divelab/Sys2Bench huggingface dataset:
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
Options:
A)288
B)266
C)120
D)277
E)6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (132 - x)
(x * 5 * 2) / 100 = (132 - x)
10x = 13200 - 100x
110x = 13200 => x = 120.
Answer: C
Answer: C
Question: In an examination, 35% of the students passed and 455 failed. How many students appeared for the examiantion?
Options:
A)490
B)620
C)700
D)845
E)None
Rationale: Solution
Let the number of students appeared be x.
Then, 65% of x = 455
‹=›65 / 100 x = 455
‹=› x= [455 x 100 / 65]
= 700.
Answer C
Answer: C
Question: The average age of a class of 32 students is 16 yrs. if the teacher’s age is also included, the average increases by one year. Find the age of the teacher
Options:
A)48
B)49
C)47
D)44
E)40
Rationale: Explanation:
Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher’s age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher’s age is 16+(33X1) = 49 Years
Answer: B
Answer: B
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party R. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
Options:
A)15
B)20
C)30
D)35
E)45
Rationale: S=100
not( R and B ) =35
only R=20
(R and B)/B=1/2
let ( R and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: A
Question: The average of five numbers id 27. If one number is excluded, the average becomes 25. The excluded number is
Options:
A)25
B)27
C)30
D)35
E)None
Rationale: Solution
Excluded number	= (27 x 5 ) - ( 25 x 4)
= 135 - 100
= 35.
Answer D
Answer: D
Question: If Daniel is 18 years old in December and is 10 years younger than his sister, which of the following could be true?
I. Daniel's Sister will be 28 years in December.
II. When Daniel is 20 years, his sister will be 25 years.
III. Daniel is older than his sister.
Options:
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
Rationale: Let’s check each statement.
Statement I: Daniel's Sister will be 28 years in December. There is 10 years difference in their ages so the sister's age will be 20 + 8 = 28, in which case Statement I is TRUE.
Statement II: When Daniel is 20 years, his sister will be 25 years. There is 10 years difference in their ages so the sister's age will be 20 + 8 = 28, in which case Statement II can NEVER be TRUE.
Statement III: Daniel is older than his sister. When Daniel is 10 the sister will be 28, in which case Statement III can NEVER BE TRUE
Only Statement I is TRUE
So, the Correct answer is A
Answer: A
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)10000
B)14000
C)15000
D)16000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: Let A, B, and C be three points on circle O such that AC is a diameter of O. Extend line AC
to a point D such that DB is tangent to O at B, and suppose that \ADB = 20o. Compute
\ACB.
Options:
A)32o
B)47o
C)55o
D)68o
E)71o
Rationale: Since we did not specify in which direction to extend the line AC, we also accepted
35 as an acceptable answer.
Let O be the center of the circle. Through angle chasing, we can determine that
\BOD = 90o - \ADB = 70o
\ACB =
180o - \BOD/2= 55o
correct answer C
Answer: C
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 80, and what number?
Options:
A)35
B)30
C)25
D)20
E)15
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -90 = 15
E
Answer: E
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections T of the 4 items can Amanda make?
Options:
A)9
B)12
C)14
D)15
E)60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
T=3*20=60
E. 60
Answer: E
Question: Let the function E(n) represent the product of the first n prime numbers, where n > 0. If x = E(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
Options:
A)ii only
B)iii only
C)i and ii only
D)i and iii only
E)ii and iii only
Rationale: E(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of E(n). Thus, E(n) + 1 = even + 1 = odd. So, (i) is always true.
Now, use logic:
If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since onlyi and iii onlyis among the options, then it must be true.
Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.
Answer: D.
Answer: D
Question: 35 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 4:3. How many liters of Liquid Q must be added to make the ratio 5:7?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Let x be the amount of liquid Q to be added.
(3/7)*35 + x = (7/12)*(35+x)
1260 + 84x = 1715 + 49x
35x = 455
x = 13
The answer is D.
Answer: D
Question: 12,31,?,129,220,347,516
Options:
A)129
B)220
C)347
D)68
E)520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
4*4*4 + 4 = 68
ANSWER : D
Answer: D
Question: If the sum of two numbers is 24 and the sum of their squares is 404, then the product of the numbers is
Options:
A)40
B)44
C)80
D)86
E)90
Rationale: Sol.
Let the numbers be x and y.
Then, (x+y) = 24 and x2 + y2 = 404.
Now, 2xy = (x+y)2 - (x2 + y2)
= (24)2 - 404 = 576- 404 = 172
xy = 86.
Answer D
Answer: D
Question: If a=2 and b=3,then 2^(a+1)+2^(b+1)=?
Options:
A)2^b(3)
B)2^(a + b)
C)2^a
D)2a^(b + 1)
E)3(2^b)
Rationale: If a=2 and b=3 then 2^3+2^4
=2^3(1+2^1)=2^3(3)
=2^b(3){b=3}
Answer is option A
Answer: A
Question: A student has to obtain 33% of the total marks to pass. He got 92 marks and failed by 40 marks. The maximum marks are?
Options:
A)400
B)300
C)500
D)610
E)175
Rationale: Let the maximum marks be x
Then, 33% of x = 92+40
33x/100 = 132
x = 400
Answer is A
Answer: A
Question: The line y = 5x/3 + b goes through the point (7, –1). What is the value of b?
Options:
A)3
B)–5/3
C)–7/5
D)16/3
E)–38/3
Rationale: “finding the equation” procedure. Plug (x, y) = (7, –1) into this equation:
{-1} = {{5(7)}/3} + b = {35/3} + b
b = {-35/3} - 1 = {-35/3} - {3/3} = -{38/3}
Answer = E
Answer: E
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3648
Options:
A)3648
B)9654
C)5945
D)7963
E)8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3648. Hence, it is the odd one.
The answer is 3648.
ANSWER:A
Answer: A
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
Options:
A)31.6
B)31.9
C)31.6
D)31.4
E)31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: A
Answer: A
Question: What day of the week does May 28 2006 fall on
Options:
A)Saturday
B)Monday
C)Sunday
D)Thursday
E)Wednesday
Rationale: 28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday.
Answer is C
Answer: C
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?
Options:
A)1:1
B)2:3
C)5:2
D)4:3
E)None of these
Rationale: Explanation :
Let,the actual amount of A and B be 4x and 3x respectively.
Amount of 1st basic element in the new alloy T is (5/8)*4x + (1/3)*3x = (7x)/2.
Similarly, the amount of 2nd basic element in the new alloy T is (3/8)*4x + (2/3)*3x= (7x)/2.
So, the ratio of 1st basic element to 2nd basic element is [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1.
Answer : A
Answer: A
Question: After working for 8 days, Anil finds that only 1⁄3 of the work has been done. He employs Rakesh who is 60 % efficient as Anil. How many more days will Anil take to complete the job?
Options:
A)15 days
B)12 days
C)10 days
D)8 days
E)None of these
Rationale: In 8 days, Anil does = 1⁄3 rd work
∴ in 1 day, he does = 1⁄24 th work.
∴ Rakesh’s one day’s work
= 60% of 1⁄24 = 1⁄40 th work.
Remaining work = 1 - 1⁄3 = 2⁄3
(Anil and Rakesh)’s one day’s work
= 1⁄24 + 1⁄40 = 1⁄15 th work.
Now, 1⁄15 th work is done by them in one day.
∴ 2⁄3 rd work is done by them in 15 × 2⁄3 = 10 days
Answer C
Answer: C
Question: If Rs.420 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)s.575
B)s.595
C)s.590
D)s.600
E)s.585
Rationale: 80 = (420*4*R)/100
R = 7.14%
I = (420*6*7.14)/100 = 180
420 + 180 = 600
ANSWER:D
Answer: D
Question: A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?
Options:
A)22 days
B)21 days
C)25 days
D)24 days
E)23 days
Rationale: Here LCM of 12 and 16 is taken as total work. ( becomes easy to solve)
Assume total work =48 units
Then workdone by (A+B) in one day = 48/12 = 4 units
Similarly, by (B+C) in one day = 48/16 = 3 units
Now according to question,
A works 5 days , B for 7 days and C for 13 days to complete total work
So, 5A + 7B + 13C = 48 units
5(A+B) + 2(B+C) + 11C = 48 units
5*4 + 2*3 +11C =48 units
11C = 22 units
C = 2 units ( C does 2 units of work daily)
Therefore, 48/2 = 24 days
C requires 24 days to complete the work alone.
Answer D
Answer: D
Question: If 20 typists can type 42 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Options:
A)189
B)72
C)144
D)216
E)400
Rationale: 20 typists can type 42 letters, so 30 typists can type = 42*30/20
42*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 42*30*60/20*20= 189
A is the answer
Answer: A
Question: A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?
Options:
A)337
B)268
C)144
D)772
E)997
Rationale: Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144
Answer:C
Answer: C
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
Options:
A)5%
B)8%
C)3%
D)9%
E)1%
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: A
Question: When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?
Options:
A)96
B)75
C)48
D)25
E)12
Rationale: x = qy+9 , where q is the quotient
x/y = (q y+9) /y = q + (9/y) = 96.12 = 96 + 0.12
=> q =96
9/y = 0.12 = > y = 75
Answer is B.
Answer: B
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a train, having same speed, coming from opposite side?
Options:
A)125 seconds
B)27 seconds
C)40 seconds
D)128 seconds
E)18 seconds
Rationale: Effective Speed = (36+36) Km/hr = 72*(5/18) m/sec = 20 m/sec
Total distance = 360 meter
Time = Distance/speed
= 360 * (20) = 18 seconds
Answer: E
Answer: E
Question: The average age of applicants for a new job is 31, with a standard deviation of 8. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Options:
A)8
B)14
C)15
D)17
E)30
Rationale: within one standard deviation of the average age means 31 +/- 7
23--31--39
number of dif.ages -23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
total=17
D
Answer: D
Question: In how many different ways can the letters of the word ‘INDIGO’ be arranged ?
Options:
A)420
B)520
C)620
D)720
E)820
Rationale: D
720
Required number of arrangements = 6! = 720
Answer: D
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)277m
B)887m
C)350m
D)188m
E)126m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.Answer: C
Answer: C
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
Options:
A)15:8
B)11:8
C)18:8
D)12:8
E)10:8
Rationale: B
15:8
Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Answer: A
Question: If a and b are different values and a – b = 5(√a - √b), then in terms of b, a equals:
Options:
A)√b
B)b
C)b - 2√b + 1
D)b - 10√b + 25
E)b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 5(√a - √b) -----> ( √a + √b) ( √a - √b) = 5(√a - √b) -------> √a + √b = 5, so
√a = 5 - √b, square both sides and solve. Answer is D.
Answer: D
Question: In the next Cricket World Cup T-20, Team Q has decided to score 200 runs only through 4s and 6s. In how many ways can the Team Q score these 200 runs?
Options:
A)13
B)15
C)16
D)17
E)18
Rationale: Team Q can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: D
Question: The compound ratio of 5:8, 3:2 and 4:5?
Options:
A)1:1
B)1:87
C)3:4
D)1:9
E)1:2
Rationale: 5/8 * 3/2 * 4/5 = 3/4
1:1
Answer: C
Answer: C
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Options:
A)2
B)5
C)6
D)9
E)4
Rationale: 4.5 4.5
30% 70%
30% ----- 4.5
70% ------? => 10.5 - 4.5 = 6 ml
Answer:C
Answer: C
Question: Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
Options:
A)1
B)9
C)4
D)6
E)3
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer: A
Answer: A
Question: Wavid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
Options:
A) 5/6*d
B) 7/3*d
C) 10/3*d
D) 7/2*d
E) 9/2*d
Rationale: Wavid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C.
Answer: C
Question: In how many different number of ways 5 boys and 2 girls can sit on a bench?
Options:
A)5020
B)5040
C)5060
D)5080
E)5000
Rationale: npn = n!
7p7 =7 x 6 × 5 × 4 × 3 × 2 × 1 = 5040
B
Answer: B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 58, what is the compound interest on the same sum at the rate and for the same time?
Options:
A)s. 59.45
B)s. 56.22
C)s. 51.219
D)s. 59.18
E)s. 51.11
Rationale: Explanation:
Sum = (58 * 100) / (2 * 5) = Rs. 580
Amount = [580 * (1 + 5/100)2] = Rs. 639.45
C.I. = (639.45 - 580) = Rs. 59.45
Answer:A
Answer: A
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.
Options:
A)1/2
B)7/15
C)8/15
D)1/9
E)2/9
Rationale: Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4) = 10C2 = 10x9/2x1 =45
Let E = event of getting both balls of same colour
Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)
=6C2 + 4C2 = 6x5/2x1 + 4x3/2x1 15+6 =21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15
Answer is B
Answer: B
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)16
B)18
C)13
D)20
E)12
Rationale: 1/2 * d (10 + 6)
= 640
d = 80
Answer: D
Answer: D
Question: A car travels first 160 km at 70 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
Options:
A)71.11
B)71.12
C)71.1
D)74.66
E)71.13
Rationale: Car travels first 160 km at 70 km/hr
Time taken to travel first 160 km = distancespeed=160/70
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=160/80
Total distance traveled = 160+160=2×160
Total time taken = 160/70+160/80
Average speed = Total distance traveled/Total time taken=320/(160/70+160/80)=74.66 km/hr
Answer:D
Answer: D
Question: Machine A can produce 1,000 sausages in 4 hours. Machine B can produce 1,000 sausages in 8 hours. Working together at their respective rates, how long will it take the machines to produce 1,000 sausages?
Options:
A)1 hr 40 min
B)2 hrs
C)2 hrs 40 min
D)3 hrs
E)4 hrs 20 min
Rationale: ARate = 1000/4 = 250 Sausages/Hour
BRate = 1000/8 = 125 Sausages/Hour
TotalSausages = (ARate + BRate) * Hours
Hours = TotalSausages / (ARate + BRate)
Hours = 1000 Sausages / (250 Sausages/Hour + 125 Sausages/Hour) = 2.667 Hours
C. 2 hrs 40 mins
Answer: C
Question: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
Options:
A)12
B)36
C)72
D)24
E)18
Rationale: Sol: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72
Ans: C
Answer: C
Question: A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?
Options:
A)5 kmph
B)6 kmph
C)8 kmph
D)1 kmph
E)2 kmph
Rationale: Explanation:
Speed of the boat downstream =
Speed of the boat upstream
\small \therefore The speed of the stream =
Answer: A
Answer: A
Question: A rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 48 inches and the width is 72 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches?
Options:
A)a 8
B)b 22
C)c 27
D)d 40
E)e 51
Rationale: l = 48 /12 = 4 ft
w = 72 / 12 = 6 ft
Area of paper = 24
Area of cube = 4 * side^2
side of cube = 2
V of cube = 8
Answer: A
Question: Faiza has 4 purses, she gives 3 purse as gift. Now how many purse did she have ?
Options:
A)2
B)5
C)1
D)9
E)4
Rationale: 4-3=1. Answer is C
Answer: C
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30sec respectively. Find the length of the train is?
Options:
A)100 m
B)130 m
C)150 m
D)160 m
E)190 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: C
Question: By selling a watch for Rs.480/-, a man loses 20% what is that watch cost price
Options:
A)s. 700/-
B)s. 600/-
C)s. 880/-
D)s. 900/-
E)s. 990/-
Rationale: 80 % ------> 480 (80 * 6 = 480)
100 % ------>600 (100 * 6 = 600)
Cost price = Rs. 600/-
B
Answer: B
Question: The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is
Options:
A)620
B)610
C)630
D)625
E)635
Rationale: Let the price of one apple = a and price of one orange = b
The price of 80 apples is equal to that of 120 oranges
80a = 120b
=> 2a = 3b
⇒b=2a/3-----(Equation 1)
price of 60 apples and 75 oranges together is Rs.1320
=>60a + 75b = 1320
=> 4a + 5b = 88
⇒4a+5(2a)/3=88(∵ Substituted the value of b from equation 1)
=> 12a + 10a = 88 × 3
=> 6a + 5a = 44 × 3
=> 11a = 44 × 3
=> a = 4 × 3 = 12
b=2a/3=(2×12)/3=8
Total price of 25 apples and 40 oranges
= 25a + 40b = (25 × 12) + (40 × 8) = 300 + 320 = 620
Answer is A.
Answer: A
Question: nine children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
Options:
A)600
B)720
C)1440
D)1650
E)4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 1650
D is the right answer.
Answer: D
Question: A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even?
Options:
A)1/3
B)2/3
C)5/9
D)6/11
E)7/11
Rationale: Probability of getting an even number = 2/3
Probability of getting an odd number = 1/3
since the dice is biased.
The sum is even if
(even,even) or (odd,odd)
[P(even).P(even)] + [P(odd).P(odd)]
2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9
ANSWER:C
Answer: C
Question: Working alone, pump A can empty a pool in 4 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
Options:
A)65
B)70
C)75
D)80
E)85
Rationale: Pump A can empty (1/4) of the pool per hour.
Pump B can empty (1/2) of the pool per hour.
Together the pumps can empty 1/4+1/2=3/4 of the pool per hour.
1 pool / (3/4) pool per hour = 4/3 hours = 80 minutes.
The answer is D.
Answer: D
Question: A father purchase dresses for his three daughters.The dresses are of same color but of different size. The dress is kept in dark room.What is the probability that all the three will not choose their own dress.
Options:
A)1/3
B)2/3
C)4/3
D)5/3
E)6/3
Rationale: For he first girl: probability for not selecting correct dress is 2/3
for the second girl: it is 1/2
for the third girl: it is 1
2/3*1/2*1=1/3
ANSWER:A
Answer: A