MU-NLPC/Calc-aqua_rat huggingface dataset:
In a game of 80 points. A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60?  Choose the correct answer:
A) 9 points
B) 6 points
C) 8 points
D) 10 points
E) 11 points

Solution: A can give B 5 points :- A / B = 80 / 75   A can give 8 points 15 points :- A / 8 points = 80/ 65   B can give 8 points a points of ( B / A ) * ( A / 8 points)   (75 / 80) * ( 80 / 65)   (75 / 65) = 15/13   As we have to find in a game of 60 , so multiply numerator and denominator with 4 such that the ratio becomes 60/52   therefore B can give 8 points of   (60-52)= 
  (60-52) = 8
8 points   ANSWER:8 points
Answer: C
In a jar there are 20 white balls, 24 green balls and 30 blue balls. How many balls must be taken out in order to make sure we have 21 balls of the same color?	Choose the correct choice from the following answers:
A) a)	23  B) b)	46  C) c)	57  D) d)	60  E) e)	67

Solution: Here, we need to find minimum number of marbles to be taken out to get 21 marbles of same color.   For a instance, if we take 19 white marbles 1st and followed by 20 Green and then 20 Blue.   Total will be   19 + 20+ 20= 
  19 + 20+ 20 = 59
59 draws.   If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 21.   So Minimum we need to take 59+1= 
59+1 = 60
60 Times to get 21 marbles of same color(either Green or Blue).   Answer : d)	60.
Answer: D
A bowl of nuts is prepared for a party. Brand P mixed nuts are 20% almonds and Brand Q's Deluxe nuts are 25% almonds. If a bowl contains a total of 65 ounces of nuts, representing a mixture of both brands, and 15 ounces of the mixture are almonds, how many ounces of Brand Q's Deluxe mixed nuts are used?	Options:
A) 16	B) 20	C) 32	D) 40	E) 48

Solution: lets say x ounces of P is mixed with Q.   => 65-x ounces of Q is present in the mixture (as the total = 65 ounces)   given total almond weight = 15 ounces   (20x/100)+(25/100)(65-x) = 15   => x = 25   => 65-25= 
65-25 = 40
40 ounces of Q is present in the mixture.   Answer is 40.
Answer: D
Product of two natural numbers is 17. Then, the sum of reciprocals of their squares is
Choices.
A) 290/289  B) 1/289  C) 290/90  D) 290/19  E) None of these

Solution: Explanation:   If the numbers are a, b, then ab = 17,   as 17 is a prime number, so a = 1, b = 17.   1/a2+1/b2=1/1(2)+1/17(2)   1/ 2+1/ 2= 
1/ 2+1/ 2 = 1
1/1(2)+1/17(2)=290/289   Option 290/289
Answer: A
Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 10% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be  Select.
A) 9% less than N
B) 25% less than N
C) equal to N
D) 20% greater than N
E) 25% greater than

Solution: Correct answer is (A).   This year, the price of a tree is price1=P/N.   If this price increases by 10% it becomes price2=P/N*1.10   Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.10) i.e. N/1.1 i.e. .91%
Answer: A
If 4x=6y=z, what is x+y, in terms of z? Select.
A) z/2  B) 5z/12  C) z/3  D) 3z/5  E) z/9

Solution: 4x=6y=z   x = z/4   and y = z/6   x+y = z/4 + z/6 = 5z/12   Answer is 5z/12
Answer: B
By walking at 3/4th of his usual speed, a man reaches office 15 minutes later than usual. What is his usual time?
Choices:
A) 45min B) 50min C) 65min D) 60min E) 70min

Solution: let T be the usual time.   time spent=4T/3   therefore, 4T/3=T+15   4T=3T+45..therefor T=45min   45minNSWER:45min
Answer: A
the sides of a triangle are in the ratio 37.if the perimeter is 60 cms, the longest side is Pick one:
A) 7  B) 30  C) 28  D) 14  E) 16

Solution: Triangle property: sum of any two sides is always greater than the third one.   and Here we have been asked for longest side...   now we can have longest side as 29 or 28 but not 30   because 31>29 and 32>28 is true but 30>30 is not true   hence Answer is 28   ANSWER:28
Answer: C
Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? Choose the correct choice from the following options.
A) 4:3:2  B) 4:2:3  C) 3:2:4  D) 2:3:4  E) None of them

Solution: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.   Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).   = (140/100 x 5x), (150/100 x 7x) and (175/100 x 8x)   = 7x, 21x/2 and 14x.   Therefore, The required ratio = 7x : 21x/2 : 14x   = 14x : 21x : 28x   = 2 : 3 : 4.   Answer is 2:3:4.
Answer: D
Find the compound interest and the amount on Rs.5000 at 5% per annum for 3 years when C.I is reckoned yearly?
Choices
A) s.1261.13 B) s.1440.13 C) s.1185.13 D) s.1346.13 E) s.788.13

Solution: A = 5000(21/20)3   = 5788.13   = 5000   ---------   788.13   ANSWs.788.13R:s.788.13
Answer: E
When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?	Choose the correct choice from the following options:	A) 4.5	B) 5	C) 5.6	D) 5.7	E) 6.5

Solution: if $x$ is the number, x/6 * 12 = 9   => 2x = 9   => x = 4.5   4.5
Answer: A
In a is a positive integer smaller than 200 and (14a)/60 is an integer, then a has how many different positive prime factors?	Choose the correct choice:	A) 2	B) 3	C) 5	D) 6	E) 8

Solution: 7a/30 tells us that a is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.   Answer: 3
Answer: B
A thief goes away with a MARUTHI car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?	Choose one.
A) 8 hrs  B) 2 hrs  C) 5 hrs  D) 4 hrs  E) 1 hrs

Solution: Explanation:   |-----------20--------------------|   50 40   Difference = 20kms   Relative Speed = 50 â€“ 40 = 10 kmph   Time = 20/10= 
20/10 = 2
2 hours.   Answer: 2 hrs
Answer: B
A room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.  Select
A) 107  B) 144  C) 175  D) 165  E) 130

Solution: Let us calculate both the length and width of the room in centimeters.   Length = 7 meters and 68 centimeters = 768 cm   width = 4 meters and 32 centimeters = 432 cm   As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.   Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 768 and 432 = 48   Thus, the number of square tiles required = (768 x 432 ) / (48 x 48) = 16 x 9 = 144   Answer: 144
Answer: B
In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school? Choose the correct choice from the following answers:
A) 100 B) 102 C) 110 D) 90 E) None of these

Solution: Explanation :   Let the total number of students = x   Given that 20% of students are below 8 years of age   then The number of students above or equal to 8 years of age = 80% of x -----(Equation 1)   Given that number of students of 8 years of age = 48 -----(Equation 2)   Given that number of students above 8 years of age = 2/3 of number of students of 8 years of age   => number of students above 8 years of age = (2/3) × 48 = 32-----(Equation 3)   From Equation 1,Equation 2 and Equation 3,   80% of x = 48 + 32= 
48 + 32 = 80
80   ⇒ 80x/100= 80   ⇒ x/100 = 1   ⇒ x = 100   100nswer : Option 100
Answer: A
The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?	Choose the correct choice from the following answers.
A) 210
B) 220
C) 230
D) 240
E) 250

Solution: distance covered in 1 min=(66*1000)/60= 
(66*1000)/60 = 1_100
1100m   circumference of the wheel=(2*(22/7)*.70)= 
(2*(22/7)*.70) = 4.4
4.4m   no of revolution per min=1100/4.4= 
1100/4.4 = 250
250   ANSW250R:250
Answer: E
If a number p is prime, and 2p+5 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?	Choose the correct option.
A) 1  B) 3  C) 5  D) 7  E) 9

Solution: 1/7 = 014285... (a repeating pattern one digit long)   1
Answer: A
Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
Choose the correct choice from the following.
A) 81000  B) 81028  C) 81287  D) 29766  E) 81372

Solution: 64000* 9/8 * 9/8= 
64000* 9/8 * 9/8 = 81_000
81000   81000nswer: 81000
Answer: A
7log7(8) = ?
Pick.
A) 1
B) 2
C) 3
D) 4
E) 8

Solution: Exponential and log functions are inverse of each other. Hence   aloga(x) = x , for all x real and positive.   and therefore   7log7(8) = 8   correct answer 8
Answer: E
In a certain population, there are 4 times as many people aged thirtty-one or under as there are people over thirtty-one. The ratio of those thirty-one or under to the total population is
Pick:
A) 1 to 2	B) 1 to 3	C) 4 to 5	D) 2 to 3	E) 3 to 4

Solution: 4 to 5onsider the ratio of the under population of 21 to over the 21 as 4:1   therefore 4x:1X   Now the ratio of the under to the whole population becomes 4x/4x+1x   = 4/5   Answer is 4 to 5
Answer: C
† and ¥ represent nonzero digits, and (†¥)² - (¥†)² is a perfect square. What is that perfect square?
Choose one:
A) 121 B) 361 C) 576 D) 961 E) 1089

Solution: If AB is a 2 digit number such that A is the tens digit and B is the units digit, the place value of A is 10 and place value of B is 1.   So AB = 10A + B   Say, AB = 15   A = 1   B = 5   Is AB = A + B? No. 15 is not equal to   1 + 5= 
  1 + 5 = 6
6   AB= 10A + B = 10*1 + 5= 
10*1 + 5 = 15
15   When you square AB, what will you get?   Is it (A + B)^2= (1 + 5)^2 = 36? No. 15^2 = 225   Then what is missing? A's place value of 10.   So it will be (10A + B) = (10*1 + 5)^2 = 225   So, in terms of AB, AB^2 = (10A + B)^2.   Answer: 1089.
Answer: E
If a 3-digit integer is selected at random from the integers 300 through 349, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to two more than the middle digit? Pick
A) 50/349  B) 1/313  C) 1/49  D) 1/100  E) 1/50

Solution: Hundreds digit has to be 3 . So units digit needs to 3 as well   And both Hundreds and Units digit needs to be 2 more than ten's digit   The number is 313   Total numbers between 300 and 349 = (349-300)+1= 
(349-300)+1 = 50
50   Probability= 1/50   Answer 1/50
Answer: E
18 men can complete a piece of work in 20 days. In how many days can 15 men complete that piece of work?
Choose the correct choice from the following options
A) 23  B) 27  C) 20  D) 24  E) 11

Solution: 18 * 20 = 15 * x => x = 24 days   Answer:24
Answer: D
A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey.
Choose the correct answer:
A) 24 km  B) 26 km  C) 21 km  D) 23(23/59) km  E) None

Solution: Solution: Average speed = total distance covered/ total time   Total distance = (16+40+10) = 46 km   Time taken = (16/20)+ (20/40)+ (10/15) = 59/30   Average speed = 46*30/59 = 23(23/59) km/hr.   Answer: Option 23(23/59) km
Answer: D
The circumferences of two circles are 268 meters and 380 meters. Find the difference between the areas of the larger and the smaller circles.	Choose the correct choice from the following choices:
A) 388.15
B) 2992
C) 4312.5
D) 2887.27
E) 5773.09

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 268 and 2∏l = 380   s = 268/2∏ and l = 380/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1902/∏2 - 1342/∏2}   = 1902/∏ - 1342/∏   = (190 - 134)(190 + 134)/∏   = (56)(324)/(22/7) = (18144)/(22)(7) = 5773.09 sq m.Answer: 5773.09
Answer: E
If m=9^(x−1), then in terms of m, 3^(4x−6) must be which of the following?  Select the correct option.
A) m/3
B) 9m
C) 9m^2
D) m^2/3
E) m^2/9

Solution: m = 9 ^ (X-1)   m = 3 ^ (2x-2)   m^2 = 3 ^ (4x-4)   m^2/9 = 3 ^ (4x-6)   Answer m^2/9
Answer: E
A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half? Choose the correct choice from the following options:
A) 67 min  B) 45 min  C) 97 min  D) 30 min  E) 16 min

Solution: Part filled by (A + B) in 1 minute   = (1/60 + 1/40) = 1/24   Suppose the tank is filled in x minutes.   Then, x/2(1/24 + 1/40)   = 1   x/2 * 1/15 = 1 => x   = 30 min.   Answer: 30 min
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	Choices:	A) 1	B) 3	C) 5	D) 7	E) 9

Solution: P ÷ 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 31= 19008 / 31 = 613, remainder = 5   5
Answer: C
4 dice are thrown simultaneously on the board. Find the probability show the same face.	Options:
A) 1/209 B) 1/211 C) 1/216 D) 1/117 E) 1/119

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
3 candidates in an election and received 1136, 8236 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?  Options.
A) 40% B) 55.4% C) 57% D) 60% E) 62%

Solution: Total number of votes polled = (1136 + 8236 + 11628)= 
(1136 + 8236 + 11628) = 21_000
21000   So, Required percentage= 11628/21000 * 100 = 55.4%   55.4%
Answer: B
There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess?	Pick one.
A) 320 B) 120 C) 400 D) 420 E) 514

Solution: Sol. Let the original average expenditure be Rs. x. Then,   42 (x - 1) - 35x=42		7x= 84		x =12.   Original expenditure = Rs. (35 x 12) =Rs. 420. .   ANSWER 420
Answer: D
What is the sum of natural numbers between 20 and 100  Choose the correct choice: A) 4800 B) 4860 C) 5000 D) 5500 E) 5550

Solution: a = first number   l = last number   Sn = n/2[a + l]   between 20 and 100 numbers = 81 => 100 - 20= 
100 - 20 = 80
80 + 1= 
80 + 1 = 81
81   Sn= 81/2 × 120 = 81 × 60 = 4860   4860)
Answer: B
Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.12000 at the end of the year, B's share is	Choose the correct choice from the following answers:
A) Rs.4000 B) Rs.4320 C) Rs.7500 D) Rs.6600 E) None

Solution: Solution   Let C = x.   Then, B = 4x and 2A = 3x4x = 12x or A = 6x.   âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.   So B's capital	= Rs(12000 x 4 / 11)   = Rs.4320.   Answer Rs.4320
Answer: B
An plane covers a distance at a speed of 180 kmph in 5 hours. To cover the same distance in 3/2 hours, it must travel at a speed of ?  Answers
A) 100 B) 200 C) 720 D) 600 E) 500

Solution: We know   600istance = speed * time   = 180 * 5= 
180 * 5 = 900
900 km   Now to cover 900 km in 3/2 hrs ,   speed= distance / time   = 900 / (3/2)= 
900 / (3/2) = 600
600 KMPH   Ans- 600
Answer: D
A Water Heater is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
Options
A) 18%	B) 19%	C) 21.2%	D) 21.81%	E) 22.07%

Solution: Simple interest SI = (P*R*T)/100   where P is the principal amount   R is the rate of interest   and T is time in years   the way I see it: Water Heater on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000   For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)   thus, SI = 2000 or   2000 = (P*R*T)/100   2000 = (22,000*R*5)/(100*12)   R = (2,000*12*100)/22,000*5   R = 21.81%   Therefore answer is 21.81%
Answer: D
In a business there are three partners sum of A and B investments to total investment is in the ratio 4 : 5, and sum of B and C investments to total investment is in the ratio 4 : 5, then which of the following is correct with regard to investments, if investments of two of the partners are equal ?	Pick one:
A) A = B
B) B = C
C) A = B = C
D) B > (A + C)
E) A > C

Solution: If ( A + B ) : ( A + B + C ) = 4 : 5, then C = 5 – 4 = 1 unit   If ( B + C ) : ( A + B + C ) = 4 : 5, then A = 5 – 4 = 1 unit   Therefore B = ( A + B + C ) – ( A + C ) = 5 – 2 = 3   Clearly B > ( A + C )   Option B > (A + C)
Answer: D
One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.36 for operating-system overhead, $0.023 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ?
Answers
A) $7.15  B) $8.87  C) $35.96  D) $40.21  E) $59.92

Solution: Operating system overhead for 1 run = 1.36 $   Mounting of data tape = 4.35$   Cost per 1 millisecond of computer time = .023 $   Total cost of 1 run of a program that requires 1.5 seconds of computer time   = 1.36 + (.023*1500) + 4.35   =1.36 + 34.5 + 4.35= 
1.36 + 34.5 + 4.35 = 40.21
40.21$   Answer $40.21
Answer: D
15 times a positive integer is more than its square by 56, then the positive integer is Choose the correct answer:  A) 13  B) 8  C) 11  D) 12  E) 14

Solution: Explanation:   Let the number be x. Then,   15x = x2 + 56   => x2 - 15x + 56 = 0   =>(x - 7)(x - 8) = 0   => x = 7 or 8   Answer: Option 8
Answer: B
if a@b = a * b^(1/2) then 2@9 = ?  Choose the correct option
A) 2	B) 6	C) 3	D) 8	E) 4

Solution: a@b = a * b^(1/2)   2@9 = 2*9^(1/2) = 2*3= 
2*3 = 6
6   Correct Option: 6
Answer: B
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 8 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? Select the correct option: A) 33:1 B) 33:7 C) 33:8 D) 33:5 E) 33:2

Solution: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/1 litres   Quantity of alcohol in the mixture formed = 5/4 + 7/1 = 33/4= 
33/4 = 33/4 = around 8.25
8.25 litres   As 10 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 8.25 : 1.75 = 33:7.   Answer: 33:7
Answer: B
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m? Choose the correct answer:
A) 127.8 m
B) 127.5 m
C) 127.5 m
D) 227.5 m
E) 123.5 m

Solution: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.   When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8= 
6300/8 = 1_575/2 = around 787.5
787.5 m.   In a race of 1000 m, A beats C by   (1000 - 787.5)= 
  (1000 - 787.5) = 212.5
212.5 m to C.   In a race of 600 m, the number of meters by which A beats C= (600 * 212.5)/1000= 
(600 * 212.5)/1000 = 127.5
127.5 m.   Answer: 127.5 m
Answer: B
The sum of money will be double itself in 40 years and simple interest find rate of interest? Choices:
A) A)1.5%	B) B)2.5%	C) C)3.5%	D) D)4.5%	E) E)5.5%

Solution: T = 40 years   P= principle amount = x   A = total amount = 2x   SI = simple interest = A-P = 2x-x = x   R = 100SI/PT = 100x/40x =2.5%   Answer is 2.5%100 /40= 
100 /40 = 5/2 = around 2.5
2.5%   Answer is 2.5%
Answer: B
In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 18000*10^(-3) Petri dishes. How many germs live happily in a single dish? Choose the correct choice from the following answers.
A) 100 B) 200 C) 300 D) 400 E) 500

Solution: 0.036*10^5 can be written as 3600   18000*10^(-3) can be written as 18   Required= 3600/18= 
3600/18 = 200
200   ANSWER:200
Answer: B
A man buys an article and sells it at a profit of 5%. If he had bought it at 5% less and sold it for Rs.25 less, he could have gained 5%. What is the cost price?
Choose the correct choice: A) 197 B) 476 C) 279 D) 278 E) 268

Solution: CP1 = 100 SP1 = 105   CP2 = 95 SP2 = 95 * (105/100)= 
95 * (105/100) = 399/4 = around 99.75
99.75   5.25 ----- 100   25 ----- ?=> 476   Answer:476
Answer: B
The length of a bridge in meters, which a train 110-meters long and traveling at 45 km/hr can cross in 30 seconds is? Choose the correct choice from the following answers
A) 245  B) 265  C) 295  D) 325  E) 375

Solution: 45 km/h = 45000 m/3600 s = 12.5 m/s   In 30 seconds, the train can go 30(12.5) 45000  /3600= 
45000  /3600 = 25/2 = around 12.5
12.5 m/s   In 30 seconds, the train can go 30(12.5)= 375 meters   Let x be the length of the bridge.   x+110 = 375 meters   x = 265 meters   The answer is 265.
Answer: B
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 4,000 have been vaccinated against both, how many have been vaccinated only against rubella?
Choose the correct choice: A) 2,5000 B) 8,000 C) 10,000 D) 15,000 E) 17,500

Solution: Use a single variable as far as possible.   Number vaccinated only against mumps = x   Number vaccinated against both = 2x = 4000 (so x = 2000)   Then, number vaccinated against mumps (including both) = x + 2x = 3x   Number vaccinated against rubella = 2*3= 
2*3 = 6
6x   Then, number vaccinated against only rubella= 6x - 2x = 4x 6  - 2= 
6  - 2 = 4
4x= 4*2000 = 8,000   Answer (8,000)
Answer: B
Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 26 have long fur, 22 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?	Choose one.
A) 26  B) 19  C) 11  D) 8  E) 6

Solution: No of dogs=45   Long fur=26   Brown=22   Neither long fur nor brown=8   Therefore, either long fur or brown=45-8= 
45-8 = 37
37   37=26+22-Both   Both=11   Answer 11
Answer: C
A man can row 5 kmph in still water. If the river is running at 1kmph, it takes him 75 minutes to row to a place and back. How far is the place?
Pick one:
A) 3km
B) 2.5 km
C) 4 km
D) 5 km
E) 6 km

Solution: Speed downstream = (5+1)km/hr = 6 km/hr Speed upstream = (5-1)km/hr = 4 km/hr Let the required distance be x km x/6 + x/4 = 75/60 2x+3x = 15 x = 3km .   3kmNSWER:3km
Answer: A
At a recent small town election for mayor a total of 983 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?  Answers:  A) 134  B) 178  C) 200  D) 166  E) 194

Solution: The number of votes the winning candidate received was   983 + 53 + 79 + 105	/4= 305.   The second received 305 – 53 = 252,   The fourth place received 305 – 105 = 200.   200
Answer: C
Convert the following unit:
6.5 hectares in mÂ²
Select:
A) 55000 mÂ²	B) 80000 mÂ²	C) 70000 mÂ²	D) 67500 mÂ²	E) 65000 mÂ²

Solution: 6.5 hectares in mÂ²   1 hectare = 10000 mÂ²   Therefore, 6.5 hectares = 6.5 Ã— 10000 mÂ²   = 65000 mÂ²   ANSW65000 mÂ²R : OPTION 65000 mÂ²
Answer: E