RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A and B are two partially filled buckets of water. If 4 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 4 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
A.44/5
B.13
C.17
D.21
Answer: A.44/5
Explanation: Let Bucket A be A and Bucket B be B
Scenario 1
A-4 = 1/3 (B+4) ----> 3A-12 =B+4
Scenario 2
B-4 = 1/2 (A+4) -----> 2B-8 = A+4
From Scenario 1, B = 3A-16
Substitute B with this information in Stmt 2
2 (3A-16) -8 = A+4 ------> 6A -32-8 = A+4 ------> 6A- A = 40+4 ---> 5A= 44
A= 44/5, Answer choice A
Question: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 24.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
A.one
B.two
C.three
D.four
Answer: B.two
Explanation: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-24,4=75,6. There are only two numbers below 75,6. The answer is B
Question: If p^2 – 13p + 40 = l, and p is a positive integer between 1 and 10, inclusive, what is the probability that l < 0?
A.1/10
B.1/5
C.2/5
D.3/5
Answer: B.1/5
Explanation: p2 – 13p + 40 = l
so (p – 8)(p – 5) = l
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Question: The number that does not have a reciprocal is ____________.
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: O does not have any reciprocal
as 1/0 is not defined ANSWER:A
Question: One packet of flower seeds was enough to just fill the area of the smaller garden in #3. How
many packets of seed are needed for the larger garden? Round each answer to the nearest square
foot before continuing.
A.1 seed packet
B.2 seed packets
C.3 seed packets
D.4 seed packets
Answer: D.4 seed packets
Explanation: 3.14 x 32 = 28.26 sq. ft. area of small garden
28 sq. ft. rounded
3.14 x 62 = 113.04 sq. ft. area of large garden
113 sq. ft. rounded
113 ÷ 28 = 4.04 or 4 seed packets (rounded)
correct answer D
Question: Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A. 6.24
B. 8
C. 10
D. 15
Answer: A. 6.24
Explanation: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/35 = 10*12/7 = 17.14
Time difference = 6.24
Ans:A
Question: How many seconds does a train 125 meters long, traveling at 72 km/h, take to completely cross a bridge of 205 meters in length?
A.12.5
B.14.5
C.16.5
D.18.5
Answer: C.16.5
Explanation: 72 km/h = 72000/3600 = 20 m/s
Time = 330 / 20 = 16.5 seconds
The answer is C.
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(5) - f(2), in terms of k?
A. 3k
B. k
C. 7k - 1
D. k^2 + k
Answer: A. 3k
Explanation: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(5) and f(2):
f(5) = k(5) - k^2 = 5k - k^2
f(2) = 2k - k^2
f(5)-f(2)= 3k... Answer A
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 70 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.12 sec
B.24 sec
C.36 sec
D.60 sec
Answer: C.36 sec
Explanation: Relative speed = 70 + 30 = 100 km/hr.
100 * 5/18 = 250/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/250 = 36 sec.
ANSWER:C
Question: If a number p is prime, and 2p+3 = q, where q is also prime, then the decimal expansion of 1/q will produce a decimal with q-1 digits. If this method produces a decimal with 166 digits, what is the units digit of the product of p and q?
A.1
B.3
C.5
D.7
Answer: A.1
Explanation: 1/5 = 0.2.. (a repeating pattern one digit long)
A
Question: Find the odd man out. 15, 25, 30, 51, 85, 90, 115
A.15
B.25
C.51
D.90
Answer: C.51
Explanation: Explanation :
All except 51 are multiples of 5
Answer : Option C
Question: Plane leaves from Chelsea every 40 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
A.5:35 p.m
B.6:45 p.m
C.7:35 p.m
D.8:35 p.m
Answer: B.6:45 p.m
Explanation: Solution:
Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 40 min = 6:20 p.m
As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:20 p.m + 25 min = 6:45 p.m
Answer B
Question: 100 identical coins each with probability 'pp' showing up heads & tossed. If 0<p<10<p<1 and the probabilityof heads showing on 50coins is equal tothat of heads on 51 coins, then the value of pp is?
A.50/107
B.53/103
C.51/101
D.65/101
Answer: C.51/101
Explanation: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Question: All of the stocks on the over-the-counter market are designated by either a 7-letter or a 6-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A.a. 2(26^5)
B.b. 26(26^4)
C.c. 27(26^4)
D.d. 27(26^6)
Answer: D.d. 27(26^6)
Explanation: no of different stocks for 7-letter code = 26^7
no of different stocks for 6-letter code = 26^6
total = 26^7 + 26^6 = 26^6(26+1) = 27(26^6)
[Reveal]Spoiler:
Option D
Question: A certain junior class has 1,000 students and a certain senior class has 400 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?
A.3/20,000
B.1/3,600
C.9/2,000
D.1/60
Answer: A.3/20,000
Explanation: Total number of ways of choosing one student from each group is = 400 * 1000
Number of cases in which a sibling pair will be got is = 60
Thus the probability that the 2 students selected will be a sibling pair is
= 60 /(400 * 1000)
= 3/20,000
A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
A.Rs.24098
B.Rs.24090
C.Rs.24000
D.Rs.24006
Answer: C.Rs.24000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000)
= Rs.24000
Answer: C
Question: If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?
A.a/2
B.b/2
C.b/2
D.(a+b)/2
Answer: D.(a+b)/2
Explanation: A and B both have to be even to fulfill the condition.
a could be = 4, 6, 8 ...., b = 2,4, ....
so a - b = 2 (Even)
a/b= 2k (Even)
a/2=2k
a = 4k
so a must be multiple of 4
now try the options
Ans. D
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
A.288
B.299
C.266
D.450
Answer: D.450
Explanation: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
Answer: D
Question: The numbers 272738 and 232342, when divided by n, a two digit number, leave a remainder of 13 and 17 respectively. Find the sum of the digits of n?
A.7
B.8
C.9
D.4
Answer: A.7
Explanation: From the given information, (272738 - 13, 232342 - 17) are exactly divisible by that two digit number.
We have to find the HCF of the given numbers 272725, 232325.
HCF = 25.
So sum of the digits = 7.
Answer:A
Question: Two letters from the word KYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
A.14/27
B.15/28
C.27/28
D.16/28
Answer: C.27/28
Explanation: There are 6 consonants and 2 vowels in KYANTKAR .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : C
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
A.3%
B.5%
C.2.5%
D.4%
Answer: A.3%
Explanation: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.05 x 30 = 1.5
Therefore, total number of defective products = 3.
Answer : A
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
A.Rs. 50
B.Rs. 160
C.Rs. 200
D.Rs. 225
Answer: C.Rs. 200
Explanation: Let C.P. be Rs. x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
ANSWER:C
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time, how many books of the special collection were loaned out during that month?
A.20
B.30
C.35
D.40
Answer: A.20
Explanation: Total = 75 books.
65% of books that were loaned out are returned --> 100%-65%=35% of books that were loaned out are NOT returned.
Now, there are 68 books, thus 76-68=7 books are NOT returned.
{loaned out}*0.35=7 --> {loaned out}=20.
Answer: A.
Question: What is the 10th digit of (5!*4!*4! - 5!*4!*3!)/2880?
A.4
B.1
C.6
D.7
Answer: B.1
Explanation: (5!*4!*4! - 5!*4!*3!)/2880?
=5!*4!(4! -3!)/4!*5!
=4!-3!
=18
Sum of digits =1
Answer B
Question: How many trailing zeroes would be found in 4617!, upon expansion?
A.1150
B.1151
C.1152
D.1153
Answer: B.1151
Explanation: for no of trailing zeros we have to find the no of 5 in 4617!,because 4617!=1*2*3*4*5*.........4616*4617.
no of 5 in 4617!= (4617/5^1)+(4617/5^2)+(4617/5^3)+(4617/5^4)+(4617/5^5)+... up to 5^n 4617.
now no of 5 =4617/5 + 4617/25 + 4617/125 + 4617/625 +4617/3125
=923 + 184 + 36 + 7 + 1 ( only take the integer value )
=1151
so the no of zeros at the end of 4617! is 1151.
ANSWER:B
Question: A store has 10 bottles of juice, including 6 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 2 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
A.1/7
B.1/12
C.1/14
D.1/18
Answer: C.1/14
Explanation: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 2 bottles of apple juice is 6C2*4C4 = 15*1 = 15
P(selling 2 bottles of apple juice) = 15/210 = 5/70 = 1/14
The answer is C.
Question: At what time between 2 and 3 o'clock will the hands of a clock be together?
A.10x10/11
B.10x11/10
C.11x10/11
D.12x10/11
Answer: A.10x10/11
Explanation: At 2 o'clock, the hour is at 2 and the minute hand is at 12,i.e. they are 10 min. Spaces apart. To be together, the minute hand must gain 10 minutes over the hour hand. Now,55 minutes will be gained in 60 min. 10 minutes spaces will be gained in (60/55 x10) min. = 10x10/11 min. The hands will coincide at 10x10/11 min.past 2.
Answer A
Question: Goldenrod and No Hope are in a horse race with 6 contestants. How many different W arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
A. 720
B. 360
C. 120
D. 24
Answer: B. 360
Explanation: no hope finishing before goldenrod= 1/2 of the times
therefore the different arrangements W are 1/2* 6! = 360 = B
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
A.33
B.40
C.99
D.277
Answer: B.40
Explanation: We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer:B
Question: In a stack of boards at a lumber yard, the 25th board counting from the top of the stack is immediately below the 15th board counting from the bottom of the stack. how many boards are in the stack?
A.38
B.36
C.35
D.34
Answer: A.38
Explanation: 1 2 3 ... 14 15 16 ...................
..............25 24 ................. 1
So the number of boards = 25+13 =38
Option: A
Question: The wages earned by Robin is 20% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin?
A.18.75%
B.33%
C.30%
D.50%
Answer: B.33%
Explanation: Let wage of Erica = 10
Wage of Robin = 1.2*10 = 12
Wage of Charles = 1.6 *10 = 16
Percentage by which wage earned by Charles is more than that earned by Robin = (16-12)/12 * 100%
= 4/12 * 100%
=33%
Answer B
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 6 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?
A.2 miles
B.4 miles
C.4.8 miles
D.9.2 miles
Answer: D.9.2 miles
Explanation: Answer: D) 9.2 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*6*20/(6+20) = 9.2m/hr
the distance between schoolhome should be half of that. ie. 9.2 miles
Answer D
Question: An even and an odd integer are multiplied together. Which of the following numbers could not be the square of their product?
A.16
B.36
C.49
D.144
Answer: C.49
Explanation: 49 = 7^2 so it can not be the square of an even number multiplied by an odd number.
The answer is C.
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
A.19
B.88
C.77
D.14
Answer: D.14
Explanation: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs.Answer:D
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
A.277
B.268
C.287
D.480
Answer: D.480
Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer:D
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 4 specified cars. In how many ways cars can be arranged?
A.1210
B.650
C.576
D.1640
Answer: C.576
Explanation: we arranged 2 specified cars in 4 slots = 4!
remaining 4 cars in 4 slots = 4!
number of ways = 4!*4! = 576
correct option is C
Question: A train 150 m long crosses a platform 100 m long in 10 sec; find the speed of the train?
A.100
B.70
C.95
D.90
Answer: D.90
Explanation: D = 150 + 100 = 250
T = 10
S = 250/10 * 18/5 = 90 kmph.
Answer: D
Question: Tom drives from town T to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between T and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour?
A.12
B.20
C.24
D.30
Answer: B.20
Explanation: Let's assume that it takes 4 hours to go from point T to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
A.337
B.267
C.176
D.100
Answer: D.100
Explanation: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Question: If two men starting from same point, walking in the opposite directions with 9km/hr and 11km/hr as average speeds respectively. Then the distance between them after 8 hours is?
A.106
B.160
C.610
D.155
Answer: B.160
Explanation: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (9Ã— 8) + (11Ã— 8)
= 72+ 88
= 160 Km
Answer:B
Question: The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is?
A.22
B.27
C.18
D.19
Answer: C.18
Explanation: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice
(20-x)/(x-15) = 2/3 60 - 3x = 2x - 30
5x = 90 x = 18.
Answer: C
Question: 5,6,8,11,?,20,26,33
A.10
B.13
C.15
D.8
Answer: C.15
Explanation: The Pattern is + 1, + 2, +3, ...
11+4=15
Answer :C
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
A.Rs.6850
B.Rs.7268
C.Rs.6871
D.Rs.6150
Answer: D.Rs.6150
Explanation: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
Answer:D
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
A.31
B.35
C.32
D.38
Answer: A.31
Explanation: A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.
ANSWER A
Question: If |x|/6 < 1, which of the following must be true?
A.x>6
B.x<6
C.x=6
D.x=12
Answer: B.x<6
Explanation: if x <6, then If |x|/6 < 1
Like x=2
Then |2|/6 < 1
1/3<1
ANSWER B x<6
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 140?
A.3
B.6
C.28
D.42
Answer: C.28
Explanation: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
140 = 4*5*7
The GCF could be 4 or 28
The answer is C.
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
A.11 min
B.56 min
C.13 min
D.20 min
Answer: D.20 min
Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:51 -------- 5 4 --------- ? è 20
Answer:D
Question: A family X went for a vacation. Unfortunately it rained for 13 days when they were there. But
whenever it rained in the mornings, they had clear afternoons and vice versa. In all they enjoyed 11
mornings and 12 afternoons. How many days did they stay there totally?
A.16
B.18
C.20
D.13
Answer: B.18
Explanation: Explanation :
Clearly 11 mornings and 12 afternoons = 23 half days
=> Since 13 days raining means 13 half days.
=> So 23-13 =10 halfdays ( not effecetd by rain )
=> So 10 halfdays =5 fulldays
Hence ,
Total no. of days = 13+5 =18 days
Answer : B
Question: Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
A.1.5
B.1.7
C.2.3
D.2.5
Answer: C.2.3
Explanation: Ratio of A to B in the final mixture = 50-30 : 30-15 = 4:3
Gallons of A used = 4/7*4 = 2.28
ANSWER:C
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
A.32 6/7%
B.22 6/7%
C.72 6/7%
D.42 6/7%
Answer: D.42 6/7%
Explanation: Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Question: If the remainder is 8 when positive integer n is divided by 12, what is the remainder when n is divided by 6?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: Assume x is quotient here,
n=12x+8 ----------(1)
and n=6x+ ?
We can also write equation (1) as:
n=(12x+6)+2.
ie 6(2x+1)+2 ie the first term is perfectly divisible by 6.
So,the remainder left is 2.
So,answer (C) is right choice.
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.175 m
B.180 m
C.185 m
D.170 m
Answer: B.180 m
Explanation: Explanation:
Length of the train be â€˜Xâ€™
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
ANSWER IS B
Question: A and B start a business with Rs.5000 and Rs.7000 respectively. How should they share their profits at the end of one year?
A.3:5
B.3:4
C.5:7
D.3:2
Answer: C.5:7
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 7000 => 5:7
Answer:C
Question: In the quadratic equation ax2 - x - 12 = 0, if the sum of two roots is 1, what is the product of the two roots?
A.-12
B.-6
C.12
D.6
Answer: A.-12
Explanation: Explanation:
The sum of the roots of the quadratic equation ax2 + bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 1 and c = -12.
we get, sum of the roots = 1 / a = 1
a = 1
Product of the roots = -12 / 1 =-12
ANSWER: A
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 5. What are the coordinates of P?
A.(5/2, 5/2)
B.(7/2, 7/2)
C.(9/2, 9/2)
D.(11/2, 11/2)
Answer: D.(11/2, 11/2)
Explanation: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 5/6 of the distance from 3 to 6.
x = 3 + (6-3)*(5/6) = 3 + 5/2 = 11/2 = y
The answer is D.
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
A.1243 toys
B.1375 toys
C.1543 toys
D.1212 toys
Answer: B.1375 toys
Explanation: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 * 4 = 1375 toys
correct answer B