MU-NLPC/Calc-aqua_rat huggingface dataset:
The equation (M )/63 = (p )/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
Choose the most appropriate option:
A) P	B) 2P	C) 4P	D) 3P	E) 7P

Solution: M/63 =(P)/21   M = (P)*63/21   =(P)*3 =3P   3P
Answer: D
what is the unit digit in [(6273)^1793x(625)^317x(341)^491]?  Pick one:
A) 0
B) 2
C) 3
D) 5
E) None of them

Solution: Unit digit in (6374)^1793=Unit digit in (4)^1793   =Unit digit in [(4^2)^896 x 4]   =Unit digit in (6x4)=4   Unit digit in (625)^317=Unit digit in (5)^317=5   Unit digit in (341)^491=Unit digit in (1)^491=1   Required digit = Unit digit in (4x5x1)=0   0nswer is 0
Answer: A
A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? Choose the most appropriate option.
A) 1:2	B) 3:4	C) 2:5	D) 3:7	E) 2:1

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and 3:4 =   6000 : 8000 => 3:4   ANSWER:3:4
Answer: B
Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.5. If he has a total of $10.15, then which of the following represents the number of dimes in Andrew’s pocket? Choose the correct choice from the following answers:
A) 9
B) 10
C) 16
D) 20
E) 18

Solution: E.   Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.   Total value = 18q(.05) + 3q(0.1) + .5q =1.7q   Given total value = 10.15   therefore, 1.7q=10.15 or q=6   Number of dimes = 3q or 18   Answer : 18
Answer: E
A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 66 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 Choose the correct choice from the following answers:
A) 2000  B) 2100  C) 2200  D) 2300  E) 2400

Solution: 1 percent for 3 years= 66   1 percent for 1 year = 22   => 100 percent = 2200   ANSWER:2200
Answer: C
A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Choose the correct option:
A) 25600.24  B) 25600.27  C) 25600.28  D) 25600.21  E) 25600.29

Solution: 6 1/4% = 1/16   x *15/16 * 15/16 * 15/16 = 21093   x = 25600.24   25600.24nswer:25600.24
Answer: A
When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in e hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of e?
Choose the most appropriate option.
A) 3/4  B) 1[1/5]  C) 1[2/5]  D) 1[3/4]  E) 2

Solution: Rate*Time=Work   Let Painter W's rate be W and Painter X's rate be X   R*T = Work   W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2   X * e = 1 => X = 1/e   When they both work together then their rates get added up   Combined Rate = (W+X)   R*T = Work   (W+X) * 3/4 = 1   => W+X = 4/3   => 1/2 + 1/e = 4/3   => 1/e = (8-3)/6 = 5/6   => e = 6/5 = 1[1/5]   Answer 1[1/5]
Answer: B
A new apartment complex purchased 60 toilets and 20 shower heads. If the price of a toilet is three times the price of a shower head, what percent of the total cost was the cost of all the shower heads?
Options: A) 13 B) 297 C) 26 D) 19 E) 10

Solution: Explanation:   Let the cost of shower head is x. Then the cost of the toilet = 3x.   Total cost of 60 toilets and 20 shower heads = 60 × 3x + 20 × x = 200x   So shower heads cost as a percentage of total cost = 20x20x20x20x × 100 = 10%   Answer:10
Answer: E
The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:  Choose the correct choice from the following: A) 28 B) 32 C) 40 D) 53 E) 54

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M. = 6x.   So, 6x = 48 or x = 8.   The numbers are 16 and 24.   Hence, required sum = (16 + 24)= 
(16 + 24) = 40
40.   Answer: Option 40
Answer: C
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 48, the dividend is?  Choose the correct choice from the following answers:
A) 5808 B) 5825 C) 5830 D) 5835 E) 5836

Solution: Divisor = (5 * 48)= 
(5 * 48) = 240
240= 10 * Quotient = Divisor   => Quotient = 240/10= 
240/10 = 24
24   Dividend= (Divisor * Quotient) + Remainder   Dividend = (240 * 24) + 48= 
(240 * 24) + 48 = 5_808
5808   5808
Answer: A
Point (e,f) is on the circle represented by e^2+f^2=10, and e, f are integers. How many such points are possible?
Answers
A) 0	B) 2	C) 4	D) 6	E) 8

Solution: e^2+f^2=10 and e, f are integers means that 10 is the sum of two perfect squares.   10 is the sum of only one pair of perfect squares 1 and 9.   So, there can be 8 such points, 4 in each quadrant:   (1, 3);   (1, -3);   (-1, 3);   (-1, -3);   (3, 1);   (3, -1);   (-3, 1);   (-3, -1).   Answer: 8.
Answer: E
In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Pick one:
A) 0.9	B) 0.72	C) 0.45	D) 0.35	E) 0.28

Solution: Let x be the total number of students.   The number students who are younger than 25 is 0.6*0.4x+0.8*0.6x = 0.72x   The answer is 0.72. 0.6*0.4 +0.8*0.6= 
 0.6*0.4 +0.8*0.6 = 0.72
0.72x   The answer is 0.72.
Answer: B
What will come in place of the x in the following Number series? 2, 2, 4, 12, 48, 240, x
Pick one:
A) 2560 B) 960 C) 1440 D) 480 E) 540

Solution: There is one series here   (the multiply by number increases by 1 to get the next number)   2 x 1 = 2   2 x 2 = 4   4 x 3 = 12   12 x 4 = 48......   Hence: 240 x 6= 1440   1440 is the correct choice
Answer: C
Two good train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.  Choose the correct choice from the following options:
A) 12 sec B) 24 sec C) 48 sec D) 60 sec E) None

Solution: Sol.   Relative Speed = (45 + 30) km / hr   = (75 x 5 / 18) m/sec   = (125/6) m/sec.   Distance covered = (500 + 500)= 
(500 + 500) = 1_000
1000 m.   Required time= (1000 x 6 / 125) sec = 48 sec.   Answer 48 sec
Answer: C
2x + y = 14
|y| <= 14
For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
Choose one
A) 7  B) 12  C) 13  D) 14  E) 15

Solution: Hi - The questions says |y| <=14 so the values of y will range from 0 to 14. So the values of y will be 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14. So 15 (E) is the answer. remember sign doesn't matter for y as y will always be positive.
Answer: E
Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs.100, then find the CP of sugar?  Choose the correct choice from the following answers:  A) Rs. 1(1/9)  B) Rs. 2(2/9)  C) Rs. 2(2/7)  D) Rs. 2  E) Rs. 3(1/9)

Solution: Here r = 10 % ,x = 100 and A = 5 kg   Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)   Rs. 2(2/9)
Answer: B
A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Choices
A) 12 B) 20 C) 88 D) 77 E) 14

Solution: 1: 2/5 = 5: 2   2/7 * 70= 
2/7 * 70 = 20
20   Answer: 20
Answer: B
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Choose the correct answer: A) 4991 B) 5991 C) 5491 D) 6991 E) 6491

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991   4991nswer: Option 4991
Answer: A
With out any halt a train travels a certain distance with an average speed of 40 km ph , and with halts it covers the same distance at an average speed of 25 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?  Choose the most appropriate option.
A) 48 min. B) 12min. C) 15min. D) 36min. E) 19min.

Solution: With halt in 1 hour the train travels 60km   With out halt for traveling same distance it take 40/25 = 8/5 = 96 minutes   :. 36 minutes is the halting time per hour   ANSWER:36min.
Answer: D
A milkman sells his milk at CP but he mixes it with water and thereby gains 25%. What is the % of water in the mixture? Choose the correct choice from the following options.
A) 10%  B) 12%  C) 20%  D) 25%  E) 30%

Solution: Here Gain= 25%   error = quantity of water he mixes in the milk =x   true value = true quantity of milk = T   So the formula becomes, 25=x(T−x)×100   ⇒1=x(T−x)×4⇒T−x=4x⇒T=5x   Percentage of water in the mixture   =xT×100=x5x×100=15×100=20%   20%
Answer: C
A person has four iron bars whose lengths are 24 m, 36 m, 48 m and 72 m respectively. This person wants to cut pieces of same length from each of four bars. What is the least number of total pieces if he is to cut without any wastage? Choices:
A) 11	B) 12	C) 15	D) 13	E) 17

Solution: 15   15   24 = 12 × 2,   36 = 12 × 3,   48 = 12 × 4,   and 72 = 12 × 6   ∴ H15F (24, 36, 48, 72) = 12   Total pieces = 2 + 3 + 4 + 6= 
2 + 3 + 4 + 6 = 15
15
Answer: C
165 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Pick one:
A) 66 liters  B) 32 liters  C) 41 liters  D) 50 liters  E) 34 liters

Solution: Milk = 3/5 * 165= 
3/5 * 165 = 99
99 liters   Water= 66 liters   99 : (66+P) = 3:4   198 + 3P = 396 => P = 66   66 liters of water are to be added for the ratio become 3:4.   66 litersnswer:66 liters
Answer: A
The present worth of Rs.338 due in 2 years at 4% per annum compound interest is
Choose the correct choice from the following answers:
A) Rs.312.5
B) Rs.154.75
C) Rs.156.25
D) Rs.158
E) None

Solution: Solution   Present Worth	= Rs.[338/(1+4/100)²]   = Rs.(338x25/26x25/26)   = Rs.312.5   Rs.312.5nswer Rs.312.5
Answer: A
How many numbers between 100 and 600 are divisible by 2, 3, and 7 together? Choose the correct choice from the following answers
A) 11  B) 12  C) 14  D) 16  E) 18

Solution: Explanation:   As the division is by 2, 3, 7 together, the numbers are to be divisible by:  2*3*7= 
 2*3*7 = 42
42   The limits are 100 and 600   The first number divisible is 42*3= 
42*3 = 126
126   To find out the last number divisible by 42 within 600:   600/42= 14.28   Hence, 42*14 = 588 is the last number divisible by 42 within 600   Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12   ANSWER: 12
Answer: B
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choose the correct choice from the following options:	A) 230 m	B) 240 m	C) 260 m	D) 320 m	E) 520 m

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 270)/9 = 500/9 => x = 230.   230 mNSWER:230 m
Answer: A
Which one of the given numbers is divisible by 11?
Choose the correct option.
A) 4823718	B) 8423718	C) 8432718	D) 4238718	E) 4852718

Solution: Explanation:   4238718 = (4+3+7+8) – (2+8+1)= 
(2+8+1) = 11
11   So, the given number is divisible by 11   Answer:4238718
Answer: D
If a certain toy store's revenue in November was 3/5 of its revenue in December and its revenue in January was 1/6 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Choose the correct choice from the following:
A) 3/2 B) 5/4 C) 10/3 D) 20/7 E) 25/9

Solution: N = 3D/5   J = N/6 = D/10   The average of November and January is (N+J)/2 = 7D/10 / 2 = 7D/20   D is 20/7 times the average of November and January.   The answer is 20/7.
Answer: D
The three digits of a number add up to 17. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?	Choose the correct choice:	A) 160	B) 72	C) 78	D) 88	E) 125

Solution: Say the three-digit number is abc.   The leftmost digit is double the middle digit --> a=2b;   The number is divisible by 5 --> c is either 0 or 5;   The three digits of a number add up to 17 --> a+b+c=17   So, either a+b+c=2b+b+0=17 or a+b+c=2b+b+5=17. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=4 --> a=8 and c=5 --> a*b*c=160.   160nswer: 160.
Answer: A
Peter's One tap, working alone at its maximum constant rate, can fill a certain sink in 220 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 224 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to Answers.
A) 111 seconds B) 130 seconds C) 177 seconds D) 200 seconds E) 270 seconds

Solution: Tap 1 : 220 secs   Tap 2 : 224 secs   Considering the average of these 2 taps : 222 secs.   So 1 tap can fill the tank in 222 secs, so 2 taps can fill the tank in 222/2= 
222/2 = 111
111 secs.   Closest answer is 111 seconds.
Answer: A
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 52 years now, the son's age five years back was?  Choose the correct choice from the following choices
A) 18years  B) 19years  C) 20years  D) 21years  E) 21years

Solution: Let the son's present age be x years. Then, (52 - x) = x   2x = 52.   x = 26.   Son's age 5 years back (26 - 5)= 
(26 - 5) = 21
21 years.   21years)
Answer: D
A college has classes from 10:00 AM until 2:00 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?  Choices:  A) 38 min  B) 41 min  C) 40 min  D) 42 min  E) 44 min

Solution: The total time is 240 minutes.   There are four breaks of five minutes between the classes for a total of 20 minutes.   The total class time is 220 minutes.   220 / 5= 
220 / 5 = 44
44 minutes per class   The answer is 44 min.
Answer: E
Lokesh started a business with Rs.30,000 and Ramesh joined him afterwards with Rs.30,000. If profits of both are same after one year then for how many months did Ramesh invest his money?	Choices
A) 9 months	B) 8 months	C) 6 months	D) 5 months	E) 12 months

Solution: let us assume ramesh has joined after "X" moths.   It has been told that profit is same   Therfore 30,000*12=30,000*X   X=12 months   ANSW12 monthsR:12 months
Answer: E
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is? Select:
A) 7 km/h
B) 5 km/h
C) 3 km/h
D) 2 (1/2) km/h
E) None

Solution: 100 --- 10 2 (1/2) km/hS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 ½ kmph   ANSWER:2 (1/2) km/h
Answer: D
x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to?  Choose the correct choice from the following options:
A) 1/6
B) 1/3
C) 1/0
D) 1/9
E) 1/5

Solution: Given x = k/y2, where k is a constant.   Now, y = 2 and x = 1 gives k = 4.   x = 4/y2 => x = 4/62, when   y = 6 => x = 4/36 = 1/9.   Answer:1/9
Answer: D
What is the approximate value of b in the following equation?
18% of 4514 + 25% of 3415 = b
Pick
A) 1620  B) 1670  C) 1680  D) 1690  E) 1630

Solution: b = 18% of 4514 + 25% of 3415   b = 18/100* 4514 + 25/100* 3415= 
18/100* 4514 + 25/100* 3415 = 166_627/100 = around 1_666.27
1666.27   ≈ 1670   Answer 1670
Answer: B
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?	Pick one:	A) 3%	B) 5%	C) 6%	D) 4%	E) 2%

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R = 5%   Answer :5%
Answer: B
John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?  Choose the most appropriate option
A) $18.44  B) $28.44  C) $48.44  D) $58.44  E) $38.44

Solution: let x be the price before the first discount. The price after the first discount is   x - 25%x (price after first discount)   A second discount of 25% of the discounted price after which the final price is 16   (x - 25%x) - 25%(x - 25%x) = 16   Solve for x   x = $28.44   correct answer $28.44
Answer: B
When the positive integer x is divided by the positive integer y, the quotient is 3 and the remainder is z. When z is divided by y, the remainder is 2. Which of the following could be the value of x?
I. 5
II. 8
III. 32  Choose the correct choice:	A) I only	B) II only	C) III only	D) I and II only	E) I, II and III

Solution: When x is divided by y, the quotient is 3 and the remainder is z: x=3y+z, where 0≤z<y (the remainder must be less than the divisor).   When z is divided by y, the remainder is 2: when divisor (y in our case) is more than dividend (z in our case), then the reminder equals to the dividend (for example, 2 divided by 5 gives the remainder of 2). Therefore, z=2 and 2<y.   So, we have that x=3y+2 and 2<y. This implies that the least value of x is x=3∗3+2=11: x cannot be 5 or 8.   Could x be 32? Yes. If y=10, then x=3∗10+2=32.   Answer: III only.
Answer: C
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Choose the correct choice from the following answers.
A) 16 2/3% loss B) 16 2/9% loss C) 16 2/2% loss D) 16 2/3% loss E) 16 3/9% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
Consider the following game, in which a referee picks a random integer between 1 and 100.
One after the other, each of three players tries to guess the number the referee picked. Each
player announces his or her guess before the next player guesses. Each guess has to be different
from the previous guesses. The winner is the player who comes closest to the referee’s
number without exceeding it. (It is possible for none of the players to win.)
Suppose that Player 1 guesses 24, and that Player 3 will guess a number that gives her/him the
best chance of winning. What number should Player 2 guess to maximize his/her chances of
winning? Select:
A) 1
B) 25
C) 62
D) 63
E) 64

Solution: First of all, observe that it always gives the third player the best chances to win if   [s]he guesses the lowest number in some range which the other players left open. Thus, if you   choose 63, this narrows the third player’s choices down to 1, 25, and 64. Guessing 25 gives   a range of 38 numbers (25 through 62 inclusive) which win for the third player if the referee   picked one of them, while a choice of 64 would only give 37 favorable numbers, and a choice   of 1 only gives 23 favorable numbers.   Note that 63 gives you 38 favorable numbers also (63 through 100 inclusive) so this way you   and the third player both have a 38% chance of winning, while the first player only has a 24%   chance.   The other four given answers do not give you such a good result. Answer (e), 64, still makes   25 the best choice for the third player, but cuts your chances down to 37% while raising the   third player’s to 39%. Answer (a), 1, is even worse than (e) because it only gives 23 chances   for you. Answer (c), 62, would give the third player 63 as the best guess, (38% versus 37%   if 25 is guessed instead) drastically reducing your winning chances to 1%. You would get the   same baleful result if you guessed 25 [answer (b)], because then the obvious best guess for   the third player is 26.   correct answer 63
Answer: D
The average monthly salary of 20 employees in an organisation is Rs. 1700. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
Choose the correct choice from the following answers:
A) Rs.6003
B) Rs.3800
C) Rs.1288
D) Rs.6108
E) Rs.6011

Solution: Explanation:   Manager's monthly salary Rs. (1800 * 21 - 1700 * 20) = Rs.3800.   Answer: Rs.3800
Answer: B
Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many W applicants majored in political science and had a GPA higher than 3.0?	Pick.
A) 5	B) 10	C) 15	D) 25	E) 35

Solution: Total applicants = 40   Political science = 15 and Non political science = 40 - 15= 
40 - 15 = 25
25   GP5 > 3.0= 20 and GP5 <= 3.0 = 20   10 Non political science students had GP5 <= 3.0 --> 15 Non political science students had GP5 > 3.0   GP5 > 3.0 in political science = Total - (GP5 > 3.0 in non political science) W= 20 - 15= 
20 - 15 = 5
5   5nswer: 5
Answer: A
A certain bridge is 4,424 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 10 miles per hour? (1 mile = 5,280 feet) Choose the correct choice from the following answers: A) 1 B) 2 C) 4 D) 5 E) 7

Solution: Distance: 4424 feet. This is (4424/5280) miles = 0.84 miles   Speed: 10 miles per hour   Time: (Distance / Speed) (0.84/10) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 5.04 minutes.   Answer to be 5 minutes.   ANS 5
Answer: D
A train 900 m long passed a pole in 9 sec. How long will it take to pass a platform 800 m long? Select the correct option.
A) 17
B) 18
C) 19
D) 20
E) 21

Solution: Speed = 900/9= 
900/9 = 100
100 m/sec.   Required time= (900 + 800)/100= 
(900 + 800)/100 = 17
17 sec.   17nswer:17
Answer: A
Two pipes can fill a tank in 18 minutes and 60 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?	Choose the correct choice from the following options:
A) 1/15
B) 1/16
C) 1/20
D) 1/10
E) 1/12

Solution: Part of the filled by all the three pipes in one minute   = 1/18 + 1/60 - 1/45 = 1/20   So, the tank becomes full in 20 minutes.   Answer:1/20
Answer: C
In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 9th Rd and 6th Ave in the shortest possible time, how many different routes could he take?
Choose the most appropriate option
A) 90	B) 120	C) 150	D) 180	E) 210

Solution: Bills needs to walk 7 blocks north and 3 blocks east.   One possible solution is NNNNNNNEEE.   There are 10C7 = 120 possible solutions.   The answer is 120.
Answer: B
It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 60 pages? Pick one:
A) 12  B) 18  C) 20  D) 24  E) 30

Solution: If it takes 4 more minutes for A to print 40 pages than it takes B,   it takes 5 more minutes for A to print 50 pages than it takes B.   Thus if b is the number of minutes than 18 takes to print 50 pages,   we can write:   1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)   6(2b+5)=b(b+5)   b^2-7b-30=0   (b-10)(b+3)=0   b=10   Thus it takes A 15 minutes to print 50 pages and   15*60/50= 
  15*60/50 = 18
18 minutes to print 60 pages (ANSWER 18)
Answer: B
In a 2000 m race, A beats B by 100 meters or 15 seconds. Find the speed of B?	Select the correct option
A) 10m/s  B) 2m/s  C) 5m/s  D) 6.7m/s  E) 3m/s

Solution: Since A beats B by 100 m or 15 seconds,   it implies that B covers 100 m in 15 seconds.   Hence speed of B = 100/15 = 6.7 m/s.   Answer: 6.7m/s
Answer: D