mathewhe/aqua_rat huggingface dataset:
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 18% of all the students at Morse have cars, how many students are in the three lower grades?
(A) 600
(B) 900
(C) 1200
(D) 1350
(E) 1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.18(x+300)
0.08x = 96
x = 1200
The answer is C.
Answer: (C) 1200
Question: The average age of 25 students in a group is 12 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
(A) 31
(B) 38
(C) 39
(D) 40
(E) 57
Rationale: age of the teacher=(26*13-25*12)
=38 years.
ANSWER:B
Answer: (B) 38
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 30%
(E) Can't be calculated
Rationale: The owner buys 100kg but actually gets 130kg;
The owner sells 100kg but actually gives 90kg;
Profit: (130-90)/90*100=30%
Answer: D.
Answer: (D) 30%
Question: Tina has 5 socks and 3 pair of shoes. How many combinations does Barbara have, if she doesn’t wear 2 specific socks with 1 specific pair of shoes?
(A) 4
(B) 7
(C) 10
(D) 11
(E) 13
Rationale: Total no of combinations available is= 5 Socks X 3 pair of shoes = 15
Eliminate the 2 socks X 1 pair of shoes combo = 2 which gives.......>> 15-2=13
ANSWER: E
Answer: (E) 13
Question: Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114.
(A) 2 or ½
(B) 2/3 or 3/2
(C) ¾ or 4/3
(D) 4 or ¼
(E) 5 or 1/5
Rationale: Let the terms be a/r, a , ar
a/r *a * ar = a 3 =216, a =6
(a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114
a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114
6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,
On solving, r = 2/3 or 3/2
ANSWER:B
Answer: (B) 2/3 or 3/2
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 5 more than the average expenditure of all the nine. The total money spent by all of them was
(A) 26
(B) 40
(C) 29.25
(D) 32.625
(E) None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 5 = 9x
⇒ x = 3.625
∴ Total money spent = 9x = 9 × 3.625 = 32.625
Answer D
Answer: (D) 32.625
Question: The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 21 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken in 10 minutes ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 21
Rationale: a must be an integer as it is the number shoots at a rate of 21sec/shoot
3*60 + 21a = 10*60
21a = 420
a = 20
The total number of shoots -->1 +20 = 21 and
22th shoot will be taken at 621 seconds which is above 10 minutes
ANSWER: E
Answer: (E) 21
Question: What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400
(A) 6400
(B) 6900
(C) 7340
(D) 7500
(E) 7900
Rationale: (A)
25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: (A) 6400
Question: A group of 10 representatives is to be selected out of 13 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) 13C₅ * 10
(B) 13C₇ * 10
(C) 13C8 * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: Here, five seniors out of 13 seniors can be selected in 13C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 13C₅ * ¹⁰C₅ = 13C8 * ¹⁰C₅
since 13C₅ = 13C8
ANSWER:C
Answer: (C) 13C8 * ¹⁰C₅
Question: From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 5 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 43
Rationale: Soln:-
5x=45 --> 21/20*x=45 --> x=45*20/21=300/7=~43.
Answer: E.
Answer: (E) 43
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 4 sec
(E) 2 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec
= 6 sec
Answer:B
Answer: (B) 6 sec
Question: What will be the fraction of 25%
(A) 1/4
(B) 1/5
(C) 1/10
(D) 1/8
(E) None of above
Rationale: Explanation:
It will 25*1/100 = 1/4
Answer: Option A
Answer: (A) 1/4
Question: 9/8, 4/3, 17/8 ,3 1/3, 7/3, 42/8, 3 1/3, 7 1/4 ,1 3/3 , 7/2, 5 1/3, ?
(A) 3/2
(B) 1/2
(C) 11/2
(D) 5/2
(E) 7/2
Rationale: divide series into 2 parts
9/8,17/8,7/3,10/3,13/3,16/3..
9/8+1=17/8,7/3+1=10/3...n so on
4/3,10/3,42/8,29/4,7/2....
4/3+2=10/3 ....n so on.....7/2+2=11/2
ANSWER:C
Answer: (C) 11/2
Question: At a summer camp with 1,500 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 1,500 campers will the 8- to 12-year-olds represent?
(A) 33 1/3%
(B) 50%
(C) 55%
(D) 60%
(E) 66 2/3%
Rationale: Total - 1,500 participants
campers are aged 8 to 12 = (1/2)*1500 = 750
Next year, campers are aged 8 to 12 = (4/3)*750 = 1000
Percentage = (1000/1500)*100 = 66 2/3%
Answer: Option E
Answer: (E) 66 2/3%
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 20.23
(B) 20.13
(C) 30.93
(D) 20.93
(E) 10.93
Rationale: A:B = 4:3
B:C = 4:5
A:B:C = 16:12:15
12/43 * 75 = 20.93
ANSWER:D
Answer: (D) 20.93
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should A pay?
(A) 240
(B) 270
(C) 276
(D) 271
(E) 272
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
8/29 * 870 = 240
Answer: A
Answer: (A) 240
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/4 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
(A) 2.5%
(B) 17.67%
(C) 28.3%
(D) 45.2%
(E) 32.5%
Rationale: Fiction Novels = 5,508
Transferred to another location = 6,120
Transferred fiction novels = 1,530
Non Transferred Fiction Novels = 3,978
Percent of the remaining collection was fiction novels = 3978/(18360 - 6120 ) * 100 => 32.5%
Hence answer will be (E)
Answer: (E) 32.5%
Question: In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 40, what is the least possible difference between n and m.
(A) a.1
(B) b.3
(C) c.5
(D) d.7
(E) e.9
Rationale: 2n+5m=40
try with n=5 and m=6 the equation will be satisfied
2(5)+5(6)=40
so difference between M and N is 1,
Answer A
Answer: (A) a.1
Question: What is the ratio between perimeters of two squares one having 7 times the diagonal then the other?
(A) 3: 7
(B) 3: 5
(C) 3: 8
(D) 7: 1
(E) 3: 5
Rationale: d = 7d d = d
a√2 = 7d a√2 = d
a = 7d/√2 a = d/√2 => 7: 1
Answer: D
Answer: (D) 7: 1
Question: In a certain country 1/3 of 4 = 6. Assuming the same proportion, what would be the value of 1/6 of 20 ?
(A) 14
(B) 15
(C) 20
(D) 22
(E) 25
Rationale: B
15
Answer: (B) 15
Question: In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
(A) 1:7
(B) 2:3
(C) 1:8
(D) 2:3
(E) 1:3
Rationale: Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1 : 3.
Answer:E
Answer: (E) 1:3
Question: A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 227
(B) 400
(C) 230
(D) 288
(E) 271
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 50/3
3(x + 300) = 2100 è x = 400m.
Answer: B
Answer: (B) 400
Question: If the compound interest on a sum of Rs.7000 for 2 years is Rs.1470 then the rate of interest is (interest compounded yearly)
(A) 10 % p.a.
(B) 12 % p.a.
(C) 11 % p.a.
(D) 9 % p.a.
(E) None
Rationale: Given CI=1470
P=7000
Thus A=CI+P=8470
Now A=p(1+R/100)^n
So,8470=7000(1+R/100)^2
(11/10)^2=(1+R/100)^2
11/10=1+R/100
Thus R=10%
ANSWER:A
Answer: (A) 10 % p.a.
Question: A straight line in the xy- plane has slope 2 . On this line the x-coordinate of the point is 300 and y-coordinate is 900 then what is the y intercept of the plane?
(A) 200
(B) 250
(C) 100
(D) 300
(E) 220
Rationale: Eq of line = Y = MX +C
M= 2
X=300
Y=300*2+ C,
Substitute Y by 900 as given in question.
900=600+C , C =200
correct option is A
Answer: (A) 200
Question: A person can swim in still water at 8 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 8km?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: M = 8
S = 4
US = 8 - 4 = 4
D = 4
T = 8/4 = 2 Answer:A
Answer: (A) 2
Question: There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students.
(A) 200
(B) 210
(C) 220
(D) 230
(E) 240
Rationale: 210
ANSWER:B
Answer: (B) 210
Question: When N is divided by T, the quotient is S and the remainder is C. Which of the following expressions is equal to N?
(A) ST
(B) S + V
(C) ST + C
(D) T(S+V)
(E) T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + C C is correct
Answer: (C) ST + C
Question: A certain team consists of 3 professors and 4 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
(A) 25
(B) 28
(C) 31
(D) 34
(E) 37
Rationale: The total number of ways to form a group of 3 from 7 people is 7C3 = 35
The number of ways to form a group without a professor is 4C3 = 4
The total number of ways to form a valid group is 35 - 4 = 31.
The answer is C.
Answer: (C) 31
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 100 metres
(D) 228 metres
(E) 150 metres
Rationale: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3	x 6 m = 100 m.
Option C
Answer: (C) 100 metres
Question: A certain team has 6 members, including Joey. A three-member relay team will be selected as follows: one of the 6 members is to be chosen at random to run first, one of the remaining 5 members is to be chosen at random to run second, and one of the remaining 4 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/2
(B) 2/3
(C) 1/3
(D) 1/6
(E) 2/5
Rationale: Each member has an equal probability to run second (1/6) or third (1/6).
The probability that Joey runs second or third is 1/6 + 1/6 = 1/3
The answer is C.
Answer: (C) 1/3
Question: What is the smallest integer q greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
(A) q=21
(B) q=41
(C) q=121
(D) q=241
(E) q=481
Rationale: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder q as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C
Answer: (C) q=121
Question: Find the value of x from the below equation? : 3x^2-5x+2 = 0
(A) 2/3
(B) -1
(C) 0
(D) -2/3
(E) 2
Rationale: a = 3, b = -5, c = 2
x1,2 = (5 Â± âˆš((-5)^2 - 4Ã—3Ã—2)) / (2Ã—3) = (5 Â± âˆš(25-24)) / 6 = (5 Â± 1) / 6
x1 = (5 + 1)/6 = 6/6 = 1
x2 = (5 - 1)/6 = 4/6 = 2/3
A
Answer: (A) 2/3
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.15000. A's share is?
(A) 2999
(B) 2778
(C) 6000
(D) 5000
(E) 6612
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 15000 = 5000
Answer:D
Answer: (D) 5000
Question: An investment yielded an interest payment of $350 each month when the annual interest rate was 9%, what is the amount of the investment that should be invested with an annual interest rate of 8% if We want to gain 15% more each month?
(A) $60,375
(B) $50,400
(C) $41,300
(D) $32,500
(E) $25,100
Rationale: An investment yielded an interest payment of $350 each month when the annual interest rate was 9%, what is the amount of the investment that should be invested with an annual interest rate of 8% if We want to gain 15% more each month?
Based on first statement the total interest earned = 350 * 12 = Principal * interest rate(9/100)
No need to solve for principal here, just continue....
So find the new principal for revised interest rate and 10% more interest, so 350 * 12 * 1.15 = Principal * interest rate (8/100)
solving for Principal = 60,375
Answer is A : 60,375
Answer: (A) $60,375
Question: The average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years. Find the average age of the women?
(A) 30.5
(B) 26
(C) 30
(D) 18
(E) 11
Rationale: Explanation:
18 + 22 + 7 * 3 = 61/2 = 30.5
Answer: A
Answer: (A) 30.5
Question: The length of the longest rod that can fit in a cubical room of 4 m side is?
(A) 6.978 m
(B) 6.928 m
(C) 6.829 m
(D) 6.248 m
(E) 6.982 m
Rationale: The length of the longest rod=4 sq.root of 3=6.928 m
Answer: B
Answer: (B) 6.928 m
Question: Gabriela’s grade was in the 90th percentile out of 100 grades in her class. In another class of 100 students there were 80 grades lower than Gabriela’s. If nobody had Gabriela’s grade, then Gabriela was what percentile of the two classes combined?
(A) 90
(B) 85
(C) 80
(D) 75
(E) 70
Rationale: Being in 90% percentile out of 100 grades means was 91st (from the least grade) in the class (as long as nobody had Gabriela 's grades), she outscored 90.
In another class her grade would rank her 61 (from the least grade out of 101, 100+ Gabriela), 60 had the grades lower than Gabriela.
So in combined classes she outscored 90+60=150. There are 200 students 150/200=0.75
Answer: D (75%)
Generally being in x% means that x% has the grades less than you.
Gabriela in 90% --> she outscored 90% of of 100=90 (Gabriela is 91st).
Of the 100 grades from another class, 60 were lower than Gabriela, hence Gabriela outscored 60.
So out of total 100+100=200, Gabriela outscored 90+60=150. Hence she is in 150/200=75%.
Answer:D
Answer: (D) 75
Question: At present the age of the father is five times that of the age of the son. Three years hence the father's age would be 4 times that of his son. Find the present age of the father?
(A) 9years
(B) 25years
(C) 45years
(D) 30years
(E) 50years
Rationale: Age of the son = (4-1)*3 / (5-4) = 9 years
Age of the father = 9*5 = 45 years
Answer is C
Answer: (C) 45years
Question: The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?
(A) 120
(B) 240
(C) 360
(D) 720
(E) 1440
Rationale: X-X-X-X-X --> there are 4 odd digits from 1 to 7, inclusive thus options for the first and the last X's are: 4-X-X-X-3. Other X's can take following values: 4-5-4-3-3 --> 4*5*4*3*3=720.
Answer: D.
Answer: (D) 720
Question: A van takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 32 Kmph
(D) 80 Kmph
(E) 90 Kmph
Rationale: Time = 6
Distence = 288
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 288/9 = 32 Kmph
C
Answer: (C) 32 Kmph
Question: It is decided to construct a 2 metre broad pathway around a rectangular plot on the inside. If the area of the plots is 96 sq.m. and the rate of construction is Rs. 50 per square metre., what will be the total cost of the construction?
(A) Rs.3500
(B) Rs. 4200
(C) Insufficient Data
(D) Rs. 4400
(E) None of these
Rationale: Explanation : Let length and width of the rectangular plot be l and b respectively
Total area of the rectangular plot = 96 sq.m.
=> lb = 96
Width of the pathway = 2 m
Length of the remaining area in the plot = (l - 4)
breadth of the remaining area in the plot = (b - 4)
Area of the remaining area in the plot = (l - 4)(b - 4)
Area of the pathway
= Total area of the rectangular plot - remaining area in the plot
= 96 - [(l - 4)(b - 4)] = 96 - [lb - 4l - 4b + 16] = 96 - [96 - 4l - 4b + 16] = 96 - 96 + 4l + 4b - 16
= 4l + 4b - 16
= 4(l + b) - 16
We do not know the values of l and b and hence area of the pathway cannot be found out. So we cannot determine total cost of the construction. Answer : Option C
Answer: (C) Insufficient Data
Question: If n is the product of all the integers from 5 to 20, inclusive, what is the greatest integer k for which 2^k is a factor of n ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: 20/2=10
10/2=5
Ans:10+5=15
ANSWER:E
Answer: (E) 15
Question: The true discount on a bill of Rs.540 is Rs.90.The banker's discount is
(A) Rs.60
(B) Rs.108
(C) Rs.110
(D) Rs.112
(E) None of these
Rationale: Solution
P.W	= Rs.(540 - 90)
= Rs. 450
S.I on Rs. 540	=Rs.(90/450 x 540)
= Rs. 108.
Answer B
Answer: (B) Rs.108
Question: A train running at 25 km/hr takes 50 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
(A) a) 200/3m175/3m
(B) b) 36m178m
(C) c) 50m45m
(D) d) 100/3 m200/3
(E) e) none of these
Rationale: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/50*12=6m so the train covered a distance in 12 sec= 25*5/50*12=30
so the length of the train(Lt) is 6+30=36m
Now crossing the platform means length of train+length of platform(Lt+p)= 50*25*5/50=125m Now the length of platform (Lp) is= 125-36=89m
So answer is 36m and 89m Must beBeven though its mentioned 36m and 178m thinking so typo mistake...........
Answer: (B) b) 36m178m
Question: If two projectiles are launched at the same moment from 2520 km apart and travel directly towards each other at 432 km per hour and 576 km per hour respectively, how many minutes will it take for them to meet?
(A) 130
(B) 135
(C) 140
(D) 145
(E) 150
Rationale: The projectiles travel a total of 1008 km per hour.
The time to meet is 2520/1008=2.5 hours = 150 minutes
The answer is E.
Answer: (E) 150
Question: A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 130 pounds?
(A) 8
(B) 14
(C) 12
(D) 9
(E) none of the above
Rationale: Ans is B:
39 pounds --> 6 days
130 pounds --> x days
x = 130*6/39 = 20
the animal has already consumed food in 6 days so the the number of days
for it's total consumption be 130 pounds is 20-6 = 14
Answer: (B) 14
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 41 what is the value of a1 ?
(A) 1
(B) 6
(C) 21
(D) 16
(E) 21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 41
a4 = 36
a3 = 31
a2 = 26
a1 = 21 <<<< Ans C
Answer: (C) 21
Question: If two positive numbers are in the ratio 1/7 : 1/4, then by what percent is the second number more than the first?
(A) 67%.
(B) 70%.
(C) 75%.
(D) 68%.
(E) 80%.
Rationale: Given ratio = 1/7 : 1/4 = 4 : 7
Let first number be 4x and the second number be 7x.
The second number is more than first number by 3x.
Required percentage = 3x/4x * 100 = 75%.
Answer: C
Answer: (C) 75%.
Question: Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 40
(B) 45
(C) 48
(D) 51
(E) 36
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 375 + 375 = 750 m.
Required time = 750 * 6/125 = 36 sec.
Answer: Option E
Answer: (E) 36
Question: There are 4 baskets. The first basket has 3 apples and 4 oranges, the second one has 4 apples and 5 mangoes, the third one has 6 Mangoes and 2 bananas and the last one has 7 bananas and 2 apples. If a fruit is randomly chosen from any basket and it comes out to be an apple, then what is the probability that it was taken out from the second basket?
(A) 27/69
(B) 28/69
(C) 29/69
(D) 25/69
(E) 28/64
Rationale: P(A|1)=3/7
P(A|2)=4/9
P(A|3)=0/8
P(A|4)=2/9
Hence event 1,2,3,4 are the partitions of the sample space.
The probability of choosing an apple, by the law of total probability
P(A)=P(A|1)P(1)+P(A|2)P(2)+P(A|3)P(3)+P(A|4)P(4)
=3/7*1/4+4/9*1/4+0/8*1/4+2/9*1/4
=23/84
By Baye's theorem,
P(2|A)=P(A|2)*P(2)/P(A)
=4/9*(1/4)/(23/84)
=28/69
ANSWER:B
Answer: (B) 28/69
Question: Convert the following unit:
2.3 hectares in ares
(A) 200 ares.
(B) 210 ares.
(C) 220 ares.
(D) 230 ares.
(E) 240 ares.
Rationale: 2.3 hectares in ares
1 hectare = 100 ares
Therefore, 2.3 hectares = 2.3 × 100 ares
= 230 ares.
ANSWER : OPTION D
Answer: (D) 230 ares.
Question: The area of a triangle will be when a = 2m, b = 4m, c = 6m, a, b, c being lengths of respective sides?
(A) 3
(B) 7
(C) 5
(D) 6
(E) 4
Rationale: S = (2 + 4 + 6)/2
= 6
Answer: D
Answer: (D) 6
Question: If it is true that x > -3 and x < 7, which of the following must be true?
(A) x > 3
(B) x > -7
(C) x < 3
(D) -7 < x < 3
(E) none of the above.
Rationale: the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x > -7 -- the answer is true, because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -7 < x < 3 - no because x can be between 3 < x < 7
E. none of the above.
Answer: B
Answer: (B) x > -7
Question: The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 40%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 35%
(E) 79%
Rationale: take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 40% then output equals 154
To restore new holidy demand output to original 100.
final -initial/final*100
=54/154*100=35% approxiamately.
option D is correct.
Answer: (D) 35%