MU-NLPC/Calc-aqua_rat huggingface dataset:
A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? Choices:
A) 81 km/hr	B) 88 km/hr	C) 62 km/hr	D) 46 km/hr	E) 34 km/hr

Solution: Explanation:   Let x is the length of the train in meter and y is its speed in kmph   x/8.4 = (y-4.5)(10/36) ---(1)   x/8.5 = (y-5.4)(10/36) ---(2)   Dividing 1 by 2   8.5/8.4 = (y-4.5)/ (y-5.4)   => 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4   .1y = 8.5×5.4 - 8.4×4.5   => .1y = 45.9-37.8= 
45.9-37.8 = 8.1
8.1=> y = 81 km/hr   81 km/hrnswer: Option 81 km/hr
Answer: A
Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: Pick one:  A) three times as much  B) twice as much  C) the same  D) half as much  E) a third as much

Solution: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.   We know that   Speed = Distance/Time.   Or, Time = Distance/Speed.   So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.   And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.   = 100/x hr.   So we can clearly see that his new time compared with the old time was: twice as much.   correct answer twice as much
Answer: B
There are 32 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?	Choose the correct choice from the following:
A) 1800	B) 1820	C) 1150	D) 1122	E) 1900

Solution: The total number of stations= 34   From 34 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 34P2 ways.   34P2= 34*33= 
34*33 = 1_122
1122   ANSWER:1122
Answer: D
There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?	Select the correct option.
A) 110	B) 100	C) 120	D) 140	E) 150

Solution: Let the number of persons in building P = p   and the number of persons in building Q = q   If 15 persons are sent from P to Q,   then the number of persons in each building is the same   => p-15 = q+15   => p - q = 30 ----(Equation 1)   If 20 persons are sent from Q to P,   then the number of persons in P is double the number of persons in Q   => 2(q - 20) = (p + 20)   => 2q - 40 = p + 20   => 2q - p = 60 ----(Equation 2)   (Equation 1) + (Equation 2)=> q = 90   From Equation 1, p = 30 + q = 30 + 90= 
30 + 90 = 120
120   i.e., Building P has 120 persons   Answer is 120.
Answer: C
In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes W of the competition are possible?
Choose the correct choice from the following options.
A) 18
B) 20
C) 54
D) 84
E) 120

Solution: the ways the three teams can be selected is..   i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..   ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60   total W=84 outcomes   84
Answer: D
A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.	Pick
A) $180000  B) $280000  C) $380000  D) $480000  E) None

Solution: Solution:   The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.   In general for independent activities   [1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount   [1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000   [1 – 9/10] × Total salary = $18000   Therefore total salary = $18000 × 10 = $180000   $180000nswer $180000
Answer: A
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? Choose the correct choice:
A) 3
B) 5
C) 6
D) 7
E) 9

Solution: M = 4   S = 2   US = 4 - 2= 
4 - 2 = 2
2   D= 6   T = 6/2= 
6/2 = 3
3   3nswer:3
Answer: A
Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and twice the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?	Choices:
A) (16/3)b  B) (17/4)b  C) (13/4)b  D) (9/2)b  E) (7/12)b

Solution: Step 1: Categorize the problem   This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.   Step 2: Think like the test maker   What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.   Step 3: Solve the problem   b = Bradley’s total   3b = Andrew’s total   (1/2)b = Charlie’s total   Add each total   b + 3b+ (1/2)b = 4b + (1/2)b = (16/4)b + (1/2)b = (9/2)b   Therefore,choose (9/2)b.
Answer: D
If a - b = 2 and a2 + b2 = 25, find the value of ab.	Pick one.
A) A)10.5  B) B)12  C) C)15  D) D)18  E) E)20

Solution: Explanation:   2ab = (a2 + b2) - (a - b)2   = 25 - 4= 
25 - 4 = 21
21   ab=10.5   10.5nswer: 10.5
Answer: A
3, 7, 15, 31, 63, ? Options:
A) 125  B) 112  C) 153  D) 173  E) 127

Solution: 127   127   127ach number in the series is the preceding number multiplied by 2 and then increased by 1.
Answer: E
If the complement of a certain angle is two times the measure of that certain angle, then what is the measure of that certain angle?  Select the correct option.
A) 45°  B) 30°  C) 22.5°  D) 18°  E) 15°

Solution: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is 2x, and together, these add up to 90 degrees.   x + 2x = 90   3x = 90   x = 30°   Answer = (30°)
Answer: B
If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in  Pick:
A) 2 days  B) 1 day  C) 3 days  D) 5 days  E) 7 days

Solution: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.   1 day)
Answer: B
If the sum of 1/3 and 22/99 is converted to a decimal, what is the 3000th digit to the right of the decimal place?
Options:  A) 2  B) 3  C) 5  D) 8  E) 9

Solution: 1/3 +22/99 = 5/9=0.555555555...   hence, the 3000th digit would also be 5   Ans: 5
Answer: C
Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?  Choose the most appropriate option.
A) 1/11 B) 2/13 C) 4/13 D) 3/17 E) 3/19

Solution: Here, n(S) = 52   There are 13 cards of diamond (including one king) and there are 3 more kings.   Let E = event of getting a diamond or a king.   Then, n(E) = (13 + 3)= 
(13 + 3) = 16
16   P (E)= 16 / 52 = 4/13   4/13
Answer: C
If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy? Select the correct option:
A) -16  B) -10  C) 0  D) 14  E) 16

Solution: (x+1)^2 <= 16   x <= 3   x >= -5   (y-1)^2< 64   y < 9   y > -7   Max possible value of xy is -5 × -6 = 30   minimum possible value of xy is -5 × 8 = -40   -40 + 30 = -10   Answer : -10
Answer: B
If points A and B are (10-5) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB Choose the correct answer:
A) I only
B) II only
C) III only
D) I and II only
E) I and III only

Solution: I. The area of a square region with side AB --> side=AB=(10-5) or 5 --> the area of a square is 5^2=25, so only one possible value;   II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;   III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).   I onlynswer: I only.
Answer: A
The banker's discount on a sum of money for 1 1/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:  Choices
A) 10% B) 13% C) 12% D) 15% E) 11%

Solution: B.D. for 3/2 years	= Rs. 558.   B.D. for 2 years   = Rs.(558 x 2/3 x 2)   = Rs. 744   T.D. for 2 years = Rs. 600.   Therefore, Sum = B.D. x T.D./B.D. - T.D   = Rs. (744 x 600/144	)= Rs. 3100.   Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.   Therefore, Rate =(100 x 744/3100 x 2)%   = 12%   Answer is 12%
Answer: C
If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?	Choose one
A) 90
B) 100
C) 110
D) 120
E) 130

Solution: The projectiles travel a total of 999 km per hour.   The time to meet is   1998/999= 
  1998/999 = 2
2 hours= 120 minutes   The answer is 120.
Answer: D
A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? Choose the correct choice from the following choices
A) 525.  B) 412.  C) 432.  D) 502.  E) 522.

Solution: Pastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35   Only option 525. satisfies the condition, and hence is the answer
Answer: A
Worker A takes 8 hours to do a job. Worker B takes 6 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Choices
A) 20/9 B) 40/9 C) 50/9 D) 24/7 E) 80/9

Solution: one day work of A = 1/8   one day work of B = 1/6   so one day work of A and B together = 1/8 + 1/6 = 7/24   so total days required = 24/7   ANSWER:24/7
Answer: D
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?	Choices
A) Rs. 10000	B) Rs. 5896	C) Rs. 2580	D) Rs. 3697	E) Rs. 60000

Solution: Explanation:   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,   1/3x=1/2(150000-x)   x/3+x/2=75000   x=75000*6/5= 
75000*6/5 = 90_000
90000   Savings in Public Provident Fund= Rs.(150000-90000)=Rs. 60000   Answer:Rs. 60000
Answer: E
If the average (arithmetic mean) of (2a+16) and (3a-8) is 84, what is the value of a?	Pick one
A) 25 B) 30 C) 28 D) 32 E) 42

Solution: ((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 84   a= 32   The answer is 32.
Answer: D
Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Choose one: A) 20*(sqr2 -1) B) 8*(sqr3 -1) C) 4*(sqr7 - 1) D) 12* (sqr7 -1) E) None of these

Solution: I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1).   20*(sqr2 -1)nswer 20*(sqr2 -1)
Answer: A
If k^3 is divisible by 120, what is the least possible value of integer k?
Select the correct option:
A) 12	B) 30	C) 60	D) 90	E) 120

Solution: 120 = 2^3*3*5   Therefore k must include at least  2 * 3 * 5= 
 2 * 3 * 5 = 30
30.   The answer is 30.
Answer: B
x is the product of each integer from 1 to 25, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Choose the correct choice from the following choices
A) 5	B) 4	C) 3	D) 6	E) 7

Solution: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:   n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n   x = 1*2*3....*25 = 25!   No. of trailing zeros in 25! = 25/5 + 25/5^2 = 6   100^k = 10^2k → k = 6/2= 
6/2 = 3
3   3
Answer: C
If n is a positive integer, which of the following expressions must be even? Pick one:	A) (n − 1)( n + 1)	B) (n − 4)( n + 1)	C) (n − 2)( n + 6)	D) (n − 5)( n + 1)	E) (n − 3)( n + 3)

Solution: Whether n is even or odd, (n-4)(n+1) will have one odd factor and one even factor.   The product will be even.   The answer is (n − 4)( n + 1).
Answer: B
30 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 3:4?  Choose the correct choice from the following answers
A) 8
B) 10
C) 12
D) 14
E) 16

Solution: Let x be the amount of liquid Q to be added.   (2/5)*30 + x = (4/7)*(30+x)   420 + 35x = 600 + 20x   15x = 180   x = 12   The answer is 12.
Answer: C
The speed at which a man can row a boat in still water is 21 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 90 metres?	Choose the correct choice from the following answers
A) 23.46 B) 27.46 C) 28.46 D) 12.46 E) 25.46

Solution: Speed of the boat downstream = 21 + 5= 
21 + 5 = 26
26 kmph= 26 * 5/18 = 7.22 m/sHence time taken to cover 90 m = 90/7.22= 12.46 seconds.Answer:12.46
Answer: D
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.28 at the candy store. What is John’s weekly allowance?	Choose the correct answer:
A) $2.40
B) $3.00
C) $3.20
D) $3.60
E) $4.80

Solution: Total allowance=X   Amount spent at the arcade=3/5X   Amount Remaining=2/5X   Amount Spent at the toy store=2/5*1/3X=2/15X   Amount Remaining=2/5X-2/15X=4/15X   Now, 4/15X=$1.28   Therefore, X=$4.80. Answer $4.80
Answer: E
The simple interest at z% for z years will be $z on a sum of  Choose the correct choice
A) $ (1000)/z B) $(100)z^2 C) $ z D) $ (100)/z E) $ 100z

Solution: Principal =$(100*z)/(z*z)=$(100/z).   Answer is $ (100)/z
Answer: D
The ratio of two quantities is 3 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities? Choose one.
A) It cannot be determined from the information given.	B) 5/9	C) 12/13	D) 15/14	E) 16/14

Solution: let the actual ratio be 3k/5k, increase numerator and denominator by 6 => 3k+6/5k+6   Until the value of k is unknown we can not determine the actual ratio.   OR   let the actual be 3/4. After increasing 6 => 9/10   let the actual be 6/8. After increasing 6 => 12/14   Therefore without actual quantities we cannot determine the actual ratio.   It cannot be determined from the information given.nswer : It cannot be determined from the information given.
Answer: A
A box contains 4 red chips and 4 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
Pick one: A) 1/2 B) 4/7 C) 7/12 D) 2/3 E) 7/10

Solution: Total selection ways: 8C2=8!/4!4!=28   Selecting one blue chip out of two: 4C1=4!/1!3!=4   Selecting one red chip out of four: 4C1=4!/1!3!=4   Thus, (4C1*4C1)/8C2=(4*4)/28=16/28=4/7=4/7
Answer: B
For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2? Choose the correct answer
A) 12.6.
B) 14.4.
C) 15.8.
D) 16.2.
E) 16.4.

Solution: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2   = 6*0 + 2*7.2 + 8 - 6.2   = 0 +14.4 +1.8   16.2   Answer 16.2.
Answer: D
the price of a commodity(in rupees per kilogram) is 100+0.1n, on the nthvday of 2007(n=1,2,,,,,100), and then remains constant. On the other hand, the price of another commodity is 89+0.15n on the nth day of 2007(n=1,2,,,,,,365). On which date in 2007, will the price of these twocommodities be equal???? Choose the correct choice from the following options:
A) 11th may
B) 12th may
C) 20th may
D) 22th may
E) 24th may

Solution: price of both the commodity cannot be same within 100days( by puttng n=100 in both the price)   price of 1st commodity after 100 days =100+0.1*100= 
100+0.1*100 = 110
110   day on which 2nd commodity becomes equal to 1st= 89+0.15n=110   n=140   140th day of 2007 is 20th may   ANSWER:20th may
Answer: C
At 3.40, the hour hand and the minute hand of a clock form an angle of Choose the correct choice:  A) 120°  B) 125°  C) 130°  D) 135°  E) None

Solution: Solution   Angle traced by hour hand in 17/2 hrs	= (360/12x17/2 )°   = 255.   Angle traced by min hand in 30 min	= (360/60x30)°   = 180.   Required angle	= (255 - 180)= 
(255 - 180) = 75
75°   Answer 125°
Answer: B
The average age of 15 students of a class is 14 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?  Choose the correct choice from the following answers.
A) 3years
B) 4years
C) 5years
D) 6years
E) 7years

Solution: Age of the 15th student   =[15 * 14 - (14 * 5 + 16 * 9)]   = (210 - 214) = 4 years.   Answer:4years
Answer: B
A train is 320 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Choose the correct choice:
A) 11 seconds  B) 38 seconds  C) 40 seconds  D) 88 seconds  E) 36.8 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 320+140= 
320+140 = 460
460 meter   Time= Distance/speed   = 460 * (2/25)= 
460 * (2/25) = 184/5 = around 36.8
36.8 seconds   Answer: 36.8 seconds
Answer: E
The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is? Choose the correct choice from the following options:
A) 11 years B) 16 years C) 33 years D) 14 years E) 18 years

Solution: Age of the 15th student   =[15 * 15 - (14 * 5 + 16 * 9)]   = (225 - 214)= 
(225 - 214) = 11
11 years.   11 yearsnswer:11 years
Answer: A
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Select:
A) 3 : 1
B) 1 : 3
C) 1 : 2
D) 2 : 1
E) None of these

Solution: Explanation :   Let speed upstream = x   Then, speed downstream = 2x   Speed in still water = (2x + x)/2 = 3x/2   Speed of the stream = (2x − x)/2 = x/2   Speed in still water : Speed of the stream = (3x/2) (2x/2) = 3 : 1. 3 : 1nswer : Option 3 : 1
Answer: A
Two numbers are in the ratio of 1 : 2. If 6 be added to both, their ratio changes to 3 : 5. The greater number is Choose the correct choice:  A) 20  B) 24  C) 28  D) 32  E) 36

Solution: Let the ratio be X : Y,   Given X/Y = 1/2 ,   (X + 6)/(Y + 6) = 3/5   => X = 12   And Y = 24   ANSWER:24
Answer: B
On flipping 3 coins together what is the outcomes for at least two tail? Choose the correct choice from the following: A) 1/7 B) 3/8 C) 3/11 D) 4/13 E) 5/13

Solution: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}   Favorable outcomes for at least two heads   = favorable outcomes for exactly two heads and favorable outcomes for more than two heads   = {TTH, HTT, TTT}   3/8   3/8
Answer: B
If x is 20 percent more than y and y is 60 percent less than z, then x is what percent of z?  Choose one
A) 500%	B) 48%	C) 500/3%	D) 125%	E) 60%

Solution: Z = 100 ; Y = 40 so X = 48   X as % of Z = 48/100 * 100= 
48/100 * 100 = 48
> 48%   Answer will be (48%)
Answer: B
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
Choose the correct choice from the following answers:
A) 500
B) 277
C) 222
D) 297
E) 111

Solution: Explanation:   110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (110 * 560)/112 = Rs. 500   500nswer:500
Answer: A
A ladder 18 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 6 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?
Choose the correct option.
A) 12.5 B) 15 C) 18 D) 19 E) 25

Solution: 18^2-6^2=288   it means that the height is equal to 16.9.   since the top of the ladder slips down 4 feet, then the height of the wall =16.9-4= 
16.9-4 = 12.9
12.9   the bottom=sqrt(18^2-12.9^2)=sqrt(324-166.41)=12.5   ans is 12.5
Answer: A
For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal?  Select the correct option.
A) 4% B) 5% C) 8% D) 10% E) 12%

Solution: Expected minimum rating = 8   Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4   Current rating is 0.4 less than 8.   Percentage = (0.4/8)*100= 
(0.4/8)*100 = 5
5%   Answer: 5%
Answer: B
he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person ?	Choose the most appropriate option
A) 75 kg	B) 95 kg	C) 45 kg	D) 85 kg	E) 25 kg

Solution: Explanation:   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (75 + 20)= 
(75 + 20) = 95
95 kg.   Answer: 95 kg
Answer: B
The value of x is to be randomly selected from the integers from 1 to 11, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?	Choose the correct choice from the following answers:
A) 5/11  B) 4/11  C) 3/11  D) 2/11  E) 1/11

Solution: y will only be negative for x=2.   (We can check the values from 1 to 11 to be certain.)   P(y is negative) = 1/11   The answer is 1/11.
Answer: E
A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Choose the correct choice from the following choices:
A) 287m	B) 278m	C) 400m	D) 228m	E) 282m

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 42   = 50/3   3(x + 300)   = 2100 è x   = 400m.   Answer:400m
Answer: C
Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to
Pick one
A) 40
B) 80
C) 95
D) 100
E) 120

Solution: Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively.   Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95.   95
Answer: C
One night 40 percent of the female officers on a police force were on duty. If 240 officers were on duty that night and half of these were female officers, how many female officers were on the police force?  Choices
A) 90 B) 300 C) 270 D) 500 E) 1,000

Solution: Let total number of female officers in the police force = F   Total number of officers on duty on that night = 240   Number of female officers on duty on that night = 240/2= 
240/2 = 120
120   (40/100)*F= 120   =>F = 300   Answer 300
Answer: B