MU-NLPC/Calc-aqua_rat huggingface dataset:
If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio W of the resistors’ sum of A and C to the resistors’ sum of A and B? Choose the most appropriate option
A) 2(R1+R2):(R1+2R2)  B) (R1+R2):(R1+2R2)  C) (2R1+R2):(R1+2R2)  D) 2(R1+R2):(2R1+R2)  E) 2(R1-R2):(R1+2R2)

Solution: two resistors A (r1) and B (r2).   total or sum of two resistors appear as   r1r2/r1+r2. It is looks like inversion of sum of rates.   1/r1+1/r2= r1+r2/r1r2.   same way sum of A(r1) and c(2r2)=1/r1+1/2r2   =2r2+r1/r12r2.   inversion rate = r12r2/2r2+r1.   ratio W of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2   =2(r1+r2)/2r2+r1.2(R1+R2):(R1+2R2)
Answer: A
A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 50 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne? Pick:
A) 1 hour
B) 1 hour 20 minutes
C) 2 hours 30 minutes
D) 1 hour 40 minutes
E) 2 hours 10 minutes

Solution: v1 and V2 are speeds.   v1.t /50 = v2   v2.t/40 = v1   v1/v2 = 5/4   which train A would 50. 4/5 mins to cover the same distance     40 + 40= 
  40 + 40 = 80
80 mins (ANS 1 hour 20 minutes)
Answer: B
A train of 24 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? Choices:	A) 5 mins	B) 3 mins	C) 7 mins	D) 9 mins	E) 2 mins

Solution: D = 25 * 60 + 1500= 
25 * 60 + 1500 = 3_000
3000 m   T= 3000/60 * 18/5= 
3000/60 * 18/5 = 180
180 sec= 3 mins   Answer: 3 mins
Answer: B
The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 4 per metre approximately Choose the most appropriate option: A) 4457 B) 4567 C) 5943 D) 4547 E) 4675

Solution: Explanation:   Area = (17.56 x 10000) m2= 175600 m2.   ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.   Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.   Cost of fencing = Rs. (1485.78 x 4) = Rs. 5943.   Answer: Option 5943
Answer: C
If n is a natural number, then (6n2 + 6n) is always divisible by:
Choose the correct choice from the following answers: A) Both 6 and 12 B) 6 only C) 12 only D) None of these E) Cannot be determined

Solution: Explanation :   6n2 + 6n = 6n(n + 1)   Hence 6n2 + 6n is always divisible by 6 and 12 (∵ remember that n(n + 1) is always even) Both 6 and 12nswer : Option Both 6 and 12
Answer: A
A train 150 m long is running at a speed of 62 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train? Choose the most appropriate option.
A) 5 sec
B) 10 sec
C) 12 sec
D) 18 sec
E) 15 sec

Solution: Answer : B.   Speed of the train relative to man = (62 - 8) kmph   = (54* 5/18) m/sec = 15m/sec   Time taken by the train to cross the man   = Time taken by It to cover 150 m at 15 m / sec = 150 *1/ 15= 
150 *1/ 15 = 10
10sec
Answer: B
There are how many hours between x minutes past 12 noon and 8:10 p.m. of the same day, where x < 60? Pick
A) (490-x)/60 B) (480-x)/60 C) (470-x)/60 D) 60 (60 – x + 7) E) 60 (60 – x + 17)

Solution: Let's just say that X is equal to 10 so we will have that the number of hours will be 8, this is our target value. Now plug 10 in the answer choices to see which gives 8.   (490-x)/60 is correct here.
Answer: A
P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work? Choose one
A) 16	B) 88	C) 29	D) 14	E) 12

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.   Hence, P can do the work in 16 days. 16nswer: 16
Answer: A
If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 60 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?	Choose the correct choice from the following answers.
A) 100	B) 120	C) 140	D) 150	E) 160

Solution: Case 1:   let rate = R, Time = T, and Distance =D   so D=RT   Case 2:   (D+60)=(R+5)(T+1)   Case 3:   (D+X)=(R+10)(T+2)   X=120   Ans 120
Answer: B
A BISCUIT manufacturer produces 300 units of a certain model each month at a cost to the manufacturer of £30 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs) on the sales of these units will be at least £30,000?	Choose the correct choice from the following options.
A) 110	B) 330	C) 220	D) 440	E) 550

Solution: 300(x-30)≥30,000   x-30≥300   x≥330   Answer: Option 330
Answer: B
210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? Pick: A) 25 B) 40 C) 50 D) 60 E) 75

Solution: 120 = 60(Mac) + x(Window) + 20(both) => x=40   ANSWER:40
Answer: B
Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, if Magnabulk charges m dollars for each crate? Choices:  A) 100bd/m  B) 100m/(bd)  C) bd/(100m)  D) m/(bd)  E) bd/m

Solution: crate has = bd magnates   C crate cost = m dollars = 100 m cents   each magnate cost for each crate = m / bd   Ans; m/(bd)
Answer: D
The overall age of X and Y is 12 year greater than the overall age of Y and Z. Z is how many decades younger that X?
Choose the correct choice from the following options
A) 11  B) 15  C) 12  D) 17  E) 19

Solution: 12   12   (X + Y) – (Y + Z) = 12   X – Z = 12
Answer: C
In the formula V = (4r)^2, if r is halved, then V is multiplied by	Choose the correct choice from the following options: A) 64 B) 8 C) 1/4 D) 1/8 E) 1/64

Solution: Say r=2 => V1 = 16   when r=1; V2 = 4   V2 = 1/4*V1.   Answer : 1/4
Answer: C
An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired? Choose the correct choice.
A) 0.6976	B) 0.7013	C) 0.789	D) 0.8356	E) 0.8666

Solution: Required probability:   =(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976=0.6976   Edit: Thank you Vaibhav for providing an alternative method.   0.6976lternate Method:   probability that the plane is hit when all the four shots are fired,   P=1−probability of not hitting the targetP=1−probability of not hitting the target   =1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)   =1−0.3024=1−0.3024   =0.6976   0.6976
Answer: A
Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose? Select the correct option:
A) 3/140
B) 1/280
C) 27/280
D) 3/35
E) 7/56

Solution: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.   Answer: 27/280
Answer: C
From a group of 3 MEN and 3 WOMEN, 4 ADULTS are to be randomly selected. What is the probability that equal numbers of men and women will be selected? Choose the correct choice from the following answers:  A) 1/5  B) 2/5  C) 3/5  D) 4/5  E) 1

Solution: Using the first example, here is the probability of THAT EXACT sequence occurring:   MMWW = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10   Each of the other 5 options will yield the exact SAME probability....   eg   MWMW = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10   So we have 6 different options that each produce a 1/10 chance of occurring.   6(1/10) = 6/10 = 3/5   Final Answer:   3/5
Answer: C
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get ?	Choose the correct answer:
A) 57% B) 60% C) 65% D) 90% E) None of these

Solution: Solution   Total number of votes polled= (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400.   ∴ Required percentage= ( 11628/20400x 100)%= 57%   57%nswer 57%
Answer: A
Find the area of a parallelogram with base 28 cm and height 32 cm.
Answers
A) 200	B) 384	C) 345	D) 244	E) 896

Solution: Area of a parallelogram = base * height = 28 * 32= 
28 * 32 = 896
896 cm2   Answer: Option 896
Answer: E
At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 400-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
Choose the correct choice from the following options
A) 1,108  B) 3,300  C) 2,108  D) 2,124  E) 2,256

Solution: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.   Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 400 for $22.95.   For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 400x8 = 3200 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 3300 hot dogs.   2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 3300 (ANSWER 3,300)
Answer: B
A bike covers a certain distance at the speed of 62km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?	Choose the correct choice from the following answers
A) 85 km/h  B) 82.66 km/h  C) 87.67 km/h  D) 90.25 km/h  E) 90.64 km/h

Solution: Ans.(B)   Sol. Total distance = 62 × 8 = 496 km   Now speed = 496/6 = 82.66 km/h
Answer: B
A restaurant meal cost $75 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between	Choose the correct choice from the following answers:
A) $75 and $80	B) $85 and $90	C) $83 and $87	D) $82 and $87	E) $81 and $87

Solution: Hence it will be between 75 * (1+10/100) and 75 * (1+15/100).   i.e b/w 82.5 and 86.25. Hence the answer $81 and $87 (b/w 81 and 87).
Answer: E
Cindy paddles her kayak upstream at c kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip? Choose the most appropriate option
A) cnp B) cn/p C) (c + n)/p D) cnp/(c + n) E) pm/n- pn/m

Solution: let t1 and t2 be the time taken to row upstream and downstream respectively   now,   t1=distance/speed=d/c   similarly,   t2=d/n (as same distance has to be rowed)   also,   t1+t2=p   therefore,   p=(d/c)+(d/n)   =d(c+n)/cn   d=pcn/(c+n)=cnp/(c + n)
Answer: D
Three workers have a productivity ratio of 2 to 4 to 8. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?  Choose one
A) 20 to 3
B) 6 to 1
C) 5 to 1
D) 1 to 6
E) 1 to 5

Solution: The fastest worker who does 8 units of job worked for all 10 hours, so he did   8*10= 
  8*10 = 80
80 units of job;   The slowest worker who does 2 unit of job worked for only   4+2= 
  4+2 = 6
6 hours (first 4 hours and last 2 hours), so he did   2*6= 
  2*6 = 12
12 units of job;   The ratio thus is 80 to 12, or 20 to 3.   20 to 3nswer: 20 to 3.
Answer: A
There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?	Choose the correct choice:
A) 1 : 2
B) 3 : 5
C) 5 : 7
D) 6 : 11
E) 5 : 3

Solution: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6   ∴A∶B∶C∶D= 3 : 4 : 5 : 6.   Thus, 1 : 2 : D = 3 : 6 or, 1 : 2   1 : 2
Answer: A
If (y - 1)(z - 3) + 5(y - 1) = 0, then which of the following must be true?  Choose the correct answer.
A) y = -4 and z = -3
B) y = 4 or z = -3
C) y = -4 or z = 3
D) y = 1 and z = 3
E) y = -1 or z = 3

Solution: factor out:   (y-1)(z-3+5)=0   (y-1) (z+2) = 0   So by checking options we get ,   Ans - y = 1 and z = 3
Answer: D
Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ?  Options:
A) 32 years, 23 years
B) 32 years, 29 years
C) 35 years, 29 years
D) 35 years, 33 years
E) 35 years, 34 years

Solution: Explanation:   When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.   Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.   Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.   Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.   32 years, 23 yearsnswer: Option 32 years, 23 years
Answer: A
In expressing a length of 81.472 km as nearly as possible with the three significant digits, find the percentage error
Choose the correct answer:
A) 0.35%	B) 0.34%	C) 0.034%	D) 0.035%	E) None of these

Solution: Explanation:   Error = (81.5 - 81.472)= 
(81.5 - 81.472) = 0.028
0.028   Required percentage=   0.028/ 81.472×100=0.034   Option 0.034%
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?  Answers
A) 10 kmph B) 13 kmph C) 65 kmph D) 55 kmph E) 14 kmph

Solution: Speed of the boat in still water   = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.   10 kmphnswer: 10 kmph
Answer: A
Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choices
A) 10 min
B) 12 min
C) 18 min
D) 20 min
E) 15 min

Solution: Due to stoppages, it covers 15 km less.   Time taken to cover 15 km = (15/60x 60) min = 15 min   Answer :15 min
Answer: E
There are 400 wolfs at a large zoo. The number of wolfs is 4 times the number of all the other animals combined. How many more wolfs are there than non wolfs animals at the zoo?	Choose the correct choice from the following.
A) 450 B) 420 C) 400 D) 390 E) 350

Solution: Answer is D.   Total wolfs= 400 = 4 * Other Animals (X)   or X = 10.   So, 390ifference in wolfs and X = 400-10= 
400-10 = 390
390.
Answer: D
Which of the following is not a leap year?	Choose the most appropriate option.
A) 1200  B) 800  C) 700  D) 2000  E) None of these

Solution: Explanation :   1. Every year divisible by 4 is a leap year, if it is not a century.   2. Every 4th century is a leap year, but no other century is a leap year.   800,1200 and 2000 comes in the category of 4th century (such as 400,800,1200,1600,2000 etc).   Hence 800,1200 and 2000 are leap years   700 is not a 4th century, but it is a century. Hence it is not a leap year   Answer : Option 700
Answer: C
In a simultaneous throw of 2 dice what is the probability of getting a total of 11?  Choose the most appropriate option:
A) 1/4 B) 1/18 C) 2/11 D) 3/13 E) 1/5

Solution: n(S) = 6*6= 
6*6 = 36
36   E= {(5,6),(6,5)}   Probability = 2/36 = 1/18   Answer is 1/18
Answer: B
Find the odd man out. 1, 3, 9, 12, 19, 29
Select:
A) 12 B) 9 C) 1 D) 3 E) 19

Solution: 12 is an even number. 12ll other given numbers are odd   12nswer : Option 12
Answer: A
A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days? Choose one.
A) 11  B) 12  C) 14  D) 13  E) 15

Solution: D   13   Let the number of men initially be x. we have M1 131 H1= M2 132 H2   So, x * 65 * 6 = (3x)/4 * 40 * h2   => h2 = (65 * 6 * 4)/(3 * 40)= 
(65 * 6 * 4)/(3 * 40) = 13
13.
Answer: D
In a certain college, 20% of the boys and 40% of the girls attended the annual college outing. If 35% of all the students are boys, what percent of all the employees went to the outing? Choose the correct choice from the following options:
A) 33%
B) 34%
C) 35%
D) 36%
E) 37%

Solution: assume total students =100 in that 35 students are boys ,remaining 65 are girls........   20% of boys(35) =7   40% of girls(65) =26   totally   (26+7)= 
  (26+7) = 33
33 mens went to outing...... 33 is 33% in 100   so, the answer is 33%   33%NSWER:33%
Answer: A
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:	Choose one.
A) 7 4/5 B) 9 3/5 C) 4 1/6 D) 7 7/12 E) 8 6/7

Solution: A + B + C's 1 day's work = 1/4   A's 1 day's work = 1/16   B's 1 day's work = 1/12   Therefore C's 1 day's work = 1/4	- ( A's 1 day's work + B's 1 day's work )   => C's 1 day's work = 1/4 - ( 1/16 + 1/12 )   => C's 1 day's work = (12-3-4)/48 = 5/48   So, C alone can do the work in 48/5 = 9 3/5 days.   So correct answer is 9 3/5
Answer: B
If |4x+6| = 46, what is the sum of all the possible values of x? Choose the correct choice
A) 2
B) -2
C) 4
D) -5
E) 6

Solution: There will be two cases   4x+6= 46 or 4x+6 = -46   => x =10 or x= -12   sum of both the values will be -12 +10 = -2   Answer is -2
Answer: B
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?  Choose the correct choice from the following answers:
A) 17 1/4 min	B) 28 1/7 min	C) 15 min	D) 17 1/8 min	E) 17 5/7 min

Solution: 1/20 + 1/30 - 1/60 = 4/60 = 1/15   15/1= 
15/1 = 15
15   Answer:15 min
Answer: C
Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by 66.66%. However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit.
How many units should Mr. David produce daily ?	Choose the most appropriate option:	A) 130	B) 100	C) 70	D) 150	E) None of these

Solution: Explanation :   Cost price function f(x) = cx2 + bx + 240.   When x = 20, f(20) = 400c + 20b + 240.   => f(40) = 1600c + 40b + 240   66.67% is 2/3.   => f(40) – f(20) = 2/3 * f(20).   Substituting f(40) and f(20), we get, 1200c+ 20b =(2/3) * (400c + 20b + 240)   Solving, we get 20b + 2800c = 480.   Now, f(60) = 3600c + 60b + 240.   f(60) – f(40) = ½ * f(40)   Substituting, and solving, we get, 360 + 60b + 2400c = 240 + 60b + 3600c   c = 1/10.   Substituting we get, b = 10.   So, the cost function f(x) = 0.1x2 + 10x + 240.   Selling price = 30 * x. ( Each unit SP is 30)   So, profit = SP – CP = 30x – (0.1x2 + 10x + 240) = -x2/10 + 20x – 240.   For maximum profit, differentiating this should give 0.   dp/dt = 0, dp/dt = -x/5 + 20   20 – x/5 = 0. x= 100.   Also double differentiating d2p / dt2, we get a negative number, so profit is maximum.   So, profit is maximum when 100 units are produced daily.   Answer : 100
Answer: B
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Select
A) 1234  B) 1356  C) 1567  D) 1546  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
In a building there are 5 rooms.Each having a equal area .The length of the room is 4m and breadht is 5 m.The height of the rooms are 2m. If 17 bricks are needed to make a square meter then how many bricks are needed to make the floor of a particular room ?
Choose the correct choice from the following answers: A) 320 B) 340 C) 300 D) 310 E) 330

Solution: Area of the floor = 4m x 5m = 20 m2   17 bricks are needed to make 1 m2 area.   So to make 20 m2 no of bricks needed = 17 x 20 = 340 Answer : 340
Answer: B
A boy & a girl appear for an interview against 2 vacant posts in an office. The probability of the boy's selection is 1/5 and that of the girl's selection is 1/3. What is the probability that only 1 of them is selected? Answers.
A) 1/3  B) 2/5  C) 2/7  D) 3/8  E) 4/9

Solution: Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)   = = 2/5   2/5
Answer: B
Find the no.of ways of arranging the boy and 9 guests at a circular table so that the boy always sits in a particular seat? Choose the correct choice from the following choices.
A) 3!
B) 8!
C) 7!
D) 9!
E) 11!

Solution: Ans.(D)   Sol. Total number of persons = 10 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 9 places in 9P9 = 9! Ways ... The number of required arrangements = 9! x 1= 9! = 9! ways
Answer: D
Otto and Han are driving at constant speeds in opposite directions on a straight highway. At a certain time they are driving toward each other and are 50 miles apart. One and a half hours later, they are again 50 miles apart, driving away from each other. If Otto drives at a speed of x miles per hour, then, in terms of x, Han drives at a speed of how many miles per hour?  Select:
A) a) 66.67-x	B) b) 40-x	C) c) 80-2x	D) d) 120-x	E) e) 40-x/2

Solution: Let's say the two cars have speeds V1 and V2. The fact that they are moving in opposite direction means that their relative speed is (V1 + V2). In other words, any gap between them will be changing in size at a rate of (V1 + V2). It doesn't matter whether they are moving toward each other or away from each other. If they are approaching each other, the gap between them is decreasing at a rate of (V1 + V2). If they are moving away from each other, the gap between them is increasing at a rate of (V1 + V2). Either way, the number for the rate of change remains the same.   Here, the two cars approach a distance 50 mi, then move away from each other another distance of 50 miles. That's a total distance of 100 miles in 1.5 hr, which gives a rate of:   R = (100 mi)/(1.5) = 66.67 mph   That's the rate of change of the gap, so it must equal the sum of the speeds of the two cars.   One of the speeds is x, and let's call the other y. We want y.   x + y = 66.67   y = 66.67 - x   a) 66.67-xnswer =(a) 66.67-x)
Answer: A