MU-NLPC/Calc-aqua_rat huggingface dataset:
Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?
Select the correct option
A) 6 min 45 sec B) 5 min 45 sec C) 2min 45 sec D) 5 min 55 sec E) 5 min 28 sec

Solution: Part filled by pipe A in 1 minute = 18   Part filled by pipe 5 min 45 sec in 1 minute = 1/14   Part filled by pipe A and pipe 5 min 45 sec in 1 minute = 1/8+1/14=11/56   Pipe A and pipe 5 min 45 sec were open for 3 minutes   Part filled by pipe A and pipe 5 min 45 sec in 3 minutes = (3×11)/56=33/56   Remaining part = 1−(33/56)=23/56   Time taken by pipe 5 min 45 sec to fill this remaining part =(23×14)/56=23/4 minutes= 5 minutes 45 seconds   Answer is 5 min 45 sec
Answer: B
Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams G could be selected from the eight candidates? Select:
A) 56	B) 120	C) 210	D) 1120	E) 6720

Solution: If an executive team is considered different if any of the same people hold different offices,....   so you will not have answer as 6720..   president could be by any of 8 person..   treasurer could be any out of remaining 7 person..   remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..   total ways G= 8*7*20=1120..   ans 1120...
Answer: D
The probability that a visitor at the mall buys a pack of candy is 50%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?	Choose one
A) 0.225	B) 0.25	C) 0.325	D) 0.375	E) 0.5

Solution: One case is: candy - candy - no candy   The probability is 5/10*5/10*5/10 = 125/1000   There are 3 such cases, so we should multiply this probability by 3.   P(exactly 2 buy candy) = 125/1000 * 3 = 375/1000= 
375/1000 = 3/8 = around 0.375
0.375   The answer is 0.375.
Answer: D
A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.8 that the job will be completed on time if there is no strike, 0.32 that the job will be completed on time. If there is a strike. Determine the probability that the job will be completed on time.  Options:
A) 0.488
B) 0.485
C) 0.486
D) 0.458
E) 0.487

Solution: 0.488ssume 0.488 = There will be a strike   B = Construction Job will be completed on time   P(0.488) = 0.65 and P(0.4881)P(0.4881) = 1 - 0.65= 
1 - 0.65 = 0.35
0.35   P(B|0.488)= 0.32 and P(B|0.4881)=0.8   P(B)=P(0.488).P(B|0.488)+P(0.4881).P(B|0.4881)   = 0.65×0.32+0.35×0.8=0.488   0.488nswer 0.488
Answer: A
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number W of employees who take the subway to work?
Choose the most appropriate option:
A) 12 B) 13 C) 14 D) 15 E) 16

Solution: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2   P/3 + F/3 = (P+F)/3 = 48/3= 
48/3 = 16
16   P/4 + F/4= 12   P/3 + F/3 > P/3 + F/4 > P/4 + F/4   --> 16> 12 + P/12 > 12   GREATEST Possible W: 12 + p/12 = 15 --> p = 36 ( integer --> good)   15 or 15 is the answer
Answer: D
In a garments industry, a loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?  Select
A) 194 sec  B) 195 sec  C) 196 sec  D) 200 sec  E) None of these

Solution: Explanation :   Let the time required by x seconds.   Then, More cloth means More time (Direct Proportion)   So,   0.128 : 1 :: 25 : x   => x = 25 * 1/0.128   => x = 195.31   So time will be approx 195 seconds   Answer : 195 sec
Answer: B
A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly ?	Pick:  A) 12  B) 16  C) 18  D) 24  E) 26

Solution: Explanation:   Suppose the boy got x sums right and 2x sums wrong.   Then, x + 2x = 48 3x = 48 x = 16.   Answer:16
Answer: B
If a:b=2:8 and b:c=3:4 find a:b:c? Choose one.
A) 3:12:16
B) 12:3:6
C) 6:12:3
D) 4:3:14
E) 5:2:6

Solution: a:b = 2:8, b:c = 3:4   2:8   3:4   (a = a × b, b = b × b and c = b × c)   a:b:c = 3:12:16   3:12:16
Answer: A
How many times will the digit 4 be written when listing the integers from 1 to 1000?	Select the correct option:	A) 512	B) 300	C) 294	D) 264	E) 385

Solution: Many approaches are possible. For example:   Consider numbers from 0 to 999 written as follows:   1. 000   2. 001   3. 002   4. 003   ...   ...   ...   1000. 999   We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000= 
3*1000 = 3_000
3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 4) 3000/10=300 times.   Answer: 300.
Answer: B
Find the odd man out
385, 462, 572, 427, 671, 264 Answers:
A) 385  B) 427  C) 671  D) 264  E) 462

Solution: add 1st and 3rd term nd get mid term     3+5= 
  3+5 = 8
8   4+2= 
4+2 = 6
6   5+2= 
5+2 = 7
7   4+7= 
4+7 = 11
11   6+1= 
6+1 = 7
7   2+4= 
2+4 = 6
6   ANSWER:427
Answer: B
A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?  Select the correct option.
A) 276
B) 30
C) 88
D) 266
E) 12

Solution: The circumference of the circle is equal to the permeter of the rectangle.   Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5   => x = 1   Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5= 
6 * 5 = 30
30 cm2   Answer:30
Answer: B
If x - y =1 and
x2+y2=25
, find the value of ab.	Choose the correct choice from the following answers
A) 8  B) 12  C) 16  D) 32  E) 48

Solution: Explanation:   We know   2ab=(a2+b2)âˆ’(aâˆ’b)2   2xy=25âˆ’1=24   =>xy=12   Option12
Answer: B
A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 80 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year? Choose the correct choice from the following choices.
A) −5%  B) 5%  C) 15%  D) 26%  E) 80%

Solution: The actual answer is obtained by multiplying 180% by 70% and subtracting 100% from this total. That is: 180% × 70% = 126%; 126% − 100% = 26%.   Answer: 26%
Answer: D
There are cats got together and decided to kill the mice of 999936. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
Choose the correct choice from the following
A) 941,1009
B) 991,1001
C) 991,1009
D) 992,1008
E) 931,1009

Solution: 999936 can be written as 1000000 â€“ 64   = 10002 â€“ 82 ie of the form a2-b2=(a+b)(a-b)   =(1000+8)*(1000-8)   = (1008)*(992)   Given that number of cats is less than number if mice.   So number of cats is 992 and number of mice were 1008   Answer 992,1008
Answer: D
The distance between X&Y is 600km. A person is traveling from X to Y at 60km/hr started at 10AM and another person is traveling from Y to X at 40km/hr and started at same time. Then at what time they meet together.?
Choose the correct choice from the following choices.
A) A)2PM B) B)4PM C) C)1PM D) D)3PM E) E)5PM

Solution: Let x hours be they will meet together   distance covered by 1st person+distance covered by 2nd person = 600km   60x+40x = 600   x= 6 hr   They will meet = 10AM +6hr = 4PM   Answer is 4PM
Answer: B
Double of Quarter of 3 percent written as a decimal is :  Choose the correct choice from the following:	A) 0.003	B) 0.015	C) 0.25	D) 0.005	E) None of these

Solution: Explanation :   Solution: (2)*(1/4)*3% = 2*(1/4 * 3/100) = 0.015.   Answer : 0.015
Answer: B
A person travels from P to Q a speed of 60 km/hr and returns by increasing his speed by 20%. What is his average speed for both the trips?
Choose the correct choice from the following.
A) 33 B) 77 C) 48 D) 66 E) 21

Solution: Speed on return trip = 120% of 60 = 72 km/hr.   Average speed of trip = 60 + 72 /2 = 132/2= 
132/2 = 66
66 km/hr   Answer : 66
Answer: D
The least number which should be added to 3725 so that the sum is exactly divisible by 5, 6, 4 and 3 is? Pick one
A) 45 B) 55 C) 65 D) 75 E) 85

Solution: L.C.M. of 5, 6, 4 and 3 = 60.   On dividing 3725 by 60, the remainder is 5.   Number to be added = (60 - 5)= 
(60 - 5) = 55
55   55)
Answer: B
A train 360 m long is running at a speed of 45 km / hr. In what time will be pass a bridge 140 m long?	Answers.
A) 40 sec	B) 42 sec	C) 45 sec	D) 48 sec	E) None

Solution: Sol.   Speed = [45x5/18] m/sec = 25/2 m/sec.   Total distance covered = (360 + 140)= 
(360 + 140) = 500
500 m.   ∴ Required time= (500 x 2/25)sec = 40 sec.   40 secnswer 40 sec
Answer: A
The concentration of spirit in three different vessels A, B and C are 45%, 30% and 10% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.	Options: A) 26% B) 33% C) 34% D) 35% E) 24%

Solution: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*10/100)=1.8+1.5+0.6= 
1.8+1.5+0.6 = 3.9
3.9 liters   So % concentration of spirit=100*3.9/(4+5+6)= 
100*3.9/(4+5+6) = 26
26%   26%NSWER:26%
Answer: A
A water tank has two pipes to fill water in it. One of the pipes fills water at the rate of 100 litres per hour. The tank is filled by the other pipe in 6 hours and by both pipes together in 4.2 hours. What is the capacity of the tank in litres ? Choose the correct choice.
A) 860 litre
B) 980 litre
C) 1120 litre
D) 1400 litre
E) None of these

Solution: Explanation:   Let the time taken by the 1st pipe to fill the tank be x hours.   When both the pipes are open, it is given that:   1/x + 1/6 = 1/(4.2) of tank is filled in 1 hour.   1/x + 1/6 = 5/21   21(6 + x) = 30 x   9x = 126   x = 14 hours   Therefore, capacity of the tank = 100 * 14= 
100 * 14 = 1_400
1400 litres.   ANSWER 1400 litre
Answer: D
A bowl was filled with 10 ounces of water, and 0.00008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? Choose the correct choice from the following
A) 0.004%  B) 0.04%  C) 0.40%  D) 4%  E) 40%

Solution: Total amount of water evaporated each day during a 50-day period = .00008 * 50   =.00008 * 100/2   = .008/2= 
.008/2 = 0.004
.004   percent of the original amount of water evaporated during this period= (.004/10) * 100= 
(.004/10) * 100 = 0.04
0.04 %   Answer 0.04%
Answer: B
what is rate of interest if principal.amount be 400,simple interest 120 and time 2year. Choose the correct choice from the following options:
A) 10
B) 12.5
C) 25
D) 12
E) 15

Solution: s.i=(p*r*t)/100   120=800r/100   r=120/8= 
120/8 = 15
15%   answer 15
Answer: E
How many 4-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 2 different consonants?  Choose the correct choice from the following answers.
A) 4!*5c2 *21c2
B) 5P2 * 21P3 * 5!
C) 5C2 * 21C3 * 5!
D) 5P2 * 21P3
E) 5C2 * 21C3

Solution: combination for 2 vowels out of 5 =5c2 ways   combination for 2 consonants of 21 = 21c2 ways   4!*5c2 *21c2dditionally the arrangement can be = 4!   total arrangements =4!*5c2 *21c2   4!*5c2 *21c2
Answer: A
a student reached his school late by 20mins by travelling at a speed of 9kmph.if he had travelled at a speed of 12kmph,he would have reached his school 20mins early.what is the distance between house and school?  Pick one
A) 24
B) 25
C) 26
D) 27
E) 28

Solution: distance = distance either student reaches school before time or after time   9(t+20/60) = 12(t-20/60)   i.e   9(t+1/3) = 12(t-1/3)   9(3t+1) = 12(3t-1)   t=7/3   put t value in any of distance equation   put t= 7/3 in 9(t+1/3)   we get 24 km   24NSWER:24
Answer: A
A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
Select the correct option
A) A.0.6 B) B.1 C) C.2.1 D) D.3 E) E.2.4

Solution: 30% of 6 = 1.8   50% of 6 = 3   shortage is 1.2   so we need to have 1.2/50% to get 50% alcohol content.   = 2.4 E.2.4
Answer: E
Rajesh can finish 1/3 of his home work in one hour. Seema can finish 3/7 of
her homework in 70 minutes and Ramya can finish 3/4 of her homework in
three and a quarter hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.00 PM for 30 minutes?  Choose the most appropriate option.
A) 4:30pm
B) 5:30pm
C) 6:30pm
D) 4:50pm
E) 3:30pm

Solution: ajesh can finish his work in 3 hr,   ramya can finish her work in 2.7 hr   seema can finish in 4.3 hr   so 4:50pm they can go to play   ANSWER:4:50pm
Answer: D
Which of the following is a even number ?
Choices:
A) 9
B) 11
C) 4
D) 3
E) 1

Solution: Explanation :   4 is a even number   Hence the even numbers are 2,4,6,8,10,12,14,... Answer : Option 4
Answer: C
in a certain tournament certain rules are followed: any player is eliminated the moment he losses for the third time (irrespective of how many wins he has), any player can play another player any number of times. If 512 contestants enter the tournament what is the largest number of games that could be played?	Choose the correct choice from the following options
A) 1535  B) 1533  C) 1536  D) 1534  E) 1556

Solution: Explanation :   As there are 512 contestants , 511 contestants must be eliminated so that there can be only 1 winner.   In a single match there is only 1 loss and for elimination of a contestant he must lose 3 matches;   therefore for eliminating 511 contestants , the nos of matches required is : 511 x 3 = 1533   The last contestant i.e the winner can also lose a maximum of 2 matches.   So the maximum nos of games that could be played is  1533+2= 
 1533+2 = 1_535
1535   1535nswer : 1535
Answer: A
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: Choose the correct option
A) 9000	B) 9400	C) 9600	D) 9670	E) 9800

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600. Answer: Option 9600
Answer: C
Amul's Ice Cream Shop sells ice cream at a cents a scoop. For an additional b cents, a customer can add 7 toppings to his or her sundae. How much would a sundae with 7 scoops and 7 toppings cost, in terms of a and b?  Options.
A) 7a+2b  B) 7a+b  C) 6a+b  D) 5a+b  E) 5a+3b

Solution: Answer 7a+b 7a+b
Answer: B
At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 50 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 40 km/h. If the distance between City P and City Q is 230 km, at what time will the truck and the car meet each other?  Choose the correct choice from the following answers
A) 4:00 B) 4:30 C) 5:00 D) 5:30 E) 6:00

Solution: At 2:00 pm, the truck and the car are 180 km apart.   The truck and the car complete a distance of 90 km each hour.   The time it takes to meet is   180/90= 
  180/90 = 2
2 hours.   They will meet at 4:00 pm.   The answer is 4:00.
Answer: A
A train 450 m long running at 108 kmph crosses a platform in 25 sec. What is the length of the platform?	Choices
A) 271
B) 266
C) 350
D) 277
E) 300

Solution: Length of the platform = 108 * 5/18 * 25= 
108 * 5/18 * 25 = 750
750 – 450= 300   Answer:300
Answer: E
A set consist of 2m-1 element. What is the number of subsets of this set which contain at most m-1 elements?	Pick one
A) 2^(2m-2) B) 2^(2m) - 2 C) 2^(2m) -1 D) 2^(2m) E) 2^(2m-1)

Solution: I used m=3, so then we have   5!/2!3! + 5!/4!1! + 5!/0!5!    10 + 5 + 1= 
 10 + 5 + 1 = 16
16   So our target is 16   Now replace in answer choices   2^(2m-2) gives us 2^4= 16   Hence 2^(2m-2) is the correct option   Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes   2^(2m-2)void 2 since you will get 1 arrangement (m-1) and may be risky since 1 is a number with certain unique properties
Answer: A
A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
Select the correct option.
A) 7/2 kmph B) 8/2 kmph C) 5/2 kmph D) 1/2 kmph E) 2/2 kmph

Solution: Explanation:   Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.   Speed in downstream = 3 x 60/18 = 10 km/hr   Rate of current = (10-9)/2 = 1/2 km/hr.   Answer: 1/2 kmph
Answer: D
Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long K would it have taken for him to walk both ways. Choices
A) 8 h 45 min B) 7 h 45 min C) 6 h 45 min D) 5 h 30 min E) None of these

Solution: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes   2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.   3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.   4.Walking to to a viewpoint+Walking back K=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.   8 h 45 minnswer: 8 h 45 min.
Answer: A
Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
Choose the correct option
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: First, reach to the point of getting the equation W: x + y = 18   It should take about 20 seconds.   Then Substitute the answer choices into the equation.   I don't know what the answer choices in this case are.   But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).   Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)   The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).   Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=3
Answer: D
A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $420 less than the sum lent. What was the sum lent?	Choose the correct choice from the following answers:
A) 500
B) 600
C) 700
D) 800
E) 900

Solution: P - 420 = (P*5*8)/100   P = 700   The answer is 700.
Answer: C
Departments A, B, and C have 6 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible? Answers.
A) 19,000
B) 41,040
C) 100,000
D) 190,000
E) 400,000

Solution: 6c1 * 6c1* 6c1*20c2 = 6*6*6*190=41,040. Hence 41,040 is the correct answer.
Answer: B
An investor invests in a new fund. The fund averages 10% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?	Choose the correct choice
A) 97.64%	B) 100.98%	C) 103.45%	D) 106.48%	E) 109.78%

Solution: 0.8*1.1^3 = 1.0648   The answer is 106.48%.
Answer: D
Which of the following is closest to (-2/3)^199？ Select.
A) -1 B) -1/2 C) 0 D) 1 E) 2

Solution: (-2/3)^4 = 16/81 which is already less than 1/2.   For larger exponents, the expression will get closer and closer to zero.   The answer is 0.
Answer: C
If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. a-c=-2
II. abc is an even integer
III. (a+b+c)/3 is an integer	Pick one: A) All are correct B) II C) I and II D) II and III E) None are correct

Solution: 1. a-c=-2 --> a, b, c are consequitive positive integers and a<b<c then c=a+2 --> a-c=2. So this statement is always true;   2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;   3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.   All are correctnswer: All are correct.
Answer: A
E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?
A.
B.
C.
D.
E.
Choose the correct choice from the following options.
A) 9√3	B) 9√2	C) 12	D) 9	E) 6√2/3

Solution: Since BE is the median, Area of triangle ABE = Area of triangle EBC = 1/2 * Area of triangle ABC = 12.   Also, since Angle C = 45, AB = AC.   But, 1/2 * AB*AC = 24 => AC = \sqrt{48} = 4\sqrt{3}   AE = AC/2 = 2\sqrt{3}   Now, triangle EDC is again right angled. so area of triangle EDC = 1/2 * ED * DC .   But ED = DC and ED^2 + DC^2 = 12 => ED = \sqrt{6}   So area of triangle EDC = 1/2 *\sqrt{6} *\sqrt{6} = 3   Now area of triangle BCD = Area of triangle EBC - Area of triangle EDC => 12 -3= 
12 -3 = 9
9.   ANSWER:9
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?  Pick one:
A) 768	B) 268	C) 260	D) 480	E) 269

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: 480
Answer: D
What is the area of an equilateral triangle whose one side length is 90? Choose the most appropriate option:
A) 4025√3
B) 3525√3
C) 3025√3
D) 2525√3
E) 2025√3

Solution: -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(90^2)/4=2025√3 and the answer is 2025√3.
Answer: E
The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is Pick:
A) 20 B) 25 C) 30 D) 35 E) 40

Solution: Let breadth = x m   Then, length = (x+5)m   x(x+5) = 750   x² + 5x - 750= 0   (x+30)(x-25)= 0   x = 25 Answer: 25
Answer: B
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Choose the correct choice from the following
A) 600 cm
B) 800 cm
C) 400 cm
D) 1000 cm
E) None of these

Solution: Area of the square = s * s = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   ANSWER:800 cm
Answer: B
Two cars, A and B, travel along interstate 20 from Atlanta to Dallas. Car A left Atlanta at 10 PM traveling at a constant speed of 60 mph. Car B left the same point in Atlanta 30 minutes later traveling at a constant speed of 80 mph. In how many minutes will Car B overtake Car A if neither car stops at any exit or experiences traffic (and thus both cars maintain their constant speeds)?	Choose one
A) 90  B) 95  C) 100  D) 110  E) 120

Solution: We need to use a form of D=RT [distance=rate*time]   Car 90 will have travelled 30 minutes longer than car B when they meet, so   Car 90 travel time: T+.5 (use 1/2 hour since the rates are in hours)   Car B travel time: T   Car 90 rate: 60 mph   Car B rate: 80 mph   Car 90 distance = Car B distance   so   (R car 90)*(T car 90) = (R car B)*(T car B)   60*(T+.5) = 80*T   60T + 30 = 80T   30 = 20T   1.5 = T   1.5 hours = 90 minutes   90
Answer: A
In a class of 27 students in an examination in maths 5 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?	Pick one: A) A)47 B) B)45.6 C) C)44 D) D)48 E) E)49.3

Solution: 49.3xplanation:   Total marks obtained by a class of 25 students   = 5*95 + 3*0 + 19 * 45= 
5*95 + 3*0 + 19 * 45 = 1_330
1330   Average marks of whole class= 1330/27 =49.3   Answer: Option 49.3
Answer: E