MU-NLPC/Calc-aqua_rat huggingface dataset:
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? Choose the correct choice from the following choices
A) 339
B) NONE
C) 349
D) 369
E) 379

Solution: x = 13p + 11 and x = 17q + 9   13p + 11 = 17q + 9   17q - 13p = 2   q =	2 + 13p   17   The least value of p for which q =	2 + 13p	is a whole number is p = 26   17   x = (13 x 26 + 11)   = (338 + 11)= 
(338 + 11) = 349
349   ANSWER 349
Answer: C
A farm has chickens, horses and sheep. There are six times the number of chickens and cows than sheep. If there are more horses than chickens or sheep, and together, horsess and chickens have a total of 100 feet and heads, how many sheep live at the farm?	Answers.
A) 5 B) 4 C) 10 D) 14 E) 17

Solution: Chicken - ch   horses - H   Sheep -S   ch+H=6S   H> ch and H>s   Each Horse has 4 legs and 1 head   Each chicken has 2 legs and 1 head   So 5h+3ch=100 (sum of legs and head)   There are 2 possible solutions to this equation   h=11 and ch=9 or   h=14 and ch=10   Since from first equation where ch+h=6s   The sum of ch and c should be divisbile by 6. 20 is not so the only possible solution is h=14 and ch=10. So s=4   Answer : 4
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream? Select the correct option
A) 77 B) 88 C) 14 D) 12 E) 17

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer:14
Answer: C
A fort had provision of food for 180 men for 45 days. After 25 days, 40 men left the fort. The number of days for which the remaining food will last, is: Choose the correct choice from the following answers:  A) 29	1/5  B) 25	3/4  C) 42  D) 54  E) 45

Solution: we have food for 180 men for 45 days.   After 25 days food left for 180 men for 20 days.   so   180 : 20   now we have 140 men and x days   140 : 180 :: 20 : x   x = (180*20)/140 = 25 3/4 days.   ANSWER:25	3/4
Answer: B
A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Number of toys sold.
II. Cost price of each toy.	Options:
A) Only I is necessary  B) Only II is necessary  C) Both I and II are necessary  D) Either I or II ins necessary  E) None of these

Solution: EXPLANATION   S.P. = Rs. 250 each.   To find gain percent, we must know the C.P. of each.   answer is (Only II is necessary).
Answer: B
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Choose the correct choice from the following options
A) 10.9 sec  B) 10.1 sec  C) 10.6 sec  D) 10.8 sec  E) 10.2 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other   = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250   = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer:10.8 sec
Answer: D
Mr. Yutaro’s class contains 6 boys and 10 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?	Choose the correct choice from the following answers:	A) 9/48	B) 9/20	C) 1/2	D) 27/48	E) 13/16

Solution: Probability of a boy being chosen first, then a girl:   6/16 * 10/15   Probability of a girl being chosen first, then a boy:   10/16 * 6/15   Probability of a boy and a girl being chosen:   (6*10+6*10) / (15*16)   =1/2   Answer:1/2
Answer: C
David started a business investing Rs. 70,000. Robert joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio amoung David, Robert and Sagar respectively, 3 years after David started the business?  Choose the correct option.
A) 12 : 10 : 16	B) 12 : 15 : 16	C) 15 : 12 : 16	D) 16 : 15 : 12	E) None

Solution: Sol.   David : Robert : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)   = 12 : 15: 16.   Answer 12 : 15 : 16
Answer: B
A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1860 are infected, how manyworkersinhabit the colony? Choose the correct choice from the following:
A) 1500	B) 2500	C) 2750	D) 3000	E) 3250

Solution: From two question we get wo equations:   (1) 0,3s + 0,14w = 1860   (2) s + w = 7000   From (2) we get w=7000-s   In (1) 0,3s + 980-0,14s= 1860   0,16s=880   88000:16= 5500 =s   In (2) 5500 + w = 7000   w= 1500 1500
Answer: A
A travel agent offers a vacation plan which costs 'a' dollars for the first day, and a/10 for each additional day. How much does a vacation of b days cost, where b > 1. Choose the correct choice from the following choices:
A) (ab+9a)/5
B) (ab+8a)/10
C) (ab+9a)/2
D) (ab+5a)/10
E) (ab+9a)/10

Solution: Cost = a + (b-1)*a/10 = (10a + (b - 1)*a)/10 = (ab+9a)/10   Answer is (ab+9a)/10
Answer: E
Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?
Choose the correct choice from the following: A) 110 B) 1,100 C) 9,900 D) 10,000 E) 12,100

Solution: P can take a total of 10*11 co-ordinates.   for a given P, R can take a total of 9 co-ordinates and Q can take a total of 10 co-ordinates.   Hence, total = 110*9*10= 
110*9*10 = 9_900
9900   ANS:9,900
Answer: C
How many cases do you need if you have to pack 50 dozens of bar soaps into cases that each hold 50 soaps?  Choose the correct choice from the following options.
A) 15 B) 14 C) 13 D) 12 E) 10

Solution: 12   12   50 dozens of bar soaps = 600 soaps   600 ÷ 50 = 12.
Answer: D
In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always come together? Pick
A) 610  B) 720  C) 825  D) 920  E) 925

Solution: The word 'OPTICAL' contains 7 different letters.   When the vowels OIA are always together, they can be supposed to form one letter.   Then, we have to arrange the letters PTCL (OIA).   Now, 5 letters can be arranged in 5! = 120 ways.   The vowels (OIA) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   ANSWER:720
Answer: B
For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.	Choose the correct choice from the following answers:
A) 13  B) 42  C) 55  D) 27  E) 19

Solution: f(x) = -3(x - 10)(x - 4) = -3x2*square* + 42x - 120 : expand and obtain a quadratic function   h = -b/2a = -42/-6= 
-42/-6 = 7
7 : h is the value of x for which f has a maximum value   f(h)= f(7) = 27 : maximum value of f.   correct answer 27
Answer: D
Find the average of first 60 natural numbers.  Select the correct option.
A) 20.5	B) 18	C) 30.5	D) 19	E) 17

Solution: Exp. Sum of first n natural numbers = n( n+1)/2   So, sum of first 60 natural numbers = 60*61/2= 
60*61/2 = 1_830
1830   Required average=1830/60= 
1830/60 = 61/2 = around 30.5
30.5   Answer:30.5
Answer: C
On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?  Select:	A) 82	B) 83	C) 84	D) 85	E) 86

Solution: Mabel handled 90 transactions   Anthony handled 10% more transactions than Mabel   Anthony = 90 + 90 × 10%   = 90 + 90 × 0.10   = 90 + 9= 
90 + 9 = 99
99   Cal handled 2/3rds of the transactions than Anthony handled   Cal= 2/3 × 99   = 66   Jade handled 16 more transactions than Cal.   Jade = 66 + 16= 
66 + 16 = 82
82   Jade handled= 82 transactions.   Correct 82nswer:82)82
Answer: A
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job. How long should it take both A and B, working together but independently, to do the same job? Choose one:
A) 6 days
B) 40 days
C) 5 days
D) 12 days
E) 40/9 days

Solution: A’s 1 hour's work = 1/8   B's 1 hour's work = 1/10   (A + B)'s 1 hour's work = (1/8) +(1/10)=9/40   Both A and B will finish the work in 40/9 days.   Ans: 40/9 days
Answer: E
A says " the horse is not black".
B says " the horse is either brown or grey."
c says " the horse is brown"
At least one is telling truth and atleast one is lying. Tell the colour of horse? Answers.
A) Black B) grey C) Brown D) White E) blue

Solution: The color of the horse can be any color other than Black and Brown.   If the color of the horse is Black - all are lying. If the color of the horse is Brown - all are telling truth. Thus, the horse is neither Black nor Brown. If the color of the horse is Grey - A and B are telling truth whereas C is lying. If the color of the horse is other than Black, Brown and Grey - A is telling truth whereas B and C are lying. You must have noticed that for the given conditions, A is always telling truth whereas C is always lying.   So ans is grey.   ANSWER:grey
Answer: B
If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 10 men in 3 days?
Pick:
A) 65mtr.
B) 28mtr
C) 70mtr.
D) 78mtr.
E) 17mtr.

Solution: 20 men is 6 days can build 112 metres   10 men in 3 days can build = 112*(10/20)x(3/6)   = 28 meters   Answer: 28mtr.
Answer: B
The value of x + x(x^x) when x = 2 is  Choose the correct choice from the following choices:
A) 10
B) 16
C) 18
D) 36
E) 64

Solution: Solution:   x + x(x^x)   Put the value of x = 2 in the above expression we get,   2 + 2(2^2)   = 2 + 2(2 × 2)   = 2 + 2(4)   = 2 + 8= 
2 + 8 = 10
10   10nswer: (a)
Answer: A
Geetha 's home has One tap, working alone at its maximum constant rate, can fill a certain sink in 210 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 214 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to  Choose the correct choice from the following options
A) 106 seconds
B) 130 seconds
C) 177 seconds
D) 200 seconds
E) 270 seconds

Solution: Tap 1 : 210 secs   Tap 2 : 214 secs   Considering the average of these 2 taps : 212 secs.   So 1 tap can fill the tank in 212 secs, so 2 taps can fill the tank in 212/2= 
212/2 = 106
106 secs.   Closest answer is 106 seconds.
Answer: A
Solution for 2.75+.003+.158  Pick one.
A) 2.91 B) 2.911 C) 2.938 D) 2.986 E) 2.999

Solution: 2.75+.003+.158=0   0=0-2.75-0.003-0.158   0=-2.911   answer :2.911
Answer: B
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?	Pick one.
A) 1898 B) 1098 C) 1000 D) 2008 E) 1082

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer:1000
Answer: C
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?	Choose the correct choice from the following answers
A) 42 6/9%  B) 42 3/7%  C) 42 7/7%  D) 42 6/7%  E) 22 6/7%

Solution: SP = CP + g   50 SP = 50 CP + 15 SP   35 SP = 50 CP   35 --- 15 CP gain   100 --- ? => 42 6/7%   Answer: 42 6/7%
Answer: D
A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is Choices
A) 3.34 B) 3.39 C) 3.37 D) 3.33 E) 3.31

Solution: 3.34rea of the path = 3.34rea of the outer circle - 3.34rea of the inner circle = ∏{4/2 + 25/100}2 - ∏[4/2]2   = ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }   = (3.14)(1/4)(17/4) = 53.38/16   = 3.34 sq m   3.34nswer:3.34
Answer: A
If 40% of a number is equal to two-thirds of another number, what is the ratio of the first number to the second?	Select the correct option
A) 7 : 3 B) 3 : 7 C) 2 : 5 D) 5 : 3 E) None of these

Solution: Suppose the first number is x and the second numbery.   Therefore, 40% of x = 2⁄3 of y   ∴ x⁄y = 2⁄3 × 100⁄40 = 5⁄3   Answer 5 : 3
Answer: D
Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is	Choose the correct choice from the following answers
A) 10.2  B) 10.4  C) 10.6  D) 10.8  E) 11.2

Solution: 10.8istance = 140+160= 
140+160 = 300
300 m   Relative speed= 60+40= 
60+40 = 100
100 km/hr= (100×10)/36 m/s   Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s   Answer is 10.8.
Answer: D
In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Choose the correct option.
A) 11 Years	B) 12.6 Years	C) 13 Years	D) 13.5 Years	E) 14 Years

Solution: Total age of 50 students   (30X 13+20 X 12) = 630   Average = 630/50= 
630/50 = 63/5 = around 12.6
12.6 Years   12.6 Years)
Answer: B
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?  Select the correct option.
A) 5768  B) 5760  C) 5762  D) 5766  E) 5712

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 4= 
 24 * 60 * 4 = 5_760
5760   Answer: 5760
Answer: B
On his first 4 tests, Rajeev received an average score of X points. If on his fifth test, he exceeds his previous average score by 20 points, what is his average score for his first 5 tests?  Options
A) X + 5
B) X + 1
C) X + 4
D) X + 2
E) X + 3

Solution: Total of 1st 4 tests= 4X   5th test score = X + 20   Total of all 5 tests = 5X + 20   Average = X + 4   Answer : X + 4
Answer: C
One train is traveling 18 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Pick:
A) 1:2  B) 5:6  C) 5:0  D) 5:4  E) 5:1

Solution: 18 * 5/18 = 10   5:10 => 1:2   1:2nswer: 1:2
Answer: A
What approximate value should come in plce of question mark (?) in the following equations ?
728.038 x 54.978 - 72.016 x 85.250 = ? Choices
A) 31400  B) 32700  C) 33900  D) 34400  E) 32400

Solution: Explanation :   ? = 728 x 55 - 72 x 85.25   = 40040 - 6138 = 339900   Answer : Option 33900
Answer: C
A train cruising at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.
Choose the correct choice from the following options:
A) 200/3m175/3m
B) 40m85m
C) 50m45m
D) 100/3 m200/3
E) none of these

Solution: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 3 seconds to pass a man walking at 3 km/hr in the same direction. Find the length of the train and that of the platform.   Distance = Speed*time   It's probably best to convert to meters so we can find the length of the platform.   Distance = 50000 meters/h * 9 seconds*(1/60*60)   Distance =(55000*9 / [3600] ) = 125m   I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.   As for the problem involving the man, the man is moving forward at a speed of 3km/h while the train is moving forward at a speed of 50km/h. Therefore, the train is moving past the man at a total speed of 47km/h.   distance = speed * time   distance = 47km/h * 3 seconds   distance (length of train) = 39.16 m   We know the length of the train is roughly 39.16m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-39.16 or roughly 85m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.   ANSWER: 40m85m) 40m85m
Answer: B
What is the area of a regular hexagon with sides 1 in. long? Answers:
A) 1.59 square inch
B) 2.59 square inch
C) 3.59 square inch
D) 4.59 square inch
E) 2.69 square inch

Solution: A regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch.   Area of each triangle = (root 3/4)* side^2 = (root 3/4)   Area of 6 triangles = 6*(root 3/4)= 1.5 root 3= 2.59 square inch   ANSWER:2.59 square inch
Answer: B
In business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2, If Rs 157300 was their profit, how much amount did B receive.	Choose the correct choice from the following choices:
A) Rs 48000
B) Rs 47000
C) Rs 47400
D) Rs 48400
E) None of these

Solution: Explanation:   A:B = 3:2 = 6:4   => A:C = 2:1 = 6:3   => A:B:C = 6:4:3   B share = (4/13)*157300= 
(4/13)*157300 = 48_400
48400   Option Rs 48400
Answer: D
Average of 10 matches is 32, How many runs one should should score to increase his average by 6 runs.
Select the correct option.
A) A)70
B) B)76
C) C)78
D) D)98
E) E)88

Solution: Explanation:   Average after 11 innings should be 38   So, Required score = (11 * 38) - (10 * 32)   = 418 - 320= 
418 - 320 = 98
98   Answer: Option 98
Answer: D
What is the probability of getting a sum 9 from two throws of a dice? Choose the correct choice from the following:
A) 1/6
B) 1/8
C) 1/9
D) 1/12
E) None

Solution: Solution   In two throws of a die, n(S) = (6×6)   = 36.   Let E = event of getting a sum 9= {{3,6),(4,5),(5,4),(6,3)}   P(E)	= n(E) / n(S)   = 4/36   ‹=›1/9.   Answer 1/9
Answer: C
The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
Choose the correct answer:  A) 5.025%  B) 5.25%  C) 6.125%  D) 7.34%  E) 8.43%

Solution: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W   Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%   6.125%
Answer: C
Three cubes of metal whose edges are 5, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? Choose the most appropriate option:  A) 28  B) 77  C) 17.3  D) 18  E) 99

Solution: 53 + 123 + 153 = a3 => a   = 17.3   Answer: 17.3
Answer: C
(3x + 4) (2x - 5) = ax^2 + kx + n . What is the value of a - n + k ?  Answers
A) 5  B) 8  C) 9  D) 10  E) 15

Solution: 15xpanding we have 6x^2 -15x + 8x -20   6x^2 - 7x - 20   Taking coefficients, a = 6, k= -7, n = -20   Therefore a - n + k = 6 - (-20) - 11 = 26 - 11= 
26 - 11 = 15
15   The answer is 15.
Answer: E
A number is missing from the number series below.
Can you find it ?
84, 155, 258, ? , 584, 819.	Pick one: A) 275 B) 350 C) 399 D) 421 E) 449

Solution: C   The missing number is 399.   84 = 4^3 + 3^2 + 4   155 = 5^3 + 5^2 + 5   258 = 6^3 + 6^2 + 6   584 = 8^3 + 8^2 + 8   819 = 9^3 + 9^2 + 9   Thus,   399 = 7^3 + 7^2 + 7
Answer: C
A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?	Pick:  A) 3  B) 6  C) 7  D) 8  E) 12

Solution: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do,. 3   3
Answer: A
If 35% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?  Choices:
A) 110	B) 330	C) 572	D) 430	E) 880

Solution: Students enrolled in biology are 35% and therefore not enrolled are 65%. so of 880 is  880*.65= 
 880*.65 = 572
572   Answer is 572 572
Answer: C
If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is? Choose the correct choice.
A) 1.44%  B) 1.43%  C) 1.34%  D) 4.44%  E) 1.74%

Solution: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.   In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%   1.44%nswer: 1.44%
Answer: A
Eighteen dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 18 dots that do not form an equilateral triangle?	Options: A) 792 B) 798 C) 804 D) 810 E) 816

Solution: The total number of ways we can choose three dots is 18C3=816.   We can form six equilateral triangles from these eighteen dots.   There are  816 - 6= 
 816 - 6 = 810
810 combinations which do not form an equilateral triangle.   The answer is 810.
Answer: D
How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 42 kmph? Pick one.
A) 21.4 sec
B) 77 sec
C) 25 sec
D) 18 sec
E) 17 sec

Solution: D = 100 + 150= 
100 + 150 = 250
250   S= 42 * 5/18 = 11.7 mps   T = 250/11.7 = 21.4 sec   21.4 secnswer:21.4 sec
Answer: A
What is the smallest positive integer x such that 108x is the cube of a positive integer?  Answers:
A) 2  B) 4  C) 8  D) 10  E) 7

Solution: Given 108x is a perfect cube   so we will take 216 = 6*6*6   108x = 216   x = 216/108= 
216/108 = 2
2   correct option is 2
Answer: A
Calculate the sum of first 89 natural numbers. Select the correct option.
A) 2017 B) 2647 C) 2147 D) 2045 E) 4005

Solution: Solution   We know that(1+2+3+.....+89)	= n(n+1)/2   Therefore (1+2+3+....+89)	=(89×90 / 2)   = 4005.   Answer 4005
Answer: E
A and B can do a work in 18 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?  Select
A) 360/13 days B) 350/13 days C) 160/13 days D) 260/13 days E) 960/13 days

Solution: One day work of A and B = 1/18   One day work of B and C = 1/30   One day work of C and A = 1/36   2(A + B + C) = 1/18 + 1/30 + 1/36   2(A + B + C) = 21/180   (A + B + C) = 13/360   Number of days required = 360/13 days.   360/13 daysNSWER:360/13 days
Answer: A
Einstein walks on an escalator at a rate of 5steps per second and reaches the other end in 10 sec. while coming back, walking at the same speed he reaches the starting point in 40secs. What is the number of steps on the escalator?
Pick one
A) 22	B) 80	C) 28	D) 17	E) 11

Solution: Escalator problems are similar to boats and streams problems. If we assume man's speed as 'a m/s' and escalator speed as 'b m/sec' then while going up man's speed becomes 'a -b' and while coming down 'a + b'.   In this question, Let the speed of escalator be b steps per sec. And length of escalator be L. Einstein's speed = 5 steps/ sec   While going down, L5+x=10L5+x=10 ⇒⇒ L = 50 + 10x   While coming up, L5−x=40L5−x=40 ⇒⇒ L = 200 - 40x   Multiply the first equation by 4, and add to the second, we get L = 80   Answer:80
Answer: B
If n is a natural number, then (7(n2) + 7n) is always divisible by:
Choose one
A) 3 and 7	B) 14 only	C) 7 only	D) 7 and 14	E) NONE

Solution: Solution   (7n2 + 7n) = 7n(n + 1), which is always divisible by 7 and 14 both, since n(n + 1) is always even.   Answer 7 and 14
Answer: D
a * b = 2a - 3b + ab, then 3*5 + 5*3 = ? Choose one
A) 20  B) 21  C) 22  D) Bedford is at one end.  E) Mercedes is at one end.

Solution: Mercedes is at one end.xplanation:   = 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)   = 6-15+15+10-9+15 = 31-9= 
31-9 = 22
22   Option Mercedes is at one end.
Answer: E
If |y + 5| = 8, what is the sum of all the possible values of y? Select the correct option:
A) -14
B) -13
C) -8
D) -12
E) -10

Solution: There will be two cases   y+5 = 8 or y+5 = -8   => y = 3 or y= -13   sum of both the values will be -13 + 3 = -10   Answer: -10
Answer: E