MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?	Choose the correct choice from the following options:
A) 180
B) 88
C) 278
D) 268
E) 267

Solution: Let the five numbers be P, Q, R, S and T.   => P + Q + R + S + T = 655.   (P + Q)/2 = 85 and R = 125   P + Q = 170 and R = 125   P + Q + R = 295   S + T = 655 - (P + Q + R) = 360   Average of the last two numbers = (S + T)/2 = 180.   180nswer: 180
Answer: A
When a is divided by b, the quotient is c with remainder 3. What is a in terms of 3, b, and c? Choose the correct choice from the following answers: A) b+c+3 B) b+c C) bc D) bc+3 E) bc-3

Solution: a/b =c with remainder 3   i.e, a-3 = bc   a= bc+3   Answer : bc+3
Answer: D
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Options:
A) 299
B) 240
C) 288
D) 161
E) 921

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15   ==> x + 300 = 540 ==> x   = 240 m.   Answer:240
Answer: B
The Computer Store has reduced the price of a computer by 15%.
What is the original price of the computer if the sale price is $1275? Select the correct option
A) 1600  B) 2500  C) 1500  D) 1200  E) 2100

Solution: Selling price = 1275/-   Reduction rate : 15%   Orginal price is : 1500/-   Answer is Option 1500
Answer: C
A certain sum is invested at simple interest at 14% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?  Choices:
A) s. 7000 B) s. 9000 C) s. 14000 D) s. 17000 E) s. 42000

Solution: Let the sum be Rs. x.   (x * 14 * 2)/100 - (x * 12 * 2)/100 = 840   => 28x/100 - 24x/100 =840   => 4x/100 = 840   => x = 42000.   ANSWs. 42000R:s. 42000
Answer: E
The length of the train which is moving at 66 km/hr, can crosses a bridge of length 345 m in 60 sec, is ?	Choose the correct choice from the following answers:	A) 575 m.	B) 645 m.	C) 555 m.	D) 655 m.	E) 755 m.

Solution: Speed = [66 X 5/18] m/sec = [55/3] m/sec Time = 60 sec Let the length of train be x metres. Then, (345 + x)/60= 55/3   345+x=1100   755 = x   x= 755 m.   Answer:755 m.
Answer: E
A boy has 4 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? Choose the correct answer:	A) 299	B) 60	C) 67	D) 89	E) 271

Solution: The boy can select one trouser in 4 ways.   The boy can select one shirt in 15 ways.   The number of ways in which he can select one trouser and one shirt is   4 * 15= 
  4 * 15 = 60
60 ways.   Answer: 60
Answer: B
Two trains 140 m and 160 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) 10.6
B) 10.5
C) 10.1
D) 10.8
E) 10.2

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer: 10.8
Answer: D
How many positive integers less than 5,000 are evenly divisible by neither 13 nor 21?  Choices:
A) 4,514  B) 4,475  C) 4,521  D) 4,428  E) 4,349

Solution: integers less than 5000 divisible by 13 5000/13 =333.something , so 333   integers less than 5000 divisible by 21 5000/21 = 238.## , so 238   we have double counted some, so take LCM of 13 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 13 and 21 = 333 +238 -47= 
333 +238 -47 = 524
524   now subtract that from 4999. 4999- 524= 4349 answer 4,349.
Answer: E
The ratio of incomes of C and D is 3 : 4 and their expenditures is 4 : 5. If the savings of C is one fourth of his income then what is the ratio of savings of C and D?	Choose the correct choice from the following answers:
A) 11/19
B) 12/19
C) 13/19
D) 14/19
E) 15/19

Solution: According to the given condition   3x - 4y = (1/4)3x   => (3/4)3x = 4y   => 9x = 16y   => x/y = 16/9   so ratio of savings = (3x - 4y)/(4x - 5y) = (3*16 - 4*9)/(4*16 - 5*9) = 12/19   ANSWER:12/19
Answer: B
A train 140 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.  Select:
A) 45 kmph
B) 50 kmph
C) 55 kmph
D) 60 kmph
E) 79 kmph

Solution: Explanation:   Let the speed of the train be x kmph.   Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.   Therefore 140/((x+5)×5/18)=6 <=> 30 (x + 5) = 2520 <=> x = 79   Speed of the train is 79 kmph.   Answer: Option 79 kmph
Answer: E
A car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?
Choose the most appropriate option.
A) 9  B) 8  C) 7  D) 6  E) 5

Solution: Let the time for which car averages 75 mph = t   60*(t+5)= 65*4 + 70 t   =>10t= 40   => t = 4   Total duration of the trip = 5+4= 
5+4 = 9
9   9nswer 9
Answer: A
A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Select the correct option.
A) 15/2	B) 14/2	C) 15/4	D) 14/4	E) 13/4

Solution: Let the total units of work done be 60.   Units of work done by A in one day = 5.   Given, B is 60% more efficient than A.   Thus, B will be able to finish 8 units of work in a day.   Therefore, time taken by B alone to complete the total work = 60/8 =15/2 days.   15/2NSWER:15/2
Answer: A
If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)? Options.
A) 9. B) 12. C) 15. D) 16 E) 18.

Solution: Expand this to get: (2X + Y)(2Z + W) = 4XZ + 2XW + 2YZ + YW   = 4 XZ + YW + 2XW + 2YZ [I rearranged the terms]   = 3 + 2XW + 2YZ [replaced 4XZ + YW with 3]   = 3 + 2(XW + YZ) factored out a 2   = 3 + 2(6)   = 3 + 12= 
3 + 12 = 15
15   ANSWER:15.
Answer: C
A chemical supply company has 60 liters of a 40% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?	Choose the correct choice from the following options.
A) 12  B) 15  C) 20  D) 24  E) 30

Solution: 60 liters of a 40% HNO3 solution means HNO3 = 24 liters in 60 liters of the solution.   Now, let x be the pure HNO3 added.   As per question,   24 + x = 50% of (60 + x)   or x =12. Hence, 12
Answer: A
A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 22 per kg, then his gain percent is Choose the correct option:  A) 12%  B) 13%  C) 14%  D) 15%  E) 17%

Solution: Explanation:   Suppose he bought 5 kg and 3 kg of tea.   Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.   Selling price = Rs. (8 x 22) = Rs. 176.   Profit = 176 - 150= 
176 - 150 = 26
26   So, Profit %= (26/150) * 100 = 17%   Option 17%
Answer: E
A,B,C can complete a piece of work in 24,6,12 days. Working together, they complete the same work in how many days?  Choose the correct choice:  A) 2  B) 4/5  C) 7/9  D) 10  E) 24/7

Solution: A+B+C 1day work = 1/24 + 1/6 + 1/12 + +  1= 
+ +  1 = 1
1/24 + 1/6 + 1/12= 7/24   A,B,C together will complete the job in 24/7 days   Answer is 24/7
Answer: E
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $60,000?
Choose the correct option
A) $38,796. B) $40,000. C) $38,976. D) $58,464. E) $36,796.

Solution: 60,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.   Only option $58,464. fulfills the condition and hence is the answer
Answer: D
A positive integer which when added to 100, gives a sum which is greater than when it is multiplied by 100. What is the number? Options
A) 6 B) 5 C) 4 D) 1 E) 8

Solution: Explanation:   The number is 1   ANSWER: 1
Answer: D
If the number is divided by 3, it reduced by 36. The number is  Choose the correct choice from the following answers.
A) A)51
B) B)50
C) C)45
D) D)54
E) E)36

Solution: Explanation:   Let the number be x. Then,   x - (x/3) = 36 => 2x/3 = 36   => x = 54   Answer: Option 54
Answer: D
When n is divided by 32, the remainder is 5. What is the remainder when 4n is divided by 8?	Select the correct option.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Let n=5 (leaves a remainder of 5 when divided by 32)   4n = 4(5) =20, which leaves a remainder of 4 when divided by 8.   Answer 4
Answer: B
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y?  Choose the most appropriate option:
A) 14
B) 12
C) 10
D) 16
E) 18

Solution: we know that : x > 1, y > 1, and x + 3y < 1000,   and it is given that length means no of factors.   for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.   hence, lets start with smallest no 2.   2^1 =2   2^2 =4   2^3=8   2^4=16   2^5=32   2^6=64   2^7=128   2^8=256   2^9=512   2^10 =1024 (it exceeds 920, so, x can't be 2^10)   so, max value that X can take is 2^9 , for which has length of integer is 9.   now, since x =512 ,x+3y<920   so, 3y<408   ==> y<136   so, y can take any value which is less than 136. and to get the maximum no of factors of smallest integer, we can say y=2^7   for 2^7 has length of integer is 7.   SO, combined together : 9+7= 
9+7 = 16
16.   16
Answer: D
A waiter's salary consists of his salary and tips. During one week his tips were 7/4 of his salary. What fraction of his income came from tips ?  Choices: A) 4/9 B) 5/4 C) 5/8 D) 5/9 E) 7/11

Solution: Income = salary (s) +tips = s + s*7/4 = s*11/4   Tips = s*7/4   fraction of his income came from tips = (s*7/4)/(s*11/4)= 7/11   ANSW7/11R:7/11
Answer: E
Mark is playing poker at a casino. Mark starts playing with 150 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?  Choices.
A) $1,960	B) $1,740	C) $1,540	D) $3,080	E) $2,100

Solution: Total chips 150   20% of $100 chips = 30 chips * $100 = $3,000   80% of $20 chips = 120 chips * $20 = $2,400   If x is the number of chips bet and y is the amount of chips remaining:   x + y = 150   y = 150 - x ~ (1)   [First round bet] + [Second round bet] = $3,000 + $2,400   [0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $5,400   10x + 18x + 30y + 14y = 5400   28x + 44y = 5400 ~ (2)   Substitute (1) into (2) to solve for x:   28x + 44(150 - x) = 5400   28x + 6600 - 44x = 5400   16x = 1200   x = 75   Substituting x:   [First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(75)($100)+0.9(75)($20) = $750 + $1,350 = $2,100   Answer is $2,100
Answer: E
Given 2x + y + z = 3 and 5x + 3y + z = 14, what is the value of x + y - z? Choose the most appropriate option.
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: (1) 5x + 3y + z = 14   If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6   Let's subtract equation (2) for equation (1).   x + y - z = 8   The answer is 14.
Answer: D
Departments A has 20 employees, B, and C have 20 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?	Pick one:
A) 19,000 B) 40,000 C) 100,000 D) 190,000 E) 380,000

Solution: 20c1 * 10c1* 10c1*20c2 = 20*10*10*190=380,000. Hence 380,000 is the correct answer.
Answer: E
The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 400 per sq. metre.	Choose the correct option:
A) Rs. 15000 B) Rs. 8250 C) Rs. 15600 D) Rs. 16500 E) None of these

Solution: Solution   Area of the floor = (5.5 × 3.75) m2 = 20.625 m2   ∴ Cost of paving = Rs. (400 × 20.625) = 8250. Answer Rs. 8250
Answer: B
City X has a population 3 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?  Pick one
A) 1:8
B) 1:4
C) 2:1
D) 6:1
E) 8:1

Solution: x= 3y, y= 2*z   X : Y , Y : Z   3 : 1 , 2 : 1   6 : 2 , 2 : 1   So, X : Z = 6 : 1   (6:1)
Answer: D
Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for z dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?	Choose one.
A) x/(y - z)  B) x/(z - y)  C) x  D) x/z  E) x/y

Solution: Two ways...   1) let t be the total number, so cost = t*y+x and selling price=t*z..   No profit no loss....t*y+x=t*z.....T=x/(z-y)...   2) choices..   The answer has to use all 3 variables x,y and z....   Only A and B are left...   In A, y will be lesser than z, so A will become NEGATIVE..   ANSWER:x/(z - y)
Answer: B
Henry answered 4/5 of the questions he was given for homework in the first hour, 5/19 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework? Choose the correct option:
A) x	B) (95/7)*x	C) (95/14)*x	D) (95/21)*x	E) (95/28)*x

Solution: Let Q be the number of homework questions.   Q = 4Q/5 + (5/19)(Q/5) + x   Q = 76Q/95 + 5Q/95 + x   14Q/95 = x   Q = (95/14)*x   The answer is (95/14)*x.
Answer: C
Jagan went to the book shop and bought things worth Rs. 30, out of which 25 paise went on sales tax on taxable purchases. If the tax rate was 5%, then what was the cost of the tax free items?  Choose the correct option:
A) Rs 22.75  B) Rs 25  C) Rs 24.75  D) Rs 26  E) None of these

Solution: Explanation :   Solution: let the amount of taxable purchases be Rs. X.   Then, 5% of x= 25/100   => x= (25/100 *100/5) = Rs. 5   .'. Cost of tax free items = Rs.[30-(5+0.25)] = Rs. 24.75   Answer : Rs 24.75
Answer: C
A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit.
Choose the correct option:  A) 2205  B) 2201  C) 2229  D) 2289  E) 2202

Solution: 2205 = 2000(21/20)2   = 2205   2205nswer:2205
Answer: A
An inlet pipe fill a tank in 5 hrs and outlet pipe empty same tank in 36 hrs working indiviually.how many additional number of outlet pipes of same capacity required to be opened so that tank never over flows Choose the correct option.
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: Inlet pipe fills the tank in 5 hr and outlet pipe empties the tank in 36 hr.   So inlet pipe is   36/5= 
  36/5 = 36/5 = around 7.2
7.2 times efficient than , ensure that the an outlet pipe.   Therefore , in order to tank never overflows , we will need total 8 outlet pipes.   Already we have 1 outlet pipe , thus we need only  (8-1)= 
 (8-1) = 7
7 outlet pipes   ANSWER:7
Answer: B
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/6 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?	Choices:
A) 50  B) 70  C) 100  D) 105  E) 10

Solution: Rented = 4/7*490= 
4/7*490 = 280
280.   Rented two-bedroom= 6/7*280= 
6/7*280 = 240
240;   Rented one-bedroom= 1/7*280= 
1/7*280 = 40
40 (or 280-240= 
280-240 = 40
40).   Rented one-bedroom units are 1/5 of all one-bedroom: 1/6*{All one bedroom}= 40 --> {All one-bedroom} = 240.   {All two-bedroom} = 490 - 240= 
490 - 240 = 250
250.   Two-bedroom not rented= 250 - 240= 
250 - 240 = 10
10   Answer: 10
Answer: E
Sony and Johnny caught 80 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?	Choose the correct option:	A) 12	B) 16	C) 34	D) 38	E) 42

Solution: s+j=80   s=4*j   j=16   ANSWER:16
Answer: B
A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Choose the correct choice from the following
A) 420 m
B) 200 m
C) 240 m
D) 320 m
E) None

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 48= 15 ⇔ x + 300 = 720 ⇔ x = 440 m.   420 mnswer 420 m
Answer: A
If 9 pumps can raise 1085 tonnes of water in 10 days, working 7 hours a day; in how many days will 8 pumps raise 868 tonnes of water, working 9 hours a day?	Pick one:	A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Explanation :   Let the required number of days be x. Then,   Less pumps, More days (Indirect Proportion)   Less water, Less days (Direct Proportion)   More hours / day, Less days (Indirect Proportion)   Pumps 8 : 9   Weight 1085 : 868   Hours/day 9 : 7 :: 10 : x   (8 x 1085 x 9 x x) = (9 x 868 x 7 x 10)   x = 9 x 868 x 7 x 10/ (8 x 1085 x 9)   x = 7   Answer : 7
Answer: B
Starting from 1 if you are asked to write first 172 digits of the natural numbers , which digit you stop at?  Pick:
A) 4
B) 7
C) 8
D) 9
E) 10

Solution: 12345678910=11digits   11-20=20digits   21-90=140 digits   total 171digits are completed   next number is 91 9is 172th digit & 1 is 173rd digit   ANSWER:9
Answer: D
when n divided by 3, the remainder is 2.
when n divided by 4, the remainder is 1
what is the the remainder when divided by 11
Choose the correct choice:
A) 1
B) 3
C) 4
D) 5
E) 6

Solution: case1   N=5,8,11,14,17,20   case 2   M=5,9,13,17,21   Therefore n=17   Remainder of 17/11 will be 6   6 6 correct
Answer: E
At the end of year X, automobile installment credit accounted for 20% of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time? Answers.
A) 171  B) 855  C) 870  D) 788  E) 684

Solution: System of Equations   a = (20/100) c   (1/3) a = 57 --> a = 171   Substitution   171 = (20100) c   c = (100/20) 171   - Calculate 171/20 * 100   The Correct answer B. The answer is 855.
Answer: B
A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Choose the correct answer.
A) 27 B) 27 C) 20 D) 25 E) 2

Solution: M = 20   S = 5   25S = 20 + 5= 
20 + 5 = 25
25   Answer:25
Answer: D
A positive number x is multiplied by 7, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? Choose one:
A) 7/3 B) 3/2 C) 4/3 D) 2/3 E) 1/2

Solution: sq rt(7x/3) = x   => 7x/3 = x^2   => x = 7/3   7/3ns - 7/3
Answer: A
One fast typist type some matter in 3 hrs and another slow typist type the same matter in 5hrs. If both do combine in how much time they will take to finish.	Choose the correct option:	A) 1 hr 5 mins	B) 1 hr 10 mins	C) 1 hr 12 mins	D) 3 hr 10 mins	E) 4 hr 5 mins

Solution: Fast's 1 hr work = 1/3   slow's 1 hr work = 1/5   1/3 + 1/5 = 8/15   they ll finish in 15/8hrs= 1 7/8 ==> 1 hr 12 mins   ANSWER:1 hr 12 mins
Answer: C
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
Choose the correct choice from the following answers: A) 3 hrs 45 min B) 3 hrs 15 min C) 4 hrs D) 4 hrs 15 min E) 5 hrs 15 min

Solution: time taken by one tap in hr = (4*1/6)=2/3   remaining part = (1-1/2)=1/2   x=3/4 hrs => 3hrs 45 min   3 hrs 45 minNSWER 3 hrs 45 min
Answer: A
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is John’s weekly allowance? Pick:	A) $1.50	B) $2.00	C) $2.50	D) $3.00	E) $3.50

Solution: x = 3x/5 + 1/3*2x/5 + 40   4x/15 = 40   x = 150 = $1.50   The answer is $1.50.
Answer: A
10x + 2y = -4
4x + y = 1
In the system of equations above, what is the value of x?	Choose the correct choice from the following choices:  A) -5  B) -3  C) -1  D) 1  E) 3

Solution: 10x + 2y = -4 can be written as 5x + y = -2   Let's subtract the second equation from this equation.   x = -3   The answer is -3.
Answer: B
If p and r are positive integers such that p > r > 1, what is the remainder when 92p × 5p+r + 11r × 6pr is divided by 10?
Choose the correct choice from the following.
A) A.0	B) B.1	C) C.3	D) D.4	E) E.5

Solution: 92p × 5p+r + 11r × 6pr--1=B.1
Answer: B
There are 750 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?  Choose the correct answer:
A) 75 B) 100 C) 125 D) 175 E) 225

Solution: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 750.   Hence, we have m+f= 750   Now, we have that half the female participants and one-quarter of the male participants are Democrats.   Let d equal the number of the Democrats.   Then we have the equation f/2 + m/4 =d   Now, we have that one-third of the total participants are Democrats. Hence, we have the equation   d = 750/3= 
750/3 = 250
250   Solving the three equations yields the solution   f= 250,m= 500, and d= 250.   The number of female democratic participants equals half the female participants equals   250/2= 
250/2 = 125
125.   ANSWER:125
Answer: C
If a - b = 3 and a2 + b2 = 29, find the value of ab.	Pick one
A) 10
B) 12
C) 13
D) 14
E) 15

Solution: 2ab = (a2 + b2) - (a - b)2   = 29 - 9= 
29 - 9 = 20
20   ab= 10.   10
Answer: A
The average weight of three boys M, N and P is 54 1/3 kg, while the Average weight of three boys N, Q and R is 53 kg. What is the average weight of M, N, P, Q and R?
Choose the correct answer.
A) 52.4 kg	B) 53.2 kg	C) 53.8 kg	D) Data Inadequate	E) None of these

Solution: Explanation :   Total weight of (M + N + P) = 54 1/3 x 3 kg = 163 kg.   Total weight of (N + Q + R) = (53 x 3) kg = 159 kg.   Adding both, we : M + 2N + P + Q + R = (163 + 159)= 
(163 + 159) = 322
322 kg.   So, to find the average weight of M, N, P, Q and R, we ought to know Ns weight, which is not given. So, the data is inadequate.   Answer : Data Inadequate
Answer: D
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:40 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
Choices
A) 5:00 B) 5:30 C) 6:40 D) 6:30 E) 7:00

Solution: Train C has traveled 20 mi in the half hour before Train D has started its journey.   140-20= 
140-20 = 120
120   40+20= 
40+20 = 60
60 mph   120 mi/ 60 mph= 2 hrs   4:40pm + 2 hrs = 6:40pm   Answer:   C. 6:40
Answer: C
If a2 - b2 = 8 and a*b = 2, find a4 + b4. Choose the correct option: A) 62 B) 72 C) 82 D) 92 E) 62

Solution: a2 - b2 = 8 : given   a4 + b4 - 2a2b2 = 82 : square both sides and expand.   a*b = 2 : given   a2b2 = 22 : square both sides.   a4 + b4 - 2(4) = 82 : substitute   a4 + b4 = 72   correct answer 72
Answer: B