MU-NLPC/Calc-aqua_rat huggingface dataset:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length Q of a cube whose surface area is equal to 6z?	Choose the correct option:
A) Q=16	B) Q=8√2	C) Q=8	D) Q=2√2	E) (√2)/3

Solution: 800score Official Solution:   The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.   The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (Q=2√2).
Answer: D
Primary batteries, unlike secondary batteries, may be:	Choose the correct choice from the following
A) 2  B) 7  C) 6  D) 8  E) 9

Solution: Explanation:   Primary batteries (disposable batteries), which are designed to be used once and discarded when they are exhausted.   Secondary batteries (rechargeable batteries), which are designed to be recharged and used multiple times.   Answer: Option 7
Answer: B
A contractor hires 100 men to finish a job in 50 days. After 8 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work? Choose the most appropriate option:
A) 21  B) 18  C) 16  D) 12  E) 8

Solution: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.   Step 2 : After 8 Days = 8* 2= 
8* 2 = 16
16% of work is finished. remaining is 84% ( which means if same 100 men were about to complete the job they would have required 42 more days)   Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 42 days to compete for n people. at present 2n people are present to finish job. hence 21 more days.   21
Answer: A
A man drives his car and starts with the speed of 25 kmph with its speed increasing every hour by 5 kmph. In how many hours would it take him to drive 100 kms?	Choices.
A) 4 1â„4 hours
B) 3 1â„2 hours
C) 3 hours 15 minutes
D) Cannot be determined
E) None of these

Solution: Distance covered in first hour = 25 Ã— 1 = 25 km   Distance covered in next second hour = 30 Ã— 1 = 30 km   Distance covered in next third hour = 35 Ã— 1 = 35 km   Distance covered in first three hours    25 + 30 + 35= 
 25 + 30 + 35 = 90
90 km   Remaining distance= 100 â€“ 90 = 10 km.   Now, this distance will be covered at the speed of 40 km/hr.   âˆ´ Time taken = 10â„40 = 1â„4 hour.   Total time= 3 + 1â„4 = 3 1â„4 hour   Answer 3 hours 15 minutes
Answer: C
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?  Choose the correct choice from the following options:  A) 29  B) 92  C) 30  D) 32  E) 23

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer:30
Answer: C
The population of a bacteria culture doubles every 3 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria  Choose the correct choice from the following answers:
A) 27
B) 12
C) 14
D) 16
E) 18

Solution: This one's easy.   1000 * 2^t = 500,000   2^t = 500   Now gauging, since 2^8 = 256, then 2^9 = 512   So t = 9   But be careful, 't' is in time intervals of 3 minutes   So answer is 9*3= 
9*3 = 27
27 minutes   27nswer (27)
Answer: A
If 3^p - 3^(p-1) = 162 then p(p-1) =  Choose the correct answer:
A) 12 B) 16 C) 20 D) 30 E) 81

Solution: It seems like you were really close but you solved for p - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of p(p -1), e.g. (3)(4) = 12. Even then, had you figured p has to be a little bigger (plugging in 4 for p gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (p - 1) exponent place.   Again, a quick plugging in should get you (20) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: C
total dinning bill of 7 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . Pick one
A) 21.84	B) 22.84	C) 23.84	D) 24.84	E) 25.84

Solution: dinner bill of 7 person = 139 + 10% tip   so,   10% of 139 = (139*10)/100= 
(139*10)/100 = 139/10 = around 13.9
13.9   So, the actual total amount= 139+13.9= 
139+13.9 = 152.9
$ 152.9   so per head bill= 152.9/7 = $ 21.84   21.84NSWER:21.84
Answer: A
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?	Choose the most appropriate option.
A) 10	B) 17	C) 15	D) 11	E) 16

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days   10nswer: 10
Answer: A
If the areas of the three adjacent faces of a cuboidal box are 120 cm², 72 cm² and 60 cm² respectively, then find the volume of the box.	Pick.
A) 120 m³	B) 400 m³	C) 660 m³	D) 720 cm m³	E) None

Solution: Sol.   Let the length, breadth and height of the box be, l, b, and h respectively, Then,   Volume = lbh = √(lbh)² = √lb * bh * lh = √120 * 72 * 60 = 720 cm³   Answer 720 cm m³
Answer: D
Two stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?  Choose the most appropriate option:
A) 9 am	B) 12 am	C) 10.30 am	D) 12.30 am	E) 11 am

Solution: 9 amssume both trains meet after x hours after 7 am   Distance covered by train starting from P in x hours = 20x km   Distance covered by train starting from Q in (x-1) hours = 25(x-1)   Total distance = 65   => 20x + 25(x-1) = 65   => 45x = 90   => x= 2   Means, they meet after 2 hours after 7 am, ie, they meet at 9 am   9 amnswer is 9 am.
Answer: A
A bag contains 9 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls? Choose the correct choice.
A) 1/7  B) 2/9  C) 3/11  D) 3/55  E) 2/3

Solution: Total number of balls = 9+2= 
9+2 = 11
11   n(S)= 11C3 = 11*10*9 / 3*2 = 165   n(E) = 2C2* 9C1 = 9   Probability = 9/165 = 3/55   Answer is 3/55
Answer: D
Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 70th number in this set? Choose the correct answer:
A) 557  B) 608  C) 613  D) 616  E) 621

Solution: The set S = {5, 13, 21, 29, ..................... }   1st Number = 8 * 0 + 5= 
8 * 0 + 5 = 5
5   2nd Number= 8 * 1 + 5= 
8 * 1 + 5 = 13
13   3rd Number= 8 * 2 + 5= 
8 * 2 + 5 = 21
21   70th Number= 8 * (70-1) + 5= 
8 * (70-1) + 5 = 557
557   557nswer= 557
Answer: A
What is the least value of x, So that 2x5476 is divisible by 9	Choose one:
A) 7 B) 8 C) 9 D) 3 E) 2

Solution: Explanation:   The sum of the digits of the number is divisible by 9.   Then the number is divisible by 9.   2 + x + 5 + 4 + 7 + 6 = 24 + x   Least value of x may be '3',   So that the total 24 + 3= 
24 + 3 = 27
27   is divisible by 9.   Answer: Option 3
Answer: D
A rectangle having length 120 cm and width 50 cm. If the length of the rectangle is increased by ten percent then how much percent the breadth should be decreased so as to maintain the same area.  Choose the correct choice from the following options:
A) 25%	B) 33.33%	C) 40%	D) 7.69%	E) None of these

Solution: Explanation :   Solution: (10/(120+10) * 100)% = 7.69%   Answer : 7.69%
Answer: D
A trader bought a car at 20% discount on its original price. He sold it at a 65% increase on the price he bought it. What percent of profit did he make on the original price?  Choose the correct choice from the following answers.
A) A)2%	B) B)12%	C) C)14%	D) D)20%	E) E)32%

Solution: Original price = 100   CP = 80   S = 80*(165/100)= 
80*(165/100) = 132
132   100 - 132= 32%   32%)
Answer: E
A 260 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?  Pick one
A) 230m B) 240m C) 250m D) 260m E) 270m

Solution: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s   time= 9sec   let the lenght of second train is x   total distance covered= 260 + x   therefore, D= speed*time   thus 260 + x = 500/9 * 9= 
500/9 * 9 = 500
500-260= 
500-260 = 240
240 m   ANSWER:240m
Answer: B
A man travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the distance amount?
Choose the correct choice from the following options:
A) 2	B) 4	C) 5	D) 1	E) 3

Solution: dist 3x km ==> x/3+x/4+x/5 = 47/60   47x/60 = 47/60   x=1 then tot dist = 3*1= 
3*1 = 3
3 km   ANSW3R 3
Answer: E
The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Answers.
A) 38 cm2	B) 85 cm2	C) 50 cm2	D) 45 cm2	E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 40/2= 
2.5 * 40/2 = 50
50 cm2   Answer:50 cm2
Answer: C
If the HCF of two numbers is 2 and their LCM is 70, then the numbers are: Choose one:
A) 2, 235  B) 6, 70  C) 4, 70  D) 14, 10  E) 15, 20

Solution: Explanation:   HCF of the two numbers is 2   Let us take two numbers are x and y   Their LCM= 70   LCM is the product of two numbers.   LCM/HCF = 70/2 = XY/2   xy=70×2 = 140   xy = 140   x = 14, y = 10 or x = 70, y = 2.   But according to the options, the numbers are x = 14 and y = 10.   Answer: 14, 10
Answer: D
What will be the compound interest on a sum of Rs. 29,000 after 3 years at the rate of 12% p.a.?  Choose the most appropriate option
A) s.11123.77 B) s.11742.91 C) s.11123.20 D) s.10123.28 E) s.10123.21

Solution: Amount = [29000 * (1 + 12/100)3]   = 29000 * 28/25 * 28/25 * 28/25   = Rs. 40742.91   C.I. = (40742.91 - 29000)   = Rs. 11742.91   Answer:s.11742.91
Answer: B
Special codes are designated by either a 7-letter or an 8-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system?  Choices.
A) 2 (26)^8 B) 26(26)^7 C) 27(26)^7 D) 26(26)^8 E) 27(26)^8

Solution: 26^7+26^8 = 26^7(1+26)=27*26^7   The answer is 27(26)^7.
Answer: C
The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?	Options:
A) 281  B) 771  C) 440  D) 767  E) 1981

Solution: r = 7 h = 3   2πr(h + r) = 2 * 22/7 * 7(10) = 440   Answer:440
Answer: C
The sum of the even numbers between 1 and n is 89*90, where n is an odd number, then n=? Choose the correct choice from the following answers:
A) 167  B) 173  C) 179  D) 185  E) 193

Solution: Let n-1 = 2a.   2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 89*90   Then a = 89 and n = 179.   The answer is 179.
Answer: C
A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Select
A) 88 B) 27 C) 32 D) 80 E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 200 + 120= 
200 + 120 = 320
320 m.   Time taken= 320/10= 
320/10 = 32
32 sec.   Answer: 32
Answer: C
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of D feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?	Answers:	A) 100xy	B) 100y - x	C) 100x/y	D) 100y/x	E) 100x - y

Solution: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)   Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   100 = D/(x*pi)   D = 100 * x * pi ---------- (3)   From equation (2)   Revolutions = D/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y   Answer (100x/y)
Answer: C
How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?
Choose the most appropriate option:  A) 12.1 sec  B) 10 sec  C) 11 sec  D) 13 sec  E) 13.2 sec

Solution: Speed = 72 km/hour = 72*(5/18) m/sec   = 20 m/sec   Total distance = 110+132 = 142 m   Time = D/S   = 242/20= 
242/20 = 121/10 = around 12.1
12.1 seconds   12.1 secNSWER 12.1 sec
Answer: A
What is the maximum number of pieces of birthday cake of size 4” by 4” that can be cut from a cake 20” by 20”?	Select the correct option:
A) 5
B) 10
C) 16
D) 20
E) 25

Solution: 25ach length =20" each piece =4"   Cake could be divided to maximum of 25 pieces   Answer: 25
Answer: E
How many ways are there to split a group of 4 girls into two groups of 2 girls each? (The order of the groups does not matter)
Choose the correct choice from the following answers:	A) 7	B) 6	C) 5	D) 4	E) 3

Solution: the combination is 4C2 /2   = 4!/2!*2! *2 = 3   3
Answer: E
Find the total number of prime factors in the expression (4)^11 x (7)^5 x (11)^2	Select the correct option
A) 26	B) 22	C) 25	D) 27	E) 29

Solution: (4)^11x (7)^5 x (11)^2   = (2 x 2)^11 x (7)^5 x (11)^2   = 2^11 x 2^11 x7^5x 11^2   = 2^22 x 7^5 x11^2   Total number of prime factors = (22 + 5 + 2)= 
(22 + 5 + 2) = 29
29.   Answer is 29.
Answer: E
A certain restaurant offers 8 different curry, 5 different main courses, 6 different ice creams. If customers choose one salad, one main course and two different ice creams for their meal, how many different meals are possible? Pick:  A) 120  B) 240  C) 480  D) 500  E) 600

Solution: MAGOOSHOFFICIAL SOLUTION:   To count the number of curry, we have to count the possibilities for the three components, and then, according to the Fundamental Counting Principle, we multiply. For more on the FCP, see this blog.   For salads, there are 8 possibilities. Done.   For main courses, there are 5 different possibilities. Done.   For ice creams, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can use the shortcut, nC2 = (n*(n-1))/2.   6C2 = (6*5)/2= 
(6*5)/2 = 15
15   So, there are 15 combinations of two different desserts.   For the number of meals, we multiply 8*5= 
8*5 = 40
40. Then, we need 40*15. Well, 4*15= 60, so 40*15 must be 600.   Answer = (600)
Answer: E
In a certain corporation, there are 300 male employees and 150 female employees. It is known that 40% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female? Choose the correct choice from the following options: A) 1/2 B) 2/3 C) 3/5 D) 7/10 E) 11/15

Solution: P(female) = 150/450 = 1/3   P(male with advanced degree) = 0.4*300/450 = 120/450 = 4/15   The sum of the probabilities is 9/15 = 3/5   The answer is 3/5.
Answer: C
A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Choose the correct choice from the following options.
A) 40	B) 55	C) 60	D) 79	E) 80

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 10) km/hr.   x - 10 = 45 => x = 55 km/hr.   Answer: Option 55
Answer: B
A began business with 12000 and is joined afterwards by B with 72000. When did B join, if the profits at the end of the year are divided equally?
Choose the correct choice.
A) 8 months	B) 9 months	C) 10 months	D) 7 months	E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12000 : (12 – x) × 72000   or 12 : 6(12 – x)   Since profit is equally divided so   12 =6(12 – x) or x = 10. Thus B joined after 10 months.   Answer 10 months
Answer: C
A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?  Answers.
A) 1200
B) 1260
C) 1301
D) 1340
E) 1400

Solution: sol. let the new sp be Rsx.then   (100-loss%) : (1st sp)=(100+gain%) (2nd sp)   {(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95= 
(105*1140)/95 = 1_260
1260.   Option 1260
Answer: B
The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?	Choose one
A) 100 % B) 200% C) 300% D) 600% E) None of these

Solution: Explanation:   Let the salaries of A, B, C be x, 2x and 3x respectively.   Then,2x + 3x = 6000 => x = 1200.   A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.   Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.   Answer: 200%
Answer: B
A certain number of persons can finish a piece of work in 100 days. If there were 10 persons less, it would take 10 more days finish the work. How many persons were there originally?	Choose the correct choice from the following choices:
A) 90
B) 100
C) 110
D) 120
E) 130

Solution: Explanation:   Assume that x persons can finish a piece of work in 100 days   Also it is given that (x−10) persons can finish a piece of work in 110 days (∵ 100 + 10 = 110)   More persons, less days(indirect proportion)   Hence we can write as(persons) x : (x−10) :: 110 : 100   ⇒100x=110(x−10)   ⇒100x=110x−1100   ⇒10x=1100   ⇒x=1100/10= 
1100/10 = 110
110   Answer: Option 110
Answer: C
In how many ways can a team 16 be chosen out of a batch of 20 players?  Choose the most appropriate option: A) 4845 B) 6852 C) 3125 D) 5846 E) 7846

Solution: Required number of ways= 20C16= 20C(20-16) = 20C4   = (20*19*18*17)/(4*3*2*1)= 
(20*19*18*17)/(4*3*2*1) = 4_845
4845.   4845NSWER:4845
Answer: A
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in meterr? Choose the correct choice from the following choices.
A) 40 m
B) 60 m
C) 65 m
D) 70 m
E) 80 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
Two trains run in opposite directions on a circular track. Train Q travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?	Choices: A) 3 B) 6 C) 9 D) 18 E) 22

Solution: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.   My solution is as follows, and I ask anyone to correct me if I am wrong.   Solution 1   Let the distance covered by train Q be X, thus that covered by the train B will be 12*3.14-X   dQ = X dB = 12*3.14 - X   Times taken by A and B are   tQ= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)   Since they have been traveling for the same period of time, then   X/4*3.14 = (12*3.14 - X)/6*3.14   X/2 =(12*3.14 -X)/3   3X = 2(12*3.14 -X)   5X = 24*3.14   X = 24*3.14/5   Plugging that in either equation of (ii) yields t = 6/5   Solution 2   We add the speed of Q and B: totalSpeed = 4*3.14 + 6*3.14 = 10*3.14   Total distance covered = 12*3.14   t ime = distance / speed = 12*3.14/10*3.14 = 6/5.   tQ =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5.
Answer: B
Complete the numerical series by replacing the question mark with the correct numbers.
5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
9+5+5 = ??????	Pick one:
A) 454584	B) 454585	C) 454586	D) 454587	E) None

Solution: Solution:   454585   Explanation:   Number is formed as (numA*num454585)(num454585*numC)(numC*numA)   Following the formular, 1st row will be like   5+3+2 => 5*3 3*2 2*5 => 151022   Simillarly   (9*5)(9*5)(9*5+9*5-5) => 454585   Answer 454585
Answer: B
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is  Choose the correct choice from the following choices:	A) 5/1	B) 5/9	C) 5/8	D) 5/6	E) 5/2

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 =5/9.   Answer:5/9
Answer: B
If 12 machine can finish a job in 40 days, then how many more machines would be needed to finish the job in one -fourth less time? Choose the correct choice from the following answers:
A) a. 4
B) b. 8
C) c. 10
D) d. 12
E) e. 16

Solution: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5= 
6*5 = 30
30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign   30/3= 
  30/3 = 10
10 employees to do the job, because you want to get a total of 30 hours of work from the employees.   We can solve this problem identically. If 12 machines (identical ones, I assume) work simultaneously for 40 days, they will do a total of 12*40 machine-days of work. So the job requires 12*40 days of machine work in total. We instead want the job done in 1/4 less time, so in 30 days. So we'll need 12*40/30= 
12*40/30 = 16
16 machines, or 4 additional machines.   a. 4
Answer: A
In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?	Choose the correct choice from the following options
A) $2.4 million  B) $2.9 million  C) $3.0 million  D) $3.1 million  E) $3.6 million

Solution: Let the number of pairs of shoes sold in 1985 = N   let price per pair of shoe sold in 1985 = P   In 1986,number of pairs of shoes sold decreased by 20 % = .8N   Price per pair increased by 20% = 1.2P   Company's revenue from sale of shoes in 1986 = 3 million$   => .8N * 1.2 P = 3   =>.96 NP = 3   => NP = 3/.96= 
3/.96 = 3.125
3.125 million $   Answer $3.1 million
Answer: D
If E is an integer greater than 6, which of the following must be divisible by 3?	Choose the correct option:
A) E(E+1)(E-4)
B) N(N+2)(N-1)
C) N(N+3)(N-5)
D) N(N+4)(N-2)
E) N(N+5)(N-6)

Solution: Now take E = 3k , E = 3k+1 E = 3k+2..put in all the choices. If by putting all the values of E we get it is divisible by 3, then it is correct answer choice.   A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: A
The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?  Choose the correct choice from the following answers:  A) 76 m  B) 178 m  C) 235 m  D) 187 m  E) 176 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2   => 2(140 + x)= 750 => x = 235 m.   Answer: 235 m
Answer: C
For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 45 true?  Choices.
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: Answer 3   (a+b)(a-b)=45   3cases For (a+b), (a-b)   45, 1   15, 3   9, 5   Answer 3
Answer: B