MU-NLPC/Calc-aqua_rat huggingface dataset:
In the line xy plane line m has the equation y = 3x - 10, then the line m passes through which of the following points? Pick one.
A) (3, 1)	B) (3, 4)	C) (4, 2)	D) (6, 9)	E) (6, 15)

Solution: Yes it is y=3x-8....extremely sorry for mistake....   IF that's the case then answer is (4, 2)   y=3x-8   2=3X4-10   2=12-10   2=2 (satisfied)
Answer: C
How many diagonals does a polygon with 13 sides have, if one of its vertices does not connect to any diagonal? Choose one.
A) 65
B) 62
C) 58
D) 54
E) 60

Solution: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals   n= 13-1 then 12*(12-3)/2= 
12*(12-3)/2 = 54
54   Correct Option:54
Answer: D
The greatest possible length which can be used to measure exactly the length 6m, 4m 20cm, 4m is	Choose the correct choice from the following
A) 20 B) 27 C) 35 D) 87 E) 98

Solution: Explanation:   Required Length = H.C.F of 600 cm, 420 cm and 400 c   = 20 cm.   20nswer: 20) 20 cm
Answer: A
Look at this series: 544, 509, 474, 439, ... What number should come next?  Choose the most appropriate option.
A) 414 B) 404 C) 420 D) 445 E) 500

Solution: Option A   Explanation:   This is a simple subtraction series. Each number is 35 less than the previous number.   ANSWER 404
Answer: B
Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?  Options: A) 1/5 B) 1/4 C) 3/8 D) 2/5 E) 1/2

Solution: Let A be any person from Couple A and B be any person from Couple B.   There are only two cases how the single person could be distributed to split the couples:   (1) * A1 * B1 * A2 * B2 *   (2) A1 B1 * A2 B2   where * denotes the possible seating arrangements for the single person.   (1) There are 5∗2!∗2!∗2!=40 different seating arrangements. We multiply by 2! because there are two options for couple A and two options for couple B to be seated. Furthermore, couple B could be seated to the left of A. Consider these possibilities:   * A2 * B1 * A1 * B2 *   * A1 * B2 * A3 * B1 *   * B1 * A1 * B2 * A2 *   etc.   (2) There are 2!∗2!∗2!=8 different seating arrangements. Same reason as above. Consider these possibilities:   A2 B1 * A1 B2   B1 A1 * B2 A2   etc.   Overall we have  40+8= 
 40+8 = 48
48 possible arrangements and 5!=120 ways to arrange 5 people. The probability is 48/120=2/5   Answer: 2/5.
Answer: D
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different N arrangements of plays can be run, if the same play can’t be run more than once?	Select the correct option
A) 24	B) 125	C) 243	D) 504	E) 729

Solution: Number of N ways to choose the first play: 9   Second play: 8   Third:7   9*8*7= 504.504
Answer: D
What is the next number in this Sequence ?
6, 14, 36, 98, 276, ?  Choose one:
A) 657 B) 794 C) 453 D) 564 E) 123

Solution: B   794   The nth term in the series is given by the sum of x^n for x in the range 1 to 3, i.e. 1^n + 2^n + 3^n.   Thus the first term is 1^1 + 2^1 + 3^1 = 1 + 2 + 3= 
1 + 2 + 3 = 6
6,   the second term is 1^2 + 2^2 + 3^2= 1 + 4 + 9= 
1 + 4 + 9 = 14
14,   and so on.   The sixth term is then 1^6 + 2^6 + 3^6= 1 + 64 + 729= 
1 + 64 + 729 = 794
794.
Answer: B
The product of x and y is a constant. If the value of x is increased by 80%, by what percentage must the value of y be decreased?
Choices:
A) 45%  B) 55%  C) 35%  D) 40%  E) 44.44%

Solution: x*y = constt.   Let x = y = 100 in beginning   i.e. x*y = 100*100= 
100*100 = 10_000
10000   x (100) ---becomes---> 1.8x (180)   i.e. 180*New 'y'= 10000   i.e. New 'y' = 10000/180 = 55.55   i.e. y decreases from 100 to 55.55 i.e. Decrease of 44.44%   Answer: option 44.44%
Answer: E
How many sides does the polygon have if the sum of the interior angles measures up to 360 degrees?	Options:
A) 4
B) 6
C) 3
D) 7
E) None of these

Solution: 4 sides...answer 4
Answer: A
A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Pick one:
A) 8 months
B) 6 months
C) 4 months
D) 2 months
E) None

Solution: Sol.   Suppose B joined for x months. Then, 85000 * 12 / 42500 * x = 3/1 or   x = 85000 * 12 / 42500 * 3 = 8.   So, B joined for 8 months.   8 monthsnswer 8 months
Answer: A
If 2x+3y+z=55,x-y=4 and y - x + z=12,then what are the values of x , y and z?	Choose the correct choice from the following options.
A) 7,11,8
B) 5,8,9
C) 4,2,5
D) 3,9,8
E) None of them

Solution: The given equations are:   2x+3y+z=55 …(i); x + z - y=4 …(ii); y -x + z =12 …(iii)   Subtracting (ii) from (i), we get: x+4y=51 …(iv)   Subtracting (iii) from (i), we get: 3x+2y=43 …(v)   Multiplying (v) by 2 and subtracting (iv) from it, we get: 5x=35 or x=7.   Putting x=7 in (iv), we get: 4y=44 or y=11.   Putting x=7,y=11 in (i), we get: z=8   7,11,8nswer is 7,11,8.
Answer: A
If a man travels f miles an hour for h hours and r miles an hour for s hours, what is his average rate in miles per hour for the entire distance traveled? Choices
A) fh + rs  B) (fh + rs)/2  C) h/f + s/r  D) (fh + rs)/(h - s)  E) (fh + rs)/(h + s)

Solution: Average Speed = Total Distance /Total Time Taken   Total Distance travelled in t hours = fh   Total Distance travelled in s hours = rs   Total Time taken = h+s   Therefore , Average Speed = (fh+hs)/(h+s)   Answer (fh + rs)/(h + s)
Answer: E
X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.14300 ?	Pick one
A) 3200
B) 4000
C) 3250
D) 4160
E) 3985

Solution: Ratio of investment, as investments is for different time.   Investment x Number of units of time.   Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.   X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.   Ratio of investments => X : Y : Z = 18 : 21 : 16.   Investment Ratio = Profit sharing Ratio.   Z = 14300 Ã— 16/55 = Rs.4160.   Share of Z in the profit is Rs.4160.   Option 4160
Answer: D
2x<4y<0 which of the following is the greatest?	Choose the correct choice from the following choices:
A) 3x+3y
B) -(5x+4y)
C) 2x-2y
D) x-3y
E) 0

Solution: Plugging in -1 for both x and y we get   A. 3x+3y =-6   B. -(5x+4y) =9   C. 2x-2y=0   D. x-3y =2   E. 0 =0   Answer: -(5x+4y)
Answer: B
In what ratio should a variety of rice costing Rs. 5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Choose one
A) 1/2 B) 5/9 C) 5/1 D) 5/3 E) 7/6

Solution: Let us say the ratio of the quantities of cheaper and dearer varieties   = x : y   By the rule of allegation, x/y   = (8.75 - 7.50) / (7.50 - 5) =1/2   1/2nswer: 1/2
Answer: A
A car travels first 160 km at 75 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?  Pick:
A) 71.11
B) 71.12
C) 71.1
D) 71.17
E) 77.42

Solution: Car travels first 160 km at 75 km/hr   Time taken to travel first 160 km = distancespeed=160/75   Car travels next160 km at 80 km/hr   Time taken to travel next 160 km = distancespeed=160/80   Total distance traveled = 160+160=2×160   Total time taken = 160/75+160/80   Average speed = Total distance traveled/Total time taken=320/(160/75+160/80)=77.42 km/hr   Answer:77.42
Answer: E
The positive number a is q percent greater than the positive number b, which is y percent less than a itself. If a is increased by y percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a  Choose the correct option
A) I only B) II only C) III only D) I and II only E) II and III only

Solution: Let q = 10% then y = 100/11 %   let b = 100 then a = 110   after increasing a by y and decreasing b yq we get c= 108   therefore c<a   III only it is answer
Answer: C
The length of a rectangular floor is more than its breadth by 200%. If Rs. 300 is required to paint the floor at the rate of Rs. 5 per sq m, then what would be the length of the floor?	Choose the correct choice from the following answers:
A) 65 B) 13.42 C) 18 D) 16 E) 14

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 300/5= 
300/5 = 60
60 sq m   l b= 60 i.e., l * l/3 = 60   l2 = 180 => l = 13.42   Answer: 13.42
Answer: B
A girl has nine jeans and 11 shirts. In how many different ways can she select a jeans and a shirts?  Choose the correct choice from the following answers:
A) A)100  B) B)99  C) C)108  D) D)110  E) E)112

Solution: The girl can select one jeans in nine ways.   The girl can select one shirt in 11 ways.   The number of ways in which he can select one jeans and one shirt is 9 * 11= 
9 * 11 = 99
99 ways.   99
Answer: B
A Jar contains a mixture of AB in the ratio 3:2. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.  Choose the correct choice from the following answers: A) 18 B) 15 C) 16 D) 20 E) 25

Solution: 10 litres of mixture that is replaced will contain 6 litres of 18 and 4 litres of B (as 18:B = 3:2)   Let the initial volume of the mixture be 3K + 2K = 5K   So by condition ,   [ 3K-6 ]/ [ 2K-4+10 ]   3  + 2= 
  3  + 2 = 5
5K   So by condition ,   [ 3K-6 ]/ [ 2K-4+10 ]= 2/3 9k-18 =4k-8+20 5 k= 12+18 k = 6   Solve for K which is K = 6   So initial volume of liquid 18 = 3K = 18 litres   18nswer : 18
Answer: A
A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (7D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
Select.
A) 3D/V  B) 4D/V  C) 5D/V  D) 6D/V  E) 7D/V

Solution: The total time of the trip was:   3D/2V + 7D/3V + D/6V =   18D/12V + 28D/12V + 2D/12V =   48D/12V = 4D/V   The answer is 4D/V.48 /12= 
48 /12 = 4
4D/V   The answer is 4D/V.
Answer: B
The sum of two numbers is 110. Five times one number is equal to 6 times the other. The bigger of the two numbers is	Choose the most appropriate option.
A) 10	B) 12	C) 14	D) 15	E) 60

Solution: a:b 5:6   a+b=110   5x+6x=110   x=10   then two numbers are 50,60. The bigger number is 60   ANSW60R:60
Answer: E
If 15 oranges are bought for a rupee, how many must be sold for a rupee to gain 25%?  Choose the correct choice from the following:
A) 12	B) 10	C) 20	D) 18	E) None of these

Solution: C.P. for one orange = 1⁄15   Then S.P. = 100+25/100×1/15=125/100×15=1/12   Hence S.P. for one orange = 1⁄12   ∴ 12 oranges must be sold for a rupee   12nswer 12
Answer: A
If a*b denotes the greatest common divisor of a and b, then ((20*16)*(18*24)) = ?	Choices:
A) 24
B) 12
C) 6
D) 4
E) 2

Solution: The greatest common divisor of 20 and 16 is 4. Hence 20*16 = 4 (note that * here denotes the function not multiplication).   The greatest common divisor of 18 and 24 is 6. Hence 18*24 = 6.   Hence ((20*16)*(18*24)) = 4*6.   The greatest common divisor of 4 and 6 is 2.   Answer; 2.
Answer: E
A person travels equal distances with speeds of 5km/hr, 10km/hr, 15km/hr. and takes a total time of 11minutes. Find the total distance ? Choose the correct option.
A) 1km
B) 1500mts
C) 1600mts
D) 2km
E) 1250mts

Solution: Let the each distance be x km   total distance = 3x   then total time,   (x/5)+(x/10)+(x/15) = 11/60   x=0.5   total distance = 3*0.5= 
3*0.5 = 1.5
1.5km= 1500meters   correct option is 1500mts
Answer: B
If A(k)=(k+1)^2, and k=1, what is the value of A(A(A(A(k))))?	Choose the correct answer:
A) 328359	B) 557321	C) 258327	D) 458329	E) 4422

Solution: A(A(A(A(1))))=A(A(A(4)))=A(A(25))=A(676)= 677^2 = 458329   Thus, the answer is 458329.
Answer: D
Revathi bought an electric cooker at 90% of the regular price. She paid $270 for the cooker. What was the regular price? Choose the correct choice: A) $300 B) $200 C) $360 D) $380 E) $400

Solution: Regular price = 270/90*100= 
270/90*100 = 300
300   $300nswer : $300
Answer: A
Two trains, A and B, started simultaneously from opposite ends of a 120-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 120-mile trip in 6 hours; Train B, traveling at a constant rate, completed the 120-mile trip in 4 hours. How many miles had train A traveled when it met train B?  Choose the correct choice from the following choices:	A) 28	B) 36	C) 48	D) 50	E) 54

Solution: As the ratio of the rates of A and B is 4 to 6 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 4/(4+6)=4/10 of 120 miles:   120*4/10= 
  120*4/10 = 48
48 miles.   Answer: 48.
Answer: C
With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 1 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Select
A) 187 km  B) 480 km  C) 278 km  D) 120 km  E) 671 km

Solution: Let the distance be x km. Then,   x/(7 1/2) - x/8 = 1   2x/15 - x/8 = 1 => x = 120 km.   Answer:120 km
Answer: D
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Choose the correct choice from the following answers:	A) 8	B) 4	C) 5	D) 9	E) 1

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
A man sold 18 toys for Rs. 16800, gaining thereby the cost price of 3 toy find the cost price of a toy  Choose the correct option: A) Rs. 600 B) Rs. 800 C) Rs.500 D) Rs.900 E) Rs.970

Solution: Let the cost of one toy = X.   Then, cost of 18 toys = 18X.   Gain = 3X.   SP of 18 toys = Rs. 16800.   Gain = SP – CP   3X = 16800 – 18X   21X = 16800   X = Rs. 800.   answer : Rs. 800
Answer: B
The percentage profit earned by selling an article for Rs. 1320 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? Choose one.
A) 3000 B) 1230 C) 2000 D) 1625 E) 3400

Solution: C.P. be Rs. x.   Then, (1320 - x)/x * 100 = (x - 1280)/x * 100   1320 - x = x - 1280   2x = 2600 => x = 1300   Required S.P. = 125 % of Rs. 1300 = 125/100 * 1300 = Rs. 1625.   ANSER 1625
Answer: D
A sum of Rs. 350 made up of 110 coins, which are of either Rs. 1 or Rs. 5 denomination. How many coins are of Rs. 5?  Pick:
A) 52	B) 60	C) 62	D) 72	E) None

Solution: Explanation:   Let, the number of Rs.1 coins are x and Rs.5 coins are y.   Then x + y = 110   x + 5y = 350   Solving above two equations, we get y = 60. So number of Rs.5 coins are 60.   Correct Option: 60
Answer: B
How many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph?  Choose the most appropriate option
A) 23 sec B) 65 sec C) 25 sec D) 45 sec E) 24 sec

Solution: D = 100 + 130= 
100 + 130 = 230
230   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 230/10= 
230/10 = 23
23 sec   23 secnswer:23 sec
Answer: A
If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 14 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Choose the correct choice from the following options: A) 25 pounds B) 46 pounds C) 92 pounds D) 100 pounds E) 140 pounds

Solution: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*14 --> x = 140.   Answer: 140 pounds.
Answer: E
Two trains of length 150 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 36 kmph. In how much time will the trains cross each other?  Choose the correct choice.
A) 87/7 sec  B) 80/7 sec  C) 80/9 sec  D) 80/5 sec  E) 20 sec

Solution: Relative speed = (54 + 36)* 5/18 = 5 * 5= 
5 * 5 = 25
25 mps.   The time required= d/s = (100 + 150 + 250)/25   = 500/25= 
500/25 = 20
20 sec.   Answer: 20 sec
Answer: E
A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money R did Bob receive?	Choose the correct answer
A) 20 B) 22 C) 24 D) 26 E) 52

Solution: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.   Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.   So, we getK - Bob's $ = 32   Bob received 4 dollars plus one-third of what remained   Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.   1/3 of K-4 is (K-4)/3   So ALTOGETHER, 22ob receives4 + (K-4)/3   So, our equation becomes:K -[4 + (K-4)/3 ]= 32   Simplify to get: K - 4 - (K-4)/3 = 32   Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96   Simplify: 2K - 8 = 96   Solve: K = 52   Plug this K-value intoK - 22ob's $ = 32to get: 52 - 22ob's $ = 32   So, 22ob's $ R= 20   Answer:   22
Answer: B
A two digit number reversed and multiplied by 4 is 3 more than the original digit. what is the digit?	Choose the correct choice from the following:	A) 61	B) 62	C) 63	D) 64	E) 66

Solution: If no is xy , then   10x+y = 4*(10y+x)-3= 40y +4x-3   6x-39y +3 =0   2x-13y +1 =0   13 y =2x+1   when y=1, x=6   so number is 61.   61NSWER:61
Answer: A
In how many years does a sum of Rs. 4000 yield a simple interest of Rs. 16500 at 15% p.a.?	Pick one.
A) 27.5 years	B) 26.5 years	C) 25.5 years	D) 28.5 years	E) 29.5 years

Solution: T = (100 * 16500)/(15 * 4000)= 
(100 * 16500)/(15 * 4000) = 55/2 = around 27.5
27.5 years   27.5 yearsNSWER:27.5 years
Answer: A
How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?	Choose the correct option.
A) 8881 B) 2777 C) 2999 D) 1200 E) 2788

Solution: 50/100 * x = 30 * 20 => x   = 1200   Answer: 1200
Answer: D
Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip, at an average speed of 60 miles per hour for the next 30 miles and at a average speed of 90 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip, Myra’s average speed in miles/hr for the entire trip was closest to
Choose the correct choice from the following choices:  A) The average speed is 35 miles per hour.  B) The average speed is 40 miles per hour.  C) The average speed is 45 miles per hour.  D) The average speed is 50 miles per hour.  E) The average speed is 55 miles per hour.

Solution: Here, Myra traveled at three speeds for one-third distance each.   Average Speed = 3abc/(ab + bc + ca) = 3*30*60*90/(30*60 + 60*90 + 30*90)   Average Speed = 3*2*90/(2 + 6 + 3) = 540/11   Answer (The average speed is 50 miles per hour.)
Answer: D
The simple form of the ratio 5/3:2/5 is? Pick
A) 10:6	B) 10:3	C) 25:6	D) 25:3	E) 30:3

Solution: 5/3 : 2/5 = 25:6   ANSWER:25:6
Answer: C
How many numbers between 0 and 1770 have a prime tens digit and a prime units digit?  Choose the correct choice from the following options.
A) 266 B) 272 C) 278 D) 284 E) 290

Solution: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is  4*4= 
 4*4 = 16
16. Thus every set of 100 consecutive positive integers has 16 such numbers.   From 0 to 1700, there  16*17= 
 16*17 = 272
272 such numbers.   From 1701 to 1770, the 10s units can only use 3 numbers {2, 3, 5}. 3*4=12.   The total number is then  272+12= 
 272+12 = 284
284   The answer is 284.
Answer: D
If 4<(1-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive  Choose the correct choice from the following options
A) II only  B) III only  C) I and II only  D) II and III only  E) I, II and III

Solution: 12<7-x   x<-5   x+5<0   1.5<x...not possible   2.True.....Check for values x=-6,-7,-8....... etc   3.True.. Since x+5<0 -(x+5) will always be positive   Hence, Ans is I, II and III..
Answer: E
If two numbers are in the ratio 2:3. If 12 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?	Choose the most appropriate option:
A) A)12
B) B)18
C) C)20
D) D)24
E) E)26

Solution: 2:3   2x + 12 : 3x + 12 = 3 : 4   4[2x + 12] = 3[3x + 12]   8x + 48 = 9x + 36   9x - 8x = 48 - 36= 
48 - 36 = 12
12   Then smallest number is= 2   2x = 24   Correct Option 24
Answer: D
A train covers a certain distance at a speed of 400kmph in 3 hours. To cover the same distance in 2 2/3 hours, it must travel at a speed of
Options
A) 480km/hr  B) 450km/hr  C) 550km/hr  D) 750km/hr  E) 650km/hr

Solution: Explanation:   Distance = 400Ã—3 = 1200km   Required speed = (1200Ã— 3/8) = 450km/hr   Answer: Option 450km/hr
Answer: B
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 5 out of 7 consecutive days in Rwanda?
Answers.
A) 4/7  B) 3/7  C) 21/128  D) 4/28  E) 28/135

Solution: using Binomial. theorem   n21/128r (p)^r (q)^n-r   721/1285 (1/2)^5 (1/2)^r   which is 21/128   Answer is 21/128.
Answer: C
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?  Choose the correct choice from the following answers:
A) 18 sec	B) 16 sec	C) 87 sec	D) 17 sec	E) 11 sec

Solution: Speed = 63 * 5/18   = 35/2 m/sec   Time taken = 280 * 2/35= 
280 * 2/35 = 16
16 sec   Answer: 16 sec
Answer: B
10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?  Choose the correct choice from the following options.
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: Work done by 10 men in 1 day = 1/7   Work done by 1 man in 1 day = (1/7)/10 = 1/70   Work done by 10 women in 1 day = 1/14   Work done by 1 woman in 1 day = 1/140   Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)   = 5/70 + 10/140 = 1/7   => 5 men and 10 women can complete the work in 7 days   Answer is 7.
Answer: D
Sandy had $224 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?  Pick one: A) $260 B) $290 C) $320 D) $350 E) $380

Solution: Let the money Sandy took for shopping be x.   0.7x = 224   x = 320   The answer is $320.
Answer: C
Of the families in City X in 1992, 30 percent owned a personal computer. The number of families in City X owning a computer in 1999 was 50 percent greater than it was in 1992, and the total number of families in City X was 5 percent greater in 1999 than it was in 1994. what percent of the families in City X owned a personal computer in 1999?  Choose one
A) 43%	B) 42.85%	C) 45.25%	D) 46.23%	E) 41.66%

Solution: Say a 100 families existed in 1992 then the number of families owning a computer in 1992 - 30   Number of families owning computer in 1999 = 30 * 150/100= 
30 * 150/100 = 45
45   Number of families in 1999= 105   The percentage = 45/105 * 100 = 42.85%.   ANSWER:42.85%
Answer: B
How many positive integers will divide evenly into 320?  Choose one:
A) 8
B) 12
C) 16
D) 18
E) 20

Solution: 520 = 10*13*4 = 8*5*13 = 2^3*5*13   We need to positive integers will divide evenly into 520 or simply the factors of 520   If a number is of the form 2^a*3^b*5^c,   Total factors = (a+1)(b+1)(c+1)   Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 8   Option 8
Answer: A
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. Wbat was the original expenditure of the mess?
Pick
A) 520 B) 720 C) 425 D) 625 E) 420

Solution: 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 is 420.
Answer: E