MU-NLPC/Calc-aqua_rat huggingface dataset:
Johnop went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
Select the correct option
A) 3 km B) 6 km C) 4.5 km D) km E) none of the above

Solution: Assume the distance to the top of the hill (1 way) as: x   Now, speed=distance/time => time=distance/speed   So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.   For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5   Now, the total time for the trip is given as 4 hrs.   Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km   So, the distance one side is = 4.5 km.   The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km   4.5 kman someone assist me in understanding where am I wrong here?
Answer: C
fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___  Choose one.
A) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y B) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y C) (a) the point with coordinates (0,0) is called line of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal 0 and solve for z ; to find x- intercept , we let x equal 0 and solve for x D) (a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let z equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x E) none of the above

Solution: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (none of the above)
Answer: E
P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by: Choose the correct choice from the following choices:
A) Rs.2400	B) Rs.3000	C) Rs.3600	D) Rs.4800	E) Rs.3800

Solution: A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)   = 147 : 189 : 126 = 7 : 9 : 6.   Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22   = Rs.3600   ANSWER:Rs.3600
Answer: C
Kyle, Devon, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/2, 1/3 and 5/9, respectively, what is the probability that Kyle but not Devon and Catherine will solve the problem?
Choices.
A) 13/29  B) 1/4  C) 15/21  D) 11/19  E) 4/27

Solution: P(Kyle will solve)=1/2   P(Devon will not solve)= 1 - 1/3 = 2/3   P(Catherine will not solve) = 1- 5/9 = 4/9   P= (1/2)*(2/3)*(4/9) = 8/54 = 4/27.   Answer:4/27
Answer: E
Of the teams competing in the world archery championships, Fifty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.	Answers:
A) 13/20 B) 4/20 C) 13/15 D) 17/20 E) 13/17

Solution: Assume 100 total people.   50% of 100 = 50 --->Europeans   1/2 of 50 ---> 25 Americans   1/20 of 100 ---> 5 Africans   Now you would add them all up, and minus it by the total (100). 100 - 80= 20. So, 20 people out of 100 are not EU, US or Africans. 20/100 is also equal to 4/20.   So therefore, the answer is 4/20.
Answer: B
An empty fuel tank with a capacity of 212 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
Answers
A) 160 B) 98 C) 100 D) 80 E) 50

Solution: Say there are A gallons of fuel A in the tank, then there would be 212-A gallons of fuel B.   The amount of ethanol in A gallons of fuel A is 0.12A;   The amount of ethanol in 212-A gallons of fuel B is 0.16(212-A);   Since the total amount of ethanol is 30 gallons then 0.12A+0.16(212-A)=30 --> A=98.   Answer: 98.
Answer: B
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:	Choose the correct choice from the following
A) 2700	B) 2800	C) 2000	D) 2500	E) 2600

Solution: Number of valid votes = 80% of 7500 = 6000.   Valid votes polled by other candidate = 45% of 6000   =(45/100)x 6000= 2700.   2700NSWER 2700
Answer: A
If s > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - s) =
Choose the correct option
A) 1/4 B) 1/3 C) 1/2 D) 3/4 E) 1

Solution: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have s-x=2t. So y-x=-t, y-s=-3t. ---> (y - x)/(y - s) = 1/3.   The answer is (1/3).
Answer: B
In how many ways can the letters of wordTECHNOLOGYbe arranged such that all the Consonants always appear together?  Choose the correct choice from the following answers:
A) 9!
B) 4!*7!
C) 5!*5!
D) 5!*4!*2!
E) 6!*4!

Solution: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (10 letters, 3 vowels E, O, O and 7 consonant T, C, H, N, L, G, Y)   For all consonants together, consider them as 1 group {T, C, H, N, L, G, Y} E O O --> this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways   Thus total arrangements with all consonants together = 4!*7! --> 4!*7! is the correct answer.
Answer: B
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres? Pick one
A) 11 seconds	B) 88 seconds	C) 99 seconds	D) 12 seconds	E) 18 seconds

Solution: Speed of the boat downstream = 15 + 3= 
15 + 3 = 18
18 kmph= 18 * 5/18= 
18 * 5/18 = 5
5 m/s   Hence time taken to cover 60 m= 60/5= 
60/5 = 12
12 seconds.Answer: 12 seconds
Answer: D
If p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 and p(0)=48, what is p(5)	Answers:
A) 48
B) 24
C) 0
D) 50
E) 40

Solution: p(x)=ax^4+bx^3+cx^2+dx+e   it can be written as   p(x)=a*(x-1)*(x-2)*(x-3)*(x-4) ----(1)   put x=0 in(1), we get   p(0)=a*(-1)(-2)(-3)(-4)   => 48=a*24   => a=2   so, p(x)=2*(x-1)*(x-2)*(x-3)*(x-4)   => p(5)=2*(5-1)*(5-2)*(5-3)*(5-4)=2*4*3*2*1= 
2*4*3*2*1 = 48
48   p(5)= 48   48NSWER:48
Answer: A
Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 12 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Choose the correct choice from the following answers.
A) 13  B) 17  C) 18  D) 19  E) 12

Solution: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/12   => 1/x = 1/6 - 1/12 = (2 - 1)/12 = 1/12   => x = 12.   Answer: 12
Answer: E
The difference between the local value and the face value of 8 in the numeral 96348621 is Choose the correct choice from the following answers:
A) 6992
B) 6982
C) 7982
D) 7972
E) 7992

Solution: 7992xplanation:   (Local value of 8) - (Face value of 8) = (8000 - 8)= 
(8000 - 8) = 7_992
7992   7992)
Answer: E
A person earns 15% on investment but loses 10% on another investment. If the ratio of the two investments be 3:5, what is the gain or loss on the two investments taken together?  Choices.
A) 0.63 %	B) 0.64 %	C) 0.65 %	D) 0.66 %	E) None

Solution: Sol.   Suppose he invested 300 & 500 respectively profit : 15% of 300 = 45 loss =   500 *10 = 50 net loss = - 5 5/800 *100 = 0.63 %   0.63 %nswer 0.63 %
Answer: A
A room is 10 meters long, 8 meters wide 6 meters in height. The longest possible rod which can be placed in the room is
Choose the correct choice from the following answers
A) 13.12 meters B) 13.92 meters C) 13.52 meters D) 13.72 meters E) 14.14 meters

Solution: Square root of 10^2+8^2+6^2...(Diognal) which is square root of 200 that lies 14<√200<15. Hence the answer should be 14.14 meters
Answer: E
8103/x is a non-terminating decimal. Which of the following could be a value of x?	Choices:	A) 2	B) 5	C) 9	D) 12	E) 15

Solution: Then:   c. 9=3*3   d. 12=3*2*2   e. 15=3*5   The sum of digits in 8103 is 12, it means that 8103 is divisible by 3 (i.e. 3 is one of the factors of 8103), which will eliminate one "3" from x, leaving us with only 2's or 5's in options d. and e. Only c is left.   ANSWER:9
Answer: C
On a sum of money, the simple interest for 2 years is Rs. 320, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is  Choose the correct choice:
A) 15%	B) 14.25%	C) 12.5%	D) 10.5%	E) 11.5%

Solution: Explanation:   --------------------------------------------------------------------------------------   Solution 1   ---------------------------------------------------------------------------------------   Simple interest for 2 years is Rs. 320   => Simple interest for first year = 320/2= 
320/2 = 160
160=> Similarly, simple interest for second year is also 160   Compound Interest for first year = 160   Compound Interest for second year = 340-160= 
340-160 = 180
180   we can see that compound Interest for second year is more than   simple interest for second year by  180-160= 
 180-160 = 20
20   i.e., Rs.20 is the simple interest on Rs.160 for 1 year   R= 100 × SI/PT = (100 × 20)/(160 × 1) = 12.5%   --------------------------------------------------------------------------------------   Solution 2   ---------------------------------------------------------------------------------------   The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum   = (R × SI)/(2 × 100)   Difference between the compound interest and simple interest = 340 - 320= 
340 - 320 = 20
20   (R × SI)/(2 × 100)= 20   (R × 320)/(2 × 100) = 20   R = 20 × 100 × 2320 = 12.5%   Answer: Option 12.5%
Answer: C
A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose the correct choice from the following:	A) 298 m	B) 279 m	C) 500 m	D) 289 m	E) 700 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (600 + x)/60 = 65/3   x = 700 m.   Answer: 700 m
Answer: E
At the wholesale store you can buy an 8-pack of hot dogs for $1.65, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $250? Choose the correct option
A) 1,108  B) 2,100  C) 2,108  D) 2,124  E) 2,628

Solution: To maximize number of hot dogs with 250$   Total number of hot dogs bought in 250-pack = 22.95*10= 
22.95*10 = 229.5
229.5$   Amount remaining= 250 - 229.5= 
250 - 229.5 = 20.5
20.5$   Total number of hot dogs bought in 20-pack= 3.05*6= 
3.05*6 = 18.3
18.3$   Amount remaining= 20.5 - 18.3= 
20.5 - 18.3 = 2.2
2.2$   Total number of hot dogs bought in 8-pack= 1.55*1= 
1.55*1 = 1.55
1.55$   Amount remaining= 2.2 - 1.65= 
2.2 - 1.65 = 0.55
0.55$   This amount is too less to buy any 8- pack .   Greatest number of hot dogs one can buy with 250 $= 250*10+20*6+8*1= 
250*10+20*6+8*1 = 2_628
2628   Answer 2,628
Answer: E
What will be the compound interest on a sum of Rs. 27,000 after 3 years at the rate of 12% p.a.?  Choose the correct choice from the following:
A) s.10123.77  B) s.10123.21  C) s.10933.05  D) s.10123.28  E) s.10123.21

Solution: Amount = [27000 * (1 + 12/100)3]   = 27000 * 28/25 * 28/25 * 28/25   = Rs. 37933.0   C.I. = (37933.056 - 27000)   = Rs. 10933.05   Answer:s.10933.05
Answer: C
In an encryption code 'PLAYS' is written as '{:SUD' when encoded and 'SLEEP' is written as 'D:RR{' when encoded. How is ''SLAPPY" written in that encryption code?  Select the correct option
A) D:S{{U  B) SLAPPY  C) {RUDD:  D) {:SUU{  E) U{{S:D

Solution: D = S   : = L   S = D:S{{U   P = {   P = {   Y = U   Correct D:S{{Unswer: D:S{{U
Answer: A
The average of 10 consecutive integers is 25. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?	Choose the correct choice from the following options
A) 19 B) 19.5 C) 20 D) 20.5 E) 21

Solution: The total subtracted is (9+8+...+1) = (9*10) / 2= 
(9*10) / 2 = 45
45   On average, each number will be reduced by   45/10= 
  45/10 = 9/2 = around 4.5
4.5   Therefore, the overall average will be reduced by 4.5   The answer is 20.5.
Answer: D
Amber works 8 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?  Choices.
A) 8d	B) 20d	C) 10md/6	D) 20d/m	E) 20md

Solution: 8dNSWER: 8d The passage states that she works 8 days a month at d dollars per day, so 8 d is her monthly pay
Answer: A
Jimâ€™s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.3 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
Choose the correct choice from the following answers:
A) $3.15  B) $4.95  C) $4.80  D) $5.05  E) $5.40

Solution: Let the fixed charge of Jimâ€™s Taxi Service = 2.25 $   and charge per 2/5 mile(.4 mile) = .3$   Total charge for a trip of 3.6 miles = 2.25 + (3.6/.4) * .3   = 2.25 + 9*.3= 
2.25 + 9*.3 = 4.95
4.95 $   Answer $4.95
Answer: B
Mahesh can do a piece of work in 35days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work? Choose the correct choice from the following answers.
A) 45  B) 25  C) 37  D) 41  E) 70

Solution: Work done by Mahesh in 35days = 20*1/35 = 4/7   Remaining work = 1 - 4/7 = 3/7   3/7 work is done by Rajesh in 30days   Whole work will be done by Rajesh is   30*7/3= 
  30*7/3 = 70
70days   Answer is 70
Answer: E
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? Choose the correct choice from the following answers:
A) 50
B) 88
C) 77
D) 66
E) 55

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   50nswer: 50
Answer: A
The speed of the train, 150m long, is 50km/hr. How much time will it take to pass a platform 600m long? Pick.
A) 74 secs.  B) 64 secs.  C) 54 secs.  D) 44 secs.  E) 34 secs.

Solution: Distance covered = ( 150+600)= 
( 150+600) = 750
750 m Speed=50km/hr=(50*5/18)=125/9m/s Time taken =750/125*9= 
750/125*9 = 54
54 secs. Answer : 54 secs.
Answer: C
$392 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?	Choose the correct choice from the following answers:
A) $212  B) $216  C) $220  D) $224  E) $228

Solution: Let the shares for A, B, and C be x, 2x, and 4x respectively.   7x = 392   x = 56   4x = 224   The answer is $224.
Answer: D
If it takes 6 identical printing presses exactly 4 hours T to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers? Choose the most appropriate option:
A) 3 hours, 20 minutes
B) 4 hours, 20 minutes
C) 4 hours, 48 minutes
D) 5 hours, 48 minutes
E) 6 hours, 50 minutes

Solution: 6 presses - 5,000 newspapers - 4 hours ;   3 presses - 2,500 newspapers - 4 hours ;   3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = T.   Answer: 4 hours, 48 minutes.
Answer: C
The water level in a rectangular swimming pool measuring 50 feet by 25 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)	Pick one:
A) 100 B) 250 C) 750 D) 1200 E) 4687.5

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  50*25*1/2= 
 50*25*1/2 = 625
625 feet^3 of water must be removed, which equals to   625*7.5= 
  625*7.5 = 4_687.5
4687.5 gallons.   Answer: 4687.5.
Answer: E
A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? Choose the correct choice from the following answers:	A) 39:40	B) 40:39	C) 3:4	D) 4:3	E) 1:2

Solution: 3: 4   39:40 = 3/7*210= 
3/7*210 = 90
90   390: 400   39:40   39:40NSWER:39:40
Answer: A
How much water should be added to 11 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?	Choose the correct option
A) 25 liters
B) 29 liters
C) 30 liters
D) 32 liters
E) 35 liters

Solution: Let x ltr water to be added   2ltr alcohol to be represented as (20(1-3/4(new soln.=11+x)))   2=5%*(11+x)-------->x=29   Ans 29 liters
Answer: B
A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.50. If the company’s latest order required a truck with at least 240,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?	Choose the correct choice from the following:
A) $960
B) $1,875
C) $1,725
D) $2,050
E) $2,250

Solution: Number of boxes= Total volume/volume of one box= 240,000/ (8*10*12)= 250   One box costs 7.50, so 250 box will cost= 250*7.5= 
250*7.5 = 1_875
1875   $1,875 is the answer
Answer: B
The 80-milliliter solution of sugar and water is 25% sugar. How much water (in milliliters) must be added to make a solution that is 5% sugar?  Choose the correct answer
A) 300 B) 320 C) 340 D) 360 E) 380

Solution: In the original solution the amount of sugar is 0.25*80= 
0.25*80 = 20
20 ml.   Let the volume of the new solution be V.   0.05V=20 ml.   V=400 ml.   The amount of water we need to add is   400 - 80= 
  400 - 80 = 320
320 ml.   The answer is 320.
Answer: B
Consider a right triangle RBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle RBC
Choose the correct choice from the following answers
A) [A] x+y+z/3  B) [B] x-y+z/3  C) [C] x-y+z/2  D) [D] (x^2 + y^2 + z^2)/3  E) [E] cannot be determined

Solution: Radius of a circle inscribed in the right triangle RBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.   Answer: [C] x-y+z/2
Answer: C
How many words of 11letters could be Formed with all the vowels present only in the even places ,and the consonants only in the odd places,using letters of english alphabet each letter may appear only once.
Choices:  A) 21!  B) 26!/5!  C) 21! /(5! * 5! )  D) 21!* 5!/15!  E) 21!* 6!/5!

Solution: (21*20*19*18*17*16)*5! = 21! * 5! / 15!   ANSWER:21! /(5! * 5! )
Answer: C
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 14,260, Deepak's share is:?	Pick one:
A) s.8467	B) s.8428	C) s.8400	D) s.8429	E) s.8680

Solution: Ratio of their shares   = 22500 : 35000   = 9:14   Deepak's share   = 14260 * 14/23   = Rs.8680.   Answer:s.8680
Answer: E
A survey was sent to 65 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Choose the correct option: A) 2% B) 4% C) 14% D) 28% E) 63%

Solution: case 1: (7/65)=x/100   x=10%   case 2: (9/63)=y/100   y=14%   So percent increase is =(y-x)=(14-10)= 
(14-10) = 4
4%   Answer is 4%
Answer: B
What least value should be replaced by * in 842*124 so the number become divisible by 9	Choose the correct choice from the following answers: A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Explanation:   Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (8+4+2+*+1+2+4) = 21+* should be divisible by 9,   21+6 will be divisible by 9,   so that least number is 6.   Answer: Option 6
Answer: D
What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage?  Options.
A) 99.6
B) 96.2
C) 97.5
D) 98.25
E) None of these

Solution: Explanation:   Use the formula,   CP= 100 – discount + brokerage%   CP= 100-4+1/5   96.2   Thus the CP is Rs 96.2.   ANSWER 96.2
Answer: B
If 8 men or 12 women can do a piece of work in 35 days, in how many days can the same work be done by 6 men and 11 women? Choose one.
A) 10 days  B) 11 days  C) 13 days  D) 15 days  E) 21 days

Solution: 8men = 12women (i.e 2men = 3women)   12women 1 day work= 1/35   soln:   6men(9women)+ 11women=20women=?   1 women 1 day work =12*35= 1/420   so, 20 women work= 20/420=1/21   ans: 21 days   ANSW21 daysR:21 days
Answer: E
P and Q are in a relay race. P runs the first leg of the course in 3 seconds. Q runs the second leg of the course in 57 seconds. What was the average time they took to run a leg of the course?  Choose the correct choice.
A) 30
B) 32
C) 34
D) 36
E) 38

Solution: (3 seconds +57 seconds)/2= 30 seconds   Correct option is: 30
Answer: A
Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21? Select.
A) 21 B) 36 C) 39 D) 60 E) 65

Solution: The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room.   Therefore there are   3/8*96= 
  3/8*96 = 36
36 people in the room under the age of 21.   Answer: 36.
Answer: B
What is the sum of the multiples of 4 between 38 and 127 inclusive?	Choose the most appropriate option:
A) 1804
B) 1816
C) 1824
D) 1828
E) 1832

Solution: the fastest way in an AP is to find the average and multiply with total integers..   between 38 and 127, the smallest multiple of 4 is 40 and largest =124..   average=(40+124)/2=164/2=82..   total numbers = (124-40)/4 + 1= =84/4+1=27+1=22..   sum=82*22= 
82*22 = 1_804
1804   ans 1804
Answer: A
A fort had provision of food for 150 men for 45 days. After 10 days, 30 men left the fort. The number of days for which the remaining food will last, is: Choose the most appropriate option.
A) 29 1/5 B) 37 1/4 C) 43 3/4 D) 54 E) 48

Solution: After 10 days : 150 men had food for 35 days.   Suppose 120 men had food for x days.   Now, Less men, More days (Indirect Proportion)   Therefore 120 : 150 :: 35 : x <=> 120 x x = 150 x 35   => x =150 x 35/120   => x = 43 3/4.   43 3/4orrect answer is 43 3/4
Answer: C
A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?  Choose the correct choice from the following answers:
A) 2 mins 14 sec  B) 2 mins 34 sec  C) 180 sec  D) 4 mins 54 sec  E) 2 mins 44 sec

Solution: D = 25 * 60 + 1500= 
25 * 60 + 1500 = 3_000
3000 m   T= 3000/60 * 18/5= 
3000/60 * 18/5 = 180
180 sec   ANSWER:180 sec
Answer: C