MU-NLPC/Calc-aqua_rat huggingface dataset:
Two cyclists start from the same place to ride in the same direction. A starts at noon at 8 kmph and B at 1.30 pm at 10 kmph. How far will A have ridden before he is over taken by B ?Find also at what times A and B will be 5 km apart.
Choose the correct option
A) 5pm and 10pm
B) 6pm and 10pm
C) 4pm and 8 pm
D) 5pm and 8 pm
E) None of these

Solution: Sol. If A rides for X hours before he is overtaken, then B rides for(X – 15) hrs.   => 8X = 10 (X – 1.5) => X = 7.5   => A will have ridden 8 × 7.5 km ro 60 km.   For the second part, if Y = the required number of hours after noon, then   8X = 10 (X – 1.5) ± 5   => X = 10 or 5 according as B is ahead or behind A.   => The required times are 5 p.m. and 10 p.m. 5pm and 10pmnswer 5pm and 10pm
Answer: A
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Choose the correct choice:
A) 277m
B) 180m
C) 272m
D) 278m
E) 267m

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: 180m
Answer: B
If w/x = 1/6 and w/y = 1/5, then (x + y)/y =
Choose the correct answer: A) 4/5 B) 6/5 C) 7/5 D) 11/5 E) 9/5

Solution: W/X = 1/6=>x=6w and W/Y = 1/5=>y=5w   (X+Y)/Y = (6w+5w)/5w = 11w/5w = 11/5   Correct Option: 11/5
Answer: D
If the number 517*324 is completely divisible by 5, then the smallest whole number in the place of * will be:	Select
A) 3  B) 1  C) 2  D) 4  E) 5

Solution: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 5.   x = 3.   3
Answer: A
A boat having a length 4 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Choose the correct choice.
A) 12 kg B) 60 kg C) 72 kg D) 80 kg E) None of these

Solution: Explanation:   Volume of water displaced = (4 x 2 x 0.01) m3   = 0.08 m3.   ∴ Mass of man = Volume of Water displaced x Density of water   = (0.08 x 1000)kg   = 80 kg.   Answer: 80 kg
Answer: D
Sonika deposited Rs.9000 which amounted to Rs.10200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? Answers:
A) 9680 B) 2277 C) 2999 D) 10700 E) 10740

Solution: (9000*3*2)/100= 
(9000*3*2)/100 = 540
540   10200   --------   10740   Answer:10740
Answer: E
If the height of a cone is increased by 130% then its volume is increased by? Select the correct option.
A) 100 B) 777 C) 998 D) 729 E) 130

Solution: 100%   Answer:130
Answer: E
If 5* nP3 = 4* (n+1)P3, find n?	Choose the correct choice from the following choices.
A) 10 B) 11 C) 12 D) 14 E) None

Solution: Solution:   nP3 = n*(n–1)*(n–2).   (n+1)P3 =(n+1)*n*(n–1).   Now,   5*n*(n–1)*(n–2) = 4* (n+1)*n*(n–1).   Or, 5(n−2) = 4(n+1).   Or, 5n−10 = 4n+4.   Or, 5n−4n = 4+10.   Hence, n = 14.   Note: nPr = [n! /(n -r)!].   Answer: Option 14
Answer: D
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
Choose the correct choice from the following choices:  A) 156  B) 150  C) 137  D) 132  E) 89

Solution: Let x be the original 2-digit number.   If each digit is halved, then the sum of G and H is 3x/2.   Note the sum must be a multiple of 3 and less than 150.   Only 132 satisfies these two conditions.   The answer is 132.
Answer: D
The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?	Choices:	A) 29997	B) 28088	C) 27098	D) 19000	E) 2799

Solution: Money paid in cash = Rs. 1000   Balance payment = (20000 - 1000) = Rs. 19000.Answer:19000
Answer: D
A merchant marks his goods up by 50% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? Select:	A) 21%	B) 25%	C) 69%	D) 35%	E) 19%

Solution: Let the price be 100.   The price becomes 150 after a 50% markup.   Now a discount of 10% on 150.   Profit=135-100   35%   answer 35%
Answer: D
In a certain school, the ratio of boys to girls is 5 to 13. If there are 160 more girls than boys, how many boys are there? Pick
A) 100  B) 36  C) 45  D) 72  E) 117

Solution: The ratio of b to G is 5:13 and the other data point is G are more than boys by 160...   Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 160. so 1 part corresponds to 160/8= 
160/8 = 20
20 and so   5 parts correspond to 5*10= 100.   100
Answer: A
If p and q are both odd prime numbers andp < q, then how many different positive integer factors does2pqhave?	Choices.
A) 3	B) 4	C) 6	D) 8	E) 12

Solution: p and q are both odd prime numbers- It means either p or q is not 2   and since prime numbers have only two factors - 1 and the number itself   p and q each will have (1+1)= 
(1+1) = 2
2 factors   Hence 2pq will have (1+1)(1+1)(1+1)= 8 factors   8 is the answer
Answer: D
If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31 Select:  A) 2  B) 3  C) 5  D) 7  E) 8

Solution: P ÷ 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 31= 19008 / 31 = 613, remainder = 5   5
Answer: C
If the cost price of 35 chocolates is equal to the selling price of 21 chocolates, the gain percent is :  Choose the correct choice from the following options.
A) 66.55% B) 66.66 % C) 66 % D) 55% E) 66.33%

Solution: Explanation :   Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 21 chocolates = Rs. 21;   S.P. of 21 chocolates =Rs. 35.   .'. Gain% = 14*100/21 = 66.66%   Answer : 66.66 %
Answer: B
A coin is tossed 6 times. What is the probability that the number of Heads is equal to the number of Tails?
Choices:	A) 5/16	B) 4/13	C) 7/16	D) 5/12	E) 6/17

Solution: We have to find the probability that we get 3 heads and 3 tails in 6 tosses of the coin.   Using the binary formula and defining a head as a success,   P(3 heads in 6 tosses) = 6C3* (1/2)^2 * (1/2)^2*(1/2)^2   = 20/64   = 5/16   The answer is 5/16
Answer: A
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?  Choose the correct choice from the following choices:
A) 1/122
B) 1/129
C) 1/121
D) 1/128
E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = 4C4/9C4   = 1/126   Answer: 1/126
Answer: E
(1000)7÷(10)19=?  Choose the most appropriate option: A) 10 B) 100 C) 1000 D) 10000 E) None of these

Solution: Explanation:   =(103)7/(10)19   =(10)21/(10)19=10(2)=100   Option 100
Answer: B
In a class of 30 students in an examination in maths 3 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
Choose the correct choice from the following choices
A) A)47  B) B)45.6  C) C)44  D) D)48.5  E) E)49

Solution: Explanation:   Total marks obtained by a class of 25 students   = 3*95 + 3*0 + 26 * 45= 
3*95 + 3*0 + 26 * 45 = 1_455
1455   Average marks of whole class= 1455/30= 
1455/30 = 97/2 = around 48.5
48.5   Answer: Option 48.5
Answer: D
A certain auto manufacturer sold 4% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?  Pick one
A) 63,000  B) 2,000,000  C) 2,020,000  D) 2,040,000  E) 2,300,000

Solution: Let's assume in 2006 the manufacturer sold X.   In 2007 he sold X-4/100(X)   If sales in 2006,X= 2.1 million find X-4/100(X)   (2.1 x 10^6)-4/100(2.1 x 10^6)   2100000-84000=2,016,000-----> 2,020,000(approx)   ANSWER:2,020,000
Answer: C
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 11 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal Select the correct option:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Since (ii) holds for every real number x, it will remain valid if we replace x with   -x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 11 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 11-3= 
11-3 = 8
8. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 8
Answer: A
In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,9). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0? Choose the correct choice from the following options:	A) 1/5	B) 1/3	C) 1/2	D) 2/9	E) 4/5

Solution: The area of the right triangle is (1/2)*4*9= 
(1/2)*4*9 = 18
18.   Only the points (a,b) below the line y=x satisfy a - b > 0.   The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.   P(a - b > 0) = 8/18 = 2/9   The answer is 2/9.
Answer: D
The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? Choose the correct choice from the following answers:	A) 10	B) 12	C) 16	D) 18	E) 20

Solution: Explanation:   10 * 15 + 36 – 26 = 160/10= 
160/10 = 16
16   16)
Answer: C
In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they selected that at least one boy should be there? Select
A) 159	B) 194	C) 205	D) 209	E) 140

Solution: We may have( 1 black and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4boys)   =(6c1 x 4c3)+(6c2 x 4c2)+(6c3 x 4c1)+6c4   =24+90+80+15= 
24+90+80+15 = 209
209   ANSWER 209 209
Answer: D
If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 5 people to do 5 times of that particular work? Pick one.
A) 1 B) 2 C) 3 D) 5 E) 8

Solution: 3 people can do the work one time in one day.   1 person can do 1/3 of the work in one day.   5 people can do 5/3 of the work in one day.   5 people can do 5 times the work in 3 days.   The answer is 3.
Answer: C
A certain quantity of 80% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Choose the correct choice from the following choices:
A) 1/4
B) 1/3
C) 1/2
D) 2/3
E) 9/11

Solution: Let's say that the total original mixture A is 100 ml   The original mixture A thus has 50 ml of alcohol out of 100 ml of solution   You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 80 ml and 25 ml is 55 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 25%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 45%. Therefore, 45 out of 55 is 9/11 and 9/11 is the answer.
Answer: E
In the faculty of Reverse-Engineering, 300 second year students study numeric methods, 600 second year students study automatic control of airborne vehicles and 200 second year students study them both. How many students are there in the faculty if the second year students are approximately 70% of the total?	Choose the correct choice from the following options
A) 750  B) 800  C) 900  D) 950  E) 1000

Solution: Total number of students studying both are 300 + 600 - 200= 
300 + 600 - 200 = 700
700 (Subtracting the 200 since they were included in the both the other numbers already).   So 70% of total is 700, so 100% is 1000   Answer is 1000
Answer: E
Length of a rectangular plot is 40 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? Choose the most appropriate option
A) 46 m
B) 60 m
C) 58 m
D) 70 m
E) 80 m

Solution: Let breadth = x metres.   Then, length = (x + 40) metres.   Perimeter = 5300/26.5= 
5300/26.5 = 200
200 m.   2[(x + 40) + x]= 200   2x + 40 = 100   2x = 60   x = 30.   Hence, length = x + 40 = 70 m   70 m
Answer: D
Which of the following is the lowest positive integer that is divisible by the first 6 positive integer multiples of 3?  Choices:	A) 90	B) 100	C) 120	D) 150	E) 180

Solution: The number must be divisible by 3, 2*3, 3^2, 2^2*3, 5*3, and 2*3^2.   The lowest such number is 2^2*3^2*5 = 180.   The answer is 180.
Answer: E
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade? Select the correct option.
A) 3 : 1  B) 7 : 3  C) 3 : 2  D) 4 : 5  E) 3 : 4

Solution: The lemonade is 50% water and 20% sugar.   The limeade is 40% water and 32% sugar.   The crusade is more than 45% water and more than 24% sugar.   For the crusade to be 45% water, the ratio of lemonade to limeade must 1:1. Since the crusade is more than 45% water (the average of 50 and 40), then the ratio of lemonade to limeade must be more than 1:1. Eliminate D and E.   For the crusade to be 24% sugar, the ratio of lemonade to limeade must 2:1. Since the crusade is more than 24% water, then the ratio of lemonade to limeade must be less than 2:1. Eliminate A and B.   Answer: 3 : 2.
Answer: C
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?  Choose the correct choice from the following answers.
A) 28  B) 27  C) 29  D) 24  E) 20

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40   = 9/2 => x   = 20 km.   Answer: 20
Answer: E
The sum of digits of a two digit number is 13,The difference between the digits is 5. Find the number  Choose the correct answer
A) 85
B) 94
C) 83
D) 72
E) None

Solution: Description :   => x+y=13, x-y=5   Adding these 2x =18   => x=9, y=4.   Thus the number is 94   Answer 94
Answer: B
Which number is the odd one out?
159
248
840
357
591
582
Options.
A) 120
B) 240
C) 840
D) 360
E) 160

Solution: 840   840   In the rest there is the same difference between each digit, eg: 8 (Ã¢â‚¬â€œ4) 4 (Ã¢â‚¬â€œ4)0
Answer: C
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? Options
A) 187  B) 476  C) 268  D) 208  E) 276

Solution: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x   = 476   Answer: 476
Answer: B
Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was	Choose the correct choice from the following answers: A) 2:1 B) 3:2 C) 4:3 D) 5:4 E) 1:2

Solution: Explanation:   Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)   Therefore, Ratio of the speeds of two trains = = 3 : 2. Answer: 3:2
Answer: B
At present, the ratio between the ages of Arun and Deepak is 4:8. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?  Pick one.
A) 17 years  B) 15 years  C) 18 years  D) 40 years  E) 19 years

Solution: Let the present ages of Arun and Deepak be 4x and 8x years respectively.   Then, 4x + 6 = 26 => x   = 5   Deepak's age   = 8x   = 40 years.   Answer:40 years
Answer: D
A new sales clerk in a department store has been assigned to mark sale items with red tags, and she has marked 30% of the store items for sale. However, 20% of the items that are supposed to be marked with their regular prices are now marked for sale, and 55% of the items that are supposed to be marked for sale are marked with regular prices. What percent of the items that are marked for sale are supposed to be marked with regular prices?
Pick one
A) 30%  B) 35%  C) 40%  D) 45%  E) 50%

Solution: # of items 100 (assume);   # of items that should be marked for sale is x;   # of items that should be at the regular price is 100-x;   # of items that are actually marked for sale   0.3*100= 
  0.3*100 = 30
30.   Let's see how many items are marked for sale:   20% of 100-x (20% of the items that are supposed to be marked with their regular prices (100-x) are now marked for sale);    100-55= 
 100-55 = 45
45% of x (since 55% of the items that are supposed to be marked for sale (x) are marked with regular prices, then the remaining 45% of x are marked for sale);   So, 0.2(100-x)+0.45x=30 --> x=40 (# of items that should be marked for sale).   So, # of the items that are supposed to be marked with their regular prices is  0.2*(100-40)= 
 0.2*(100-40) = 12
12, which is  12/30*100= 
 12/30*100 = 40
40% of # of items that are actually marked for sale.   Answer: 40%.
Answer: C
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 38,000, what will be the amount A receives? Choose the correct option.
A) 14700  B) 15960  C) 14900  D) 14300  E) 14000

Solution: Total amount invested = 50000   Assume that investment of C =x.   Then investment of 15960 =5000+x,   Investment of A =4000+5000+x=9000+x   x+5000+x+9000+x=50000   ⇒3x+14000=50000   ⇒3x=50000–14000=36000   ⇒x=36000/3= 
36000/3 = 12_000
12000   Investment of C=x=12000   Investment of 15960 =5000+x=17000   Investment of A =9000+x=21000   Ratio of the investment of A, 15960 and C   =21000:17000:12000   =21:17:12   Share of A = Total profit ×21/50   =38000×21/50=15960   Answer is 15960
Answer: B
Ms.James invested in Fund T and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund T paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund T. How much did Ms. Morris invest in Fund T?
Choose the correct answer
A) $32,000  B) $36,000  C) $40,000  D) $42,000  E) $45,000

Solution: 0.17B-0.23T = 200 | * 100   17B-23T=20,000   T+B=100,000   B=100,000 - T   17(100,000 - T) - 23T = 20,000   1,700,000 - 17T - 23T = 20,000   1,680,000 = 40T   divide by 40   first two digits: 42...so answer is $42,000.
Answer: D
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 16%? Choose the correct choice from the following answers:
A) 20%
B) 26%
C) 13 1/30%
D) 12%
E) 13%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 84   2/3 SP1 = 84   SP1 = 126   100 --- 26 => 26%   ANSWER:26%
Answer: B
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?	Choose the correct choice from the following choices:	A) Rs.3250	B) Rs.6250	C) Rs.10250	D) Rs.11750	E) Rs.12750

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750   ANSWER:Rs.11750
Answer: D
The average age of husband, wife and their child 3 years ago was 33 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is  Choose the correct choice from the following answers
A) 35 years
B) 40 years
C) 50 years
D) 58 years
E) None

Solution: Solution   Sum of the present ages of husband, wife and child	= (33x3+3x3) years   = 108 years.   Sum of the present ages of wife and child	= (20x2+5x2) years   = 50 years.   âˆ´ Husband's present age	= (108 - 50)= 
(108 - 50) = 58
58 years.   Answer 58 years
Answer: D
A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 2% higher then what would the sum amount in the same time period?
Choose the correct choice from the following choices.
A) Rs. 4465	B) Rs. 3683	C) Rs. 3596	D) Data inadequate	E) None of these

Solution: 3422=2900+(2900*R*3/100)   R=6   If R is 2 more.   Then R=8   Sum=2900+(2900*8*3/100)= 
2900+(2900*8*3/100) = 3_596
3596   ANSWER:Rs. 3596
Answer: C
J is faster than P. J and P each walk 24 km. Sum of the speeds of J and P is 7 kmph. Sum of time taken by them is 14 hours. Then J speed is equal to Choices
A) 22	B) 14	C) 6	D) 8	E) 16

Solution: Given J > P   J + P = 7, only options are (6, 1), (5, 2), (4, 3)   From the given options, If J = 4 the P = 3. Times taken by them = 244+243=14   Answer:14
Answer: B
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 140 of the workers of that company are men, how many of the workers are women? Choose the correct choice from the following options:	A) 85	B) 95	C) 105	D) 120	E) 210

Solution: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.   Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.   Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.   Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.   If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.   Cavg = (80*1 + 40*2)/3 = 160/3% are men   Total = 120*300/160= 
120*300/160 = 225
225   No. of women= 225 - 140= 
225 - 140 = 85
85   85
Answer: A
An aptitude test contains 4 questions from verbal reasoning, 5 questions from simple mathematics and 6 questions testing knowledge of English. Three questions are selected at random from the list of questions. The probability that all of them are from simple mathematics section, is:	Choose the correct choice from the following:
A) 2/91
B) 1/22
C) 3/22
D) 2/77
E) None of these

Solution: Explanation :   Let S be the sample space.   Then, n(S) = number of ways of selecting 3 questions out of 15= 15C3= (15 x 14 x 13)/(3 x 2 x 1)= 455   Let E = event of getting all the 3 questions from simple mathematics section.   n(E) = 5C3 = 5C2 = (5 x 4)/(2 x 1) = 10   P(E) = n(E)/n(S) = 10/455 = 2/91 .   2/91nswer : 2/91
Answer: A
In a group of 100 cars, 49 cars do not have air conditioning. If at least 51 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?	Select.
A) 49	B) 47	C) 48	D) 51	E) 53

Solution: Lets assume AC=51(includesonly AC carsandcars with AC and racing stripes)   lets assume RS(racing stripes)>=51(includescars with AC and racing stripesandonly racing stripes).   Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=51.. we have to assign atleast 2 tocars with AC and racing stripes.   Hence AC=51-2= 
51-2 = 49
49.   The answer is 49
Answer: A
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?
Options:
A) 69.5 km/hr	B) 70 km/hr	C) 79 km/hr	D) 79.2 km/hr	E) 79.5 km/hr

Solution: Explanation:   Let the length of the train be x metres and its speed by y m/sec.   Then,   Now,   8y + 264 = 20y   y = 22.   Speed = 22 m/sec = km/hr = 79.2 km/hr.   ANSWER IS 79.2 km/hr
Answer: D
765 chairs are to be arranged in a column in such a way that the number of chairs in each column should be equal to the columns. How many chairs will be excluded to make this arrangement possible? Choose the correct choice from the following choices
A) 6	B) 36	C) 19	D) 27	E) None of these

Solution: 27(2) < 765 < 28(2)   ∴ required no. of chairs to be excluded   = 765 – 729 = 36   Answer 36
Answer: B