mathewhe/aqua_rat huggingface dataset:
Question: As a treat for her two crying children, a mother runs to the freezer in which she has four cherry ice pops, three orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 1/99
(B) 1/6
(C) 5/18
(D) 13/18
(E) 5/6
Rationale: Probability of not getting the same flavor ->
Fouvarable -> Cherry - orange [ 4C1 * 3C1 [or simply 4*3 ] or Cherry - lemon [ 4*4] or orange - lemon [3*4]
Prob = (4*3 + 4*4 + 3*4 ) / 9C2 = 40/3960 = 1/99
Answer -> A
Answer: (A) 1/99
Question: A and B walk around a circular track. A and B walk at a speed of 1 rounds per hour and 4 rounds per hour respectively. If they start at 7 a.m. from the same point in opposite directions, how many times shall they cross each other before 8.30 a.m.?
(A) 7
(B) 9
(C) 4
(D) 3
(E) 8
Rationale: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)
= 1 + 4 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 7 am to 8.30 am = 1.5 hour
Hence they cross each other 7 times before 8.30 am
Answer : A
Answer: (A) 7
Question: There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song?
(A) 15624
(B) 16478
(C) 17953
(D) 19655
(E) 28958
Rationale: 15624
A
Answer: (A) 15624
Question: If it would take one machine 15 minutes to fill a large production order and another machine 20 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 4 1/60
(B) 5
(C) 5 5/11
(D) 5 1/2
(E) 8 4/11
Rationale: Since , Machine 1-M1 take 15 mins to fill the order
The work done by M1 in a min = 1/15
Machine 2- M2 take 20 mins to fill the same order
and work done by M2 in a min = 1/20
Total work done by M1 and M2 in a min = 1/15 + 1/20 = 7/60
Time needed for M1 and M2 to complete the order = 60/7 = 8 4/11
Answer E
Answer: (E) 8 4/11
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 5:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:9
(C) 3:2
(D) 2:3
(E) 10:9
Rationale: The ratio of economy to luxury cars is 3:2 --> E:L = 3:2 = 15:10.
The ratio of economy cars to sport utility vehicles is 5:3 --> E:S = 5:3 = 15:9.
Thus, L:S = 10:9.
Answer: E.
Answer: (E) 10:9
Question: In a kilometer race, A beats B by 40 meters or 15 seconds. What time does A take to complete the race?
(A) 277 sec
(B) 285 sec
(C) 267 sec
(D) 167 sec
(E) 276 sec
Rationale: Time taken by B run 1000 meters = (1000 * 15)/50 = 300 sec.
Time taken by A = 300 - 15 = 285 sec.Answer: B
Answer: (B) 285 sec
Question: In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 600 students and the middle school enrolled 300 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?
(A) r/3
(B) r/2
(C) 2r
(D) 3r
(E) r/9
Rationale: Total per head = 2r/900
After s transfer both schools have total for head.
So at High School it will be:
r+s = (600)* (2r/900) = 12r/9=4r/3
i.e. s = 4r/3 - r/1 =4r-3r/3=r/3
Answer :A
Answer: (A) r/3
Question: The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 60 feet wide by 150 feet long by 10 feet deep and is currently at 80% capacity, how long will it take to drain the pool?
(A) 1800
(B) 1000
(C) 1200
(D) 1400
(E) 1600
Rationale: volume of pool = 60*150*10 cu.ft , 80% full = 60*150*10*0.8 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 60*150*10*0.8/ 60 min= 1200 min
C
Answer: (C) 1200
Question: Simplfy
3b - [b -(a+b) - {b - (b - a+b)} + 2a]
(A) a
(B) 2b
(C) 4a
(D) 0
(E) 1
Rationale: Explanation:
3b-[b-(a+b)-{b-(b-a+b)}+2a]
=3b-[b-a-b-{b-(2b-a)}+2a]
=3b-[-a-{b-2b+a}+2a]
=3b-[-a-{-b+a}+2a]
=3b-[-a+b-a+2a]
=3b-[-2a+b+2a]
=3b-b
=2b
Option B
Answer: (B) 2b
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 6 students is 14 years and that of the other 8 students is 16 years. The age of the 15th student is
(A) 9 years
(B) 13 years
(C) 14 years
(D) 21 years
(E) 25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x6+16x8)]
= (225 - 212)
= 13 years.
Answer B
Answer: (B) 13 years
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/9
(B) 3/10
(C) 2/9
(D) 10/19
(E) 4/9
Rationale: 9C2 ==> 5C1, 4C1
Req = (5*4)/9C2=20/36=5/9
ANSWER A
Answer: (A) 5/9
Question: Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet?
(A) 95 minutes
(B) 90 minutes
(C) 88 minutes
(D) 95 minutes
(E) None of these
Rationale: Explanation :
Let us consider that speed of train , first man and second man are respectively t, f and s.
According to first given condition goods train crossed the first person moving in same direction in 20 sec.
So length of the will be 20(t-f)
Similarly train crossed the second man in 18 sec.
So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s)
=> 2t = 20f + 18s
=> t = 10f + 9s
Now it is given that After 10 min the train crossed the other person who is coming in opposite direction.
So,If we consider this way of train as L then the next equation will be
L = 600t (here 600 is used for 10 minutes)
Finally as asked in the question the time required to meet the two man after the train has passed will
be given by
Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes}
=> = (600t-600f) / (f+s)
=> = [600(10f+9s)-600f] / (f+s)
=> = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s)
=> =600*9 seconds
=> = 600*9/60min
=> = 90 minutes
Hence (B) is the correct answer.
Answer : B
Answer: (B) 90 minutes
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/4 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
(A) 2.5%
(B) 17.67%
(C) 28.8%
(D) 45.2%
(E) 73.6%
Rationale: Fiction Novels = 5,508
Transferred to another location = 4590
Transferred fiction novels = 1530
Non Transferred Fiction Novels = 3,978
Percent of the remaining collection was fiction novels = 3978/(18360 - 4590 ) * 100 => 28.888...%
Hence answer will be (C)
Answer: (C) 28.8%
Question: If -x^2 - 2y^2 = 2xy, then (x+y)^2 =
(A) x^2
(B) 3x^2
(C) 4xy
(D) 2y^2
(E) -y^2
Rationale: Its B
-x^2 -2y^2 = 2xy
-2y^2 = 2xy + x^2
Add y^2 on both sides we get
-2y^2 +y^2 = x^2 +y^2 +2xy
-y^2 = (x+y)^2
Correct Option : E
Answer: (E) -y^2
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) 34348
(B) 37888
(C) 10560
(D) 29877
(E) 27881
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer: C
Answer: (C) 10560
Question: A = {0, 1, -3, 6, -8, 20, 4}
B = {-1, 2, -4, 7, 5}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 4/9
(E) 12/35
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 4/7*3/5 = 12/35;
P(negative, negative) = 2/7*2/5 = 4/35.
P = 12/35 + 4/35
= 12/35
Answer: E
Answer: (E) 12/35
Question: 0.002 x 0.4 = ?
(A) 8.0
(B) 0.008
(C) 0.08
(D) 0.8
(E) 0.0008
Rationale: 2 x 4 = 8.
Sum of decimal places = 4
0.002 x 0.4 = 0.0008
Answer: Option E
Answer: (E) 0.0008
Question: A bag contains 7 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
(A) 19/20
(B) 17/20
(C) 21/50
(D) 8/10
(E) 9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (7/10) x (6/10) = 21/50.
P(B) = (3/10) x (4/10) = 3/25.
Hence, the required probability is P(A) + P(B) which is nothing but 21/50.
ANSWER:C
Answer: (C) 21/50
Question: In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 4,500. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 16,000 and the lowest selling price was 5,000. What was the range of selling prices for the 25 used car sold by xiang in May and June?
(A) 15,600
(B) 15,750
(C) 16,820
(D) 18,100
(E) 19,200
Rationale: for 10 cars - 16000+ 5000 = 21,000
for 15 cars - 15000+ 4500 = 19,500
max = 21,000 min 4500
answer is approx 16,500.
Option C is closest.
Answer: (C) 16,820
Question: The purchase price of an article is $48. In order to include 5% of cost for overhead and to provide $12 of net profit, the markup should be
(A) 15%
(B) 25%
(C) 30%
(D) 40%
(E) 45%
Rationale: Cost price of article = 48$
% of overhead cost = 5
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 5 = 30%
Answer C
Answer: (C) 30%
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 94 kmph
(B) 58 kmph
(C) 54 kmph
(D) 94 kmph
(E) 59 kmph
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Answer:C
Answer: (C) 54 kmph
Question: What is the largest prime factor of 27^3−9^3−3^6?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 27^3−9^3−3^6 = 3^9 - 3^6 - 3^6 = 3^6( 3^3-1-1) = 3^6 (27-2) = 3^6 * 5^2.
Two prime factors are 3 and 5. Therefore, max prime factor is 5.
ANSWER:C
Answer: (C) 5
Question: 5358 x 81 = ?
(A) 423762
(B) 433758
(C) 433298
(D) 433998
(E) 437382
Rationale: D
273258
5358 x 81 = 5358 x (80 + 1)
= 5358 x 80 + 5358 x 1
= 428640 + 5358
= 433998
Answer: (D) 433998
Question: Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 10 percent was planted with grapes and 80 percent of the cleared land was planted with potato. If the remaining 450 acres of cleared land was planted with tomato, how many acres did the farmer own?
(A) 3500
(B) 4500
(C) 5500
(D) 5250
(E) 5000
Rationale: 10% od 90% = 9%, 80% 0f 90% = 72% so the remaining 90-9-72=9%=450 acres or 10% of 90%=9% --> 450/9*100=5000 acres Answer (E)
Answer: (E) 5000
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 62.0. What is the quiz score of the student who dropped the class?
(A) a) 10
(B) b) 25
(C) c) 40
(D) d) 55
(E) e) 70
Rationale: Total Score of 16 students is 16*62.50 = 1000
Total Score of 15 students is 15*62 = 930
So, the score of the person who left is 70 ( 1000 - 930 )
Answer will be (E)
Answer: (E) e) 70
Question: A group of men decided to do a work in 8days, but 3 of them became absent. If the rest of the group did the work in 10days, Find the original number of men?
(A) 15
(B) 20
(C) 30
(D) 25
(E) 18
Rationale: Original number of men = 3*10 / (10-8) = 15
Answer is A
Answer: (A) 15
Question: There is certain numbers of toys in the box. They are divided into such a way that the person who gets 1/4 of the whole gets thrice of what the others get on an average. Find the number of people amongst whom the toys are distributed?
(A) 8
(B) 10
(C) 12
(D) 9
(E) 4
Rationale: Explanation:
If the person who gets 1/4 of the whole gets thrice of what the others get on an average,
each one will get =1/3×1/4=112 of the whole.
Therefore, if there are k persons other than the person who gets one-fourth, then
1/4 + k/12 = 1
⇒ k=9
Hence, total number of people = 10.
Answer: B
Answer: (B) 10
Question: In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre?
(A) 2:7
(B) 1:2
(C) 2:9
(D) 2:2
(E) 2:6
Rationale: Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8  Ratio of water and milk = 4 : 8 = 1 : 2
Answer:B
Answer: (B) 1:2
Question: 9, 16, 20, 25, 36,49
(A) 9
(B) 16
(C) 20
(D) 25
(E) 36
Rationale: Each of the numbers except 20, is perfect square.
Answer: Option C
Answer: (C) 20
Question: The average of 7 numbers is 23. If each number be multiplied by 5. Find the average of new set of numbers?
(A) A)110
(B) B)122
(C) C)120
(D) D)115
(E) E)145
Rationale: Explanation:
Average of new numbers = 23 * 5 = 115
Answer: Option D
Answer: (D) D)115
Question: Tom read a book containing 100 pages by reading the same number of pages each day. If he would have finished the book 10 days earlier by reading 30 pages a day more, how many days did Tom spend reading the book?
(A) 7
(B) 7.68
(C) 8
(D) 9
(E) 10
Rationale: Actually u can set up 2 equation
P--stands for the pages
D--stands for the days
1) P*D=100 (we want to find the Days, soP=100/D)
2) (P+30)(D-10)=100 => PD-10P+30D-300=100
as the 1) stated u can put 1) into 2)
=> 100-10P+30D-300=100 => 30D-10P=100
put the bold one into it => 30D-10(100/D)=100
the we get the final equation 30D^2-1000=100D (divide 16)
=> D^2-5D-150=0
(D-15)(D+10)=0 so D=7.68 days. Ans:( B)
Answer: (B) 7.68
Question: Annie has 100 cards numbered 1 through 100. If she deals four cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
(A) 95!/100!
(B) 96!/100!
(C) (95! X 5!)/100!
(D) (96! X 5!)/100!
(E) (97! X 4!)/100!
Rationale: Alex to get 4 consecutive cards in ascending order, to have 4 consecutive at the end is good enough.
There are 97 consecutive numbers in 100: {1, 2, 3, 4, }, {2, 3, 4, 5}, ..., { 97, 98, 99, 100};{4!*97!}{100!}.
Answer: E.
Answer: (E) (97! X 4!)/100!
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/5
(C) 1/4
(D) 1/2
(E) 1/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: How many cubes of 4cm edge can be cut out of a cube of 28cm edge
(A) 343
(B) 232
(C) 216
(D) 484
(E) None of these
Rationale: Explanation:
number of cubes=(28 x 28 x 28) / (4 x 4 x 4) = 343
Answer: A
Answer: (A) 343
Question: When the price of an article was reduced by 25% its sale increased by 80%. What was the net effect on the sale?
(A) 35% increase
(B) 44% decrease
(C) 60% increase
(D) 66% increase
(E) 66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 25%, the new price is 0.75p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.75p)(1.8n) = 1.35np, which is 1.35 times the old revenue, so is 35% greater.
ANSWER:A
Answer: (A) 35% increase
Question: The number of positive integers which can be formed by using any number of digits from 0,1,2,3,4,5 without repetition.
(A) 1200
(B) 1500
(C) 1600
(D) 1630
(E) None
Rationale: Solution: One digit positive numbers = 5.
Two digit positive numbers = 25.
Three digit positive numbers = 100.
4 digit positive numbers = 300.
5 digit positive numbers = 600.
Six digit positive numbers = 600.
Total positive numbers,
= 5+25+100+300+600+600
= 1630.
Answer: Option D
Answer: (D) 1630
Question: A sum of money at simple interest amounts to Rs. 855 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) s. 650
(B) s. 690
(C) s. 738
(D) s. 700
(E) s. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (855 - 117) = Rs. 738.
Answer: Option C
Answer: (C) s. 738
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1
(B) 2/7
(C) 1/7
(D) 2/5
(E) 2
Rationale: P (getting a prize) = 10/(10 + 25) = 10/35
= 2/7
Hence Answer is B
Answer: (B) 2/7
Question: To fill an art exhibit, the ladies in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many ladies are in the art class?
(A) 80
(B) 120
(C) 240
(D) 320
(E) 400
Rationale: Let the total number of ladies in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: (C) 240
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 12 m, 10 m
(B) 13 m, 12 m
(C) 14 m, 11 m
(D) 15 m, 10 m
(E) 15 m, 12 m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
ANSWER:D
Answer: (D) 15 m, 10 m
Question: A train 200m long passes a standing man in 18 seconds. What is the speed of the train?
(A) 30km/hr
(B) 40km/hr
(C) 42km/hr
(D) 50km/hr
(E) 32km/hr
Rationale: Speed of the train = 200/18* 18/5 = 40km/hr
Answer is B
Answer: (B) 40km/hr
Question: Hiralal gave a loan of Rs. 20 to Ramlal and recovered it at the rate of Rs 3.50 for eight months, commencing from the end of 1st month. What is the effective rate of simple interest?
(A) 60%
(B) 80%
(C) 20%
(D) 90%
(E) none
Rationale: Explanation:
Principal = Rs 20
Amount = Rs 3.50 x 8 = Rs 28
Interest = Rs 28 - Rs 20 = Rs 8
Time = 8 months = 8/12 years
8 = 20×8×r/12×100
r = 12×100/20 = 60% p.a.
Answer A
Answer: (A) 60%
Question: A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is
(A) 720
(B) 900
(C) 1200
(D) 1800
(E) None
Rationale: Solution
2(15 + 12) ×h	= 2(15 x 12)
‹=›h= 180/27 m
= 20/3m
Volume	= (15×12×20/3)m3
‹=›1200 m3.
Answer C
Answer: (C) 1200
Question: Find a number such that when 15 is subtracted from 7 times the number, the results is more than twice the number?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Solution
Let the number be x.	= Then, 7x-15 = 2x+10
= 5x = 25
‹=›x = 5.
Hence the required number is 5.
Answer D
Answer: (D) 5
Question: Given that a “6-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 4-inch pizza to a 6-inch pizza gives you approximately what percent increase in the total amount of pizza?
(A) 33
(B) 50
(C) 67
(D) 80
(E) 125
Rationale: area of 4 inch pizza= 2*2*pi=4 pi
area of 6 inch pizza =3*3*pi=9 pi
5/4*100=125% increase
hence answer is E
Answer: (E) 125
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit Y on the height of vehicles that are allowed to use the tunnel?
(A) 5½ ft
(B) 7½ ft
(C) 8 ½ ft
(D) 9½ ft
(E) 10 ft
Rationale: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer YBis 8 - .5 = 7.5... choose (B)!
From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.B
Answer: (B) 7½ ft
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) 2288
(B) 2779
(C) 2779
(D) 3900
(E) 2781
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Answer: (D) 3900
Question: In doing a division of a question with zero remainder,a candidate
took 12 as divisor instead of 21.The quotient obtained by him was 35.
The correct quotient is?
(A) 12
(B) 21
(C) 20
(D) 35
(E) 10
Rationale: Dividend=12*35=420.
Now dividend =420 and divisor =21.
Therefore correct quotient =420/21=20.
ANSWER C 20
Answer: (C) 20
Question: A car drives 90 miles on local roads at 30 mph, and 75 miles on the highway at 60 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 39 mph
(D) 42 mph
(E) 38 mph
Rationale: So The Answer is Plainly C....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=90 miles , and v= 30 mph so we can obtain time : 30*t = 90 Or t= 90/30 = 3 hours the needed time to cover 90 miles
in the same way we should divide 75 to 60 to find the needed time to cover 75 miles ,so t= 1.25 hours
so the total time for covering total distance would be 3+1.25 = 4.25 hours and total distance is 90+75= 165 miles
Final stage : average speed is total distance divide to total time : 165/4.25 = 38.8 miles per hour rounded up to 39 MPH....
Answer: (C) 39 mph
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
(A) Rs. 28800
(B) Rs. 28810
(C) Rs. 28820
(D) Rs. 28880
(E) Rs. 28890
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Option A
Answer: (A) Rs. 28800