mathewhe/aqua_rat huggingface dataset:
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years
Answer: Option C
Answer: (C) 6 years
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
(A) 120
(B) 180
(C) 240
(D) 280
(E) 320
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x. This must be equal to 360.
3x=360
x=3603
x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon. So answer is C.
Answer: (C) 240
Question: Find the simple interest on $10000 at 8% per annum for 12 months?
(A) $410
(B) $500
(C) $650
(D) $800
(E) $1000
Rationale: P = $10000
R = 8%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*8*1/100 = $800
Answer is D
Answer: (D) $800
Question: Johnny borrows $50,000 from Tony at 3% daily interest compounded daily. How much does Johnny owe Tony after 4 weeks?
(A) 50000*0.02^28
(B) 50000*1.12
(C) 50000*2.12
(D) 50000*1.03^28
(E) (50000*1.02)^28
Rationale: A=A= P(1+r100)^n
So, A=50000(1+3/100)^7âˆ—4
So, A= 50000(1.03)^28
Hence answer will be (D)
Answer: (D) 50000*1.03^28
Question: 893.7 – 573.07 – 95.007 = ?
(A) 225.623
(B) 224.777
(C) 233.523
(D) 414.637
(E) None of these
Rationale: Solution
Given expression = 893.7 - (573.07 + 95.007) = 893.7 - 668.077 = 225.623. Answer A
Answer: (A) 225.623
Question: A snail, climbing a 36 feet high wall, climbs up 8 feet on the first day but slides down 4 feet on the second. It climbs 8 feet on the third day and slides down again 4 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
(A) 12
(B) 14
(C) 15
(D) 20
(E) 21
Rationale: total transaction in two days = 8-4 = 4 feet
in 15 days it will climb 36 feet
thus reaching the top
therefore , total no of days required =15
C
Answer: (C) 15
Question: A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed 1½ times of the previous in how many days will he cover 750 km?
(A) 30
(B) 31.25
(C) 31
(D) 32
(E) 33
Rationale: Distance d = 1200km
let x be the speed
he walks 15 hours a day(ie 24 - 9)... so totally he walks for 1050hrs...
x = 1200/1050 => 120/105 = 24/21 => 8/7kmph
given 1 1/2 of prev speed
so 3/2 * 8/7= 24/14 = 12/7
new speed = 12/7kmph
now he rests 10 hrs a day ... means he walks 14 hrs a day...
time = 750 * 7 /12 => 437.5hrs
=> 437.5/14 = 31.25
ANSWER:B
Answer: (B) 31.25
Question: What is the tens digit of 7^1001?
(A) 0
(B) 0
(C) 2
(D) 3
(E) 4
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
1001= 4*250 + 1
The ten's digit will be 1 .
Answer B
Answer: (B) 0
Question: A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 2%
(C) 1%
(D) 6%
(E) 7%
Rationale: S.I. = (15500 - 12500) = Rs. 3000\
Rate = (100 * 3000) / (12500 * 4) = 6%
Answer: D
Answer: (D) 6%
Question: The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?
(A) 3
(B) 6
(C) 5
(D) 7
(E) 9
Rationale: Explanation:
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 63
=> 9 (x - y) = 63
=> x - y = 7.
Thus, none of the numbers can be deermined..
Answer: D
Answer: (D) 7
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 287 m
(B) 266 m
(C) 987 m
(D) 270 m
(E) 256 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer:D
Answer: (D) 270 m
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.1800. How much third person will get?
(A) 400
(B) 800
(C) 600
(D) 1200
(E) 1000
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 1800 = 800
Answer: B
Answer: (B) 800
Question: 4 shooters are hitting 1 out of 4 different targets. What is the probability that exactly one shooter will hit each target.
(A) 4/4^4
(B) 4^4/4
(C) 4!/4
(D) 4!/4^4
(E) 1/4!
Rationale: Each shooter out of 4 has 4 options, hence total # of outcomes is 4^4;
Favorable outcomes will be 4!, which is # of ways to assign 4 different targets to 4 shooters:
1-2-3-4 (targets)
A-B-C-D (shooters)
B-A-B-C (shooters)
C-B-A-B (shooters)
...
So basically # of arrangements of 4 distinct objects: 4!.
P=favorable/total=4!/4^4
Answer: D.
Answer: (D) 4!/4^4
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 15, 12, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
(A) 4/15
(B) 1/2
(C) 15/22
(D) 25/12
(E) 11/4
Rationale: The time it takes printer X is 15 hours.
The combined rate of Y and Z is 1/12 + 1/18 = 5/36
The time it takes Y and Z is 36/5
The ratio of times is 15 / (36/5) = 5*15/36 = 25/12
The answer is D.
Answer: (D) 25/12
Question: The average age 15 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 18
(B) 99
(C) 30
(D) 26
(E) 12
Rationale: 15 * 2 = 30 years
Answer: C
Answer: (C) 30
Question: The circulation for magazine Y in 1971 was 5 times the average (arithmetic mean) yearly circulation for magazine Y for the years 1972-1980. What is the ratio of the circulation in 1971 to the total circulation during 1971-1980 for magazine Y ?
(A) 3/14
(B) 5/14
(C) 9/14
(D) 11/14
(E) 1/2
Rationale: There are 9 years from 1972-1980, inclusive. Let's say the average circulation every year between 1972-1980 inclusive is x.
So the total circulation is 9x from 1972-1980, inclusive.
In 1971, the circulation is 5x.
So total circulation for 1971-1980 is 5x + 9x = 14x.
Ratio of circulation in 1971 to total circulation during 1971-1980 is 5x to 14x or 5/14.
Answer : B
Answer: (B) 5/14
Question: John has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
(A) 54
(B) 55
(C) 56
(D) 57
(E) 58
Rationale: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 55 that is c is the option which is divisible by 5.
so answer is B
Answer: (B) 55
Question: The average age of three boys is 28 years and their ages are in the proportion 4 : 6 : 8. The age of the youngest boy is:
(A) 21 years
(B) 18 years
(C) 14 years
(D) 9 years
(E) None of these
Rationale: Total age of 3 boys = (28 Ã— 3) years = 84 years. Ratio of their ages = 4 : 6 : 8.
Age of the youngest = (84 Ã— 3â„18) years = 14 years.
Answer C
Answer: (C) 14 years
Question: The number 152 is equal to the sum of the cubes of two integers. What is the product of those integers?
(A) 8
(B) 15
(C) 21
(D) 27
(E) 39
Rationale: Actually, decomposition into factors can easily give you the answer here. You should just do the decomposition of the right thing i.e. the options since they represent the product of those integers.
Since the sum of cubes is 152, the numbers cannot be larger than 5 since 6^3 itself is 216.
21, 27, 39 - The factors are too large so ignore
8 - (2, 4) Does not satisfy
15 - (3, 5) Yes. 3^3 + 5^3 = 152 - Answer
ANSWER:B
Answer: (B) 15
Question: Annie has 100 cards numbered 1 through 100. If she deals eight 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) (93! X 8!)/100!
(D) (96! X 8!)/100!
(E) (97! X 4!)/100!
Rationale: Alex to get 8 consecutive cards in ascending order, to have 8 consecutive at the end is good enough.
There are 93 consecutive numbers in 100: {1, 2, 3, 4, 5,6,7,8}, {2, 3, 4, 5, 6,7,8,9}, ..., {93,94,95,96, 97, 98, 99, 100};
Total ways to pick 8 cards out of 100 is {8!*93!}{100!}.
Answer: C.
Answer: (C) (93! X 8!)/100!
Question: The current ages of 3 individuals are in the ratio 4:7:9. 0.8 decades ago, the sum of their ages was 56. Find their current ages in years
(A) 16, 28, 36
(B) 17, 28, 39
(C) 18, 30, 38
(D) 20, 32, 46
(E) None of these
Rationale: A
16, 28, 36
Let their current ages are 4A, 7A and 9A years correspondingly.
Then, (4A – 8) + (7A – 8) + (9A – 8) = 56
20A = 80
A = 4
Their current ages are
16 years, 28 years and 36 years correspondingly.
Answer: (A) 16, 28, 36
Question: How many solution does the expression x+3−−−−√=xx+3−−−−√x+3=xx+3 has?
(A) 23
(B) 27
(C) 260
(D) 175
(E) 191
Rationale: Squaring on the both sides, x+3=x2(x+3)x+3=x2(x+3)
Bring x+3 to one side and take common, (x2−1)(x+3)(x2−1)(x+3)
So roots are, 1, -1, 3. But -1 is not a root. So 1, -3 are the roots.
(∵∵ when you square the equation additional roots may be generated. So finally you have to check manually, whether the given roots satisfy the original equation or not)
Answer:B
Answer: (B) 27
Question: The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 1,000,000 bacteria
(A) 10
(B) 12
(C) 14
(D) 16
(E) 20
Rationale: The question basically asks how many minutes it takes for a population to increase by factor 1000 (1,000,000 / 1,000 = 1000).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 1000, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. i.e. the population has to double 10 times.
Since it takes the population 2 minutes to double once it takes 10*2 minutes =20 minutes to double nine times.
Thus, solution E = 20 is correct.
Answer: (E) 20
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.2
(B) 31.2
(C) 31.6
(D) 31.3
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer:C
Answer: (C) 31.6
Question: If n is a positive integer, what is the remainder when (4^(4n+3))(6^n) is divided by 10?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 7
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =8.
C or J in this problem.
Answer: (C) 4
Question: A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?
(A) 87
(B) 95
(C) 102
(D) 103
(E) 115
Rationale: Form 1 PM to 5 PM.
Excluding the actual hour chime we have 20 (1PM)+20(2PM) +20(3PM)+20(4PM) +8 (5PM) = 88
Now the hour chimes are 1+2+3+4+5 = 15
Total = 88+15 = 103
Answer D.
Answer: (D) 103
Question: If (A+B) = 4, (B+C) = 7 and (C+D) = 5, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 7.
(D) 2.
(E) -2.
Rationale: Given A+B = 4
B+C = 7
C+D = 5
(A+B)-(B+C)+(C+D)=(A+D)
=>4 - 7+5 = 2.
Option D...
Answer: (D) 2.
Question: A man buys an item at Rs. 750 and sells it at the loss of 20 percent. Then what is the selling price of that item
(A) Rs. 660
(B) Rs. 760
(C) Rs. 600
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 750
= 80/100 * 750
= 600
Option C
Answer: (C) Rs. 600
Question: Find the sum of prime numbers lying between 60 and 75.
(A) 199
(B) 201
(C) 211
(D) 272
(E) None
Rationale: Solution
Required sum	=61 + 67 + 71 + 73
= 272.
Answer D
Answer: (D) 272
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 130 m and they cross each other in 12 sec, then the speed of each train is?
(A) 30
(B) 35
(C) 36
(D) 37
(E) 39
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (130 + 130)/12 => x = 10.83
Speed of each train = 10 m/sec.
= 10.83 * 18/5 =- 39 km/hr.
Answer: Option E
Answer: (E) 39
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 32 hours and 16 hours respectively. The ratio of their speeds is
(A) 4 : 9
(B) 4 : 3
(C) 4 : 12
(D) 1 : 2
(E) 4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 32 = 1 : 2.Answer: D
Answer: (D) 1 : 2
Question: 50 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor?
(A) 14.4
(B) 180/7
(C) 50.4
(D) 64.8
(E) 90
Rationale: 50% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/50)*100 = 64.8 square feet
Answer: Option D
Answer: (D) 64.8
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 10%
(B) 30%
(C) 50%
(D) 40%
(E) None of these
Rationale: Explanation :
he total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer : D
Answer: (D) 40%
Question: Out of seven consonants and three vowels, how many words can be made so that each word contains two consonants and three vowels?
(A) 1650
(B) 1920
(C) 2240
(D) 2520
(E) 2860
Rationale: 7C2 x 3C3 x 5! = 2520
The answer is D.
Answer: (D) 2520
Question: What is the 27th digit to the right of the decimal point in the decimal form of 5/11?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 5/11 = 0.45454545...
The odd numbered positions in the decimal expansion are all 4.
The answer is B.
Answer: (B) 4
Question: In a photography exhibition, some photographs were taken by Octavia the photographer, and some photographs were framed by Jack the framer. Jack had framed 24 photographs taken by Octavia, and 12 photographs taken by other photographers. If 36 of the photographs in the exhibition were taken by Octavia, how many photographs were either framed by Jack or taken by Octavia?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 108
Rationale: The number of photographs either framed by Jack or taken by Octavia = {Jack} + {Octavia} - {overlap} = 36 + 36 - 24 = 48 ({overlap} is green box).
Answer: B
Answer: (B) 48
Question: At a local appliance manufacturing facility, the workers received a 40% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
(A) 83%
(B) 28%
(C) 20%
(D) 17%
(E) 12%
Rationale: Let's say he works usually 40 hours and earns 100 per hour.
10 * 100 = 1000
10 * 140 = 1400 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/140 = 7.14
So he can reduce his work by 2.86 hours. Which is >28%.
Answer B
Answer: (B) 28%
Question: A circular path of 16 m radius has marginal walk 3 m wide all round it. Find the cost of leveling the walk at Rs.2 per m2?
(A) Rs.660
(B) Rs.40
(C) Rs.44
(D) Rs.42
(E) Rs.43
Rationale: Explanation:
π (19^2 - 16^2) = 22/7 * (361-256) = 330
330 * 2 = Rs.660
Answer: Option A
Answer: (A) Rs.660
Question: If n = 2×3×5×7×11×13×15, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
(A) I only
(B) II only
(C) I and III
(D) III only
(E) None of the above
Rationale: Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2: this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (C).
Answer: (C) I and III
Question: By giving Rs. 50 to M, A would have the amount equal to what M had earlier. If the sum of the amounts with A and M is Rs. 650. What is the ratio of the amount with A to that with M earlier?
(A) 7 : 4
(B) 5 : 3
(C) 2 : 1
(D) 7 : 6
(E) None of these
Rationale: Explanation:
let the amounts with A and M be Rs. “X” and Rs. “Y” respectively.
Thus, we have, X + Y = 650 and
X – 50 = Y
X – Y = 50.
Hence, X = 350 & Y = 300
Thus the required ratio is 350 : 300 = 7 : 6
ANSWER D
Answer: (D) 7 : 6
Question: At Amiee’s Pet Shop, 10 cups of bird seed are used every 4 days to feed 6 parakeets. How many cups of bird seed would be required to feed 10 parakeets for 5 days?
(A) 28.7
(B) 35.4
(C) 2 1/2
(D) 50
(E) 25
Rationale: Let's go step-by-step.
10 cups are used over a 4 day period, which means 2 1/2 cups a day. This feeds 6 parakeets, which means each parakeet needs .41 of a cup every day.
For 10 parakeets, we need 10*.41cups = 4.10 cups a day. Over 7 days, we need 28.70 cups. Choice A.
Answer: (A) 28.7
Question: If a and b are positive integers and b ≠ 1, then ab(b −1) is
(A) ab^2-ab
(B) 2/b
(C) 1/b
(D) 1/a
(E) 1/a+1/b
Rationale: Answer : A
Answer: (A) ab^2-ab
Question: The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.
(A) 4:25
(B) 4:28
(C) 4:29
(D) 4:25
(E) 4:21
Rationale: Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be
Area of square=1/2∗Diagonal2 1/2∗2x2:1/2∗5x24x2:25x2=4:25
Answer: A
Answer: (A) 4:25
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 278
(B) 272
(C) 892
(D) 750
(E) 298
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time
= 1 min.
= 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2
= 750
Answer: D
Answer: (D) 750
Question: In a certain lottery drawing, two balls are selected at random from a container with 50 balls, numbered from 1 to 50, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?
(A) $9.85 x 10^6
(B) $2.45 x 10^6
(C) $1.00 x 10^7
(D) $1.05 x 10^7
(E) $9.90 x 10^7
Rationale: The max product of any two balls can be 49 * 50 = 2450 = 2.45 * 10^3
If you multiply it by $1000 the max amount will be 2.45 * 10^6.
B
Answer: (B) $2.45 x 10^6
Question: A man walking at a constant rate of 6 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 12 miles per hour. The woman stops to wait for the man 10 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
(A) 5
(B) 15
(C) 10
(D) 20
(E) 25
Rationale: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 10*12/60 =2 miles and the man walks the distance mM, which is 10*6/60 = 1 mile.
The difference of 2 - 1 =1 miles (MW) will be covered by the man in (1)/6 = 1/6 of an hour, which is 10 minutes.
Answer C.
Answer: (C) 10
Question: In how many different ways can the letters of the word ‘RED’ be arranged ?
(A) 0
(B) 6
(C) 24
(D) 120
(E) 720
Rationale: B
6
Required number of arrangements = 3! = 6
Answer: (B) 6
Question: An empty wooden vessel weighs 16% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
(A) 3/5
(B) 5/9
(C) 1/24
(D) 4/9
(E) 7/15
Rationale: An empty wooden vessel weighs 16% of its total weight when filled with paint:
Vessel = 0.16(Vessel + Paint);
16V = V + P (so the weight of completely filled vessel is 16V)
P = 15V (so the weight of the paint when the vessels is completely filled is 15V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*16V;
P' = 7V (so the weight of the paint when the vessels is partially filled is 7V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 7V/15V = 7/15.
Answer: E.
Answer: (E) 7/15
Question: What is the smallest number which is a perfect square and is divisible by 16, 20 and 24?
(A) 3600
(B) 2778
(C) 2677
(D) 97Y67
(E) 272
Rationale: Explanation:
3600. The number is perfect square of 60.
It is divisible by 36 24 and 20. Only two numbers 3600 and 7200 fit these conditions.
It is clear that 3600 is the smaller number.
ANSWER: A
Answer: (A) 3600
Question: Find the number of Zeros in: (1)^1 x (2)^2 x (3)^3 x (4)^4 x ......(99)^99 x (100)^100
(A) 1200
(B) 1300
(C) 1400
(D) 1500
(E) None of these
Rationale: Explanation :
Consider number of 5's only.
(5+10+15+20+50+30+35+40+45+100+55+60+65+70+75+150+80+85+90+95+200)
=1300
Answer : B
Answer: (B) 1300
Question: What is the area D of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
(A) 60.
(B) 85.
(C) 125.
(D) 225.
(E) It cannot be determined from the information given
Rationale: Length of one side= 15 (20-5)
Since, its a square, the area will be D= 15^2= 225
D is the answer
Answer: (D) 225.
Question: An ice cream cone is three inches tall and its top is a circle with diameter two
inches. The cone is lled with ice cream, such that the interior of the cone is entirely full.
The cone is topped with a hemisphere of ice cream with diameter two inches. What is the
total volume, in cubic inches, of the ice cream in and atop the cone?
(A) π
(B) 4/3 π
(C) 3/2 π
(D) 5/3 π
(E) 2π
Rationale: The volume consists of that of the cone, plus that of the hemisphere on top. The
volume of a cone of radius r and height h is 1/3πr2h, so with h = 3 and r = 2
2 = 1 this volume
is 1
312 3 = . The volume of a sphere of radius r is 4
3r3, and we have half this, or 2
3: The
total volume is 5/3 π
correct answer D
Answer: (D) 5/3 π