MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the probability of getting exactly three heads on five flips of a fair coin?	Choose the correct choice from the following options:
A) 1/32  B) 3/32  C) 1/4  D) 5/16  E) 1/2

Solution: 5 Flips of a fair coin to get = HHHTT = no. of ways this can be achieved = 5!/3!x2! = 10   Probability to get any of the above 10 arrangements (HHHTT) = (1/2)^5 = 1/32   Total probability = 1/32 x 10 = 5/16   Answer:5/16
Answer: D
The average of first seven multiples of 8 is:
Choose the correct choice.
A) 9  B) 16  C) 15  D) 32  E) 10

Solution: Explanation :   (8(1+2+3+4+5+6+7)/7   = 8x28/7   = 32   Answer : 32
Answer: D
A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
Choices.
A) 11	B) 99	C) 89	D) 10	E) 12

Solution: lb = 150   2(l + b) = 50 => l + b = 25   l – b = 5   l = 15 b = 10   Answer:10
Answer: D
A and B can complete a job in 30 and 20 days respectively. They start working together and B leaves 5 days before the work is finished. In how many days is the total work finished?
Answers:
A) 15	B) 6	C) 5	D) 4	E) 3

Solution: A and B can do the job in 30 and 20 days individually, so together they will take 30*20/(30 + 20) = 600/50= 
600/50 = 12
12 days.   The work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after  (5/6)*12= 
 (5/6)*12 = 10
10 days   Total time taken= 10 + 5= 
10 + 5 = 15
15 days.   15NSWER:15
Answer: A
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Choose the most appropriate option:
A) 5.98  B) 8.98  C) 5.76  D) 5.87  E) 5.82

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76
Answer: C
The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?	Select the correct option.
A) 432  B) 300  C) 252  D) 992  E) 212

Solution: 2(3x + x) = 80   l = 30 b = 10   lb = 30 * 10= 
30 * 10 = 300
300   Answer:300
Answer: B
The average (arithmetic mean) of six numbers is 9. If 3 is subtracted from each of four of the numbers, what is the new average? Choose the correct choice from the following answers
A) 1.5	B) 2	C) 7	D) 4	E) 4.5

Solution: Sum of 6 numbers = 6*9= 
6*9 = 54
54   If 3 is subtracted from each of four of the numbers , we subtract  3*4= 
 3*4 = 12
12 from the total sum   Sum of 6 number after subtracting 3 from each of four of the numbers= 54 - 12= 
54 - 12 = 42
42   New average= 42/6= 
42/6 = 7
7   Answer 7
Answer: C
The speed of a boat in upstream is 50 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?
Choose the correct choice from the following choices:
A) 10 kmph.
B) 17 kmph.
C) 15 kmph.
D) 11 kmph.
E) 12 kmph.

Solution: Speed of the boat in still water = (50+80)/2= 
(50+80)/2 = 65
65 kmph. Speed of the stream= (80-50)/2= 
(80-50)/2 = 15
15 kmph.   Answer:15 kmph.
Answer: C
A and B run a 1 km race. If A gives B a start of 50m, A wins by 14 seconds and if A gives B a start of 22 seconds, B wins by 20 meters. Find the time taken by A to run 1 km.
Choose the correct choice from the following.
A) 222  B) 100  C) 287  D) 2976  E) 111

Solution: To solve these type of questions, always keep in your mind that, the ratio of the speeds of two contestents never change.   A gives B a start of 50 m means, A runs 1000 m and B runs only 950. By the time A reaches the target, B has to take 22 seconds to reach the target.   ab=1000950−14b=9801000−22bab=1000950−14b=9801000−22b   50,000 -1100b = 46550 -686b   Solving we get b = 25/3   Now Assume A's speed = x   1000950−14(25/3)=x25/31000950−14(25/3)=x25/3   x = 10   So x takes   1000/10= 
  1000/10 = 100
100 seconds.   Answer:100
Answer: B
How many multiples of 4 are there between 16 and 112, inclusive?	Choose the most appropriate option
A) 21
B) 22
C) 23
D) 24
E) 25

Solution: The multiples of 4 are from 4*4 up to 4*28.   28-4+1= 
28-4+1 = 25
25.   The answer is 25.
Answer: E
The value of 1 + 1/(4 x 3) + 1/(4 x 32) +1/(4 x 33) up to four places of decimals is ?
Choose one.
A) 1.1202	B) 1.1203	C) 1.1204	D) None of these	E) Cannot be determined

Solution: Answer   Given expression = (108 + 9 + 3 +1) / 108   = 121 / 108   = 1.1203   Correct Option: 1.1203
Answer: B
The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. the numbers are:	Options: A) 7,2 B) 8,9 C) 5,12 D) 2,7 E) 12,5

Solution: x(x+y)=204   x^2+xy=204....(1)   y(x-y)=35   xy-y^2=35....(2)   x^2+Y^2=169   Thus, x=12, y=5   correct answer 12,5
Answer: E
A number when divided by 342 gives a remainder 47. When the same number ift divided by 19, what would be the remainder ?
Answers.
A) 9  B) 7  C) 6  D) 5  E) 3

Solution: On dividing the given number by 342, let k be the quotient and 47 as remainder.   Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.   The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder.   9nswer is 9.
Answer: A
(540 - ?) × 1/7 + 12 = 25  Choose the most appropriate option.
A) A)227	B) B)449	C) C)32	D) D)600	E) E)3

Solution: Explanation:   => (540 - ?) × 1/7 + 12 = 25   => (540 - ?) × 1/7 = 25 - 12= 
25 - 12 = 13
13=> 540 - ? = 13 × 7 = 91   => ? = 540 - 91= 
540 - 91 = 449
449   Answer: Option 449
Answer: B
A housewife wishes to purchase three articles A, B and C from a sum of Rs. 200. The unit prices of the articles A, B and C are Rs. 20, Rs. 35 and Rs. 25 respectively. If she spends the entire amount by purchasing 5 numbers of articles of type C, what is the ratio of the number of articles purchased of type A to that of, type B?
Choose the correct choice from the following answers:	A) 1 : 2	B) 2 : 1	C) 1 : 1	D) None of these	E) Cannot be determined

Solution: Explanation:   After spending Rs. 125 (25 * 5) for articles of type C, the housewife is left with Rs. 75 (200 – 125). Since this amount has to be spent in totality, she must have purchased 2 articles of type A (equivalent to Rs. 40) and 1 article of type B (equivalent to Rs. 35). Thus, the required ratio is 2 : 1.   ANSWER 2 : 1
Answer: B
A money lender lent a total of $1900 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1900, how much did he lend to each of the two customers?
Choose the correct choice from the following options
A) 700; 1100
B) 1273; 627
C) 1000; 800
D) 1200; 800
E) None of the above

Solution: The method given above is the one given in the book.   However the method I used was   (1*x*5)/100 + (1900-x)*6/100 = 1900*5.67/100   Simplifying we get x=627   1273; 627
Answer: B
There are three numbers. 5/7th of the first number is equal to 48% of the second number. The second number is 1/9th of the third number. If the third number is 1125, then find 25% of the first number?
Pick one.
A) 168  B) 84  C) 42  D) 21  E) None of these

Solution: Let the first number and the second number be F and S respectively.   5/2 F = 48/100 S ----> (1)   S = 1/9 * 1125 ----  (1)= 
----  (1) = 1
1/9 * 1125= 
1/9 * 1125 = 125
125   (1)=> 5/7 F = 48/100 * 125   => F = 84   25% of F = 1/4 * 84= 
1/4 * 84 = 21
21   ANSWER:21
Answer: D
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg?
Choose the correct option:
A) s.50	B) s.46	C) s.49	D) s.41	E) s.42

Solution: 1000*(25/100)= 
1000*(25/100) = 250
250 ---- 5   ? ---- 1=> Rs.50   s.50nswer: s.50
Answer: A
A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country W. If calls to country W are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country W in a certain month?  Options.
A) $8.75
B) $12
C) $13.40
D) $17.40
E) $24.40

Solution: Discount = 40% of spending   We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.   Max discount = (40/100)* 60 * 1.6 = (40/100)*96   This would be slightly less than 40. About 38 to 39.   Saving = (Slightly less than 40) - 25 = Slightly less than 15 charged in W country   Answer ($13.40)
Answer: C
For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 161?  Choose the correct choice from the following answers:
A) 1090 B) 2060 C) 3080 D) 4030 E) 5040

Solution: 100 + 102 +...+ 160 = 31*100 + (2+4...+60) = 31*100 + 2(1+2+...+30) =   31*100 + 2(30)(31)/2 = 130*31= 
130*31 = 4_030
4030   The answer is 4030.
Answer: D
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?  Choices:
A) 321  B) 65  C) 120  D) 100  E) 80

Solution: 1 million distinct 3 digit initials are needed.   Let the number of required alphabets in the language be ‘n’.   Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.   Note distinct initials is different from initials where the digits are different.   For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.   This n3 different initials = 1 million   i.e. n3 = 106 (1 million = 106)   => n3 = (102)3 => n = 102 = 100   Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.   Ans: 100
Answer: D
The sum of all solutions for x in the equation x^2 – 8x + 21 = |x – 5|+ 4 is equal to:  Answers.
A) –7 B) 7 C) 20 D) 12 E) 14

Solution: x^2 - 8x + 17 = |x-5|   RHS can be -ve or +ve   x^2 - 9x + 22 = 0   x^2 - 7x + 12 = 0   x= 11,4,3,2   We test all 3 values in original equation, all ok.   Thus, Sum = 11 + 4 +3 + 2= 
11 + 4 +3 + 2 = 20
20   Ans (20)
Answer: C
If log10 2 = 0.3010, the value of log10 80 is: Choices:
A) 2.65
B) 1.903
C) 3.05
D) 6.487
E) 5.98

Solution: Explanation:   log10 80	= log10 (8 x 10)   = log10 8 + log10 10   = log10 (23 ) + 1   = 3 log10 2 + 1   = (3 x 0.3010) + 1   = 1.9030.   answer 1.903
Answer: B
Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?	Select the correct option:	A) 10.45	B) 10.35	C) 10.15	D) 10.05	E) 10.25

Solution: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4= 
80 * 9/4 = 180
180 hrs.   Time taken to cover remaining distance= (350 - 180)/60 = 17/6 hrs   = 2 5/6 = 2 hrs 50 min   Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.   So, Anna reached city A at 10.25 a.m.   Answer:10.25
Answer: E
Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 4000 Km?  Select:
A) 10.  B) 25.  C) 30.  D) 38.  E) 200.

Solution: Total distance= Distance travelled by A +Distance travelled by car B   Distance= speed*time   Distance of A= 3x * 6   Distance of B= x*2   (3x * 6) + (x*2) = 4000   x= 200 KM/hr   200. is the answer
Answer: E
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:
A) 3377 B) 2788 C) 27999 D) 11750 E) 17881

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750   Answer: 11750
Answer: D
John is traveling to a meeting that is 24 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
Choose the correct choice from the following choices
A) 25 mph	B) 37 mph	C) 48 mph	D) 49 mph	E) 56 mph

Solution: Well 48mph. C. Time*rate=distance --> 0.5*rate=24 --> rate=48
Answer: C
What is the units digit of (493) (915) (381) (756) (22) Select the correct option:
A) 0
B) 1
C) 4
D) 5
E) 6

Solution: Just multiply the digits in the units place for each term and you will get the answer. It should be 0. you got a 5 as a unit digit and an even number term. so the multiplication of this will definitely yield a 0. Answer has to be 0.   I also tried it using the calculator and the answer is 1.   IMO 1.
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?  Choose the correct choice:
A) 186 m  B) 176 m  C) 120 m  D) 178 m  E) 187 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer:120 m
Answer: C
Tomy started a software business by investing Rs.50,000. After 6months, Nanda joined her with a capital of $80,000. After 3years, they earned a profit of $24,500. What was Simran's share in the profit?
Select
A) $8,500 B) $9,500 C) $10,500 D) $11,500 E) $12,500

Solution: Tomy : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.   Tomy 's share = $24500 x	3/7	= $10,500.   $10,500
Answer: C
If n = 7^11 – 7, what is the units digit of n? Choose the most appropriate option.
A) 0
B) 1
C) 4
D) 6
E) 8

Solution: Always divide the power (incase 11) by 4 and use the remainder as the new power. The question now becomes 7^3 - 7. Now 7^3 has last digit 3. Since 7^11 (or for that matter 7^3) is greater than 7, we subtract 7 from 13 ( the 10+3 --> 10 has come from carry over from the tenth place). thus 13 - 7= 
13 - 7 = 6
6 is the answer. Option 6
Answer: D
Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there be three persons ahead of C and 21 persons behind A, what could be the minimum number of persons in the queue?	Choose one
A) 33
B) 37
C) 28
D) 36
E) 19

Solution: Explanation:   Three persons A, B, C can be arranged in a queue in six different ways, ie ABC, CBA, BAC, CAB, BCA, ACB. But since there are only 3 persons ahead of C, so C should be in front of the queue. Thus, there are only two possible arrangements, ie CBA and CAB.   We may consider the two cases as under:   Case I:   Clearly, number of persons in the queue = (3+1+8+1+5+1+21=) 40   Case II:   Number of persons between A and C   = (8 - 6)= 
(8 - 6) = 2
2   Clearly number of persons in the queue= (3+1+2+1+21)= 
(3+1+2+1+21) = 28
28   Now, 28 < 40. So, 28 is the minimum number of persons in the queue.   Answer: 28) 28
Answer: C
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 6 p.c?	Choose the correct choice from the following choices
A) 38028  B) 38000  C) 32977  D) 37600  E) 38982

Solution: CP + CP/8 = 45000   CP = 40000   SP = 40000*(94/100)= 
40000*(94/100) = 37_600
37600   Answer:37600
Answer: D
A number when divided by a divisor leaves a remainder of 21. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Choose the correct option:
A) 12 B) 13 C) 34 D) 37 E) 59

Solution: Let the number is N, the divisor = D,   I will make the two equations-   N = xD+21   2N = yD+11   where x and y are integers   Solving them: D(y-2x) = 34   as D is also integer and 34 is a prime number, the D should be 34 to satisfy the above equation.   Hence answer is '37'
Answer: D
A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 65%. Staff are allowed a further 60% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
Choose the most appropriate option:
A) 0.15D  B) 0.16D  C) 0.65D  D) 0.14D  E) 0.05D

Solution: Effective discount = a + b + ab/100 = - 65 - 60 + (-65)(-60)/100 = -86   Sale price = 0.14D * ( 1 - 86/100)   Sale price = .14 * 0.14D   Answer (0.14D)
Answer: D
A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ? Choose the correct option
A) 25 km/hr
B) 35 km/hr
C) 40 km/hr
D) 42 km/hr
E) 45 km/hr

Solution: Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr   35 km/hr
Answer: B
A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate? Select
A) 12 1/2 years	B) 12 1/8 years	C) 17 1/2 years	D) 12 3/2 years	E) 15 1/2 years

Solution: 100 ---- 200 ---- 5   200 ---- 5   100 ---- 2 1/2   ------------------   600 ---- 12 1/2 years   12 1/2 yearsnswer:12 1/2 years
Answer: A
If sum of three numbers in A.P is 33 and sum of their squares id 491, then what are the three numbers. Answers.
A) 5,11,17
B) 7,11,15
C) 9,11,13
D) 3,11,19
E) 3,12,19

Solution: a + (a + d ) + ( a + 2d ) = 3( a + d ) = 33,   a + d = 11, or second term = 11 , first term = 11– d ,   Then ( 11- d ) 2 + 11 2 + ( 11 + d ) 2 = 491   2 d 2 = 491 - ( 3 * 121 ) = 491 - 363= 
491 - 363 = 128
128   d 2= 64, d = 8, a = 3,   ANSWER:3,11,19
Answer: D
How many number are immediately preceded and immediately followed by different numbers?
7 7 7 5 7 5 7 5 7 7 7 7 5 7 5 7 5 7 7 7 7 7 5 7 5  Choose the correct choice from the following options:  A) 2  B) 3  C) 4  D) 5  E) 1

Solution: five   ANSWER:5
Answer: D
An exhibition was conducted for 4 weeks. The number of tickets sold in 2nd work week was increased by 20% and increased by 16% in the 3rd work week but decreased by 20% in the 4th work week. Find the number of tickets sold in the beginning, if 1392 tickets were sold in the last week Choose the correct option.
A) 6 B) 35 C) 120 D) 1250 E) 740

Solution: Answer: 1250   Explanation:   let initially A ticket has been sold.   So now in 2nd week 20% increases so   A × 120100120100   In 3rd week 16% increases so   A × 120100120100 × 116100116100   In 4th week 20% decrease so   A × 120100120100 × 116100116100 × 120100120100 = 1392   A = 1250   Answer:1250
Answer: D
Let exp(m,n) = m to the power n. If exp(10, m)= n exp(2,2) where m and n are integers then n= ___?  Choose the correct choice from the following: A) 24 B) 25 C) 26 D) 27 E) 28

Solution: 10^m=n*(2^2)   (2*5)^m=n*(2^2)   (2^m)*(5^m)=n*(2^2) now equate both side we get m=2 and (5^m)=n   (5^2)=n=>n=25   ANSWER:25
Answer: B
Difference of 2 numbers is 100. If 5% of one number is 10% of the other number, find the addition of2 numbers? Options:	A) 150	B) 300	C) 210	D) 290	E) 180

Solution: Let the numbers be x and y   5% of x = 10% of y   x = 2y   x-y = 100   2y - y =100   y = 100   x = 2y = 200   x+y = 300   Answer is 300
Answer: B
If y = 30p, and p is prime, what is the greatest common factor of y and 24p, in terms of p?	Choose the correct answer:	A) p	B) 2p	C) 6p	D) 8p	E) p^2

Solution: y = 30p = 2*3*5*p   24p = 2^3*3*p   The greatest common factor of 30p and 20p is the product of all the common prime factors, using the lower power of repeated factors. The greatest common factor is 2*3*p = 6p   The answer is 6p.
Answer: C
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be	Choose the correct choice from the following answers.
A) 22	B) 24	C) 26	D) 20	E) 28

Solution: Explanation :   Let number of hens = h and number of cows = c   number of heads = 48   => h + c = 48 ---(Equation 1)   number of feet = 140   => 2h + 4c = 140   => h + 2c = 70 ---(Equation 2)   (Equation 2) - (Equation 1) gives   2c - c = 70 - 48   => c = 22   Substituting the value of c in Equation 1, we get   h + 22 = 48   => h = 48 - 22= 
48 - 22 = 26
26   i.e., number of hens= 26   Answer : 26
Answer: C
It takes 8 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 8 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 2:00 pm? Choose the correct option:
A) 5:10 pm	B) 5:30 pm	C) 5:50 pm	D) 6:10 pm	E) 6:30 pm

Solution: Each student paints at a rate of 1/80 of the house per hour.   In 5 hours, the 8 students can paint 40/80 of the house.   From 2 pm to 3 pm, 9 students paint another 9/80 for a total of 49/80.   From 3 pm to 4 pm, 10 students paint another 10/80 for a total of 59/80.   From 4 pm to 5 pm, 11 students paint another 11/80 for a total of 70/80.   12 students can paint the remaining 10/80 of the house in 10/12 of an hour = 50 minutes.   The house is completed at 5:50 pm.   The answer is 5:50 pm.
Answer: C
If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
Choose one
A) 23267	B) 2677	C) 1800	D) 2778	E) 76611

Solution: Explanation:   Least Cost Price = Rs. (200 * 8) = Rs. 1600.   Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.   Required profit = Rs. (3400 - 1600) = Rs. 1800.   Answer: 1800) 1800
Answer: C
There are 8 stores in town that had a total of 23 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 8 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
Choose the correct choice from the following options
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: 8 people visited 2 stores each for 16 visits.   To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is   23 - 16 - 3= 
  23 - 16 - 3 = 4
4, which is the maximum that one person could have visited.   The answer is 4.
Answer: C
A car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km/hour. At what speed, in km/hr, is the car traveling? Select the correct option
A) 70 B) 72 C) 74 D) 75 E) 78

Solution: Time to cover 1 kilometer at 80 kilometers per hour is 1/80 hours = 3,600/80 seconds = 45 seconds;   Time to cover 1 kilometer at regular speed is  45 + 4= 
 45 + 4 = 49
49 seconds= 49/3,600 hours = 1/74 hours;   So, we get that to cover 1 kilometer 1/74 hours is needed --> regular speed 74 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   Answer: 74
Answer: C
One night a certain hotel rented 3/5 of its rooms, including 2/3 of their air conditioned rooms. If 3/5 of its rooms were air conditioned, what percent of the rooms that were not rented were air conditioned?
Choices: A) 50% B) 55% C) 60% D) 65% E) 70%

Solution: The rooms which were not rented is 2/5   The 50%C rooms which were not rented is (1/3)*(3/5) = 1/5   The percentage of unrented rooms which were 50%C rooms is (1/5) / (2/5) = 1/2 = 50%   The answer is 50%.
Answer: A
How many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Choose the correct choice.
A) 28 sec
B) 23 sec
C) 29 sec
D) 30 sec
E) 36 sec

Solution: 30 sec   30 sec = 150 + 150= 
150 + 150 = 300
300   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 300/10= 
300/10 = 30
30 sec
Answer: D
A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?  Choose the correct choice from the following answers:	A) 65 kmph	B) 28 kmph	C) 54 kmph	D) 26 kmph	E) 87 kmph

Solution: D = 100 + 125= 
100 + 125 = 225
225   T= 15   S = 225/15 * 18/5= 
225/15 * 18/5 = 54
54 kmph   Answer:54 kmph
Answer: C