting of 5 odd multiples of 5?  Choices:
A) 383 B) 80 C) 160 D) 320 E) 40

Solution: Solution: sequence of 5 lets say sequence is 5n, 5(n+1), 5(n+2), 5(n+3), 5(n+4)   so range is 5n+20-5n = 20   if we put the different values of n we will get different but the range will be multiple of 20   and only 386 is not multiple of 20   383nswer : 3835 +20-5= 
5 +20-5 = 20
20   if we put the different values of n we will get different but the range will be multiple of 20   and only 386 is not multiple of 20   383nswer : 383
Answer: A
Each truck from David Removal Company can haul 1000 pounds of trash at a time.
On Wednesday the company has jobs to remove 2,500 pounds of trash from one
site, 500 from another site, and 3,500 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
Jones Company to remove all of the trash? Choose the correct choice from the following answers.
A) 5500 lbs.-2 Trips
B) 4500 lbs.-9 Trips
C) 2500 lbs.-3 Trips
D) 3500 lbs.-7 Trips
E) 6000 lbs.-6 Trips

Solution: Total trash = 2500+500+3500 = 6000   No. of trips = 6000/1000= 
6000/1000 = 6
6   Answer : 6000 lbs.-6 Trips
Answer: E
12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for two days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days? Options.
A) 15  B) 18  C) data inadequate  D) none of these  E) 13

Solution: Explanation:   12 M or 15 W complete the work in 4 days   ie. 6 Men complete in 2 nd days 1/4 th work 12*4/1= 6 * 2/x   => x= 1/4 th work   Remaining work = 3/4 th.   15nswer: 15
Answer: A
The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?	Options
A) 240
B) 270
C) 295
D) 268
E) 252

Solution: Let the smaller number be x. Then larger number = (x + 1355).   x + 1355 = 6x + 15   5x = 1340   x = 268   Smaller number = 270.   ANSWER 268
Answer: D
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 5 miles behind the slower one. How far apart are the two trains at 5 o'clock?  Choose the correct choice
A) 60 miles	B) 80 miles	C) 90 miles	D) 120 miles	E) 85 miles

Solution: Answer = E. 85 miles   Relational speed = 130 - 100= 
130 - 100 = 30
30 miles per hour   In 3 hours, difference= 30 * 3= 
30 * 3 = 90
90 miles   Fast train trailing 5 miles, so effective difference= 90 - 5= 
90 - 5 = 85
85 miles
Answer: E
A motorcyclist goes from Bombay to Delhi, a distance of 200 kms at an average of 50 kmph speed. Another man starts from Bombay by car 2 Â½ hours after the first, and reaches Delhi Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Choose the most appropriate option.
A) 1:2  B) 1:7  C) 1:9  D) 1:4  E) 1:1

Solution: T = 200/50= 
200/50 = 4
4 h   T= 4 - 3= 
4 - 3 = 1
1   Time Ratio= 4:1   Speed Ratio = 1:4   Answer: 1:4
Answer: D
Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 62 km along the main road. What would be the distance between two cars at this point? Choose the correct answer.
A) 65 B) 38 C) 20 D) 28 E) 21

Solution: Answer: 38) 38 km
Answer: B
A monkey starts climbing up a tree of 20 feet tall. Each hour it hops 3 feet and slips back 2 feet. How long monkey will take to reach the top of the tree?	Pick one:  A) 16 hours.  B) 19 hours.  C) 12 hours.  D) 18 hours.  E) 13 hours.

Solution: The monkey hops 3 feet and slips down 2 feet. So for the first hour it climb 1 feet.   Then for 2 hours 2 feet. Continuing the same till 17 hours, the monkey might have reached 17 feet.   In 18th hour monkey hops 3 feet and reach the 20 feet. Hence the answer is 18 hours.   Answer 18 hours.
Answer: D
The average of first six prime numbers greater than 20 is? Answers
A) 10  B) 20  C) 30  D) 40  E) 34

Solution: 23 + 29 + 31 + 37 + 41 + 43= 
23 + 29 + 31 + 37 + 41 + 43 = 204
204/6= 
204/6 = 34
34   ANSW34R:34
Answer: E
The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 384 square centimeters, what is the length of the rectangle in centimeters? Choose the correct choice from the following answers:
A) 20	B) 21	C) 22	D) 23	E) 24

Solution: Perimeter = 2(W+L) = 5W   3W = 2L   W = 2L/3   WL = 384   2L^2/3 = 384   L^2 = 576   L = 24 cm   The answer is 24.
Answer: E
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get? Choose the correct option.
A) 2400  B) 7768  C) 2678  D) 2699  E) 2881

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400   2400nswer: 2400
Answer: A
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?	Select
A) Rs. 32,000
B) Rs. 34,000
C) Rs. 36,000
D) Rs. 36,500
E) Rs. 38,000

Solution: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then, 2x + 4000 = 40   3x + 4000 57   57(2x + 4000) = 40(3x + 4000)   6x = 68,000   3x = 34,000   Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.   Rs. 38,000
Answer: E
There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles .
Choose the correct answer.
A) 3 hr	B) 4 hr	C) 2 hr	D) 1 hr	E) 5 hr

Solution: Thicker candle - 6hr   thinner candle -4hr   lcm of (6,4)=12   thinner candle burn in 1 hour= 3part   thicker candle burn in 1 hour= 2part   in 1 hr length of candle left : (thicker,thinner):(10,9)   in 2 hr (8,6)   in 3 hr (6,3)   so, 3 hr   3 hrNSWER:3 hr
Answer: A
2 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place? Options:  A) 1  B) 2  C) 5  D) 0  E) 4

Solution: the formula to count handshakes is n(n−1)2n(n−1)2   Where n is the number of people   => 2(2-1)/2 = 2*1/2 = 2/2= 
2/2 = 1
1=> the answer is 1(1)
Answer: A
After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4725. What was the number of original inhabitants?	Choose the correct choice
A) 5000  B) 7000  C) 4000  D) 8000  E) 9000

Solution: Let the total number of original inhabitants be x.   (75/100) * (90/100) * x = 4725   (27/40) * x = 4725   x = 4725 * 40 / 27= 
4725 * 40 / 27 = 7_000
7000   The answer is 7000.
Answer: B
38 69 55 73 31 47 91 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
Choose the correct choice from the following answers:
A) 56
B) 68
C) 69
D) 71
E) 79

Solution: Arrange the numbers in ascending order:   31, 38, 47, 55, 69, 73, 82, 91 (Just cross check the count to ensure that you didn't miss anything)   How many numbers do we see?   8, alright.   What's (1/4)8?   2.   What's (3/4)8?   6.   We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.   31, 38, 47, 55, 69, 73, 82, 91   31, 38, 47, 55, 69, 73: Find a number greater than any of these numbers.   82, 91: Find a number smaller than any of these numbers.   Only 79 fits the description.   Ans:79
Answer: E
Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is
Choose the correct answer.
A) 50 B) 55 C) 60 D) 65 E) 66

Solution: Explanation:   Total weight increased is 1.5 * 10= 
1.5 * 10 = 15
15.   So weight of new person is 45+15= 
45+15 = 60
60   Answer: Option 60
Answer: C
Entry fee in an examination was Re. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is
Choose the correct option.
A) 60  B) 50  C) 66  D) 54  E) None

Solution: Sol.   Let the total original sale be Rs. 100. Then, original number of visitors = 100.   New number of visitors = 120 / 0.75= 
120 / 0.75 = 160
160.   ∴ Increase%= 60%.   60nswer 60
Answer: A
If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 102 to 198, inclusive?
Pick one.
A) 6  B) 5  C) 4  D) 3  E) 2

Solution: 102 x 104 x 106 x 108 => unit digit 4   112 x 114 x 116 x 118 => unit digit 4   192 x 194 x 196 x 198 => unit digit 4   So we have 10 numbers ending by 4 to multiply.   Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply   Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply   So the unit digit is 6   6nswer: 6
Answer: A
Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 15 from the product of their ages a year from today. What is their age today? Choose the correct choice.
A) 2.  B) 4.  C) 5.  D) 7.  E) 9.

Solution: ad = (a+1) (d+1) -15   0= a+d-14   a+d = 14   a=d (as they are twin brothers)   a=d=7   7. is the answer
Answer: D
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 9. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ? Select:  A) 51/625  B) 50/625  C) 4/625  D) 25/625  E) 53/625

Solution: I think most of the answers are missing a point. Let me try to put it across:   Total number of possible numbers are : 5x5 = 25   Correct number =1   Case 1: When he gets it right in first attempt: P(E1) = 1/25   Case 2: He gets 1st attempt wrong and second right:   When he gets it wrong then the probability of getting wrong is 24/25.   Now there are 24 cases with him and he chooses the right one this time.   Probability of right case is 1/24   Thus, P(E2) = 24/25 x 1/24   =1/25   Probability of getting it right in at most two cases = P(E1) + P(E2)   = 1/25 + 1/25   = 2/25   = 50/625   Option (50/625) is therefore right as most of you mentioned but the method employed was wrong.
Answer: B
If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are Answers: A) rational B) irrational C) non real D) real E) none of these.

Solution: Sol.(a) The sum of coefficients   = (b + c - a) + (c + a - b) + (a + b - c) = a + b + c = 0 (given)   ∴ x = 1 is a root of the equation   ∴ The other root is a+b−cb+c−aa+b−cb+c−a , which is rational as a,b, c, are rational   Hence, both the roots are rational.   ALTERNATIVE :   D = (c + a - b)2 - 4(b + c - a)(a + b - c)   = (-2b)2 - 4(-2a)(-2c) = 4b2 - 16ac   = 4(a + c)2 - 16ac = 4[(a + c)2 - 4ac] = 2[(a - c)2]   D is a perfect square. Hence, the roots of the equation are rational.   rationalnswer rational
Answer: A
In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes  Answers.
A) 12:7 B) 10:7 C) 8:7 D) 4:3 E) none

Solution: Solution: Boys: girls = 8:5; (let the boys = 8x; girl = 5x)   Total strength = 286;   8x+5x = 286;   13x = 286;   Or, x = 286/13= 
286/13 = 22
22;   Boys= 176 and girls = 110;   22 more girls get admitted then number of girls become,   (5x+22) = 110+22= 
110+22 = 132
132;   Now, new ratio of boys and girls= 176:132 = 4:3.   Answer: Option 4:3
Answer: D
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?  Choose the most appropriate option.
A) 3630	B) 3877	C) 2667	D) 2977	E) 2378

Solution: Explanation:   6300:4200:10500   3:2:5   3/10 * 12100= 
3/10 * 12100 = 3_630
3630   3630nswer: 3630
Answer: A
A & B are two places. C & D start walking from A and B respectively. Before meeting D, C travel 18m more than D. then C takes 13 and half minute and D take 24 minute to reach their destination. Pick:
A) 124
B) 126
C) 127
D) 128
E) 129

Solution: their speed in ratio 4:3   7*18= 
7*18 = 126
126   ANSWER:126
Answer: B