mathewhe/aqua_rat huggingface dataset:
Question: If you cut a 16ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece?
(A) 4ft
(B) 6ft
(C) 8ft
(D) 10ft
(E) 12ft
Rationale: Total length is 16ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).
(x)+ (x+4)=16
x+x+4-4=16-4
2x=12
2x/2=12/2
x=6
The piece is B) 6ft.
Answer: (B) 6ft
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 8 kilometers per hour, while Ferry Q takes a route that is two times longer. If Ferry P is slower than Ferry Q by 4 kilometers per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The distance traveled by Ferry P is 24 km.
Then the distance traveled by Ferry Q is 48 km. Ferry Q travels at a speed of 12 kph. The time of the journey for Ferry Q is 48/12 = 4 hours, which is 1 hour more than Ferry P. The answer is A.
Answer: (A) 1
Question: Harry started a 4-mile hike with a full 10-cup canteen of water and finished the hike in 2 hours with 2 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 3 miles of the hike?
(A) 1/3
(B) 2/3
(C) 3/3
(D) 3/1
(E) 3/2
Rationale: No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 6 cups.
No of cups harry drank during the first 3 miles = 3.
drink / mile = 3/3
Answer: C
Answer: (C) 3/3
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
(A) 2230 m^2
(B) 2456 m^2
(C) 2520 m^2
(D) 2678 m^2
(E) 2734 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: (C) 2520 m^2
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If six beavers start to build the same dam at noon, and one beaver per hour is added beginning at 5:00 PM, at what time will the dam be complete?
(A) 7:24 PM
(B) 8:00 PM
(C) 8:36 PM
(D) 9:12 PM
(E) 9:48 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 6 beavers in 5 hours is 6/60 *5 = 30/60
In the next hour, 7 beavers do 7/60 for a total of 37/60.
In the next hour, 8 beavers do 8/60 for a total of 45/60.
In the next hour, 9 beavers do 9/60 for a total of 54/60.
In the next 36 minutes, 10 beavers do 10/60 * 36/60 = 6/60 for a total of 60/60.
The dam will be completed at 8:36 pm.
The answer is C.
Answer: (C) 8:36 PM
Question: If q and y are integers and (15^q + 15^(q+1))/4^y = 15^y what is the value of q?
(A) 2
(B) 3
(C) 4
(D) 5
(E) Cannot be determined
Rationale: \frac{15^q( 1+ 15)}{4^y} = 15^y
(15^q . 4^2 ) / 4^y = 15^y. 4^0
15^q . 4^(2-y) = 15^y. 4^0
Equating the powers, q = y; 2-y = 0; So q = y = 2=A
Answer: (A) 2
Question: The daytime telephone rate between two cities is 70 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is:
(A)  0.4(0.70) + 35c
(B)  0.6(0.70 + 0.35c)
(C)  0.4(0.70 + 9c)
(D)  0.6(0.70 + 32c)
(E)  0.4(0.70 + 0.32c)
Rationale: For first three minutes = 70 cents
Remaining minutes = 35 -3 = 32
charge for 32 minutes = 32c
total cost (if the call was made in daytime) = 0.70 + 32c
60% chargereducedon night calls => 40% charge
=>0.4(0.70 + 32c)
Hence, Answer is E
Answer: (E)  0.4(0.70 + 0.32c)
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 4 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 4 minute mark.)
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: 4 minutes is 240 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
240/24=10.
In the time period, Lamp A and Lamp B will flash together 10 times.
Lamp A and Lamp C will flash together every 30 seconds.
240/30=8.
In the time period, Lamp A and Lamp C will flash together 8 times.
Lamp B and Lamp C will flash together every 40 seconds.
240/40=6.
In the time period, Lamp B and Lamp C will flash together 6 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
240/120=2.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 10+8+6-6=18 times.
The answer is C.
Answer: (C) 18
Question: Average expenditure of a person for the first 3 days of a week is Rs. 360 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
(A) 350
(B) 370
(C) 390
(D) 400
(E) None
Rationale: Explanation:
Assumed mean = Rs. 360
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 360 + Rs. 40 = Rs. 400
Correct Option: D
Answer: (D) 400
Question: Analyze the number square carefully and find out what number fits in place of question mark.
1	3	5
2	4	6
7	2	?
(A) 6
(B) 12
(C) 24
(D) 48
(E) 28
Rationale: 20 fits in place of question mark.
This is because (number in first column) / (number in second column) * 8 = number in third column.
Here (left number / middle number) * 8 = right number
(7 / 2) * 8 = 7*4= 28
E
Answer: (E) 28
Question: A no.when divided by 225 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
(A) 2
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: 225 + 43 = 268/17 = 13 (Remainder)
E
Answer: (E) 13
Question: In how many ways can the letters of the word SITO be arranged in a row so that the vowels appear in alphabetic order?
(A) 16
(B) 12
(C) 14
(D) 18
(E) 24
Rationale: two letters can be arranged in 2! ways.
only one combination IO is required.
4 letters can be arranged in 4! ways.
thus 4!/ 2! * 1 = 12.
B
Answer: (B) 12
Question: Using all the letters of the word "FORMED", how many words can be formed, which begin with F and end with D?
(A) 30
(B) 26
(C) 23
(D) 20
(E) 24
Rationale: There are six letters in the given word.
Consider 6 blanks ....
The first blank and last blank must be filled with F and D all the remaining four blanks can be filled with the remaining 4 letters in 4! ways.
The number of words = 4! = 24.
ANSWER:E
Answer: (E) 24
Question: The speed of a boat in still water in 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:
(A) 10.4 km
(B) 10.6 km
(C) 11.4 km
(D) 11 km
(E) 12 km
Rationale: Explanation:
Speed downstream = (22 + 4) = 26 kmph
Time = 24 minutes = 24/60 hour = 2/5 hour
Distance travelled = Time × speed = (2/5)×26 = 10.4 km
Answer: Option A
Answer: (A) 10.4 km
Question: Steve traveled the first 2 hours of his journey at 50 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
(A) 68 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 50 = 100 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 100 = 340m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 340/5 = 68mph
Answer: A
Answer: (A) 68 mph
Question: Sandy walked 25 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 25 meters. She then turned to her right and walked 12 meters. What distance is she from the starting point and in which direction?
(A) 32 meters East
(B) 32 meters North
(C) 32 meters West
(D) 42 meters East
(E) 52 meters West
Rationale: The net distance is 20 + 12 = 32 meters to the east.
The answer is A.
Answer: (A) 32 meters East
Question: If 20% of a number, then 120% of that number will be?
(A) 20
(B) 120
(C) 360
(D) 720
(E) 700
Rationale: Explanation:
Let the number x. Then,
20% of x = 120
x = (120 * 100)/20 = 600
120% of x = (120/100 * 600) = 720.
Answer IS D
Answer: (D) 720
Question: Felix earned 80% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?
(A) 10%
(B) 9.09%
(C) 48%
(D) 47.27%
(E) It cannot be determined from the information given.
Rationale: This Q is all about taking the correct BASE for taking %s..
the very first step requires taking some numbers for each..
ONE should be 100...
it is easy to take 20 and 100 here..
but the BASE is 100 here, so the salary can be 100 and 180..
100 increases 10% =110..
180 decreases 10%=162..
so the increase is 52..
again the BASE is 110, so answer 52/110 * 100= 47.27% D
without calculations,
answer cannot be equal to or greater than 48, as 52 is on 110..
so D is the only one left
Answer: (D) 47.27%
Question: In a game of chess, the moves of whites and blacks alternate with whites having the first move. During a certain chess tournament whites have made 2319 moves altogether while blacks have made 2315 moves. If in any game the side that made the last move did not lose, which of the following can be true about the tournament?
I. Blacks lost 5 games
II. Blacks won more games than whites
III. All games ended in a draw
(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: if white wins, white will always have more moves than black.
Win: White. Then, White > Black.
If Black wins, the number of moves of both white and black will be the same.
Win: Black. Then, White (moves) = Black (moves).
Why? Because, white cannot have the last move and lose the game (from the question). And white always starts so it will be WB WB WB till blacks last move.
If it is a draw, either of these possibilities exists.
Win: Draw. White > Black or Black = White.
Statement 1: Black lost 5 games. This is false because anyone who plays the last move cannot lose (from the question). IF black lost 5 games, white will have a clear lead of 5 moves. It is only 4 moves from the question.
Statement 2: This is possible. Imagine that they play about 150 games. 146 could be black wins (So black moves will be equal to white). then last 4 can be White wins (White moves > Black moves).
Statement 3: All games are draws with white having the last move in only 4 of them . Possible
the answer is D
Answer: (D) II and III only
Question: How many positive integers less than 50 have a reminder 5 when divided by 7?
(A) 3
(B) 7
(C) 4
(D) 5
(E) 6
Rationale: take the multiples of 7 and add 5
0X7+5=5 ....6X7+5=47
there are 7 numbers
answer B
Answer: (B) 7
Question: The cost of 3 kg of sugar is $30. What will the cost of 8 kg of sugar be?
(A) 20
(B) 40
(C) 80
(D) 160
(E) 180
Rationale: 3 kg costs $30
1 kg costs $10
8 kg costs $80
The answer is C.
Answer: (C) 80
Question: In the coordinate plane, points (x, 2) and (8, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 8
(B) 6
(C) 5
(D) 3
(E) 2
Rationale: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.
Thus: (x, 2)=(4, 2) and (8, y) = (8,4) --> x+y=4+4=8.
Answer: A
Answer: (A) 8
Question: The ratio 6 : 5 expressed as a percent equals
(A) 12.5%
(B) 40%
(C) 120%
(D) 125%
(E) None
Rationale: Solution
6 : 5	= 6/ 5
= (6/5 x 100)%.
= 120 %.
Answer C
Answer: (C) 120%
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
(A) Rs.1529
(B) Rs.1508
(C) Rs.1500
(D) Rs.1592
(E) Rs.1520
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer: C
Answer: (C) Rs.1500
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 226
(C) 276
(D) 266
(E) 181
Rationale: Explanation:
20000(11/10)4 - 20000(6/5)2
= 482
Answer: A
Answer: (A) 482
Question: Last year a certain bond yielded 8 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
(A) $6,000
(B) $3,750
(C) $7,425
(D) $7,500
(E) $9,375
Rationale: Interest = 0.08*face value = 0.04*7,500 --> face value = 0.04*7,500/0.08 = 3,750.
Answer: B.
Answer: (B) $3,750
Question: The width of a rectangular hall is ½ of its length. If the area of the hall is 128 sq.m, what is the difference between its length and breadth?
(A) 8m
(B) 10m
(C) 12m
(D) 15m
(E) 17m
Rationale: Let the length of the hall be x m
Breadth of the hall = 1x/2 m
Area of the hall = Length * Breadth
128 = x * 1x/2
x² = 256
x =16
Difference between the length and breadth of the hall = x - 1x/2 = x/2
=16/2 = 8m
ANSWER:A
Answer: (A) 8m
Question: find out the probability to get 1Rs coin head, 2Rs coin Tail and 5Rs coin head??
(A) 1/2
(B) 1/8
(C) 1/16
(D) 1/4
(E) None of these
Rationale: 1Rs coin head=1/2
2Rs coin Tail=1/2
5Rs coin head=1/2
=(1/2)*(1/2)*(1/2)
=1/8
ANSWER:B
Answer: (B) 1/8
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $48,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
(A) $24,000
(B) $28,000
(C) $32,000
(D) $36,000
(E) $40,000
Rationale: The answer should be -> A. $24,000
Answer: (A) $24,000
Question: The average weight of 4 person's increases by 8.5 kg when a new person comes in place of one of them weighing 95 kg. What might be the weight of the new person?
(A) 129 kg
(B) 134 kg
(C) 180 kg
(D) 185 kg
(E) 190 kg
Rationale: Total weight increased = (4 x 8.5) kg = 34 kg.
Weight of new person = (95 + 34) kg = 129 kg
Option A
Answer: (A) 129 kg
Question: Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 5. Based on this information, how many gold coins would there be in this collection after the proposed trade?
(A) 50
(B) 60
(C) 180
(D) 200
(E) 300
Rationale: The correct answer is D.
Answer: (D) 200
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $48. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) xy/360
(B) 9xy/40
(C) 40xy/9
(D) 432xy
(E) 432/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 48 / (xy/9) = 432/(xy).
The answer is E.
Answer: (E) 432/(xy)
Question: A train passes a train standing in platform in 30 sec and a man standing on the platform in 12 sec. If the speed of the train is 36 km/hr. What is the length of the platform?
(A) 250
(B) 200
(C) 300
(D) 240
(E) 180
Rationale: Speed = 36 * 5/18 = 10 m/sec.
Length of the train = 10 * 12 = 120 m.
Let the length of the platform be x m . Then,
(x + 120)/30 = 10 => x = 180 m.
Answer: E
Answer: (E) 180
Question: Three number are in the ratio 5:6:7. The sum of its largest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) 87
(B) 57
(C) 48
(D) 26
(E) 28
Rationale: Let the numbers be 5x, 6x and 7x.
Largest number = 7x
Smallest number = 5x
Third number = 6x
7x + 5x = 6x + 48
6x = 48
Third number is: 48.
Answer: C
Answer: (C) 48
Question: a man owns 2/3 of the market research beauro business and sells 3/4 of his shares for Rs.75000. what is the value of business ?
(A) 170000
(B) 120000
(C) 130000
(D) 140000
(E) 150000
Rationale: x*(3/4)=75000 this is cost of his owns value
on solving we get x=100000
now, y*(2/3)=100000 we get y=150000
so 150000 is the cost of whole business.
ANSWER:E
Answer: (E) 150000
Question: Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
(A) 75
(B) 81
(C) 85
(D) 89
(E) 91
Rationale: Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
First Number = 551/29 =19
Third Number = 1073/29 =37
Required sum = (19 + 29 + 37) = 85.
ANSWER :C
Answer: (C) 85
Question: Find the largest 4 digit number which isexactly divisible by 88?
(A) 7851
(B) 8902
(C) 9944
(D) 9578
(E) 9734
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: (C) 9944
Question: The average of temperatures at noontime from Monday to Friday is 55; the lowest one is 45, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: there are 5 days so the sum of temperature can be 55*5=275
lowest is 45. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*45=180.
on the fifth day it is 275-180=95
range is therefore 95-45=40
answer C
Answer: (C) 40
Question: How many such letter-pairs are there in the word SMUGGLER having same no.of letters left between them as they have in the series?
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: S,U
And E,G
ANSWER:A
Answer: (A) 2
Question: A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7.5
(D) 4
(E) 32
Rationale: US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer: C
Answer: (C) 7.5
Question: The profit earned by selling an article for 912 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
(A) 960
(B) 1060
(C) 1,200
(D) 1020
(E) None of these
Rationale: Let the profit or loss be x
and 912 – x = 448 + x or, x = 464⁄2 = 232
\ Cost price of the article = 912 – x = 448 + x = 680
\ SP of the article = 680 × 150⁄100 = 1020
Answer D
Answer: (D) 1020
Question: The ages of Krish and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:
(A) 10
(B) 13
(C) 15
(D) 18
(E) 19
Rationale: Explanation:
Krish’s age = 3A and Vaibhav’s age = 5A =(3A + 9)/(5A + 9)=3/4
=> 4 (3A + 9) = 3 (5A + 9)
=> A = 3
Therefore, Vaibhav’s age = 15 years. Answer: C
Answer: (C) 15
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of
(A) 3100
(B) 6220
(C) 6210
(D) 6240
(E) 6670
Rationale: Market Value = Rs. 96.
Required Income = Rs. 650.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96
To obtain Rs.650, investment = 96/10×650=6240
Answer is D.
Answer: (D) 6240
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?
(A) 37.5%
(B) 37.9%
(C) 37.8%
(D) 39.5%
(E) 31.5%
Rationale: Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 88
Gain % = 24/64 * 100 = 37.5%.
Answer:A
Answer: (A) 37.5%
Question: Mr. Bhaskar is on tour and he has Rs. 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs. 3. for how many days is Mr. Bhaskar on tour?
(A) 20
(B) 10
(C) 15
(D) 18
(E) None of them
Rationale: Suppose Mr. Bhaskar is on tour for x days. Then,
360/x - 360/x+4 = 3 <=> 1/x - 1/x+4 = 1<=> x(x+4)
= 4 x 120 =480
<=> x2 +4x –480 = 0 <=> (x+24) (x-20) = 0 <=> x =20.
Hence Mr. Bhaskar is on tour for 20 days.
Answer is A.
Answer: (A) 20
Question: Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed?
(A) 36521
(B) 25200
(C) 45127
(D) 14521
(E) 47845
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= 7C3 * 4C2
= 210
Number of groups each having 3 consonants and 2 vowels = 210
Each group contains 5 letters
Number of ways of arranging 5 letters among themselves
= 5! = (5 * 4 * 3 * 2 * 1)
= 210
Required number of words = (210 * 210)
= 25200
Ans: B
Answer: (B) 25200
Question: If a(a -1) = 20 and b(b - 1) = 20, where a ≠ b, then a + b =
(A) −48
(B) −1
(C) 2
(D) 46
(E) 67
Rationale: i.e. if a = 5 then b = -4
or if a = -4 then b = 5
But in each case a+b = -5+4 = -1
Answer: option B
Answer: (B) −1
Question: If M is the mean of x,y,z ; then what is the mean of 3x,3y and 3z
(A) M
(B) 3M
(C) 10M
(D) M+10
(E) M-10
Rationale: So new mean is 3M
Answer (B)
Answer: (B) 3M
Question: In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 5 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?
(A) 27/343
(B) 3/7
(C) 27/125
(D) 329/411
(E) 9/125
Rationale: Let us take 7*5=35 as the total number of customers. So 7*3=21 customers bought a bagel and 5*5=25 customers bought a coffee.
chances that at least 1 customer bought a coffee and a bagel = 1 - chances that no customer bought a coffee and a bagel
chances that no customer bought a coffee and a bagel= 24/35*23/34*22/33*21/32*20/31=82/411
chances that at least 1 customer bought a coffee and a bagel= 1 - 82/411 = 329/411
Answer D.
Answer: (D) 329/411
Question: The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 19/35
(B) 18/38
(C) 18/36
(D) 18/16
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 4/5 * 4/7 + 1/5 * 3/7
= 16/35 + 3/35
= 19/35
Answer: A
Answer: (A) 19/35
Question: Susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long, 7 small cubes wide and 6 small cubes deep. She realise that she has used more small cubes than she really needed. She realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions, if it were made
(A) 194
(B) 195
(C) 196
(D) 197
(E) 198
Rationale: Volume of cube of dimensions 7 7 6 is 7*7*6=294
If it were to look hollow the imaginary inside cube volume is to be deducted
which is (7-2)*(7-2)*(6-2)=100 (Here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension)
so minimum number of cubes required to make hollow cube is 294-100=194 cubes
ANSWER:A
Answer: (A) 194
Question: When height of a tree is equal to the length of its shadow, what is the angle of elevation of the sun?
(A) 45 deg
(B) 65 deg
(C) 276 deg
(D) 66 deg
(E) 165 deg
Rationale: ANSWER: A
Answer: (A) 45 deg
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.34. How much did the meal cost without the tip?
(A) $28.98
(B) $29.91
(C) $30.15
(D) $31.60
(E) $30.85
Rationale: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $36.34:
1.15x = 36.34
Divide both sides by 1.15:=>x=36.34/1.15=31.60
correct answer D)$31.60
Answer: (D) $31.60
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 B pay?
(A) 270
(B) 360
(C) 276
(D) 271
(E) 272
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 870 = 360
Answer: B
Answer: (B) 360
Question: If a class of 10 students has eight men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
(A) 8!7!
(B) 5!5!
(C) 4!4!
(D) 10!
(E) 10!/5!
Rationale: for no two men to sit together, either all are in even or odd position.
fix one at any one position then rest four can be fixed in 7! ways...
also rest five position of women can be fixed in 8!..
total ways 8!7!
A
Answer: (A) 8!7!