divelab/Sys2Bench huggingface dataset:
Question: The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age? [0.5 Decades = 5 Years]
Options:
A)35 years
B)40 years
C)45 years
D)47 years
E)None of these
Rationale: Explanation:
Let, Total of current ages of the 2 daughters is A years.
Then, father’s current age = 3A years.
(3A + 5) = 2 (A +10)
3A + 5 = 2A + 20
A = 15
Therefore, father’s current age = 45 years. Answer: C
Answer: C
Question: In a class,30 students pass in english and 20 students in maths,while some students among these pass in both.how many students do only english as compared to those doing only maths?
Options:
A)10
B)15
C)4
D)12
E)indeterminate
Rationale: For doing Union or Intersection we would need three values. In this question the missing information in this question is Total no.of Students in the class.
ANSWER:E
Answer: E
Question: In Orange County one tenth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Options:
A)60.
B)42.
C)85.
D)70.
E)252.
Rationale: The number must be an integer and multiple of both 10 and 7.
Only option D fulfill this condition and hence is the answer.
Answer: D
Question: A recipe contains 100g of sugar and milk, a quarter of sugar in butter. If it contains more milk 45g butter it contains sugar?
Options:
A)55
B)44
C)50
D)30
E)68
Rationale: We propose equations,
sugar + milk = 100g
butter = sugar / 4
45g +butter=milk
sugar = 44g
Answer: B
Answer: B
Question: What is the radius of a circle that has a circumference of 3.14 meters?
Options:
A)1.0
B)2.5
C)1.3
D)0.5
E)0.7
Rationale: Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2* 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
Answer: 0.5 meter.
correct answer D
Answer: D
Question: A train is running at a speed of 40 km/hr and it crosses a post in 17.1 seconds. What is the length of the train?
Options:
A)190 metres
B)160 metres
C)200 metres
D)120 metres
E)250 metres
Rationale: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 17.1 s
Distance Covered, d = vt = (400/36)Ã— 17.1 = 190 m
Distance covered is equal to the length of the train = 190 m
Correct answer is 190 metres
A
Answer: A
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 30 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 50 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
Options:
A)36
B)84
C)132
D)144
E)180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 84min
B
Answer: B
Question: There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?
Options:
A)2/9
B)2/5
C)7/9
D)4/5
E)8/9
Rationale: Number of students = 10
Number of ways 10 students can sit around a circular table = (10 - 1)! = 9!
Number of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2
Number of ways A and D do not sit together = 9! - (8! * 2)
Probability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9
Answer: C
Answer: C
Question: A car covers a distance of 660 km in 6 hours. Find its speed?
Options:
A)104
B)7778
C)266
D)110
E)121
Rationale: 660/6 = 110 kmph
Answer:D
Answer: D
Question: If José reads at a constant rate of 5 pages every 5 minutes, how many seconds will it take him to read N pages?
Options:
A)60
B)2N
C)5/2*N
D)24N
E)150
Rationale: Jose would read 1 page in 5/5 min
Jose would read N page in (5/5)*N min i.e. (5/5)*N*60 Seconds = 60N Seconds.
Option A is the correct Answer.
Answer: A
Question: Calculate the percentage gain if a trader bought a bicycle for Rs 950 and sold it for Rs.1500?
Options:
A)56.89%
B)52.89%
C)59.89%
D)56.89%
E)57.89%
Rationale: C.P. = 950
S.P. = 1500
Gain = 1500-950 ---- 550
% Gain => 550/950*100 => 57.89%
Answer:E
Answer: E
Question: Find the cube root of 804357?
Options:
A)22
B)88
C)93
D)19
E)18
Rationale: Unit digit of the answer is 3. (cube of 3 = 27). Now omit 357 and find after which cube 804 lies. It is 729. so our tenth place is 9.
Answer = C
Answer: C
Question: 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?
Options:
A)6
B)7 2⁄3
C)6 2⁄3
D)6 1⁄3
E)None of these
Rationale: 10 men + 15 women in 1 day do 1⁄15 + 1⁄12 = 9⁄60 work
\ Time taken = 60⁄9 days = 62⁄3 days
Answer C
Answer: C
Question: If the day before yesterday was Thursday, when will Sunday be?
Options:
A)Day after tomorrow
B)Tomorow
C)Two days after today
D)Today
E)None of these
Rationale: Explanation :
Day before yesterday was Thursday
=>Yesterday was a Friday
=> Today is a Saturday
=> Tomorrow is a Sunday. Answer : Option B
Answer: B
Question: There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg.
Options:
A)29.23 kg
B)32.56 kg
C)35.66 kg
D)37.25 kg
E)NONE OF THE ABOVE
Rationale: Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg
1) First find the total weight of all students
- Weight of batch A = (36 x 40) = 1440
- Weight of batch B = (44 x 35) = 1540
Total weight of all students = (1440 + 1540) = 2980 kg
2) Find average weight of whole class
(Batch A + Batch B) students = (36 + 44) = 80 students
Average Weight =	Total weight of all the students /	No. of Students
= 2980 / 80
= 37.25 kg
ANSWER IS D
Answer: D
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
Options:
A)87 days
B)10 days
C)55 days
D)44 days
E)22 days
Rationale: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days
Answer:B
Answer: B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)38
B)2767
C)245
D)277
E)232
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer:C
Answer: C
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
Options:
A)2888
B)2827
C)2880
D)2827
E)2837
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 4! * 5! = 24 * 120
= 2880.
Answer: C
Answer: C
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 35 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)80x/7
B)13x/20
C)80/9x
D)20x/13
E)80x/9
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 35% of the sales of imported tools = 0.35*{total}/4 = 7/20*{total}/4 = 7*{total}/80.
Since the sales of of Japanese tools was x, then 7*{total}/80 = x --> {total} = 80x/7.
Answer: A.
Answer: A
Question: Suppose two numbers are in the ratio 2:3. If 5 is subtracted from both of the numbers then the ratio becomes 1:2 then find the greatest number?
Options:
A)5
B)15
C)10
D)20
E)25
Rationale: Given Ratio -> 2:3
2x - 5 : 3x - 10 = 1 : 2
2[2x - 5] = 1[3x - 5]
4x - 10 = 3x - 5
4x - 3x = 10 - 5
x = 5
Then greatest number is = 3x
3x = 15
Ans - B
Answer: B
Question: A restaurant buys fruit in cans containing 3 1/2 cups of fruit each. If the restaurant uses 1/2 cup of the fruit in each serving of its fruit compote, what is the least number of cans needed to prepare 60 servings of the compote ?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: 7/2 cups = 1 can
1/2 cup of each serving. so 7 serving per 1 can.
Least number is 7*9=63 =60 approx
Answer -9
ANSWER:C
Answer: C
Question: The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?
Options:
A)10%
B)15%
C)12%
D)13%
E)14%
Rationale: P(Absent|Friday) = P(Friday and abscent)/P(Friday)
= 0.03/0.2
= 15%
ANSWER:B
Answer: B
Question: What was the day on 15th august 1947 ?
Options:
A)Friday
B)Sunday
C)Saturday
D)Thursday
E)Monday
Rationale: Explanation:
15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)
Odd days in 1600 years = 0
Odd days in 300 years = 1
46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug
( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.
Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.
Hence, as the number of odd days = 5 , given day is Friday.
Answer: A
Answer: A
Question: A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1% cash on their first $5000 of purchase, 2% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.2% on their total annual charges made on the credit card, then what was the customer's annual charge?
Options:
A)$13,750
B)$15,000
C)$16,250
D)$17,500
E)$18,750
Rationale: The customer receives $50 for the first $5000.
The customer receives $100 for the next $5000.
Let x be the total amount of the customer's annual charge.
$150 + 0.03(x-10,000)=0.022x
0.008x=150
x=18,750
The answer is 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 23 seconds. The ratio of their speeds is?
Options:
A)3/1
B)3/2
C)3/9
D)3/5
E)7/2
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) = 23
==> 27 x + 17 y = 23 x + 23 y
==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: B
Question: Sum of 19 odd numbers is?
Options:
A)341
B)351
C)361
D)371
E)381
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 19 odd numbers = 19^2 = 361
ANSWER:C
Answer: C
Question: if 3rd ter, and 9th term is 8 in a.p,then find the 11th term
Options:
A)61
B)62
C)63
D)64
E)65
Rationale: a3=a1+(3-1)d
8=a1+2d.....(1)equ.
a9=a1+(9-1)d
8=a1+8d....(2)equ.
solve (1) and (2) then a1=4 and d=6.
a11=a1+(11-1)d
a11=4+10*6
a11=64.
ANSWER:D
Answer: D
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
Options:
A)Rs.8429
B)Rs.8420
C)Rs.8400
D)Rs.8420
E)Rs.8412
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23
= Rs.8400.
Answer:C
Answer: C
Question: he average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)0
B)1
C)10
D)19
E)8
Rationale: Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a the 20th number is (-a).
Answer: Option D
Answer: D
Question: There are 7 red balls and 5 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that 3 balls selected are red balls?
Options:
A)19/44
B)5/44
C)3/41
D)13/44
E)7/44
Rationale: Probability = Favorable outcomes / Total Outcomes
Probability = 7C3 / 12C3 OR (7/12)*(6/11)*(5/10) = 7/55
Answer Option E
Answer: E
Question: The difference between the place values of 6 and 5 in the number 826533 is
Options:
A)5500
B)4500
C)2500
D)6970
E)None
Rationale: Sol.= (Place value of 6) – (place Value of 5)= (6000 - 500)= 5500 Answer A
Answer: A
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
Options:
A)2 Hours
B)3 Hours
C)4 Hours
D)1 Hour
E)5 Hours
Rationale: Let the duration of the flight be x hours.
Then, 600/X - 600/(X +1/2) = 200 ==> 600/X - 1200/(2X +1) = 200
==> X(2X + 1) = 3 ==> 2X sqr. + X - 3 = 0 ==> (2X +3)(X - 1) = 0.
by neglecting negative value of X we got X = 1 hr.
Answer D) 1 Hour.
Answer: D
Question: A tank is filled in FOUR hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)56 hours
B)28 hours
C)55 hours
D)14 hours
E)47 hours
Rationale: 1/A + 1/B + 1/C = 1/4 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/4
=> (1 + 2 + 4)/2B = 1/4
=> 2B/7 = 4
=> B = 14 hours.
Answer: D
Answer: D
Question: A car dealership finances the purchase of a $30,000 car by lending y over the purchase price of the car to account for interest. If the dealership also charges a separate $150 service fee for the financing, this service fee is what fraction of the amount received by the customer?
Options:
A)150/(30000-Y)
B)150Y*30000
C)30150+Y
D)150Y
E)150/(30000+Y)
Rationale: The amount of money the customer received was (30,000 + y) dollars. The $150 service fee as a fraction of the amount received was, therefore, 150/(30,000 + y).
Answer: E.
Answer: E
Question: What will be the ans of that 126th term in the series abbcccdddd......???
Options:
A)m
B)n
C)o
D)q
E)p
Rationale: use formula n(n+1)/2=126
15*16=2*126
so 15 th letter is p
ANSWER:E
Answer: E
Question: What is the ratio whose term differ by 35 and the measure of which is 2/7?
Options:
A)A)32:23
B)B)14:49
C)C)71:85
D)D)32:39
E)E)41:52
Rationale: Let the ratio be x:(x+35)
Then, x/(x+35) = 2/7
x=14
required ratio = 14:49
Answer is B
Answer: B
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1110 will be:
Options:
A)Rs. 300
B)Rs. 200
C)Rs. 240
D)Rs. 350
E)None of these
Rationale: Z share = Z,
Y = 1.2Z
X = 1.25Ã—1.2Z,
X+Y+Z =111
(1.25Ã— 1.2+1.2+1)Z=1110
3.7Z=1110, Z=300
Answer: . A
Answer: A
Question: One side of a triangle has length 7 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 10
III. 5
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 7 and 4 are the base and height of triangle .
Area = 1/2 * 7 * 4 = 14
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 14
The answer is D.
Answer: D
Question: Of the 180 people at a party, 70 were women, and 30 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
Options:
A)40
B)50
C)60
D)70
E)100
Rationale: Total people at party=180
Women=70
so Men 180-70=110
No. of pple who tried appetizer=180-50 (given info)=130
No of women who tried appetizer=30
So Remaining ppl(men) who tried the appetizer =130-30=100
Correct Option E
Answer: E
Question: 2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
Options:
A)4
B)5
C)7
D)9
E)11
Rationale: (C)
Required remainder = remainder by (13 +11)/17 = 7
Answer: C
Question: What is the value of (P + Q)/(P - Q) if P/Q is 4?
Options:
A)5/3
B)2/3
C)2/6
D)7/8
E)8/7
Rationale: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (4 + 1)/(4 - 1)
= 5/3
= 5/3
ANSWER:A
Answer: A
Question: When a is divided by b, the quotient is c with remainder 4. What is a in terms of 4, b, and c?
Options:
A)b+c/4
B)bc+4
C)b+c
D)bc*4
E)bc-4
Rationale: a/b =c with remainder 4
i.e, a-4 = bc
a= bc+4
Answer : B
Answer: B
Question: If a and b are unique prime integers, which of the following must be even?
Options:
A)a−b
B)a−2b
C)2a−2b
D)2a−b
E)ab^2
Rationale: Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Answer C
Answer: C
Question: In a coconut grove, (x + 2) trees yield 40 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (x+2)×40+x×120+(x−2)×180/(x+2)+x+(x−2)=100
⇒ 340x−280/3x = 100
⇒ 40x = 280 ⇒ x = 7
Answer E
Answer: E
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)?
Options:
A)1
B)1/4
C)2
D)2/5
E)None
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
Option is B
Answer: B
Question: What amount does an investor receive if the investor invests $4000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)$4720
B)$4840
C)$4920
D)$5080
E)$5160
Rationale: A = (1 + R/100)^n * P
(1.1)^2 * 5000 = 1.21 * 5000 = 4840
The answer is B.
Answer: B
Question: Which of the following is closest to the difference between sum W of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
Options:
A)2.82
B)2.72
C)1.82
D)1.72
E)0.82
Rationale: Sum W of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: D
Question: Antonio works in a bakery. He made cookies that cost $2 and made $420. How many customer did he have?
Options:
A)200 customers
B)210 customers
C)250 customers
D)230customers
E)170 customers
Rationale: A cookie costs $2 adding another one is $4. 420 divided by 4 is 105 x 2 is 210. He had 210 customers. The correct answer is B.
Answer: B
Question: Gold is 11 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
Options:
A)3:2
B)1:1
C)3:1
D)5:2
E)4:3
Rationale: G = 11W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
11W+5Wx = x+1 * 8W
11+5x = 8(x+1)
x = 1/1
Ratio of gold with copper = 1:1 = 1:1
Answer is B
Answer: B
Question: A gardener wants to plant trees in his garden in rows in such a way that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
Options:
A)A)63
B)B)28
C)C)48
D)D)32
E)E)33
Rationale: Required number of trees
= 24/36 * 42 = 28.
ANSWER:B
Answer: B
Question: A Orange costs Rs 11 each and a watermelon costs Rs. 7 each. If I spend Rs 40 on total what is the number of orange I purchased?
Options:
A)7
B)8
C)9
D)3
E)10
Rationale: 3*11 + 7 = 40
Answer : 3
Option : D
Answer: D
Question: Solve the following quadratic equation by factoring.
x2-5x-14=0
Options:
A)-2,7
B)2,-7
C)1,8
D)1,-8
E)2,6
Rationale: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(x+2)(x-7)=0
x=-2 and x=7
ANSWER A
Answer: A
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?
Options:
A)20km/hr
B)30km/hr
C)40km/hr
D)50km/hr
E)90km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 450
50x - 45x = 450
x = 90km/hr
Answer is E
Answer: E
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
Options:
A)10 min
B)20 min
C)30 min
D)40 min
E)50 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: D
Question: In how many ways can the letters {U, U, R, R} be arranged?
Options:
A)4
B)20
C)120
D)720
E)840
Rationale: My answer : A
There is 4! ways to arrange those letters in total, however letter U repeats 2! times and letter R repeats 2! times
=> the way to arrange without repeating = 4!/ [2!x2!] = 4
Answer: A
Question: Calculate the average of all the numbers between 7 and 49 which are divisible by 6.
Options:
A)20
B)18
C)19
D)15
E)30
Rationale: Explanation:
numbers divisible by 6 are 12,18,24,30,36,42,48,
Average = (12+18+24+30+36+42+48, ) / 7 = 210/7 = 30
ANSWER: E
Answer: E
Question: Five pieces of wood have an average length of 128cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood?
Options:
A)a) 90
B)b) 100
C)c) 110
D)d) 130
E)e) 140
Rationale: C. 110
sum of all lengths of all 5 pieces of wood = 128 * 5 = 640
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 640 - 420 = 220
each of these 2 will have length 220/2 = 110
Answer C
Answer: C
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)27 2/23 %
B)33 1/3 %
C)30%
D)19%
E)21%
Rationale: Explanation:
100
150
------
150-------50
100-------? => 331/3%
ANSWER IS B
Answer: B
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 18 kilometer long bridge, at the same speed?
Options:
A)14 min
B)20 min
C)18 min
D)19 min
E)13 min
Rationale: S = 600/40 = 15 mps
S = 18000/15 = 1200 sec = 20 min.Answer: B
Answer: B
Question: How many different ways can you select a pilot and a co pilot if you have 95 people to choose from?
Options:
A)199
B)200
C)398
D)4950
E)8930
Rationale: 1) PERMUTATION:-
since it is selection, we have to find permutation..
95P2= 95!/(95-2)!=8930
ANS:E
Answer: E
Question: If x and y are integers such that x^2= y and xy = 343, then x – y = ?
Options:
A)-42
B)-20
C)-5
D)5
E)20
Rationale: here x and y are integers .
x^2=y,xy =343.
substitute x^2=y in xy => x^3=343.
here x^3 is positive ,
x is also positive.
x=7 then y=49.
x-y=-42
so option A is correct
Answer: A