divelab/Sys2Bench huggingface dataset:
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time L will it take to fill the bucket to full capacity?
Options:
A)7/18
B)9/18
C)2
D)18/7
E)18/5
Rationale: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank L = 60/7 - 6 = 18/7 mins. ANS D.
Answer: D
Question: A 6% stock yields 8% . The market value of the stock is :
Options:
A)33
B)75
C)298
D)27
E)29
Rationale: Explanation:
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs 6, investment =Rs. \inline \left ( \frac{100}{8} \times 6\right ) = Rs. 75
Market value of Rs. 100 stock = Rs. 75.
Answer: B) Rs.75
Answer: B
Question: 220 metres long yard, 21 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2 consecutive trees
Options:
A)10
B)12
C)14
D)11
E)17
Rationale: 21 trees have 20 gaps between them,
Required distance (220/20) = 11
D
Answer: D
Question: How many 5's are there preceded by 2 but not followed by 6?
5 9 3 2 1 2 6 7 4 9 2 5 2 1 3 2 8 2 5 1 3 8 3 2 5 6 2 5 3 9 5 8 2 0 1 8 7 4 6 3
Options:
A)4
B)5
C)6
D)8
E)3
Rationale: 2 5 2
2 5 3
2 5 1
Only at these places 3 is preceded by 2 but not followed by 6
Answer: E
Answer: E
Question: How much more would Rs.60000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
A)482
B)725
C)992
D)1446
E)923
Rationale: 60000(11/10)4 - 60000(6/5)2 = 1446
Answer:D
Answer: D
Question: Martha takes a road trip from point A to point B. She drives x percent of the distance at 40 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?
Options:
A) 110
B) 300
C) 1,100
D) 3,000
E) 20,000
Rationale: total distance = d
total time taken = x/(100*40) + (100-x)/(100*50)
speed = distance / time
gives numerator = 20000
Answer : E
Answer: E
Question: A train covers a distance of 14 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)m
B)m
C)m
D)m
E)m
Rationale: Speed = (14/10 * 60) km/hr
= (84 * 5/18) m/sec = 70/3 m/sec.
Length of the train = 70/3 * 6
= 140 m.
Answer:C
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)3.12 km
B)2.88 km
C)3 km
D)2 km
E)4 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
ANSWER:B
Answer: B
Question: What is the dividend. divisor 18, the quotient is 9 and the remainder is 3
Options:
A)A)145
B)B)148
C)C)165
D)D)153
E)E)158
Rationale: D = d * Q + R
D = 18 * 9 + 3
D = 162 + 3
D = 165
Answer : C
Answer: C
Question: A boy can reach a certain place in 15 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.
Options:
A)4 km/hr.
B)6 km/hr
C)8 km/hr
D)14 km/hr
E)None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
15x - (15 * 29x/30) = 3
=> 30x-29x = 3*2
=> x = 6 km/hr.
Answer : B
Answer: B
Question: A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:1. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?
Options:
A)1:1
B)3:5
C)2:3
D)3:2
E)5:3
Rationale: ............................... Milk ............... Water ....................... Total
Initial ......................30 .................... 10 .............................. 40
20 Lts mix. taken out 30-15 ............... 10-5 ........................... 40-20
20 Lts milk added..... 15+20 ................ 5 .............................. 40
20 Lts mix. taken out 35-15 ............... 5-5 ........................... 40-20
20 Lts water added..... 20 ................ 0+20 .............................. 40
New ratio = 20:20= 1:1
A
Answer: A
Question: Due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A)A) 4.99
B)B) 8
C)C) 10
D)D) 15
E)E) 24
Rationale: Old time in minutes to cross 8 miles stretch = 8*60/55 = 8*12/11 = 8.72
New time in minutes to cross 8 miles stretch = 8*60/35 = 8*12/7 = 13.71
Time difference = 4.99
Ans:A
Answer: A
Question: John walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 10 hours 40 minutes. He would have gained 4 hours by driving both ways. How long would it have taken for him to walk both ways.
Options:
A)15 h 15 min
B)11 h 10 min
C)14 h 40 min
D)10 h 10 min
E)9 h 45 min
Rationale: 1.Walking to to a viewpoint+Driving back=10 hours 40 minutes
2.Driving to a viewpoint+Driving back=10 hours 40 minutes - 4 hours=6 hours 40 minutes, thereforeone way driving=6 hours 40 minutes/2 =3 hours 20 minutes.
3. From 1.one way driving=10 hours 40 minutes-3 hours 20 minutes=7 hours 20 minutes.
4.Walking to to a viewpoint+Walking back=7 hours 20 minutes+7hours 20 minutes=14 hours 40 minutes.
Answer: C
Answer: C
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)10 %
B)5 %
C)12 %
D)16 %
E)20%
Rationale: Explanation:
P = (P*5*R)/100
R = 20%
Answer: E
Answer: E
Question: The sum of present age of Abe and the age before 7 years is 33. Find the present age of Abe. What will be his age after 7 years?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Present age = x
Before 7yrs, y=x-7
After 7yrs, z=x+7
By the qn,
x+(x-7)=33
2x-7=33
2x=33+7
x=40/2
x=20
z=x+7
=20+7
=27
ANSWER:C
Answer: C
Question: A train 700m long takes 10 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)A)175kmph
B)B)257kmph
C)C)162kmph
D)D)145kmph
E)E)100kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
700/[(x+5)*5/18] = 10
10(x+5) = 140*18
x = 257kmph
Answer is B
Answer: B
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
Options:
A)1/60
B)1/45
C)2/45
D)3/22
E)5/22
Rationale: 5C2*3C1=10*3=30
12C3=220
3/22
Answer: D
Answer: D
Question: One pump drains one-half of a pond in 2.5 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
Options:
A)1 hour
B)1.2 hour
C)3 hours
D)1.25 hours
E)6 hours
Rationale: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.
We have the 1st pump working rate/hour = 1/2 : 5/2 = 1/5
Working rate of 2 pumps: 1/2 : 1/2 = 1.
Working rate of 2nd pump: 1 -1/5 = 4/5--> Time taken for the 2nd pump to finish: 1 : 4/5 = 5/4 = 1.25 hours.
D
Answer: D
Question: 6x – 5y + 3z = 23
4x + 8y – 11z = 7
5x – 6y + 2z = 10
Given the equations above, x + y + z = ?
Options:
A) 11
B) 12
C) 13
D) 14
E) 15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 23-10
or, x+y+z = 13
Option C is the ans
Answer: C
Question: The sum of the present age of Henry and Jill is 40. What is their present ages if 8 years ago Henry was twice the age of Jill?
Options:
A)13 and 27
B)16 and 24
C)18 and 22
D)11 and 29
E)none of these
Rationale: Let the age of Jill 8 years ago be x, age of Henry be 2x
x+8 + 2x+8 = 40
x = 8
Present ages will be 16 and 24
Answer : B
Answer: B
Question: If ‘LONDON’ is coded as ‘KNMCNM’, then ‘INDIA’ is coded as
Options:
A)EWSTF
B)RGTDF
C)HMCHZ
D)HTGCVH
E)POJYNMK
Rationale: L= 12 = 12-1 = 11 = K
O = 15 =15-1 =14 = N
SIMILARLY,
I = 9 = 9-1 = 8 = H
N = 14 = 14-1 = 13 = M
D = 4 = 4-1 = 3 = C
A = 27 = 27 -1 = 26 = Z
SO ANS IS
HMCHZ
Answer: C
Question: Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometers total did she hike east?
Options:
A)3.625
B)3.5
C)4
D)4.5
E)5
Rationale: Set up two R x T =D cases.
1. 1/10 km/ min x T = 2.75
from which T= 27.5 mins.
We know total journey time now is 45 +27.5 = 72.5
The rate is the same ie 1/10km/min.
set up second R x T =D case.
1/10 km/min x 72.5 = 7.25 km
Now the total journey would be halved as distance would be same in each direction. 7.25/2 =3.625.
A.
Answer: A
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)2888
C)2667
D)2999
E)2122
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: Out of three consecutive odd numbers eleven times the first number is equal to addition of thrice the third number and adding 16 to four times the second . What is the first number?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Description :
=> 11x=4(x+2)+16+3(x+4)
=> 11x=7x+36
=> 4x=36
X=9
Answer E
Answer: E
Question: Rahul is a cashew merchant in Kerala. He has cashews in sealed wooden boxes of 10kg
each. The price of the cashew increases by Rs.20 per kg for every year, but at the same
time, 10% of the cashews are eaten by rodents every year. If the price of a 1 kg of fresh
cashew is Rs.100, what is the change in his profits if he sells a sealed box after one year of
storage, rather than selling it fresh? (In Rs.)
Options:
A)64 more
B)64 less
C)80 more
D)80 less
E)90 less
Rationale: Price of 1kg fresh cashew = Rs.100
Therefore, price of 10kg = Rs.100 * 10 = Rs.1000
10% of 10kg which eaten by rodents = 10*10/100 = 1kg.
So, End of Year he had 10kg - 1kg = 9kg
So, he sells that 9kg with Rs.20 per kg profit = 9 * 120 = 1080.
He buy 10kg wooden box with cashew for 1000Rs and sell that for 1080Rs.
So, profit = 1080 - 1000 = 80Rs more money he get.
ANSWER:C
Answer: C
Question: Rs.8000 become Rs.10210 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)6 YEARS
B)7
C)5
D)3
E)4
Rationale: Explanation:
10210 = 8000(21/20)N
(21/20)5 = (21/20)N => N = 5
Answer: Option C
Answer: C
Question: 34.	The side surface of a cylinder is rolled with a rectangle. If the height of a cylinder is 16 feet and the perimeter of the circular base. Is 12 feet, what is the diagonal of the rectangle?
Options:
A)16
B)20
C)18
D)22
E)21
Rationale: Think of an aluminum can can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, use pythagoreans theorem or properties of 3-4-5 triangles to solve for the hypothenuse, 20. (Correct answer B)
Answer: B
Question: If 30% of 100 is greater than 50% of a number by 10, then the number is?
Options:
A)40
B)30
C)60
D)80
E)50
Rationale: Let the number be x
30% of 100 - 50% of x = 10
50/100 x = (30/100 * 100)-10
x/2 = 20
x = 40
Answer is A
Answer: A
Question: If A lends Rs.2000 to B at 15% per annum and B lends the same sum to C at 17% per annum then the gain of B in a period of 4 years is?
Options:
A)155
B)162
C)157.5
D)160
E)157.12
Rationale: (2000*2*4)/100
=> 160
Answer: D
Answer: D
Question: What is the speed of the train?
I.The train crosses a signal pole in 18 seconds.
II.The train crosses a platform of equal length in 36 seconds.
III.Length of the train is 330 metres.
Options:
A)I and II only
B)II and III only
C)I and III only
D)III and either I or II only
E)Any two of the three
Rationale: Explanation:
Let the speed of the train be x metres/sec.
Time taken to cross a signal pole = Length of the train/Speed of the train
Time taken to cross a platform = (Length of the train + Length of the Platform)/Speed of the train
Length of train = 330 m.
I and III gives, 18 =330/x => x = 330/18 m/sec = 55/3 m/sec.
II and III gives, 36 = 2X330/x = x=660/36 m/sec = 55/3 m/sec.
Answer is (D).
Answer: D
Question: Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 3z
B)(y +z) / 4
C)2y + 3z
D)3y + z
E)3y + 4.5z
Rationale: X + 2Y + 3Z = 1.5(X + Y + Z)
X + 2Y + 3Z = 1.5X + 1.5Y + 1.5 Z
Add and subtract the common terms,
0.5 X = 0.5Y + 1.5Z
Divide by 0.5,
X = Y + 3 Z
ANSWER:A
Answer: A
Question: A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar?
Options:
A)20 ounces
B)80 ounces
C)100 ounces
D)120 ounces
E)180 ounces
Rationale: 20% sugar in 60 oz solution;
Sugar = 60*20/100 = 12 oz
Water = 60-12 = 48 oz
Now; let's add "x" oz of water in the solution;
Total solution = 60+x oz
Sugar = 12 oz.(Sugar's amount will not change as we are not adding or subtracting sugar)
12 = (60+x) * 5/100
60+x = 240
x = 240 - 60 = 180 oz
Answer: "E"
Answer: E
Question: In how many ways can the letters of the word SPENCER be arranged if the S and P must always be together and the N and C must always be together?
Options:
A)12
B)24
C)60
D)120
E)240
Rationale: There are 7 letters in the word SPENCER are 2E , SP , NC , R
We will consider SP and NC as a group and there are 2 E's
No of arrangements in which S and P must always be together and the N and C must always be together
= (5! *2 *2)/2!
= 5!*2
= 120 *2
= 240
Answer E
Answer: E
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 26 seconds. The ratio of their speeds is?
Options:
A)3/1
B)9/1
C)3/3
D)3/5
E)5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 26 ==> 27 x + 17 y = 26 x + 26 y
==> 1 x = 9 y ==> x/y
= 9/1.
Answer:B
Answer: B
Question: A person has to make 146 pieces of long bar. he take $ seconds to cut piece.what is total time taken by him to make 146 pieces?
Options:
A)580 seconds
B)680 seconds
C)500 seconds
D)540 seconds
E)560 seconds
Rationale: if it is 4 seconds, as u have mistaken with SHIFT key, then....
we'll have to make 145 cuts for 146 pieces.
so 145 * 5 = 580 seconds
ANSWER:A
Answer: A
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 32 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Options:
A)17 litres
B)21.3 litres
C)11 litres
D)07 litres
E)38 litres
Rationale: 262.85(32)+3,104.35x = 1,399.45(32 + x)
Solve the equation.
262.85(32)+3,104.35x = 1,399.45(32 + x)
8,411.2 + 3,104.35x = 44,782.4 + 1,399.45x
8,411.2 + 1,704.9x = 44,782.4
1,704.9x = 36,371.2
x ≈ 21.3
Answer is B.
Answer: B
Question: The cost price of 14 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/91%
B)18 2/11%
C)27 3/11%
D)18 2/91%
E)12 2/11%
Rationale: 14 CP = 11 SP
11 --- 2 CP
100 --- ? =>27 3/11%
Answer:C
Answer: C
Question: There are 7 Physics and 1 Chemistry book in shelf A and 5 Physics books in Shelf B, one book is moved from shelf A to shelf B. A student picks up a book from shelf B. Find the probability that the Chemistry book is taken by the student.
Options:
A)7/8
B)1/8
C)1/48
D)5/48
E)5/6
Rationale: I)Probability that the book moved from A to B is Chemistry=1/8.
II)Probability that the boom taken from B is Chemistry=1/6
P=1/8∗1/6=14/8
ANSWER: C
Answer: C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)38
B)27
C)40
D)77
E)21
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: C
Question: Two pipes A and B can fill a tank in 50hour and 75 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)15hrs
B)20hrs
C)25hrs
D)30hrs
E)32hrs
Rationale: Part filled by A in 1 hour = 1/50
part filled by B in 1 hour = 1/75
Part filled by A+B in 1 hour = 1/50 + 1/75 = 1/30
Both the pipes will together will fill the tank in 30 hours.
Answer is D
Answer: D
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
Options:
A)240
B)120
C)280
D)160
E)200
Rationale: Let C's share = Rs. x
Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6
Therefore, x/6 + x/4 + x = 1360
=17x/12 = 1360
x = 1360 x 12/17= Rs. 960
Hence, B's share = Rs. (960/4)= Rs. 240.
Answer is A.
Answer: A
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/6%
B)16 3/3%
C)16 2/3%
D)16 2/9%
E)12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: C
Question: The average (arithmetic mean) of six numbers is 10. If 3 is subtracted from each of four of the numbers, what is the new average?
Options:
A)1.5
B)2
C)3
D)8
E)4.5
Rationale: Sum of 6 numbers = 6*10 =60
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 60 - 12 = 48
New average = 48/6 = 8
Answer D
Answer: D
Question: The speeds of 3 trains in the ratio 2:4:6. The ratio between time taken by them to travel the same distance is?
Options:
A)6:4:3
B)1:2:3
C)4:8:9
D)6:3:2
E)4:8:7
Rationale: Ratio of time taken is = 1/2 : 1/4 : 1/6 = 6:3:2
Answer is D
Answer: D
Question: How many diagonals does a 62-sided convex polygon have?
Options:
A)1829
B)2356
C)3458
D)3843
E)4820
Rationale: A 62-sided convex polygon has 62 vertices.
If we examine a single vertex, we can see that we can connect it with 59 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 62 vertices can be connected with 59 vertices to create a diagonal then the total number of diagonals would be (62)(59) = 3658
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3658 by 2 to get 1829.
The answer is A.
Answer: A
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 7 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)20 years
E)21 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 7 years = (x+ 7) = 21 years..
Answer: E
Answer: E
Question: A person travels from P to Q a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
Options:
A)62.5
B)77
C)48
D)99
E)21
Rationale: Speed on return trip = 150% of 50 = 75 km/hr.
Average speed of trip = 50 + 75 /2 =125/2 = 62.5 km/hr
Answer : A
Answer: A
Question: Express 5 mps in kmph?
Options:
A)22
B)88
C)90
D)18
E)24
Rationale: 5 * 18/5 = 18 kmph
Answer: D
Answer: D
Question: In your classes you counted 126 hands. How many students were at the class?
Options:
A)63
B)61
C)85
D)86
E)88
Rationale: Total number of hands = 126
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 126 by 2
126 ÷ 2 = 63
Therefore, there were 63 students at the class.
ANSWER IS A
Answer: A
Question: A man engaged a servant on the condition that he would pay him Rs.900 and a uniform after 1year service. He served only for 9 months and receiveduniform and Rs.650, find the priceof the uniform?
Options:
A)Rs.90
B)Rs.100
C)Rs.120
D)Rs.150
E)Rs.160
Rationale: 9/12 = 3/4 * 900 = 675
650
-------------
25
1/4 -------- 25
1 --------- ? => Rs.100
B
Answer: B
Question: In a certain voting district, 40 percent of registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?
Options:
A)72%
B)47%
C)42%
D)34%
E)28%
Rationale: Town A is 40%, therefore town B must be 60%
Town A registered voters:0.70∗0.40=0.28
Town B registered voters: 0.60x=0.28 --> x=28/60 which is a little bit less than 50 percent
ANSWER:B
Answer: B
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 4%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
Options:
A)16.16%
B)15.76%
C)14.14%
D)13.13%
E)12.12%
Rationale: (100%+4%)*(100%-19%) = 1.04*.81 = 0.8424.
1-0.8424 = 15.76% lost = -15.76%
The Answer is B
The organization has lost 15.76% of its total volunteers from fall to spring.
Answer: B
Question: Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?
Options:
A)1/3
B)1/5
C)1/6
D)1/7
E)2/5
Rationale: Total number of ways to go home, considering that the order order matters =
Options: SSSEEE
Slots : ------
total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2
Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =
Options: SS ????
Slots: -- ----
Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =
3P2 * 4P4 = 3! * 4! = 3*2*4*3*2
The probability is therefore:
3P2 * 4P4 = 6P6
3*2*4*3*2= 1/5
ANSWER:B
Answer: B
Question: There are 4 more women than men on Centerville's board of education. If there are 4 members on the board, how many are women?
Options:
A) 3
B) 4
C) 6
D) 7
E) 8
Rationale: Given: M=W-4 so, W+(W-4)=4 --> W=4.
Answer: B.
Answer: B
Question: If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
Options:
A)25/√π
B)30/√π
C)20
D)25
E)30
Rationale: 60/360 = 1/6
1/6 of total area = 5
5/6 of total area = 5*5 =25
ANSWER:D
Answer: D
Question: What quantity of water should taken out to concentrate 27 liters of 40% acidic liquid to 60% acidic liquid?
Options:
A)5liters
B)10liters
C)15liters
D)9liters
E)6liters
Rationale: Required answer is = 27(60-40)/60 = 9 liters
Answer is D
Answer: D
Question: A rectangular grass field is 75 m * 55 m, it has a path of 3.2 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)s.1350
B)s.1327
C)s.1328
D)s.1364
E)s.1927
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +3.2 * 2) 2*2.5 => 682
682 * 2 = Rs.1364
Answer: D
Answer: D