mathewhe/aqua_rat huggingface dataset:
Question: A quadilateral pqrs is inscribes in a circle of center o. PQ is parallel to RS and pq= 3rs,
also QR=PS. perimeter(pqrs)= perimeter of square whose area is 36sqm,then find the approx area of pqrs
(A) 6root(3)
(B) 12root(3)
(C) 9root(3)
(D) 18root(3)
(E) 12root(3)
Rationale: Lets take, QR=PS= a m and RS=b m, So, PQ=3b m
now if are of a square is 36 sqm, then perimeter is 24
now perimeter of the inscribed quadrilateral is 4b+2a= 24
so, 2b+a=12
from this we can get set of solutions like (a,b)= (6,3), (8,2), (10,2)
Now, formula for area of inscribed quadrilater is root{(s-a)(s-b)(s-c)(s-d)}
Here s= 12
now by trial and error method we can get the solution
appprox area is 18root(3)
ANSWER:D
Answer: (D) 18root(3)
Question: A man starts from B to K, another starts from K to B, at the same time. After passing each other they complete their journeys in 3.33 and 4.80 hours respectively. Find the speed of the second man if the speed of the first is 12 km/ hr
(A) 12 kms/hr
(B) 10 kms/hr
(C) 14 kms/hr
(D) Data inadequate
(E) none
Rationale: 12:x=sqrt(288):sqrt(199.8)
12:x=17:14
x=168/17 ~10km/hr
ANSWER:B
Answer: (B) 10 kms/hr
Question: Eight children — A, B, C, D, E, F, G, and H — are going to sit in eight chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?
(A) 2520
(B) 5040
(C) 10,080
(D) 20,160
(E) 40,320
Rationale: The number of ways to seat 8 people is 8! = 40,320.
Child C will sit to the left of Child D in exactly half of these arrangements.
The total number of possible arrangements is 40,320/2 = 20,160
The answer is D.
Answer: (D) 20,160
Question: If the ratio of x to y is 1 to 5, then (y-x)/(x+y)?
(A) -7/3
(B) -3/7
(C) 2/3
(D) 1
(E) 2/6
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 1 to 5 means
(x/y)=(1/5)
Cross-multiply
1x = 5y
x = (1/5)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (1/5)*y) / ((1/5)*y + y)
= ((4/5)*y) / ((6/5)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(4/5) / (6/5)
= (4/5) * (6/7)
The 5s cancel each other out, and you are left with 4/6 to 2/3.
Answer: (C) 2/3
Question: A train speeds past a pole in 15 sec and a platform 110 m long in 25 sec, its length is?
(A) 165
(B) 150
(C) 988
(D) 177
(E) 171
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 110)/25 = x/15 => x = 165 m.
Answer: A
Answer: (A) 165
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
(A) 7 years
(B) 5 years
(C) 2 years
(D) 4 years
(E) 9 years
Rationale: 4 years
Answer: D
Answer: (D) 4 years
Question: (112 x 54) = ?
(A) 67000
(B) 70000
(C) 76500
(D) 77200
(E) 85200
Rationale: Explanation:
(112 x 54) = 112 x(10/2)4=112 X10 4 /2 4 =1120000/16 =70000
ANSWER IS B
Answer: (B) 70000
Question: In a company ones salary increases 6/5 times in every year. After 4 year of joining average salary is 1342. Then what's the starting salary of the company?
(A) 900
(B) 1000
(C) 1100
(D) 1200
(E) 1300
Rationale: Let x be initial salary.
After one year it becomes 6/5*x
4 months salary is
x+6/5x +6/5*6/5x+ 6/5*6/5*6/5x + 6/5*6/5*6/5*6/5x =1342*4
By solving we get x =1000
ANSWER:B
Answer: (B) 1000
Question: There are 5 questions in a question paper. In an examination 5% students answer all questions and 5% answered none. 50% of the rest answered 3 questions and 20% answered 2 questions and 300 answered only 1 question. How many students appeared for the test?
(A) 1400
(B) 1500
(C) 1600
(D) 1700
(E) 1800
Rationale: Let total no.of students be x
x=(x*5/100)+(x*5/100)+(x*50/100)+(x*20/100)+300
100x=(5*x)+(5*x)+(50*x)+(20*x)+30000
100x=80x+30000
20x=30000
x=1500
ANSWER:B
Answer: (B) 1500
Question: The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?
(A) 375
(B) 2570
(C) 2800
(D) 3315
(E) None of these
Rationale: Explanation:
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. Of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cm. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315
ANSWER: D
Answer: (D) 3315
Question: If 0.5% of A =95 paise, then the value of A is ?
(A) Rs. 190
(B) Rs. 17
(C) Rs. 1.70
(D) Rs. 4.25
(E) None
Rationale: Answer
∵ 0.5/100 of A = 95/100
∴ A = Rs. (95 / 0.5) = Rs. 190
Correct Option: A
Answer: (A) Rs. 190
Question: Look at this series: 83, 80, 85, 82, 87, 84, ... What number should come next?
(A) 89
(B) 95
(C) 85
(D) 83
(E) 80
Rationale: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option A
Answer: (A) 89
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
(A) 3/105
(B) 3/103
(C) 1/108
(D) 2/113
(E) 2/115
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: (C) 1/108
Question: The value of (10^7-10^2)/(10^6-10^3) is closest to which of the following?
(A) 1
(B) 10
(C) 10^2
(D) 10^3
(E) 10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^7 - 10^2
10^7 is HUGE compared to 10^2.
So 10^7 - 10^2 is very close to 10^7 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^6 is HUGE compared to 10^3.
So 10^6 - 10^3 is very close to 10^6.
So we have:
10^7/10^6
or 10^(7-6) = 10.
Choose B.
Answer: (B) 10
Question: In Town X, 64 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 25%
(C) 32%
(D) 34%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 42 are employed males, hence 22% are employed females.
(employed females)/(total employed people)=22/64=34%
Answer: D.
Answer: (D) 34%
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'7" tall, which of the following is the median height of the children?
(A) 2'2"
(B) 2'7"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'7"+2'7")/2 = 2'7"
Ans:Option B
Answer: (B) 2'7"
Question: How many times digit 6 is used while writing numbers from 80 to 1000?
(A) 648
(B) 300
(C) 252
(D) 225
(E) 26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 225. Hence D.
Answer: (D) 225
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
(A) 25600.24
(B) 25600.28
(C) 25600.17
(D) 25600.28
(E) 25600.22
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: (A) 25600.24
Question: A bag consists of 30 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
(A) 5/6
(B) 2/4
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: bag consists of 20 marbles, of which 5 are blue, 9 are red
remainder are white. So, white = 30 - 5 - 9 = 16.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/30+16/30 = 25/30 = 5/6
Hence, answer will be A.
Answer: (A) 5/6
Question: If the sum of two numbers is 55 and the H.C.F. and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
(A) 55/601
(B) 601/55
(C) 11/120
(D) 120/11
(E) 120/13
Rationale: given a+b=55,hcm and lcm is 5 and 120
axb=lcmx hcf
600=120x5
1/a+1/b=a+b/ab=>55/600=>11/120
ANSWER:C
Answer: (C) 11/120
Question: An electric pump can fill a tank in 10 hours. Because of a leak in the tank, it took 20 hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
(A) 10hours
(B) 12hours
(C) 20hours
(D) 5hours
(E) 15hours
Rationale: Work done by the leak in 1 hour = 1/10 - 1/20 = 1/20
The leak will empty the tank in 20hours
Answer is C
Answer: (C) 20hours
Question: There are 7 players in a bowling team with an average weight of 76 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
(A) 78 Kg.
(B) 70 Kg.
(C) 75 Kg.
(D) 70 Kg.
(E) 72 Kg.
Rationale: The New average will be= (76*7+110+60)/9= 78 kgs
A is the answer
Answer: (A) 78 Kg.
Question: A fair coin is tossed repeatedly. If heads appears on first 7 tosses what is the probability that tail appears on the next two tosses?
(A) 1/6
(B) 1/5
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Answer: (D) 1/4
Question: Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 42 years. What is Molly's age right now?
(A) 24
(B) 27
(C) 30
(D) 33
(E) 36
Rationale: Now, Sandy is 42 - 6 = 36
Molly's age is (3/4) * 36 = 27
The answer is B.
Answer: (B) 27
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 2 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 5 hours. If at 06:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00.
(C) 20:00.
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 2 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 5 hours
Time taken by both buses to meet again in St. Louis will be LCM of 2 and 5 = 10
If the buses start at 06:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours
Answer A
Answer: (A) 16:00.
Question: A woman buys a soccer ball for rs.9.00 and sells it for rs.12.00. Find her gain %.
(A) 36.33%
(B) 9%
(C) 33.33%
(D) 24%
(E) 12%
Rationale: sol. cp=rs 9.00, sp=rs 12.00
gain=rs(12.00 –9.00)=rs 3.00
so gain%={(3.00/9.00)*100}=33.33%
Answer is C.
Answer: (C) 33.33%
Question: Which of the following is equal to 3^k*5^(k-1)?
(A) 3*15^(k-1)
(B) 5*10^(k-1)
(C) 15^k
(D) 3*15^k
(E) 15^(2k-1)
Rationale: 3^k*5^(k-1) = 3*3^(k-1)*5^(k-1) = 3*15^(k-1)
The answer is A.
Answer: (A) 3*15^(k-1)
Question: A train running at 7/11 of its own speed reached a place in 22 hours. How much time could be saved if the train would have run at its own speed?
(A) 4hrs
(B) 6hrs
(C) 8hrs
(D) 9hrs
(E) 11hrs
Rationale: New speed = 7/11 of usual speed
New time = 11/7 of usual time
11/7 of usual time = 22 hrs
Usual time = 22*7/11 = 14 hrs
Time saved = 22-44 = 8 hrs
Answer is C
Answer: (C) 8hrs
Question: Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 6 people. If only Inna or Jake can drive, how many seat allocations are possible?
(A) 30
(B) 42
(C) 120
(D) 240
(E) 720
Rationale: 5 people ,6 seats, only 2 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *2= 48 ways
4 seats can be chosen out of remaining 5 seats in 5c4 ways = 5!/(3!*2!)= 5 ways
48*5=240
D
Answer: (D) 240
Question: Point (j,k) is on the circle represented by j^2+k^2=10, and j, k are integers. How many such points are possible?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: j^2+k^2=10 and k, k are integers means that 10 is the sum of two perfect squares.
10 is the sum of only one pair of perfect squares 1 and 9.
So, there can be 8 such points, 4 in each quadrant:
(1, 3);
(1, -3);
(-1, 3);
(-1, -3);
(3, 1);
(3, -1);
(-3, 1);
(-3, -1).
Answer: E.
Answer: (E) 8
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number R of employees who take the subway to work?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible R: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: (D) 15
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 4 businessmen, how many possible team submissions are possible?
(A) 52
(B) 100
(C) 162
(D) 198
(E) 202
Rationale: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 4C2 =24
2) 2 tech1 businessman: 4C2 x 4C1 = 24
3) 3 tech0 businessmen: 4C3 = 4
Total:24+24+4 = 52
Answer: A
Answer: (A) 52
Question: Dan can fill Q cans of water in 7 minutes. If there are R cans of water in one gallon, how many gallons can Dan fill in 42 minutes?
(A) 6QR
(B) 6R/Q
(C) 6Q/R
(D) 7Q/R
(E) 7R/Q
Rationale: Dan can fill this number of cans in 42 minutes: (42/7)Q = 6Q.
One can is 1/R gallons.
Dan can fill 6Q*(1/R) = 6Q/R gallons of water in 42 minutes.
The answer is C.
Answer: (C) 6Q/R
Question: Running at the same constant rate, 15 identical machines can produce a total of 45 bags per minute. At this rate, how many bags could 150 such machines produce in 8 minutes?
(A)  9,00
(B)  1,800
(C)  2,700
(D)  3,600
(E)  4,800
Rationale: Let's take the approach that uses the answer choices to eliminate wasted time.
45/15 = 3 bags per minute per machine. 150 machines = 450 per minute. 8 minutes worth = 3600 bags.
Looking at the answers it is clear...we can only choose (D).
THE CORRECT ANSWER IS D.
Answer: (D)  3,600
Question: Given that N=a^3*b^4*c^5 where a, b and c are distinct prime numbers, what is the smallest number with which N should be multiplied such that it becomes a perfect square, a perfect cube as well as a perfect fifth power?
(A) a^3*b^4*c^5
(B) a^5*b^4*c^3
(C) a^2*b^3*c^5
(D) a^7*b^6*c^5
(E) a^27*b^26*c^25
Rationale: The powers of a, b and c have to be divisible by 2, 3 and 5 for N to be a perfect square, perfect cube and perfect 5th power.
LCM of 2, 3 and 5 is 30
The smallest integer N = (a^30)(b^30)(c^30)
Answer: E
Answer: (E) a^27*b^26*c^25
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 120 12-ounce smoothies?
(A)  120
(B)  150
(C)  180
(D)  240
(E)  600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
D
Answer: (D)  240
Question: Find the cost of fencing around a circular field of diameter 22 m at the rate of Rs.3 a meter?
(A) 288
(B) 132
(C) 772
(D) 207.3
(E) 261
Rationale: 2 * 22/7 * 11 = 69.1
69.1 * 3 = Rs.207.3
Answer: D
Answer: (D) 207.3
Question: In a sequence, each term is obtained by adding 5 to the preceding one. If the sum of the first 20 terms is equal to 350, what is the result of the addition of the first 30 terms?
(A) 1100
(B) 1175
(C) 1270
(D) 1275
(E) 1280
Rationale: a is first term and d = 5 since the preceding number is always greater than the previous one..
Now 20th term is a+19(5).
Sum of n terms is n/2(first term + last term)and here we have to get sum of 20 terms , we get 20/2 ( a + a+95) = 350 ( given sum of 20 terms is 300)
=> 10(2a+95) = 350
=> 2a+95 = 35
=> a = -30
Now to get sum of first 30 terms , we need to get 30th term value i.e. -30+29(5) = 115.
Sum of first 30 terms = 30/2( -30 + 115) =1275 .
Hence option D is correct answer..
Answer: (D) 1275
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds. The ratio of their speeds is?
(A) 3/1
(B) 4/1
(C) 3/3
(D) 3/5
(E) 5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 25 ==> 27 x + 17 y = 25 x + 25 y
==> 2 x = 8 y ==> x/y
= 4/1.
Answer:B
Answer: (B) 4/1
Question: The price of lunch for 15 people was $210.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A)  $11.73
(B)  $12.72
(C)  $13.80
(D)  $14.00
(E)  $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 210 is for 115 then we have to calculate for 100
for 115 210
for 100 x
so by cross multiplication we get 115x=100*210 => x=100*210/110 by simplifying we get x as 190.90 which is the price of lunch before gratuity so the gratuity is 19.10 so
as the question ask the average price person excluding gratuity is 190.90/15=12.72 so our answer is B)
Answer: (B)  $12.72
Question: Solve for x
if (log2)(1-x/2)=x-2.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (log2)(1-x/2)=x-2
or,log2-(x/2)log2=x-2
or,2log2-xlog2=2x-4
or,log4+4=2x+xlog2
or,4.60=2.3x i.e.x=2.
ANSWER:B
Answer: (B) 2
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.85 less, he could have gained 25%. What is the cost price?
(A) s.370
(B) s.375
(C) s.425
(D) s.350
(E) s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
85 ----- ? => 425
ANSWER:C
Answer: (C) s.425
Question: In a certain company, a third of the workers do not have a retirement plan. 10% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 120
(E) 91
Rationale: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (90*1 + 40*2)/3 = 170/3% are men
Total = 120*300/170 = 211
No. of women = 211 - 120 = 91
E
Answer: (E) 91
Question: Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%?
(A) 30000
(B) 40000
(C) 50000
(D) 60000
(E) 70000
Rationale: let first parrt is x and second part is y then x+y=50000----------eq1
total profit=profit on x +profit on y
7000=(x*10*1)/100 + (y*20*1)/100
70000=x+2y-----------------------------------eq2
70000=50000+y
so y=20000 then x =50000-20000=30000
first part =30000
ANSWER:A
Answer: (A) 30000
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/65
(B) 17/29
(C) 17/21
(D) 17/20
(E) 17/212
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D
Answer: (D) 17/20
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 75 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 97%
(C) 100%
(D) 107%
(E) 99%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.1 = 33
B = 20*1.5*1.1 = 33
C = 20*1.5*0.4 = 12
D = 20*0.6*1.75 = 21
E = 0
Total 33 + 33 + 12 + 21 = 99.
Answer: E.
Answer: (E) 99%
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 15%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
(A) 20%
(B) 25%
(C) 33.33%
(D) 40%
(E) 15%
Rationale: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.15(85)
so;
total weight=100g
fat=15g
15%
E
Answer: (E) 15%
Question: Jack and Jill are marathon runners. Jack can finish a marathon (40 km) in 4.5 hours and Jill can run a marathon in 4.0 hours.What is the ratio of their average running speed? (Jack: Jill)
(A) 14/15
(B) 15/14
(C) 8/9
(D) 5/4
(E) Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 40 /(9/2) = 80/9
Average Speed of Jill = 40/(4.0) = 10
Ratio of Average speed of Jack to Jill = (80/9)/10 = 8/9
Answer C
Answer: (C) 8/9
Question: A train sets off at 2 p.m. at the speed of 60 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 70 kmph. At what time the trains will meet?
(A) 0.37 p.m
(B) 0.20 p.m
(C) 0.30 a.m.
(D) 0.38 p.m
(E) 0.10 p.m
Rationale: D = 60 * 1 Â½ = 90 km
RS = 70 â€“60 = 10
T = 90/10 = 9 h
3.30 + 9 h = 0.30 a.m.
Answer: C
Answer: (C) 0.30 a.m.