MU-NLPC/Calc-aqua_rat huggingface dataset:
which of the following statement is not correct? Choose the most appropriate option.
A) log10 10 = 1 B) log(2+3)= log(2*3) C) log10 1= 0 D) log(1+2+3)= log1 + log2 + log3 E) none

Solution: a) loga a=1, so log10 10 = 1   b) log (2+3)= 
 (2+3) = 5
log 5 and log  (2*3)= 
  (2*3) = 6
log 6= log 2 + log 3   therefore log(2+3) # log (2*3)   c) since loga 1=0, so log10 1 = 0   d) log (1+2+3)= 
 (1+2+3) = 6
log 6= log(1*2*3)= log 1+log 2+log 3   e)none   Correct Answer (log(2+3)= log(2*3))
Answer: B
The difference between the length and breadth of a rectangle is 28 m. If its perimeter is 120 m, then its area is:	Choose the correct choice from the following
A) 704 m2  B) 720 m2  C) 620 m2  D) 820 m2  E) None

Solution: EXPLANATION   We have: (l â€“ b) = 28 and 2(l + b) = 120 or (l + b) = 60.   Solving the two equations, we get: l = 44 and b = 16.   Area = (l x b) = (44x 16) m2 = 704 m2.   704 m2nswer 704 m2
Answer: A
47% of the students in a class of 36 students has glasses or contacts. How many students in the class have either glasses or contacts?
Choose the correct choice from the following options.
A) 15	B) 16	C) 17	D) 18	E) 19

Solution: a=r⋅b   47%=0.47a   =0.47⋅36   a≈17   Option 17 is correct.
Answer: C
A used car dealer sold one car at a profit of 25 percent of the dealers purchase price for that car and sold another car at a loss of 20 percent of the dealers purchase price for that car. If the dealer sold each car for $20,000 , what was the dealers total profit or loss, in dollars, for the two transactions combined?	Answers:
A) 1000 profit  B) 2000 profit  C) 1000 loss  D) 2000 loss  E) 3334 loss

Solution: car 1 :   P1*1.25 = 20000   P1 = 16000   car2   P2*0.8 = 20000   P2 = 25000   P1+P2 = 41000   Final sale = 40000   1000 loss .. option 1000 loss
Answer: C
The present population of a town is 300. Population increase rate is 10% p.a. Find the population of town after 1 years?	Choose the correct choice from the following answers.
A) 100 B) 120 C) 200 D) 220 E) 330

Solution: P = 300   R = 10%   Required population of town = P*(1 + R/100)^T   = 300*(1 + 10/100)   = 300*(11/10)= 
300*(11/10) = 330
330   Answer is 330
Answer: E
A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
Select: A) 2/91 B) 3/91 C) 5/91 D) 6/91 E) 5/69

Solution: Total number of balls = 4 + 5 + 6= 
4 + 5 + 6 = 15
15   Let S be the sample space.   n(S)= Total number of ways of drawing 3 balls out of 15 = 15C3   Let E = Event of drawing 3 balls, all of them are yellow.   n(E) = Number of ways of drawing 3 balls, all of them are yellow   = Number of ways of drawing 3 balls from the total 5 = 5C3   (∵ there are 5 yellow balls in the total balls)   P(E) = n(E)/n(S)   =5C3/15C3   =5C2/15C3 [∵ nCr = nC(n - r). So 5C3 = 5C2. 2/91pplying this for the ease of calculation]   = 2/(7*13)   = 2/91   2/91nswer : Option 2/91
Answer: A
In a college the ratio of the numbers of boys to the girls is 8:5. If there are 120 girls, the total number of students in the college is?
Choose the correct choice from the following options:
A) 312  B) 356  C) 452  D) 416  E) 512

Solution: Let the number of boys and girls be 8x and 5x   Then , 5x = 120   x= 24   Total number of students = 13x = 13*24= 
13*24 = 312
312   312nswer is 312
Answer: A
A building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?  Choose the most appropriate option
A) 36 B) 55 C) 40 D) 45 E) None of these

Solution: Explanation :   54 men work 10 hours a day for 30 days and 5/9th of the work is completed.   Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work.   M1D1T1W2 = M2D2T2W1   54*30*10*4/9 = x*18*8*5/9   x = 90   Hence, 36 more workers should be employed.   36nswer : 36
Answer: A
What is the median from the below series 90, 89, 93, 88, 95, 88, 97, 87, and 98	Choose the most appropriate option.
A) 80
B) 85
C) 90
D) 97
E) 100

Solution: Ordering the data from least to greatest, we get:   87, 88, 88, 89, 90, 93, 95, 96, 98   The median quiz score was 90. (Four quiz scores were higher than 90 and four were lower.)   90
Answer: C
The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?	Choices:	A) 1: 5	B) 1: 8	C) 1: 9	D) 1: 1	E) 1: 4

Solution: r1: r2 = 1: 3   Πr12: Πr22   r12: r22 = 1: 9   Answer:1: 9
Answer: C
The average age of a husband and his wife was 29 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is : Choose the correct choice
A) 11
B) 23
C) 19
D) 287
E) 27

Solution: Explanation:   Sum of the present ages of husband, wife and child = (29 * 2 + 5 * 2) + 1= 
(29 * 2 + 5 * 2) + 1 = 69
69 years.   Required average= (69/3)= 
(69/3) = 23
23 years.   Answer: 23
Answer: B
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?  Choose the correct choice from the following
A) 7 min  B) 8 min  C) 9 min  D) 10 min  E) 12 min

Solution: Explanation:   1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   ANSWER IS 8 min
Answer: B
If 100<y<199 and 10<x<100, then the product xy CANNOT be equal to:  Choices:	A) 19,104	B) 19,303	C) 19,356.732	D) 19,910	E) 19,502

Solution: Correct Answer: (E)   Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 10. The largest value must be less than 199 * 100. This means that 1000 < xy < 19,900. (19,910) is outside of this range, so it is not a possible product of xy.
Answer: D
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Pick
A) 200 m B) 225 m C) 245 m D) 250 m E) 270 m

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   ANSWER:245 m
Answer: C
In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Select the correct option
A) 1/6	B) 2/9	C) 6/11	D) 9/16	E) 3/4

Solution: # defective pens = 3   # good pens = 9   Probability of the 1st pen being good = # of favorable outcomes / # of total outcomes = 9/12   Probability of the 2nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11   Total probability = 9/12 * 8/11 = 6/11   answer will be 6/11
Answer: C
There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have? Select:  A) 7/17  B) 5/12  C) 4/11  D) 3/10  E) 2/9

Solution: P(first stamp is different) = 5/10   P(second stamp is different) = 4/9   P(both stamps are different) = 5/10*4/9 = 2/9   The answer is 2/9.
Answer: E
The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area? Options:
A) 20%	B) 30%	C) 50%	D) 70%	E) 80%

Solution: Let original length = x and original breadth = y.   Original area = xy.   New length = x .   2   New breadth = 3y.   New area = x x 3y = 3 xy.   2 2   Increase % = 1 xy x 1 x 100 % = 50%.   2 xy   50%
Answer: C
A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Choose the correct choice from the following choices.
A) 22 1/8 days
B) 22 1/2 days
C) 22 6/2 days
D) 72 1/2 days
E) 23 1/2 days

Solution: 1/18 + 1/30 = 8/90 = 4/45   45/4 = 11 1/4 *2 = 22 1/2 days   Answer: 22 1/2 days
Answer: B
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?  Answers:
A) 6  B) 7  C) 8  D) 6  E) 4

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/5   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/5 :: 1 : x   x = (2/5 * 1 * 15)= 
(2/5 * 1 * 15) = 6
6 min.   So, the tank will be emptied in 6 min.6nswer: 6
Answer: A
How many even numbers greater than 300 can be formed with digits 1,2,3,4,5 no digit being repeated ?	Choose the correct answer
A) 111 B) 123 C) 124 D) 132 E) 145

Solution: Number can be 3, 4, or 5 digit (4 and 5 digit number will obviously be more than 300).   5 digit even numbers:   Last digit must be either 2 or 4 (for number to be even), so 2 choices. First 4 digits can be arranged in 4! # of ways. So total # of 5 digit even numbers possible is 4!∗2=484!∗2=48;   4 digit even numbers:   Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 3 digits out of 4 digits left when order of the digits matters is P34P43. So total # of 4 digit even numbers possible is P34∗2=48P43∗2=48;   3 digit even numbers:   Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 2 digits out of 4 digits left when order of the digits matters is P24P42. So total # of 3 digit even numbers possible is P24∗2=24P42∗2=24.   But out of these 24 3-digit even numbers some will be less than 300, the ones starting with 1 or 2. There are 9 such numbers (1X2 and 3 options for the second digit X, so 3 plus 1X4 and 3 options for X, so 3 plus 2X4 and 3 options for X, so 3), which means that # of 3 digit even numbers more than 300 is 24−9=1524−9=15;   So total 48+48+15=11148+48+15=111.   111NS:111
Answer: A
The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume? Options:
A) 20π	B) 24π	C) 25π	D) 96π	E) 100π

Solution: You have three options here. Approach is to calculate volumes for all of them and see which one is greatest.   1. Cylinder's base rests on a 4x5 side of the box. So, height becomes 6 and the maximum possible radius becomes 4/2.   So, maximum volume = π.(4/2)^2.6=π24   2. Cylinder's base rests on a 5x6 side of the box. So, height becomes 4 and the maximum possible radius becomes 5/2.   So, maximum volume = π.(5/2)^2.4=π25   3. Cylinder's base rests on a 4x6 side of the box. So, height becomes 5 and the maximum possible radius becomes 4/2.   So, maximum volume = π.(4/2)^2.5=π20   Option 2 gives maximum value and so that should be the answer, π25.   ANSWER:25π
Answer: C
From a pack of 52 cards,two cards are drawn at random together at random what is the probability of both the cards being kings?	Pick.
A) 1/221  B) 8/221  C) 4/589  D) 4/587  E) 7/654

Solution: let S be the sample space then   n(S)=52C2=(52*51)/(2*1)= 
(52*51)/(2*1) = 1_326
1326   let E be the event of getting 2 kings out of 4   n(E)=4C2=(4*3)/(2*1)= 
(4*3)/(2*1) = 6
6   P(E)=n(E)/n(S)=6/1326=1/221   1/221nswer (1/221)
Answer: A
Working alone, Mary can pave a driveway in 6 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 25%, but Hillary becomes distracted and her rate decreases by 20%. If they both work together, how many hours will it take to pave the driveway?  Options:
A) 3 hours B) 4 hours C) 5 hours D) 6 hours E) 7 hours

Solution: Initial working rates:   Mary = 1/6 per hour   Hillary = 1/6 per hour   Rate when working together:   Mary = 1/6+ (1/4*1/6) = 1/5 per hour   Hillary = 1/6 - (1/5*1/6) = 2/15 per hour   Together they work 1/5 + 2/15 = 1/3 per hour   So they will need 3 hours to complete the driveway. The correct answer is 3 hours.
Answer: A
A dishonest fruit seller professes to sell his goods at the cost price but weighs 800 grams for a kg weight. Find his gain percent.	Answers:
A) 100%  B) 150%  C) 50%  D) 200%  E) None of these

Solution: He gives 800 grams but charges the price of 1000 grams (1 kg) ⇒ on every 800 grams, he gains (1000 – 800) grams i.e. 200 grams.   ∴ His gain % = 200⁄800 × 100% = 25%   Short cut : Gain % = error/true weight−error=100%   100%nswer 100%
Answer: A
The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is ?
Select the correct option
A) 4328
B) 4322
C) 4320
D) 4332
E) 4333

Solution: x Not younger_______ ↑   The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.   The required number of ways   = 6(6!)   = 4320   Answer: 4320
Answer: C
If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 10800 ?	Choose the correct choice from the following answers.
A) 11	B) 13	C) 14	D) 18	E) 10

Solution: Required difference = [3 ½ % of Rs.10800] – [3 1/3 % of Rs.10800]   = [(7/20-(10/3)]% of Rs.10800 =1/6 % of Rs.10800   = Rs. [(1/6)8(1/100)*10800] = Rs. 18.   Answer is 18.
Answer: D
Jake and Kay drive at constant speeds toward each other on a highway. Jake drives at a constant speed of 29 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Jake is 155 km away from Kay at 6 am, and also 155 km away from Kay at 11 am, then how fast is Kay driving (in kilometers per hour)?	Choices.
A) 29 B) 30 C) 31 D) 32 E) 33

Solution: Jake and Kay complete 310 km / 5 hours = 62 km/hour   Kay's speed is  62-29= 
 62-29 = 33
33 km/hour   The answer is 33.
Answer: E
In a mixture there is ratio of alcohol and water is 4:3.if in this mixture we will add 3litre of water.then ratio become 4:5.then calculate the amount of alcohol?
Choose the correct choice from the following answers
A) 4 B) 5 C) 6 D) 8 E) 9

Solution: Let in mixture alcohol=4x litre,and water=3x litre   4x/3x+3=4/5   X=1.5   Amount of alcohol=(4×1.5)=6 litre   Answer 6
Answer: C
If a farmer wants to plough a farm field on time, he must plough 100 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?  Choose the most appropriate option:	A) 600	B) 490	C) 720	D) 1400	E) 1679

Solution: Let x be the number of days in the initial plan. Therefore, the whole field is 100â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:   100x=85(x+2)+40   15x=210   x=14   So the farmer planned to have the work done in 6 days, and the area of the farm field is 100(14)=1400 hectares   correct answer 1400
Answer: D
Which of the following statements is definitely false, if M is the sister of N and O. T is M's son and U is M's daughter? Choices:
A) N is T's uncle B) O is T's uncle C) N is U's brother D) N is M's brother E) O is M's uncle

Solution: Explanation:   All the statements are true except C (N is U's brother), U is M's daughter that makes N her uncle, not brother.   Answer: N is U's brother) Q is T's son
Answer: C
If x is a positive integer with fewer than 3 digits, what is the probability R that x*(x + 1) is a multiple of either 4 or 5?
Choose the correct choice from the following answers:
A) 4/99  B) 2/25  C) 8/99  D) 49/100  E) 86/99

Solution: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.   We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability R that x(x+1) is a multiple of either 4 or 5.   When will this happen? If either x OR (x+1) is a multiple of 4 or 5.   Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.   Out of the numbers from 1 to 20:   4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20   So, 14 out of the first 20 numbers match our criteria. Since:   probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (86/99) is the only answer greater than 1/2, we go with (86/99).
Answer: E
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 26 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the correct choice from the following.
A) 457 km	B) 444 km	C) 547 km	D) 564 km	E) 453 km

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 26 + 21= 
26 + 21 = 47
47   T= 12   564 km = 47 * 12= 
47 * 12 = 564
564   Answer:564 km
Answer: D
If a = -0.5, which of the following is true?	Answers
A) a < a^3 < a^2  B) a < a^2 < a^3  C) a^2 < a < a^3  D) a^3 < a < a^2  E) a^2 < a^3 < a

Solution: a=-0.5;   a^2=0.25;   a^3=-0.125;   a < a^3 < a^2nswer : a < a^3 < a^2
Answer: A
A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares?
Choose one
A) 600,400	B) 500,500	C) 300,700	D) 800,1200	E) 550,1450

Solution: Ratio of their works A:B = 6:4   Ratio of their wages A:B = 2:3   A's share = (2/5)2000 = 800   B's share = (3/5)2000 = 1200   correct option is 800,1200
Answer: D
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter? Choose the correct option:
A) 91.5 cm
B) 91.6 cm
C) 97.5 cm
D) 51.5 cm
E) 91.2 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5 cmnswer: 91.5 cm
Answer: A
In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite direction at 15 m/s. When will all the three meet for the first time on the track after the start?	Choose the correct choice
A) After 4 s B) After 50 s C) After 100 s D) After 200 s E) None of these

Solution: A takes (100m) / (10m/s) = 10s to finish one complete round.   B takes (100m) / (8m/s) = 12.5s to finish one complete round.   C takes (100m) / (15m/s) = (20/3)s to finish one complete round.   For them to meet, the time will be LAfter 100 sM of above three times i.e,   LAfter 100 sM(10,12.5,20/3) = LAfter 100 sM(10,25,20)/GAfter 100 sD(1,2,3)=100/1= 
100/1 = 100
100sec   ANSWER:After 100 s
Answer: C
Lakshmi invested some money in 15% stock at 200.If Latha wants to invest in an equally good 30% stock ,he must purchase a stock worth of :  Choose the correct choice from the following choices:
A) Rs. 300	B) Rs. 200	C) Rs. 450	D) Rs. 500	E) Rs. 400

Solution: Solution   For an income of Rs. 15, investment = Rs. 200   For an income of Rs. 30, investment = Rs.(200/15x30) = Rs. 400   Answer Rs. 400
Answer: E
Two pipes A and B can separately fill a tank in 20 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? Choose the correct option:
A) 12min  B) 14min  C) 15min  D) 13min  E) 10min

Solution: 4/20 + x/15 = 1   x = 12   12minNSWER:12min
Answer: A
The average weekly salary per head of the entire staff
of a factory consisting of supervisors and the laborers
is Rs 60.The average salary per head of the supervisors
is Rs 400 and that of the laborers is Rs 56.Given that
the number of supervisors is 12.Find the number of
laborers in the factory
Choose the correct choice from the following answers: A) 1000 B) 1010 C) 1020 D) 1030 E) 1040

Solution: Average salary of laborerRs 56 Average salary of supervisors Rs 400   Average salary of entire staff Rs 60   340 4   Number of laborer / Number of Supervisors = 340 / 4= 
340 / 4 = 85
85/1   Thus,if the number of supervisors is 1,number of laborers=85.   Therefore if the number of supervisors is 12 number of laborers    85*12= 
 85*12 = 1_020
1020.   ANSWER 1020
Answer: C
Reduce
368/600
to the lowest terms Choose the most appropriate option
A) 30/25  B) 28/25  C) 28/29  D) 46/75  E) None of these

Solution: Explanation:   We can do it easily by in two steps   Step1: We get the HCF of 368 and 600 which is 8   Step2: 46/75ivide both by 8, we will get the answer 46/75   Answer: Option 46/75
Answer: D
Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?  Choose the correct choice from the following options:
A) $600  B) $1000  C) $3800  D) $5300  E) $6200

Solution: Pay out for plan A: Cost-$1,000 or Cost-0.5*Cost=0.5*Cost, when 0.5*Cost<$1,000;   Pay out for plan B: 0.8(Cost-$300);   The question is: for which of the following costs the pay outs are the same.   C-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer.   Or you can use backsolving for this question:   A. C=$600: pay out for plan A will be   0.5*600= 
  0.5*600 = 300
300 (as 0.5*600<1,000) and pay out for plan B will be   0.8*(600-300)= 
  0.8*(600-300) = 240
240;   B. C=$1000: pay out for plan A will be 0.5*1,00=500 (as 0.5*1,000<1,000) and pay out for plan B will be 0.8*(1,000-300)=560;   C. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.5*3,800>1,000) and pay out for plan B will be 0.8*(3,800-300)=2,800 --> 2,800=2,800;   D. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.5*5,300>1,000) and pay out for plan B will be 0.8*(5,300-300)=4,000;   E. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.5*6,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720.   Answer: $3800.
Answer: C
An assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?  Choose one:  A) 38  B) 40  C) 42  D) 45  E) 50

Solution: The time to produce the first 60 cogs is 60/36 = 5/3 hours.   The time to produce the next 60 cogs is 60/60= 
60/60 = 1
1 hour.   The average output is 120 cogs / (8/3) hours= 45 cogs per hour.   The answer is 45.
Answer: D
Two trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is?  Answers.
A) 22
B) 98
C) 60
D) 40
E) 12

Solution: Let the speed of the slower train be x m/sec.   Then, speed of the train = 2x m/sec.   Relative speed = ( x + 2x) = 3x m/sec.   (100 + 100)/12 = 3x => x = 50/9.   So, speed of the faster train = 100/9 = 100/9 * 18/5= 
100/9 * 18/5 = 40
40 km/hr.   Answer:40
Answer: D
Square A has an area of 81 square centimeters. Square B has a perimeter of 32 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? Options
A) 17/64 B) 17/81 C) 16/25 D) 3/5 E) 6/25

Solution: I guess it's mean that square B is placed within square Aentirely.   Since, the perimeter of B is 32, then its side is 32/4= 
32/4 = 8
8 and the area is 4^2=64;   Empty space between the squares is 81-64= 
81-64 = 17
17 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=17/81.   Answer: 17/81
Answer: B