divelab/Sys2Bench huggingface dataset:
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Options:
A)Rs. 2000
B)Rs. 10,000
C)Rs. 15,000
D)Rs. 20,000
E)Rs. 26,000
Rationale: Principal = Rs.(100 x 5400)/(12x3)	= Rs. 15000.
Answer: Option C
Answer: C
Question: Pipes A and B can fill a tank in 4 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
Options:
A)3 hrs
B)3 9/77 hrs
C)3 9/17 hrs
D)3 9/27 hrs
E)3 9/19 hrs
Rationale: Net part filled in 1 hour = 1/4 + 1/6 - 1/12
= 4/12 = 1/3
The tank will be full in 3 hrs
Answer:A
Answer: A
Question: P is three times as fast as Q and working together, they can complete a work in 20 days. In how many days can Q alone complete the work?
Options:
A)26 1/2 days
B)27 1/2days
C)29 3/4days
D)14 1/4 days
E)10 1/2days
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 20 days, which means Q can do the work in 80 days.
Hence, P can do the work in 26 1/2 days.
Answer:A
Answer: A
Question: How many 3's are there in the following sequence which are neither preceded by 6 nor immediately followed by 9 ?
9 3 6 6 3 9 5 9 3 7 8 9 1 6 3 9 6 3 9
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: D
9 3 6 6 3 95 9 3 78 9 16 3 9 6 3 9
Answer: D
Question: Which of the following is closest to (-9/10)^199？
Options:
A)-1
B)-1/2
C)0
D)1
E)2
Rationale: (-9/10)^4 = 6561/10,000 which is already less than 2/3.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Answer: C
Question: "How old are you, Alchemerion?" asked one of the wizards appearances the wizards answer with a riddle, "I am still Very young as wizards go.I am only three times my son's age. My father is 40 year more than twice of my age. Together the three of us are a 1240 year old". How old is Alchemerion
Options:
A)300
B)320
C)340
D)360
E)380
Rationale: let Alchemerion be A
let son be S
let father be F
A= 3* S
F= 40 +(2*A)
therefore 1240=(S+F+A)
1240=(A/3)+ (40+(2*A) )+ A
A=360
ANSWER:D
Answer: D
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
Options:
A)35
B)36 2/3
C)37 1/2
D)40
E)42
Rationale: Let distance = x km and usual rate = y kmph.
Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)
Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)
On dividing (i) by (ii), we get: x = 40.
Answer : D.
Answer: D
Question: Jill has 14 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
Options:
A)3
B)6
C)9
D)12
E)24
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 14 1 3/4w = 14w=8The total number of jars = 3w =24Answer: E
Answer: E
Question: What is the unit digit in 15^100?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: Unit digit in 15^100 = unit digit in [(15^4)^25 ]But unit digit in 15^4=5unit digit 15^100= 5Answer is E
Answer: E
Question: What is the height of the tower ? A man standing at a distance of 1km from the bottom of the tower makes an angle 300 degrees with the top of the tower .An insect starts from the bottom of the tower and reaches the top in 25sec.
Options:
A)0.577km
B)0.477km
C)0.677km
D)0.577k7
E)0.977km
Rationale: tan = opp side/adj side
tan 30= height/1
ht=0.577km
ANSWER:A
Answer: A
Question: Find the sum of first 35 natural numbers
Options:
A)470
B)468
C)630
D)463
E)520
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)/2
=35(35+1)/2=35(36)/2=630
Answer: Option C
Answer: C
Question: To create paint with a certain shade of gray, one must combine 2.75 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)127.2
B)129.4
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 2.75 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.75:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: A
Question: A pupil's marks were wrongly entered as 83 instead of 70. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Options:
A)18
B)82
C)26
D)27
E)29
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 70) => x/2
= 13 => x = 26.
Answer: C
Answer: C
Question: If a car at 60 km/hr instead of 50 km/hr,the car would have gone 20 km more. The actual distance traveled by the car is?
Options:
A)100 km
B)58 km
C)60 km
D)90 km
E)65 km
Rationale: Let the actual distance traveled be x km. Then,
x/50 = (x + 20)/60
6x - 5x = 100 =>x = 100 km.
Answer :A
Answer: A
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 500 bolts?
Options:
A) 36
B) 72
C) 120
D) 144
E) 180
Rationale: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 500 bolts
500 * 6 / 25 = 120 mins
Ans C
Answer: C
Question: Which of the following is equal to 1(1/3)%?
Options:
A)0.012/100
B)0.12/100
C)1.3/100
D)12/100
E)12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/3
How about adding a space:Which of the following is equal to (1 1/3)%
(1 1/3)% = 1.3% = 1.3/100
Answer:
C
Answer: C
Question: A van takes 6 hours to cover a distance of 252 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)28 Kmph
B)60 Kmph
C)70 Kmph
D)80 Kmph
E)90 Kmph
Rationale: Time = 6
Distence = 252
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 252/9 = 28 Kmph
A
Answer: A
Question: Two pipes A and B can separately empty a cistern in 45 min and 30 min respectively. There is a third pipe in the top of the cistern to fill it. If all the three pipes are simultaneously opened, then the cistern is full in 90 min. In how much time, the third pipe alone can fill the cistern?
Options:
A)22.5 min
B)15 min
C)30 min
D)20 min
E)25 min
Rationale: Work done by the third pipe in 1 min = (1/45 + 1/30) - 1/60 = 4/90.
[+ve sign means filling]
The third pipe alone can fill the cistern in 90/4= 22.5 min.
ANSWER:A
Answer: A
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 11 salespeople on staff, how many different arrangements of winners are possible?
Options:
A)1,728
B)1,440
C)990
D)220
E)6
Rationale: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 11 salespeople on staff, how many different arrangements of winners are possible?
11*10*9
=990
Answer : C
Answer: C
Question: A train 1000 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)288 m
B)256 m
C)1000 m
D)278 m
E)287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (1000 + x)/60
= 65/3
x = 300 m.
Answer:C
Answer: C
Question: 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?
Options:
A)10.9
B)10.6
C)10.4
D)10.8
E)10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: D
Answer: D
Question: Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 38 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:18, at what time will they be reading the same page?
Options:
A)7:48
B)8:18
C)8:48
D)9:18
E)9:48
Rationale: Since Tom reads an average of 1 page every 2 minutes, Tom will read 24 pages in the first 48 minutes. Jan can catch Tom at a rate of 8 pages per hour, so it will take 3 hours to catch Tom.
The answer is B.
Answer: B
Question: Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 40 km per hour. At what time will Car B be 40 km ahead of Car A?
Options:
A)3:00 pm
B)3:30 pm
C)4:00 pm
D)4:30 pm
E)5:00 pm
Rationale: At 9:30 am, Car A will be 15 km ahead of Car B.
Car B travels at a rate 10 km per hour faster than Car A.
Car B needs to travel 55 km more than Car A in order to be 40 km ahead.
This will take 55 km/10 km per hour=5.5 hours.
Car B will be 55 km ahead at 3:00 pm.
The answer is A.
Answer: A
Question: There are 28 students in a class. Sixteen of those students are men.
What percent of the class are women? (Round to the nearest tenth)
Options:
A)22.9%
B)32.9%
C)52.9%
D)62.9%
E)42.9%
Rationale: 28 total students-16 men=12 women
12 is what % of 28?
Multiple the opposites
100 x 12 = 1200
Divide by the remaining number
28)42.85/1200.00
42.9%
correct answer E
Answer: E
Question: If ab - c = a(b - c), which of the following must be true?
Options:
A) a=0 and c=0
B) a=1/2 and b=2
C) b=1 and c=0
D) a=1 or c=0
E) a=1/2 or c=0
Rationale: ab-c = a (b-c)
ab - c = ab - ac
c= ac
ac-c = 0
c(a-1) = 0
Either c = 0; or a = 1
D is the answer
Answer: D
Question: What is the difference between the place value and face value of 2 in the numeral 2578?
Options:
A)2000
B)2002
C)1998
D)1990
E)1910
Rationale: Difference between the place value and face value of 2 = 2000-2 = 1998
Answer is C
Answer: C
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 9%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
Options:
A)16.16%
B)15.25%
C)14.14%
D)13.33%
E)11.71%
Rationale: (100%+9%)*(100%-19%) = 1.09*.81 = 0.8829.
1-0.8829 = 11.71% lost = -11.71%
The Answer is E
The organization has lost 11.71% of its total volunteers from fall to spring.
Answer: E
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Options:
A)17
B)65
C)12
D)27
E)92
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase
=4 * 10 = 40
The new sum = 230 + 40 = 270 The new average
= 270/10 = 27.
Answer: D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)157 m
B)717 m
C)142 m
D)150 m
E)152 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 9) m
= 150 m.
Answer:D
Answer: D
Question: How much water should be added to 14 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
Options:
A)25 liters
B)27 liters
C)26 liters
D)32 liters
E)35 liters
Rationale: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=14+x)))
2=5%*(14+x)-------->x=26
Ans C
Answer: C
Question: If f is a function defined for all k by f(k) = k^3 /16, what is f(2 k) in terms of f(k)?
Options:
A)1/8 f(k)
B)8 f(k)
C)2 f(k)
D)10 f(k)
E)32 f(k)
Rationale: f(k) = k^3 /16
f(2k) = (2k)^3 /16 =8 * k^3/16 = 8 x (k^3 /16) = 8 f(k).
So answer is B.
Answer: B
Question: Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is
Options:
A)500
B)400
C)300
D)1200
E)200
Rationale: C=x
B=x/2
A=x/4
A:B:C=1:2:4
C's Share Rs(4/7)*700 = 400
ANSWER B
Answer: B
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
Options:
A)$6,000
B)$6,750
C)$7,425
D)$7,500
E)$9,375
Rationale: Interest = 0.05*face value = 0.04*7,500 --> face value = 0.04*7,500/0.05 = 6,000.
Answer: A.
Answer: A
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs.60,000. the amount invested by Y is
Options:
A)Rs.45,000
B)Rs.50,000
C)Rs.60,000
D)Rs.90,000
E)None
Rationale: Solution
Suppose Y invested Rs.y
Then,	60000 /y = 2 / 3
â€¹=â€º y=(60000Ã—3 / 2).
â€¹=â€º y=90000.
Answer D
Answer: D
Question: 10 men and 15 women together can complete a work in 5 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
A)127 days
B)150 days
C)177 days
D)187 days
E)225 days
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/5
15 women's 1 day work = (1/5 - 10/100) = 1/10
1 woman's 1 day work = 1/150
1 woman alone can complete the work in 150 days.
Answer:B
Answer: B
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
A)10
B)25
C)30
D)45
E)50
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: C
Question: Evaluate
1916−−−−√
Options:
A)116
B)115
C)114
D)113
E)None of these
Rationale: Explanation:
=2516−−−√
=25−−√16−−√
=54
=114
Answer: C
Answer: C
Question: Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.19
B)7.18
C)7.44
D)7.15
E)7.12
Rationale: T = (135 + 165)/ (80 + 65) * 18/5
T = 7.44
Answer: C
Answer: C
Question: If the price of a TV is first decreased by 20% and then increased by 40%, then the net change in the price will be :
Options:
A)4% increase
B)12% increase
C)10% decrease
D)6% increase
E)None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 140% of(80% of 100) =Rs. 140/100 * 80/100 * 100 = Rs. 112.
.'. Increase = 12%
Answer : B
Answer: B
Question: The sum of three consecutive numbers is 75. Name the numbers.
Options:
A)24, 25, and 26.
B)34, 25, and 26.
C)29, 28, and 26.
D)44, 15, and 36.
E)54, 5, and16.
Rationale: The sum of three consecutive numbers is 75. Name the numbers.
Consecutive numbers are numbers in counting order. To solve problems of this type, let x equal
the first number. The second and third numbers can be expressed as x 1 and x 2.
Write an equation. x x 1 x 2 75
Solve. 3x 3 75
3x 72
x 24
Answer: The numbers are 24, 25, and 26.
Check: The numbers are consecutive, and their sum is 75.
correct answer A
Answer: A
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.6.6. The true discount is
Options:
A)Rs.72
B)Rs.36
C)Rs.55
D)Rs.50
E)none
Rationale: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(6.6 x 100 / 12 x 1)
= Rs.55.
Answer C
Answer: C
Question: An orphanage had provision of food for 300 boys for 90 days. After 20 days, 50 boys left the orphanage. The number of days for which remaining food will last is :
Options:
A)70
B)72
C)80
D)84
E)86
Rationale: Explanation :
Solution: After 20 days : 300 boys had food for 70 days.
Suppose 250 boys had food for x days. Now, less boys, more days (Indirect proportion)
.'. 250 : 300 : : 70 : x
=> 250*x = 300*70
=> x = 300*70/250 = 84.
Answer : D
Answer: D
Question: The owner of a local jewelry store hired two watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 5 more besides. He escaped with two diamonds. How many did he steal originally?
Options:
A)50
B)36
C)25
D)None of these
E)Cannot be determined
Rationale: Explanation :
Since, thief escaped with 1 diamond,
Before 2nd watchman, he had ( 2 + 5 ) x 2 = 20 diamonds.
Before 1st watchman, he had ( 20 + 5 ) x 2 = 50 diamonds.
Answer : A
Answer: A
Question: Which of these following integers is the square of an integer?
Options:
A)17095831562
B)17051831967
C)17127831453
D)17142831568
E)17751831696
Rationale: The unit digit of any perfect square can not be 2, 3, 7, or 8.
The answer is E.
Answer: E
Question: Fresh tomato contains 60% lycopene and dry tomato contains 20% lycopene. How much dry tomato can be obtained from 100kg of fresh tomato?
Options:
A)A)32kg
B)B)50kg
C)C)52kg
D)D)80kg
E)E)100kg
Rationale: Quantity of lycopene in 100 kg of fresh tomatoes = (100-60)% of 100kg = 40kg
Let the quantity of dry tomato obtained be x kg
then, (100-20)% of x = 40
(80/100)*x = 40
x = 50
correct option is B
Answer: B
Question: The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,980 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)
Options:
A)200π
B)450π
C)300π
D)480π
E)1,200π
Rationale: Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 1980
Revolutions in 60 seconds (one minute)= 1980*60
Total distance traveled= total revolutions *distance traveled in one revolution
1980*60 *2π10/5280= 450π
B is the answer
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 60?
Options:
A)s.3944
B)s.3948
C)s.4080
D)s.3965
E)s.3929
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 60
= Rs.4080.
Answer: C
Answer: C
Question: In the first 15 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 35 overs to reach the target of 275 runs?
Options:
A)5.55
B)6.25
C)6.75
D)7.02
E)6.48
Rationale: Required run rate = 275 - (3.2 x 15)	/35	=	227/35 = 6.48 Option E
Answer: E
Question: When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 728 more than 4times the middle integer. Find the numbers?
Options:
A)650
B)678
C)698
D)728
E)729
Rationale: x + 4 (x + 4) = 728 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 728 + 4 x + 8
x = 720
x + 2 = 722
x + 4 = 724
Check: the smallest is added to four times the largest
720 + 4 * 724 = 3616
four times the middle
4 * 722 = 2888
3616 is more than 2888 by
3616 - 2888 = 728
D
Answer: D
Question: Man is 40% more efficient than Woman. How much time will they, working together, take to complete a job which 1 Man alone could have done in 20 days?
Options:
A)11 days
B)25 days
C)22 days
D)11 2â„3 days
E)11 1â„3 days
Rationale: Ratio of times taken by Man and Woman = 100 : 140 = 5 : 7.
Suppose Woman takes x days to do the work.
Then, 5 : 7 : : 20 : x â‡’ x = (20Ã—7)/5 â‡’ x = 28
Manâ€™s 1 dayâ€™s work = 1â„20; Womanâ€™s 1 days work = 1â„28
(Man + Woman)â€™s 1 dayâ€™s work = (1â„20 + 1â„28) = 3â„35
âˆ´ Man and Woman together can complete the job in 35â„3 days or 11 2â„3 days.
Answer D
Answer: D
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 5 standard Veggiematik machines chop in 6 minutes?
Options:
A)36
B)54
C)108
D)270
E)324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 36 Carrots - 4 minutes,
1 standard Veggiematik machine - 9 Carrots - 1 minute,
Now
5 standard Veggiematik machine - ? Carrots - 6 minutes,
Hence = 9X5X6 =270 Carrots
Answer D
Answer: D
Question: What is the place value of 3 in the numeral 3259
Options:
A)2000
B)3000
C)3500
D)4000
E)4590
Rationale: Option 'D'
3 * 1000 = 3000
Answer: D
Question: If 2x + y = 7 and x + 2y = 5, then xy/y = ?
Options:
A) 1
B) 4/3
C) 3
D) 18/5
E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(3*1)/1
=3
C
Answer: C
Question: The average of 10 consecutive integers is 15. Then, 9 is deducted from the first consecutive number, 8 is deducted from the second, 7 is deducted form the third, and so on until the last number which remains unchanged. What is the new average?
Options:
A)10
B)10.5
C)11
D)11.5
E)12
Rationale: The total subtracted is (9+8+...+1) = (9*10) / 2 = 45
On average, each number will be reduced by 45/10 = 4.5
Therefore, the overall average will be reduced by 4.5
The answer is B.
Answer: B
Question: Find the value of x from the below equation: x^2−7x+10=0
Options:
A)5
B)3
C)6
D)7
E)9
Rationale: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x^2−7x+10=(x−5)(x−2)
x2−7x+10=(x−5)(x−2)
x^2−7x+10
=0
⇒(x−5)(x−2)
=0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(x−5)(x−2)
=0
⇒(x−5)
=0or (x−2)=0
⇒x= 5 or 2
A
Answer: A
Question: What is 0.1 percent of 12,356?
Options:
A)0.12356
B)1.2356
C)12.356
D)0.012356
E)0.0012356
Rationale: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.1(1/100)12,356. The answer is 12.356. Hence, the correct answer is C.
Answer: C
Question: The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
Options:
A)15 cm
B)25 cm
C)35 cm
D)42 cm
E)43 cm
Rationale: Explanation:
Required Length = H.C.F of 700 cm, 385 cm and 1295 c
= 35 cm. Answer: C
Answer: C
Question: The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
Options:
A)C
B)W
C)Y
D)I
E)A
Rationale: Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.
Ans: A
Answer: A
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.484 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
Options:
A)12
B)18
C)20
D)22
E)24
Rationale: 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 = 484/3 = 161.33 sq m
l b = 161.33 i.e., l * l/3 = 161.33
l^2 = 484 => l = 22.
D
Answer: D
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100000 and 1000000 ?
Options:
A) 10
B) 11
C) 101
D) 1011
E) 10001
Rationale: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 10=10000
1000100000/ 101 =100000
so answer is option is A
Answer: A
Question: Two trains of length 200 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)28
B)266
C)990
D)20
E)24
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 200 + 280 = 480 m.
The time required = d/s = 480/20 = 24 sec.
Answer: E
Answer: E
Question: In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
Options:
A)2:1
B)1:2
C)1:5
D)5:1
E)4:3
Rationale: 1st variety rs 18 /kg---- 2nd variety rs 24/kg
mix cost 20/kg = (24-20) (20-18)
=4:2 = 2:1
ANSWER A
Answer: A