divelab/Sys2Bench huggingface dataset:
Question: John and Steve are speed walkers in a race. John is 14 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
Options:
A)13 seconds
B)17 seconds
C)26 seconds
D)32 seconds
E)51 seconds
Rationale: Let t be the time that John spent for his final push.
Thus, per the question,
4.2t = 3.7t+14+2 ---> 0.5t = 16 ---> t = 32 seconds.
D is the correct answer.
Answer: D
Question: A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river.
They met at 500 yards away from A and after that they met 300 yards away from shore B without
halting at shores. Find the distance between the shore A & B
Options:
A)1100 yards
B)1200 yards
C)1300 yards
D)1400 yards
E)None of these
Rationale: Explanation :
The boats first met after 500yards from A.
Let the total distance between A and B be x.
Then,
500/a = x - 500 / b, ------------(1)
where, a = speed of A,
b = speed of B.
Assuming both boats are coming back to their original start place without halting at the shores,
Distance coverred by A = x + 300
Distance covered by B = 2x - 300
x+300/a = 2x-300/b -----------------------(2)
From above,
500/x-500 = x+300/2x-300
Solve, for x = 1200
Answer : B
Answer: B
Question: Aman started a business investing Rs. 50,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)120:105:118
B)60:105:112
C)12:105:110
D)12:105:112
E)60:105:111
Rationale: Explanation:
Aman : Rakhi : Sagar = (50000 * 36) : (105000 * 30) : (140000 * 24)
= 60:105:112
Answer: B
Answer: B
Question: The average of ten numbers is X and the average of five of these is Y.If the average of the remaining five is z, then
Options:
A)x = y+z
B)2x = y+z
C)x = 2y+2z
D)none of the above
E)Cannot be determined
Rationale: Explanation :
Clearly, we have x =(5y+5z/10)
or
2x = y + z
Answer : B
Answer: B
Question: The line CD is parallel to AB and crosses the angle BOA so that O,B,D lie on the same line and so do O,A,C. If OA=2, AC=4 and BD=6, determine the length of OB.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Solution:
The lines AB and CD are parallel, so by the intersect theorem, we have
OB/BD=OA/AC, or OB=OA/AC.BD=2/4.6=3
Answer A
Answer: A
Question: If a-b= 4 and a^2+b^2=80, find the value of ab
Options:
A)10
B)12
C)15
D)18
E)32
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 80 - 16 = 64
=> ab = 32
ANSWER:E
Answer: E
Question: A group of people participate in some curriculum, 30 of them practice Yoga, 25 study cooking, 15 study weaving, 6 of them study cooking only, 8 of them study both the cooking and yoga, 7 of them participate all curriculums. How many people study both cooking and weaving?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Both cooking and weaving = 25 - (6+8+7) = 4
So, the correct answer is D.
Answer: D
Question: In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 36 readers, how many reading spots do not have even a single reader?
Options:
A)8
B)16
C)15
D)14
E)9
Rationale: 1+2+3+4+5+6+7+8 = 36
so, 8 spots are occupied by users
23-8 = 15,
ANSWER:C
Answer: C
Question: A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than four times?
Options:
A)37/256
B)56/256
C)65/256
D)70/256
E)93/256
Rationale: More than 5 times tails = 6times +7times+8times = 8C5 + 8C6 + 8C7 + 8C8 = 93
2 2 2 2 2 2 2 2
2^8 times total events and 93 events where tails side up .
So probability = 93/2^8 = 93/256 (Answer E)
Answer: E
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is 3/4 empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
Options:
A)40%
B)41%
C)43.75%
D)42%
E)44%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (3/4)*(1/2) + 1/2 = 7/8
4th step: brand Z is (1/2)*(7/8) = 7/16 = 43.75%
Answer (C)
Answer: C
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
Options:
A)116.6
B)116.68
C)116.69
D)116.66
E)116.62
Rationale: Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.Answer:D
Answer: D
Question: Three years ago the average age of A and B was 18 years. with c joining them ,the average age become 22 years.how old is c?
Options:
A)26
B)31
C)24
D)22
E)27
Rationale: Present age of A+B =(18*2+3*2) years = 42 years
Present age of A+B+c =(22*3) years =66 years
C's age is = (66-42) years = 24 years
Answer =C
Answer: C
Question: 9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 42 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
Options:
A) 6
B) 7
C) 8
D) 12
E) 14
Rationale: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.
Side 1 = 8 m/h --> 4 m in 1/2 hr
Side 2 = 10 m/h --> 5 m in 1/2 hr
to complete this right angle triangle
d^2 = 4^2 + 5^2
d^2 = 41
= ~ 6
Answer option A
Answer: A
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
Options:
A)55 sec
B)40 sec
C)45 sec
D)30 sec
E)35 sec
Rationale: T = (660 + 165)/54 * 18/5
T = 55
ANSWER A
Answer: A
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 1600. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)70.00%
B)86.98%
C)76.99%
D)45%
E)None of these
Rationale: The total CP = Rs. 16000 + Rs. 1600 = Rs. 17600 and SP = Rs. 31150
Profit(%) = (31150 - 17600)/17600* 100 = 76.99%
ANSWER:C
Answer: C
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 6.5 hours, then the distance covered at 40 kmph is
Options:
A)130 km
B)120km
C)100km
D)280km
E)none of these
Rationale: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 6.5
or, x/40 + (250 - x)/60 = 6.5
or, (3x + 500 - 2x)//120 = 6.5
or 500 + x = 780
x=280
ANSWER:D
Answer: D
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
Options:
A)12
B)81
C)77
D)66
E)73
Rationale: (A + B) - (B + C) = 12
A - C = 12
Answer: A
Answer: A
Question: Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
Options:
A)12 min
B)25 min
C)40 min
D)48 min
E)58 min
Rationale: Distance = Speed * time
4*11/4 = 11km
New Speed = 16.5 kmph
Therefore time = D/S = 11/16.5 = 40min
Answer : C.
Answer: C
Question: Sam invested Rs. 5000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Options:
A)500.2
B)320.0
C)220.5
D)100.1
E)230.2
Rationale: P = Rs. 5000 ; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [5000* (1 + 5/100)2]
= (5000* 21/20 * 21/20)
= Rs.220.50
Answer:C
Answer: C
Question: A circular mat with diameter 12 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)5/12
B)2/5
C)1/5
D)3/4
E)5/6
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(6)(6)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(36/24)
I hope this is easy to follow, so with some simplification i get (1/8)(3/2) =3/16= (1/5) Answer is C
Answer: C
Question: A student got twice as many sums wrong as he got right. If he attempted 54 sums in all, how many did he solve correctly ?
Options:
A)12
B)16
C)18
D)24
E)26
Rationale: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 54 3x = 54 x = 18.
Answer:C
Answer: C
Question: A female student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
Options:
A)100
B)120
C)140
D)110
E)150
Rationale: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
D
Answer: D
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is five years older than Ellen, how old is Aaron?
Options:
A)0.5–5
B)6–10
C)11–15
D)16–20
E)21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 5
e+5-20 = 2e-40
e-15 = 2e-40
e = 25
d = 32
42 = 4a + 40
a = 0.5
Answer: A
Answer: A
Question: If x = √11 + √20, y = √15 + √17 and z = √14 + √18, then which of the following holds true?
Options:
A)x < y < z
B)Y< z < x
C)y < x < z
D)x < z < y
E)None of these
Rationale: By squaring and simplifying,
x2 = 31 + 2√220
y2 = 32 + 2√255
z2 = 32 + 2√252
x2 < z2 < y2 => x < z < y.
Answer:D
Answer: D
Question: a metallic cuboid of dimensions 27x18x12 m is melted.find the minimum amount of the volume of molten metal which should be added to mould it into a cube whose edge is 'a' cm where a is an integer.
Options:
A)16 m
B)17 m
C)18 m
D)19 m
E)15 m
Rationale: volume of cuboid = 27*18*12 = (27*27*8)= (3*3*2)^3= 18^3
so no amount of the volume of molten metal should be added to mould it into a cube whose edge is 'a' cm where a is 18 m.
ANSWER:C
Answer: C
Question: Gasoline varies in cost from $0.95 to $1.15 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
Options:
A)$15.50
B)$15.72
C)$16.10
D)$16.50
E)$17.01
Rationale: Solution:
We know that the per gallon cost of gasoline varies from $0.95 - $1.15.
Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.
Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.
So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).
Case 1: for 30 gallons the cost is 30*0.95 to 30*1.15 which is $28.50 to $34.50
Case 2: for 20 gallons the cost is 20*0.95 to 20*1.15 which is $19.00 to $23.00
Thus, the maximum cost of the 480 mile trip is $34.50 and minimum is $19.00
so the difference is $34.50 - $19.00 = $15.50
Answer: A
Answer: A
Question: Mitchell took a box of pushpins and counted how many there were of each colour. There was 1 red pushpin, 5 blue pushpins, and 2 yellow pushpins. How many pushpins were there in all?
Options:
A)02
B)04
C)03
D)05
E)08
Rationale: Add the numbers of pushpins.
1 + 5 + 2=8.
Answer is E.
Answer: E
Question: Robert spent $120 in buying raw materials, $195 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
Options:
A)A)$150
B)B)$210
C)C)$350
D)D)$160
E)E)$200
Rationale: Let the total amount be x
then, (100-10)% of x = 120+195
90% of x = 315
90x/100 = 315
x = $350
Answer is C
Answer: C
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 115. If the ratio of his marks in English and Maths is 5:1, find his marks in Science?
Options:
A)18
B)77
C)25
D)55
E)31
Rationale: S:E = 1:3
E:M = 5:1
------------
S:E:M = 5:15:3
5/23 * 115 = 25
Answer: C
Answer: C
Question: In an election, candidate A got 85% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
Options:
A)330000
B)340000
C)347000
D)356000
E)404600
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 85 %
Therefore, the number of valid votes polled in favour of candidate A = 85 % of 476000
= 85/100 × 476000
= 40460000/100
= 404600
E)
Answer: E
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 26 m * 2 m * 0.75 m?
Options:
A)29798
B)27908
C)78902
D)26000
E)27991
Rationale: 26 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
26 = 1/1000 * x => x
= 26000
Answer: D
Answer: D
Question: Helen went to the stationers and bought things worth Euro 23, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)uro 16.70
B)uro 15.70
C)uro 13.70
D)uro 18.70
E)uro 17.70
Rationale: E
Euro 17.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [23 - (5 + 0.30)] = Euro 17.70
Answer: E
Question: In the coordinate plane, the points F (-1,1), G (1,2), and H (2,1) lie on a circle with center P. What are the coordinates of point P ?
Options:
A)(0.5,0.5)
B)(1,1)
C)(1,2)
D)(1,-2)
E)(2.5, -2.5)
Rationale: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-1)
But the the center of the circle will lie on (0.5,0.5)
A
Answer: A
Question: How many meters of carpet 50cm, wide will be required to cover the floor of a room 30m * 20m?
Options:
A)1600
B)450
C)300
D)1200
E)600
Rationale: 50/100 * x = 30 * 20 => x = 1200
Answer: D
Answer: D
Question: The market value of a certain machine decreased by 15 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
Options:
A) $8,000
B) $5,600
C) $3,200
D) $4,400
E) $800
Rationale: B.
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 15/100) = 8000-1200= $ 6800
Market value in 1984 = Market value in 1983 - (15 % of $8000)= 6800-1200 = $5600
Answer: B
Question: The water level in a rectangular swimming pool measuring 60 feet by 10 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)
Options:
A)100
B)2250
C)750
D)1200
E)5625
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 60*10*1/2=300 feet^3 of water must be removed, which equals to 300*7.5=2250 gallons.
Answer: B
Answer: B
Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the
mixture must be drawn off and replaced with water so that the mixture may be half water and half
syrup?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Explanation :
Let the quantity of the initial liquid in the vessel = 8 litre and quantity of water in the initial liquid = 3
litre andquantity of syrup in the initial liquid = 5 litreLet x litre of the mixture is drawn off and replaced
with waterQuantity of water in the new mixture = 3−3x8+xQuantity of syrup in the new mixture =
5−5x8Given that in the new mixture, quantity of water = quantity of
syrup⇒3−3x8+x=5−5x8⇒10x8=2⇒5x4=2⇒x=85⇒85litre
Initially we assumed that the quantity of the initial liquid in the vessel = 8 litre for
the ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced
with water so that the mixture may be half water and half syrup
Now, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off
and replaced with water so that the mixture may be half water and half syrup
=85×18=15
It means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture
may be half water and half syrup
Answer : Option C
Answer: C
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability W that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
Options:
A)(a) 4/10
B)(b) 4/9
C)(c) 1/2
D)(d) 6/10
E)(e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability W = 50/90 = 5/9
Correct answer E
Answer: E
Question: Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next two years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
Options:
A)s.8500
B)s.6000
C)s.10880
D)s.9000
E)s.7000
Rationale: using the formula S.I=P*T*R/100
(x*6*3/100)+(x*9*2/100)+(x*13*3/100)=8160
x=10880
ANSWER:C
Answer: C
Question: a three digit number, sum of the digit is 17, the sum of square of digits is 109, if it is subtracted wit 495 the number gets reversed, find the three digit number.
Options:
A)683
B)863
C)368
D)686
E)786
Rationale: from the given options
863-495=368
therfore ans is 863
ANSWER:B
Answer: B
Question: Mohan purchased 12 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Options:
A)A)Rs.598
B)B)Rs.594
C)C)Rs.596
D)D)Rs.595
E)E)Rs.520
Rationale: Explanation:
Price of 12 kgs of rice at Rs.26/kg = 12x26 = Rs.312
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.312+Rs.208 = Rs.520.
Answer: Option E
Answer: E
Question: A can do a piece of work in 5 days and B can do it in 6 days how long will they both work together to complete the work?
Options:
A)2 6/11
B)2 8/11
C)2 7/11
D)2 9/11
E)2 10/11
Rationale: Explanation:
A’s one day work = 1/5
B’s one day work = 1/6
(A+B)’s one day work = 1/5 + 1/6 = 11/30 => time = 30/11 = 2 8/11 days
Answer: Option B
Answer: B
Question: What is the sum of the numbers between 1 and 20, inclusive?
Options:
A)310
B)200
C)215
D)285
E)210
Rationale: Sol. 1+2+3...17+18+19+20
answer. E
Answer: E
Question: The length of the shorter side of a rectangle is 2 units. The length of each
diagonal is 4 units. What is the acute angle between the diagonals?
Options:
A)15o
B)22.5o
C)45o
D)60o
E)75o
Rationale: Suppose the vertices of the rectangle are labeled A, B, C, and D in such a way
that AB is the shorter side. Let O be the intersection point of the two diagonals. Then
4AOB is equilateral
correct answer D
Answer: D
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
Options:
A)240
B)180
C)120
D)220
E)140
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 –65x/100 = 21
5 x = 2100
x = 140.
Answer is E.
Answer: E
Question: For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 2 order of $250 ?
Options:
A) $1
B) $2
C) $3
D) $4
E) $5
Rationale: Total cost involved for each 75 $ shipment: 3+2 = 5 $. Thus, for two such orders = 10$
Total cost involved for a 250$ shipment: 3+3 = 6$. Thus, for two such orders = 12$
The difference = 2$.
B
Answer: B
Question: A watch was sold at a loss of 10%. If the watch was sold for $24 more, there would have been a gain of 6%. What is the cost price?
Options:
A)$120
B)$150
C)$180
D)$210
E)$240
Rationale: 0.9x + 24 = 1.06x
0.16x = 24
x = 150
The answer is B.
Answer: B
Question: What is the absolute value of twice the difference of the roots of the equation D=5y^2 − 20y + 15 = 0 ?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: D=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: E
Question: If (2x + 2)(x + 3) = 2x^2 + x, what is a possible value of x?
Options:
A) -6/7
B) -6/8
C) -5/7
D) 8/7
E) 6/8
Rationale: Rearranging the given expression:
(2x + 2)(x + 3) = 2x^2 + x
i.e. 2x^2 + 8x + 6 = 2x^2 + x
i.e. 7x = -6
i.e. x = -6/7
Answer: Option A
Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: A
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 12 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 8 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
Options:
A) 0.22
B) 0.31
C) 2.50
D) 3.21
E) 4.8
Rationale: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/12 (R=W/T here W=1 work, T = 12hrs)
2nd outlet rate = 1/8 (R=W/T here W=1 work, T = 8hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/12+1/8 = 5/24
again apply the formula RT=W
T = W/R = 1/5/24 = 24/5 =4.8
Answer is E.
Answer: E
Question: If (2a + 3b)/(5a - 3b) = 23/5 , then the value of b : a is ?
Options:
A)4 : 1
B)1 : 4
C)4 : 5
D)5 : 4
E)1 : 2
Rationale: (2a + 3b)/(5a - 3b) = 23/5
=> 10a + 15b = 115a - 69b
=> 105a = 84b => 5a = 4b
a/b = 4/5
ANSWER:D
Answer: D
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
A)3 sec
B)5 sec
C)6 ½ sec
D)7 ½ sec
E)5 ½ sec
Rationale: D
7 ½ sec
70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 ½ sec
Answer: D