mathewhe/aqua_rat huggingface dataset:
Question: An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 60% is a passing grade, what is the probability that Brian passes?
(A) 1/16
(B) 37/256
(C) 1/2
(D) 35/256
(E) 15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 35/256.
D
Answer: (D) 35/256
Question: The ratio of numbers is 4:5 and their H.C.F is 4. Their L.C.M is:
(A) 80
(B) 16
(C) 24
(D) 48
(E) 98
Rationale: Let the numbers be 4x and 5x.
Then their H.C.F = x. So, x = 4.
So, the numbers are 16 and 20.
L.C.M of 16 and 20 = 80.
ANSWER:A
Answer: (A) 80
Question: If the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 8
(B) 27
(C) 10
(D) 7
(E) 19
Rationale: 2 * 22/7 * 21 * x = 1056
=> x = 8
Answer: A
Answer: (A) 8
Question: A fruit seller had some oranges. He sells 40% oranges and still has 300 oranges. How many oranges he had originally?
(A) 700
(B) 710
(C) 720
(D) 500
(E) 740
Rationale: 60% of oranges = 300
100% of oranges =(300×100)/6=500
total oranges = 500
ANSWER : D
Answer: (D) 500
Question: A rectangular surface have length 15m and breadth 8m.calculate its area and diagonal.
(A) 120,18
(B) 120,17
(C) 115,17
(D) 115,18
(E) 120,18
Rationale: area=length*breadth=15*8=120 sq.m
Diagonal=√(15)^2+(8)^2=√289=17 m
Answer B
Answer: (B) 120,17
Question: Three unbiased coins are tossed. What is the probability of getting at least 2 tails?
(A) 0.75
(B) 0.5
(C) 0.25
(D) 0.2
(E) 0.3
Rationale: EXPLANATION:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
E = {HTT, THT, TTH, TTT}
n(S) = 8
n(E) = 4
P(E) =n(E) / n(S) = 4/8 = 0.5
ANSWER IS B
Answer: (B) 0.5
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
(A) 20
(B) 30
(C) 50
(D) 10
(E) 40
Rationale: There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children 120 men.
50 children (120/200)	* 50 = 30 men
Answer is B.
Answer: (B) 30
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 3484
(B) 3467
(C) 3567
(D) 4567
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: If 4 (A's capital) = 6 (B's capital) = 8 (C's capital). Then the ratio of their capitals is?
(A) 6:4:5
(B) 6:4:3
(C) 6:4:2
(D) 6:2:3
(E) 6:5:3
Rationale: 4A = 6B = 8 C
A:B:C = 1/4:1/6:1/8
= 6:4:3
Answer: B
Answer: (B) 6:4:3
Question: An bus covers a certain distance at aspeed of 150 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 560 km/h
(B) 450 km/h
(C) 779 km/h
(D) 723 km/h
(E) 720 km/h
Rationale: Distance = (150 x 5) = 750 km.
Speed = Distance/Time
Speed = 750/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 750 x 3/5 km/hr = 450 km/hr.
B
Answer: (B) 450 km/h
Question: Prizes totaling $45,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
(A) (a) $5,000
(B) (b) $10,000
(C) (c) $17,000
(D) (d) $55,000
(E) (e) $65,000
Rationale: The highest prize cannot possibly be less than 1/3rd of 45,000 (because in this case the sum of 3 prizes would be less than 45,000) and cannot be more than 45,000.
Answer: C.
Answer: (C) (c) $17,000
Question: The average age of 20 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
(A) 79
(B) 86
(C) 95
(D) 72
(E) 80
Rationale: Age of the 15th student = 20*15 - (14*5+16*9) =300-214 = 86 years
Answer is B
Answer: (B) 86
Question: The rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started. If after a minute and a half the gyroscope reached a speed of 3200 meters per second, what was the speed, in meters per second, when the stopwatch was started?
(A) 25/3
(B) 25/4
(C) 25/8
(D) 25/16
(E) 25/32
Rationale: Let x be the original speed when the stopwatch was started.
In 90 seconds, the speed doubled 9 times.
2^9 * x = 3200
x = (2^7 * 25) / 2^9 = 25/4
The answer is B.
Answer: (B) 25/4
Question: In Township K, 1/4 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?
(A) 23/30
(B) 11/15
(C) 7/10
(D) 1/6
(E) 2/15
Rationale: 1/4 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/4) = 1/12
therefore only video cassette recorder = 1/10 - 1/12 = 1/60
Total = 1/4+1/60+neither cable tv nor videocassette recorders
1 = 4/15 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-4/15 = 11/15
Hence B.
Answer: (B) 11/15
Question: In 1982 and 1983, Company B’s operating expenses were $11.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
(A) 3%
(B) 16 2/3%
(C) 25%
(D) 4 1/3%
(E) 60%
Rationale: Profit in 1982 = 15.6 - 11 = 4.6 million $
Profit in 1983 = 18.8 - 14 = 4.8 million $
Percentage increase in profit = (4.8-4.6)/4.6 * 100 %
= 4 1/3%
Answer D
Answer: (D) 4 1/3%
Question: How many even multiples of 55 are there between 549 and 1101?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 11
Rationale: 550 = 10*55
1100 = 20*55
The even multiples are 55 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: (B) 6
Question: The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?
(A) 3:2
(B) 5:4
(C) 7:6
(D) 9:8
(E) 11:10
Rationale: Polly : Sandy = 5:6
Sandy : Willy = 3:2 = 6:4
Polly : Sandy : Willy = 5:6:4
Polly : Willy = 5:4
The answer is B.
Answer: (B) 5:4
Question: The speed of a railway engine is 63 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
(A) 19
(B) 18
(C) 16
(D) 17
(E) 23
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Does reduction mean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 63 - k*sqrt(N)
where k is a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 = 63 - k*sqrt(9) = 63 - 3k
k = 13
Now, we need to know: what value of N makes S go to zero?
0 = 63 - 13*sqrt(N)
13*sqrt(N) =63
n = 23
With 24 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 23 is the maximum number of cars the engine can pull and still move.
E
Answer: (E) 23
Question: A man buys a cycle for Rs.1200 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs.1090
(B) Rs.1020
(C) Rs.1190
(D) Rs.1202
(E) NONE
Rationale: Solution
S.P	= 85% of Rs.1200
= Rs.(85/100×1200)
Rs.1020.
Answer B
Answer: (B) Rs.1020
Question: An angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows he killed the Chariot driver of Bheeshm. With one arrow each he knocked down respectively the Chariot, the flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: x/2 + 6+3+1+4 sqrt(x) = x
x/2 +10 + 4 sqrt(x) = x
4sqrt(x) = x/2 - 10
squaring on both sides
16x = x²/4 +100 -10x
simplifying x² -104x +400=0
x =100, 4
x=4 is not possible therefore x=100
ANSWER:B
Answer: (B) 100
Question: Village P’s population is 800 greater than Village Q's population. If Village Q’s population were reduced by 500 people, then Village P’s population would be 3 times as large as Village Q's population. What is Village Q's current population?
(A) 1100
(B) 1150
(C) 1200
(D) 1250
(E) 1300
Rationale: P = Q+800.
P=3(Q-500).
3(Q-500)=Q+800.
2Q=2300.
Q=1150.
The answer is B.
Answer: (B) 1150
Question: A 4 digit no may consist of the digits 6,2,7,5 where none of the nos are repeated.Find the possible no of combinations divisible by 36?
(A) 18
(B) 36
(C) 38
(D) 48
(E) 58
Rationale: lcm of 36 = 3 *3 * 4 the four digit number should be divisible by 3 and 4 then it is divisible by 36 adding all the digits 6+2+7+5=20 not divisible by 20 so
any 4 digit number formed by this is not divisible by 36
ANSWER:B
Answer: (B) 36
Question: 0, 3, 9, 18, 30, 45, 63, ?What number should replace the question mark?
(A) 78
(B) 74
(C) 79
(D) 72
(E) 84
Rationale: E 84add 3,6,9,12,15,.....
Answer: (E) 84
Question: How many X ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
(A) 3
(B) 16
(C) 28
(D) 32
(E) 56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen X= 56 - 24 = 32
Ans: D
Answer: (D) 32
Question: A walks at 4 kmph and 4 hours after his start, B cycles after him at 10 kmph. How far from the start does B catch up with A?
(A) 25km
(B) 26.7km
(C) 30km
(D) 32.5km
(E) 31.2km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.
x/4 - x/10 = 4
x = 26.7 km
Answer is B
Answer: (B) 26.7km
Question: Machine A and machine B are each used to manufacture 440 sprockets. It takes machine A 10 hours longer to produce 440 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Machine B: Takes x hours to produce 440 sprockets
Machine A: Takes (x+10) hours to produce 440 sprockets
Machine B: In 1 hour, B makes 440/x sprockets
Machine A: In 1 hour, A makes 440/(x+10) sprockets
Equating:
1.1(440/(x+10)) = 440/x
484/(x+10) = 440/x
484x = 440x+4400
44x = 4400
x = 100
A makes 440/(110) = 4 sprockets per hour
Answer : C
Answer: (C) 4
Question: It takes Joey the postman 1 hours to run a 4 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
(A) 5
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: let his speed for one half of the journey be 4 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*4*x/4+x=5
8x=4x+20=>x=5
A
Answer: (A) 5
Question: Dacid obtained 90, 92, 85, 87 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 67
(B) 26
(C) 88
(D) 90
(E) 75
Rationale: Average
= (90+ 92+ 85+ 87+ 85)/5
= 439/5 = 87.8.
Answer: C
Answer: (C) 88
Question: What is the greatest positive integer x such that 5^x is a factor of 125^10?
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: 125^10 = (5^3)^10 = 5^30
ANSWER:E
Answer: (E) 30
Question: A and B started a business in partnership. A invested Rs. 40000 for 6 months. A received Rs.6000 as his share out of the total profit of Rs. 9000, What was the amount invested by B for the whole year?
(A) Rs. 10000
(B) Rs. 10002
(C) Rs. 10009
(D) Rs. 10007
(E) Rs. 122122
Rationale: Explanation:
Profits of A and B are distributed in the same ratio of their investment and period of investments.
Investment of A/ Investment of B = Profit of A/ Profit of B = 6000/3000
(40000*1/2)/X*1 = 2/1
Therefore, X = B's investment amount = Rs. 10,000.
ANSWER:A
Answer: (A) Rs. 10000
Question: In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 70% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) a) 50%
(B) b) 53%
(C) c) 54%
(D) d) 55%
(E) e) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=55%
D
Answer: (D) d) 55%
Question: In how many minimum number of complete years, the interest on 212.50 P at 3% per annum will be in exact number of rupees?
(A) 6
(B) 8
(C) 9
(D) 7
(E) None of these
Rationale: Interest for one year = 212.50 × 3⁄100 × 1 = 51⁄8
Thus in 8 years, the interest is 51.
Answer B
Answer: (B) 8
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 35 percent of the budget?
(A)  126 °
(B)  15 °
(C)  54 °
(D)  90 °
(E)  150 °
Rationale: 100 percent = 360 degrees
35 percent = 360*35/100 = 126 degrees
Answer is A.
Answer: (A)  126 °
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 65% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
(A) 1
(B) 25
(C) 35
(D) 45
(E) 75
Rationale: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 65% = 117 responded as satisfied, So remaining Satisfied are 120 - 117 = 3
so 3 is what percentage of 300 - 1%
So the answer should be A
Answer: (A) 1
Question: A car started running at a speed of 29 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
(A) 41 km
(B) 76 km
(C) 25 km
(D) 15 km
(E) 30 km
Rationale: A
41 km
The total distance covered by the car in the first 10 hours = 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 = sum of 10 terms in AP whose first term is 32 and last term is 50 = 10/2 [32 + 50] = 410 km.
Answer: (A) 41 km
Question: Three bottles contain equal mixtures of spirit and water in the ratio 6 : 1, 5 : 2 and 3 : 1 respectively. If all the solutions are mixed together, the ratio of spirit to water in the final mixture will be
(A) 64 : 65
(B) 65 : 64
(C) 19 : 65
(D) 65 : 19
(E) none of these
Rationale: Given that all bottles contain equal amount of mixture say V.
So in the first vessel -> water : spirit =1/7 : 6/7
In the second bottle -> 2/7 : 5/7
In the third bottle -> l/4:3/4.
Hence, the final ratio is=((6/7) + (5/7) + (3/4)) / ((1/7) + (2/7) + (1/4))
= 65/19
ANSWER:D
Answer: (D) 65 : 19
Question: When a student Joe, weighing 43 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
(A) 5.5 kg
(B) 11 kg
(C) 30 kg
(D) 6.5 kg
(E) 71 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 43+30 = 73
So, the average the two persons = 36.5
That gives the answer 43-36.5 = 6.5
Answer D
Answer: (D) 6.5 kg
Question: What is the remainder when 7777* 8888 * 101010 is divided by 33
(A) 110
(B) 220
(C) 330
(D) 440
(E) 550
Rationale: 7777/33==> Remainder=22
8888/33==> Remainder=11
101010/33==> Remainder=30
=22*11*30=7260/33==> Remainder=220
Answer:B
Answer: (B) 220
Question: In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
(A) 23
(B) 12
(C) 24
(D) 27
(E) 11
Rationale: You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither
78 = (41-9) + (22-9) + 9 + neither.
Not enrolled students = 24
Answer: C
Answer: (C) 24
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/1
(E) 1/2
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: (C) 1/5
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
(A) 6
(B) 73
(C) 72
(D) 35
(E) 32
Rationale: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1
= 55 - 15 - 10 + 2 = 32
Answer:E
Answer: (E) 32
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.61 then sum is
(A) s.6100
(B) s.5100
(C) s.5800
(D) s.6000
(E) s.6200
Rationale: p(r/100)^2=C.I-S.I
P(10/100)^2=61
6100
ANSWER:A
Answer: (A) s.6100
Question: In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?
(A)  $2.4 million
(B)  $2.9 million
(C)  $3.0 million
(D)  $3.1 million
(E)  $3.6 million
Rationale: Let the number of pairs of shoes sold in 1985 = N
let price per pair of shoe sold in 1985 = P
In 1986,number of pairs of shoes sold decreased by 20 % = .8N
Price per pair increased by 20% = 1.2P
Company's revenue from sale of shoes in 1986 = 3 million$
=> .8N * 1.2 P = 3
=>.96 NP = 3
=> NP = 3/.96 = 3.125 million $
Answer D
Answer: (D)  $3.1 million
Question: Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 81th number in this set?
(A)  605
(B)  608
(C)  613
(D)  616
(E)  645
Rationale: The set S = {5, 13, 21, 29, ..................... }
1st Number = 8 * 0 + 5 = 5
2nd Number = 8 * 1 + 5 = 13
3rd Number = 8 * 2 + 5 = 21
81th Number = 8 * (81-1) + 5 = 645
Answer = E
Answer: (E)  645
Question: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.07, what is value of J?
(A) 22
(B) 56
(C) 78
(D) 200
(E) 175
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.07, the decimal part of the decimal quotient, must equal the remainder, 14, divided by the divisor J.
0.07 = 14/J
0.07*J = 14
J = 14/0.07 = 1400/7 = 200
So J =200, answer = D.
Answer: (D) 200
Question: At what rate percent per annum will the simple interest on a sum of money be 3/5 of the amount in 10 years?
(A) 6%
(B) 7%
(C) 9%
(D) 3%
(E) 1%
Rationale: Let sum = x. Then, S.I. = 2x/5, Time
= 10 years.
Rate = (100 * 3x) / (x * 5 * 10)
= 6%
Answer: A
Answer: (A) 6%
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 228
(B) 75
(C) 299
(D) 267
(E) 312
Rationale: S = (90 + 60)/2 = 75 kmph
Answer: B
Answer: (B) 75
Question: When 0.232323..... is converted into a fraction, then the result is
(A) 23/99
(B) 24/99
(C) 25/99
(D) 22/99
(E) 20/99
Rationale: 0.232323... = 0.23
=	23/99
Answer is A.
Answer: (A) 23/99
Question: The function f is defined by subtracting 25 from the square of a number and the function v is defined as the square root of one-half of a number. If v(f(x))=10, then which of the following is a possible value of x?
(A) -15
(B) -5
(C) 0
(D) 5
(E) 25
Rationale: f(x) = x^2-25
v(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
v(f(x)) = 10
v(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: (A) -15
Question: John took a bus from home to market, that travels at 50 kmph. While walking back at 5 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 35 kmph. Find the average speed.
(A) 8.5 kmph
(B) 16.0 kmph
(C) 22.5 kmph
(D) 18.6 kmph
(E) none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/50, by walking =x/5, by cycling = x/35 hours
:. Average speed = Total Distance/Total time
= 5x / x/25 + x/5 + x/35
= 5 *60 / 2.4+12+1.7
= 18.6
ANSWER:D
Answer: (D) 18.6 kmph
Question: Priya covers journey from kavali to nellore by car at average speed of 80 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
(A) 50Km/hr
(B) 53.33Km/hr
(C) 60Km/hr
(D) 66Km/hr
(E) 72km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*80*40/120
= 53.33 Km/hr
Answer: Option B
Answer: (B) 53.33Km/hr
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set W, which cannot be the range of the set W?
(A) 8
(B) B.11
(C) C.14
(D) D.17
(E) E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set W becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: (B) B.11