MU-NLPC/Calc-aqua_rat huggingface dataset:
The function F is defined for all positive integers n by the following rule: f(n) is the number of position integer each of which is less than n, and has no position factor in common with n other than 6. If p is any prime number then f(p)=  Pick
A) p-1
B) p-2
C) (p+1)/2
D) (p-1)/2
E) 2

Solution: The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.   Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).   If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.   Answer: (p-1)/2.
Answer: D
In wardrobe Marry has 3trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4shirts. One of them is grey and the other 3are white. He openshiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey? Choose the correct choice from the following answers:
A) 1/2 B) 2/3 C) 3/5 D) 4/7 E) 4/9

Solution: Probability that trouser is not grey = 2/3   Probability that shirt is not grey = 3/4   ∴ Required probability = 2/3 x 3/4 = 1/2   1/2
Answer: A
What is the least value of x, So that 2x4472 is divisible by 9
Choices
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 + 4 + 4 + 7 + 2 = 19 + x   Least value of x may be '8',   So that the total 19 + 8= 
19 + 8 = 27
27   is divisible by 9.   Answer: Option 8
Answer: B
How many positive integer solutions does the equation 4x+5y = 100 have?
Select the correct option: A) 50 B) 33 C) 16 D) 5 E) 14

Solution: formula: (constant)/(lcm of two nos)   =100/(4*5)= 
100/(4*5) = 5
5   ANSWER:5
Answer: D
A 7-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?
Options.
A) 4/5  B) 6/7  C) 5/8  D) 7/9  E) 9/10

Solution: The longer wire will form a square with an area more than 1 if the wire is cut at a point within three meters of either end. The probability of this is 6/7.   The answer is 6/7.
Answer: B
How many 3 digit positive integers R exist that when divided by 7 leave a remainder of 5?	Choose the correct choice from the following choices.
A) 128  B) 142  C) 143  D) 141  E) 129

Solution: Minimum three digit number is 100 and maximum three digit number is 999.   The first three digit number that leaves remainder 5 when divided by 7 is 103.   14 * 7= 
14 * 7 = 98
98 +5= 
98 +5 = 103
103   The second three digit number that leaves remainder 5 when divided by 7 is 110.   15 * 7= 
15 * 7 = 105
105 +5= 
105 +5 = 110
110   The third three digit number that leaves remainder 5 when divided by 7 is 117   and so on   The last three digit number that leaves remainder 5 when divided by 7 is 999   142 * 7= 
142 * 7 = 994
994 + 5= 
994 + 5 = 999
999   Therefore, we identify the sequence   103,110,117.....999   use the formula of last term   Last term= first term + (n - 1) * common difference   you will get the answer 129 that is definitely 129.
Answer: E
Find the length of the wire required to go 13 times round a square field containing 24336 m2. Choices:
A) 15840
B) 3388
C) 2667
D) 8112
E) 66711

Solution: a2 = 24336 => a = 156   4a = 624   624 * 13= 
624 * 13 = 8_112
8112   Answer: 8112
Answer: D
If (x – 1)^2 = 144, which of the following could be the value of 2x? Choose the correct choice from the following answers:
A) –26
B) –22
C) –11
D) 12
E) 13

Solution: If (x-1)^2 = 144   then (x-1) = Sq rt 144   = 12 ( can have both positive and negative values)   If positive   then (x-1) = 12   => x = 13 => 2x = 26   If negative   then (x-1) = -12   => x = -12+1 = -11 => 2x = -22   Out of options given, we can see B has -22 value .   Hence option –22
Answer: B
If I walk at 5 km/h, I miss the bus by 9 minutes. If I walk at 3 km/h, I reach 6 minutes before the arrival of the bus. How far I walk to reach the bus stand ?	Choose the correct answer
A) 1.99 km	B) 1.55 km	C) 1.82 km	D) 2.87 km	E) 1.87 km

Solution: d = product of speed difference of time /difference of speed   d = 5x3/60[9âˆ’(âˆ’6)/5-3]   [Here, â€“ve sign indicates before the schedule time]   â‡’ d = 1.87 km   Answer 1.87 km
Answer: E
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
Choose the correct choice from the following choices.
A) 24	B) 77	C) 36	D) 25	E) 13

Solution: Explanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   27 : 36 :: 18 : x   [Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]   {\color{Blue} x=\frac{36\times 18}{27}}   x = 24   So 24 days will be required to get work done by 27 men.   24nswer: 24
Answer: A
The distance from City A to City B is 120 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?	Answers
A) 45 B) 48 C) 50 D) 52 E) 54

Solution: The time it takes Bob to drive to City B is 120 / 40= 
120 / 40 = 3
3 hours.   Alice needs to take less than 2.5 hours for the trip.   Alice needs to exceed a constant speed of 120 / 2.5= 
120 / 2.5 = 48
48 miles per hour.   The answer is 48.
Answer: B
Two trains are moving at 60 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?  Options:
A) 5 sec	B) 6 sec	C) 7 sec	D) 8 sec	E) 9 sec

Solution: 70 + 60= 
70 + 60 = 130
130 * 5/18= 325/9 mps   D = 150 + 100= 
150 + 100 = 250
250 m   T= 250 * 9/325 = 7 sec   Answer:7 sec
Answer: C
Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 80 litres of tomato juice?  Answers:
A) 2.8 liters.	B) 2.5 liters.	C) 8.5 liters.	D) 2.6 liters.	E) 10 liters.

Solution: Answer:   Explanation:   In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.   â‡’â‡’ 10%(80) = 80%(x)   â‡’â‡’ x = 10 liters.   Answer:10 liters.
Answer: E
Three hoses work to fill a tub at at different rate. Hose T and B, working together, can fill the tub in 6/5 of an hour. Hoses T and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution
Answers:  A) 3/10  B) 2/5  C) 1/2  D) 1  E) 6/5

Solution: Convert the given time to rate and you will be able to add it up.   Total Rate of T and B = Rate of T + Rate of B = 1/(6/5) = 5/6   Total Rate of T and C = Rate of T + Rate of C = 1/(3/2) = 2/3   Total Rate of B and C = Rate of B + Rate of C = 1/2   Adding all three,   2(Rate of T + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2= 
5/6 + 2/3 + 1/2 = 2
2   Rate of T + Rate of B + Rate of C= 1 tub/hour   Time taken by all three together to fill up the tub is 1 hour=1
Answer: D
At what rate percent on simple interest will a sum of money double itself in 30 years?	Choose the correct choice from the following:
A) 3 1/3%  B) 3 5/3%  C) 3 1/9%  D) 3 1/5%  E) 3 1/7%

Solution: P = (P*30*R)/100   R = 3 1/3%   3 1/3%nswer:3 1/3%
Answer: A
A person borrows 20000 for 6 years at 8% p.a. simple interest. He immediately lends it to another person at 9 % p.a. for 6 years. Find his gain in the transaction per year. Choose the correct choice from the following.
A) 200  B) 250  C) 210  D) 190  E) 180

Solution: Gain in 6 years   = [(20000Ã—9Ã—6/100)âˆ’(20000Ã—6Ã—8/100)]   = (10800 â€“ 9600) = 1200   âˆ´ Gain in 6 year = (1200/6)= 
(1200/6) = 200
200   200nswer 200
Answer: A
Three candidates contested an election and received 2136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got  Answers:
A) 54.3%
B) 56%
C) 57%
D) 58%
E) 59%

Solution: Explanation:   Total number of votes polled = (2136 + 7636 + 11628)= 
(2136 + 7636 + 11628) = 21_400
21400   So, Required percentage= 11628/21400 * 100 = 54.3%   54.3%nswer: Option 54.3%
Answer: A
12In dividing a no. by 585, a student employed the method of short division. He divided the no.successively by 5, 9 and 13 and got the remainders 4, 8, 12 respectively. What would havebeen the remainderif he had divided the no. by 585? Options
A) 245  B) 345  C) 560  D) 584  E) 650

Solution: Let   p   p be the number   Suppose,   p   ÷   5   =   q   p÷5=q, remainder = 4   q   ÷   9   =   r   q÷9=r, remainder = 8   r   ÷   13   =   s   r÷13=s, remainder = 12   Hence,   r   =   13   s   +   12   r=13s+12   q   =   9   r   +   8   =   9   (   13   s   +   12   )   +   8   =   117   s   +   116   q=9r+8=9(13s+12)+8=117s+116   p   =   5   q   +   4   =   5   (   117   s   +   116   )   +   4   =   585   s   +   584   p=5q+4=5(117s+116)+4=585s+584   Therefore, if   p   p is divided by 585, we will get 584 as remainder.   584
Answer: D
A customer went to a shop and paid a total of $25, out of which 90 cents was for sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Options:
A) $8.50
B) $8.70
C) $9.10
D) $10.00
E) $10.40

Solution: The total cost was $25.   The tax was $0.90   Let the original price of the taxable items = x   Given that tax rate = 6%   0.06x = 0.90   x = $15   The cost of the tax free items was $25 - $15 - $0.90 = $9.10   The answer is $9.10.25 -  15 -  0.90= 
25 -  15 -  0.90 = 9.1
$9.10   The answer is $9.10.
Answer: C
What should be the least number to be added to the 51234 number to make it divisible by 9?	Choices
A) 6
B) 4
C) 3
D) 5
E) 2

Solution: The least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits.   Sum of digits = 15.   Nearest multiple of 9 greater than sum of digits = 18.   Hence 3 has to be added.   ANSWER:3
Answer: C
How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed	Choose the correct choice from the following choices:	A) 1024	B) 5040	C) 3260	D) 1540	E) 2104

Solution: 'LOGARITHMS' contains 10 different letters   Required number of words   = Number of arrangements of 100 letters taking   4 at a time   = 10P4   = 10 * 9 * 8 * 7= 
10 * 9 * 8 * 7 = 5_040
5040   Ans: 5040
Answer: B
In a room with 10 people, 7 people have exactly 1 friend in the room and 6 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends? Choices.
A) 5/21 B) 3/7 C) 4/7 D) 5/7 E) 49/45

Solution: (7/10)(8/9) + (6/10)(7/9) if you choose one of the 7 with one other friend, then you have a 8/9 chance of not picking their friend 2nd. If you choose one of the 6 with 2 friends, you have a 7/9 chance of not picking one of their friends second. Add them up.   56/90 + 42/90   98/90 = 49/45   E. 49/45
Answer: E
In Town X, 64 percent of the population are employed, and 40 percent of the population are employed males. What percent of the employed people in Town X are females? Choose the correct choice from the following choices
A) 38%  B) 25%  C) 32%  D) 40%  E) 52%

Solution: We are asked to find the percentage of females in employed people.   Total employed people 64%, out of which 40 are employed males, hence 24% are employed females.   (employed females)/(total employed people)=24/64=38%   38%nswer: 38%.
Answer: A
A wheel of a car of radius 21 cms is rotating at 600 RPM. What is the speed of the car in km/hr? Choose the correct choice from the following answers:	A) 79.2 km/hr	B) 47.52 km/hr	C) 7.92 km/hr	D) 39.6 km/hr	E) 3.96 km/hr

Solution: Explanatory Answer   The radius of the wheel measures 21 cm.   In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.   ∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.   In a minute, the distance covered by the wheel = circumference of the wheel * rpm   ∴ this wheel will cover a distance of 132 * 600= 
132 * 600 = 79_200
79200 cm in a minute.   In an hour, the wheel will cover a distance of 79200 * 60= 
79200 * 60 = 4_752_000
4752000 cm.   Therefore, the speed of the car= 4752000 cm/hr = 47.52 km/hr   Choice 47.52 km/hr is the correct answer.
Answer: B
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?  Answers
A) Rs.1350	B) Rs.1327	C) Rs.1328	D) Rs.1397	E) Rs.1927

Solution: Rs.1350rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 2 = Rs.1350   Rs.1350nswer: Rs.1350
Answer: A
A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is. Choose the correct choice: A) 20% B) 21% C) 22% D) 23% E) 24%

Solution: Explanation:   Gain%=((100+common gain%)2/ 100−100)%   =((100+10)2/ 100−100)%   =(12100−10000/ 100)%=21%   Option 21%
Answer: B
How many 3/4 foot pieces of cable can be cut out of a piece that is 40 feet long?  Select the correct option.
A) a.50 B) b.56 C) c.57 D) d.53 E) e. 59

Solution: Pretty Simple..the answer is choice (D) 53.   All that one has to do is :   1: Convert 3/4 into an improper fraction (3/4) or a decimal (0.75)   2: d.53ivide 40 by 3/4 (or 0.75)   Answer =53 (d.53)
Answer: D
The number n yields a remainder p when divided by 12 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of n ? Choose the correct choice from the following:
A) 45  B) 34  C) 72  D) 85  E) 100

Solution: I solved this question in the following way:   Q<7 so Q can be from 0 to 6 and P<12 so P can be from 0 to 11, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 11.   n=12k + P or n= 12k + 7 to 11 and look at the answer as, place different values for k, 34 will give 34 which is 12*2 + 10, the other answers are out of the range
Answer: B
A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.360. How much does C have?	Select the correct option:
A) 60
B) 78
C) 267
D) 29
E) 27

Solution: 60+B+C = 500   60+C = 200   B+C = 360   --------------   60+B+2C = 560   60+B+C = 500   ----------------   C = 60   60nswer: 60
Answer: A
The value of (34.31*0.473*1.567)/(0.0673*23.5*7.57) is close to  Pick:
A) 2  B) 1.15  C) 2.05  D) 2.12  E) 2.35

Solution: (34.31*0.473*1.567)/(0.0673*23.5*7.57) = 25.4303/11.972   = 2.12   ANSWER:2.12
Answer: D
The LCM of two numbers is 2310 and HCF is 55. If one of the numbers is 210. Then what is the other number ?  Pick
A) 715	B) 825	C) 330	D) 605	E) 465

Solution: First number * Second Number = LCM * HCF   Other number = 2310 * 55 / 210 = 11*55= 
11*55 = 605
605   ANSWER :605
Answer: D
A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:  Answers:
A) 20 days
B) 22 1/2 days
C) 24 days
D) 25 days
E) 30 days

Solution: Ratio of times taken by A and B = 1 : 3.   The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.   If difference of time is 2 days, B takes 3 days.   If difference of time is 60 days, B takes (3/2 * 60)= 
(3/2 * 60) = 90
90 days   So, A takes 30 days to do the work.   A's 1 day's work=1/30   22 1/2 days's 1 day's work =1/90   (A + 22 1/2 days)'s 1 day's work = (1/30 + 1/90) = 4/90 = 2/45   A and 22 1/2 days together can do the work in 45/2 = 22 1/2 days   Answer = 22 1/2 days
Answer: B
A shopkeeper sells 450 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? Pick one:	A) 12	B) 27	C) 29	D) 45	E) 21

Solution: SP per metre = 18000/450 = Rs. 40 Loss per metre = Rs. 5 CP per metre = 40 + 5 = Rs. 45.Answer: 45
Answer: D
If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $17,000 is invested at the same interest rate, what is the interest from the investment?
Choose the most appropriate option:  A) $700  B) $750  C) $800  D) $850  E) $900

Solution: 5000*r*t/100=250   rt=5   17000*5/100= 
17000*5/100 = 850
850   Answer is $850
Answer: D
What is the smallest positive integer K such that the product of 720 x K is a perfect square?
Choices:
A) 5	B) 9	C) 15	D) 25	E) 63

Solution: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.   Now, 720 = 3^2 * 4^2 * 5, so if k=5 then 720 k = (3 * 4 * 5)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).   5nswer: 5.
Answer: A
Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 36 pages per hour. If Tom starts reading a novel at 4:00, and Jan begins reading an identical copy of the same book at 4:48, at what time will they be reading the same page?
Select:
A) 7:18 B) 7:48 C) 8:18 D) 8:48 E) 9:18

Solution: Since Tom reads an average of 1 page every 2 minutes, Tom will read 24 pages in the first 48 minutes. Jan can catch Tom at a rate of 6 pages per hour, so it will take 4 hours to catch Tom.   The answer is 8:48.
Answer: D
Find the missing number:
6 9 12 ? 6	Choose one.
A) 6  B) 7  C) 8  D) 9  E) 5

Solution: 6 9 12 9 6   palindrome   ANSWER:9
Answer: D
In a box of 9 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?	Options:	A) 4/7	B) 5/9	C) 6/11	D) 7/12	E) 8/15

Solution: # defective pens = 2   # good pens = 7   Probability of the 1st pen being good = 7/9   Probability of the 2nd pen being good = 6/8   Total probability = 7/9 * 6/8 = 7/12   The answer is 7/12.
Answer: D
Two trains 120 m and 150 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) 10.9 sec
B) 14.8 sec
C) 10.6 sec
D) 10.8 sec
E) 9.27 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 = 120 + 150= 
120 + 150 = 270
270 m.   Required time= 270* 9/250 = 9.27   = 9.27 sec.   Answer: 9.27 sec
Answer: E
Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?
Options.
A) 12%	B) 12.5%	C) 6.67%	D) 6.25%	E) 8.33%

Solution: Now After a time of 3years the principal P amounts to $300 and after a time of 8years ( question says after another 5years so 3+5) P becomes $400.   Formulating the above data   Amount (A1) at end of 3years   A1= P(1 + 3R/100) = 300   Amount (A2) at end of 8years   A2 = P(1 + 8R/100) = 400   Dividing A2 by A1 we get   (1 + 8R/100)/(1 + 3R/100) = 4/3   after cross multiplication we are left with 12R =100 which gives R = 8.33%   ANSW8.33%R:8.33%
Answer: E
How many two digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Choose the correct choice:
A) 30
B) 197
C) 278
D) 279
E) 274

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is   6P2 = 6 * 5= 
6 * 5 = 30
30.   30nswer: 30
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? Choose the correct choice from the following answers.
A) 150	B) 88	C) 77	D) 62	E) 13

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.   150nswer: 150
Answer: A
A can complete a certain job in 7 days. B is 40% more efficient than A. In how many days can B complete the same job?
Choose the correct choice from the following choices:
A) 5  B) 6.25  C) 7  D) 7.5  E) 4.8

Solution: Let, Total Work Unit = 70 Units   A can finish in 7 days = 70 unit work   i.e. A can finish in 1 days = 10 unit work   i.e. B can finish in 1 days = 10+(40/100)*10= 
10+(40/100)*10 = 14
14 unit work   Days in which B will complete the work alone= 70/14= 
70/14 = 5
5 days   5nswer: Option 5
Answer: A
If P represents the product of the first 18 positive integers, then P is NOT a multiple of  Select the correct option:	A) 99	B) 84	C) 72	D) 65	E) 38

Solution: Answer is E.   Since prime factor of 38 is 2x19. 19 is a prime number and not part of the first 18 positive integers.   A) 9 x 11   B) 12 x 7   C) 12 x 6   D) 13 x 5   38) 2 x 19
Answer: E
A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same)	Choose the correct choice from the following:
A) 20%  B) 33.33%  C) 100%  D) 65.66%  E) Data inadequate

Solution: Solution: Assume the cost price = 100 and selling price = 120.   Then, when price of petrol is reduced;   Cost price become 60 and selling price = 160;   Profit increased = 100%.   Answer: Option 100%
Answer: C
The total of the ages of Mahesh, Suresh, Ramesh is 120 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh? Choose the correct choice from the following options:
A) 32years
B) 50years
C) 42years
D) 35years
E) 30years

Solution: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x   2x+10 + 3x+10 +4x+10 = 120   x = 10   Ramesh present age = 4*10+10= 
4*10+10 = 50
50 years   Answer is 50years
Answer: B
A train speeds past a pole in 22 seconds and a platform 140 m long in 33 seconds. Its length is?
Answers:
A) 280 B) 260 C) 300 D) 290 E) 270

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 22 => y = x/22   x + 140 / 33 = x / 22   x = 280 m.   280nswer:280
Answer: A
At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 15 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 15 pieces of fruit is 48 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45 cents?  Choose one.
A) 1  B) 2  C) 3  D) 8  E) 9

Solution: Let number of Apples = A   number of oranges = B   A+B=15 --- 1   .48 =(.4A + .6 B)/15   => 48 = 4A + 6B ----2   Solving 1 and 2, we get   A= 9   B= 6   Let the number of oranges put back = 3   45*(15-c) = 40*9 + 60(6-3)   => 3= 3   Answer 3
Answer: C
The average age of a class of 32 students is 18 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher  Options
A) 45 Years B) 51Years C) 49 Years D) 52 Years E) 54 Years

Solution: Total age of students is 32X18 = 576 Years Total age inclusive of teacher = 33X (18+1) = 627 So, Teacher's age is 627-576= 
627-576 = 51
51 Yrs There is a shortcut for these type of problems Teacher's age is 18+(33X1)= 51Years Answer : 51Years
Answer: B
When x is divided by y, the quotient is u with remainder r. Which of the following is y in terms of r, x, and u? (Assume both y and u are nonzero.)	Select the correct option: A) x – r – u B) (x+r)/u C) x/u−r D) (x−r)/u E) xr –u

Solution: Given that when x is divided y, the quotient is u and remainder is r. This implies x-r is divisible by y and yu=(x-r) or y = (x-r)/u.   Answer (x−r)/u.
Answer: D