RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Walking 7/6 of his usual rate, a boy reaches his school 5 min early. Find his usual time to reach the school?
A.22
B.28
C.99
D.35
Answer: D.35
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
5 --------- ?
= 35 m
Answer:D
Question: 40, 45, 50, 55, 60, 75, 75, 90, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69.
1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
Question: How many diagonals does a polygon with 15 sides have, if one of its vertices does not connect to any diagonal?
A.80
B.90
C.77
D.88
Answer: C.77
Explanation: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 15-1 then 14*(14-3)/2 = 77
Correct Option:C
Question: What is the least value of x. So that 1894x is divisible by 3?
A.2
B.5
C.1
D.6
Answer: A.2
Explanation: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
1+ 8 + 9 + 4+ x= 22 +x
Least value of X may be 2
Therefore 22 +2 = 24 is divisible by 3.
A
Question: Which of the following number is divisible by 24 ?
A.31214
B.61212
C.512216
D.3125832
Answer: D.3125832
Explanation: Explanation :
24 = 3 × 8 where 3 and 8 are co-prime numbers. 3 and 8 are also factors of 24. Hence
Hence if a number is divisible by 3, and 8, the number will be divisible by their product 24 also.
If a number is not divisible by 3 or 8, it is not divisible by 24
You must learn Divisibility Rules to say whether a given number is divisible by another number
without actually performing the division.
31214 is not divisible by 3 and 8 => 31214 is not divisible 24
61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24
512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24
3125832 is divisible by 3 and 8 => 3125832 is divisible 24. Answer : Option D
Question: Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
A.22
B.25
C.26
D.27
Answer: D.27
Explanation: Solution
Given Data
3 positive integers
Average of a, b, and c = 22
So, a+b+c3a+b+c3 = 66 or a + b + c = 66
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 66 (b and c are equal and b, the median, is a + 13)
Or 3a = 40 or a = 13.33
So, b = c = 10+ 13.33 = 23.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 66
Or 3a = 39 or a=13 The value of the numbers is an integer
If a = 13, b = 26 and c = 27
The least value for c that satisfies all these conditions is 27.
Correct answer is choice D.
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-a=2
II. a-c is positive integer
III. (a+b+c)/3 is an integer
A.I
B.II
C.I and III
D.II and III
Answer: C.I and III
Explanation: If a, b, c are consequitive positive integers and a<b<c, which of the following must be true?
1. c-a=2
2. abc is an even integer
3. (a+b+c) /3 is an integer
1.
a=a
b=a+1
c=a+2
c-a=a+2-a=2.
Correct
2. a-c is negative because a<c - false
3. (a+b+c) /3 is an integer
Again;
a=a
b=a+1
c=a+2
a+b+c=(a+a+1+a+2)=3a+3
3a is always divisible by 3
3 is divisible by 3.
Thus3a+3is also divisible by 3.
Rule:
if integer x is divisible by n
and
integer y is divisible by n
then; x+y must be divisible by n
Correct.
Ans :C
Question: 9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
A.90%
B.85%
C.80%
D.75%
Answer: D.75%
Explanation: D. 75%
Question: what is the least number by which 15,625 must be divided to get a number perfect square
A.21
B.25
C.24
D.40
Answer: B.25
Explanation: 15,625/25=625
625=(25)^2
Ans-25
ANSWER:B
Question: The ratio of the adjacent angles of a parallelogram is 5 : 13. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
A.168°
B.134°
C.156°
D.224°
Answer: B.134°
Explanation: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 5x + 13x = 180°
Or, 18x = 180°
Or, x = 10°
Hence the angles of the parallelogram are 50° and 130°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 50° + 84° = 134°
Answer : B
Question: A candidate got 31% of the votes polled and he lost to his rival by 2451 votes. How many votes were cast?
A.6150
B.6250
C.6350
D.6450
Answer: D.6450
Explanation: Let x be the total number of votes.
0.31x + 2451 = 0.69x
0.38x = 2451
x = 2451/0.38 = 6450
The answer is D.
Question: Calculate the area of a triangle, if the sides are 30 cm, 21 cm and 10 cm, what is its area?
A.145 cm2
B.105 cm2
C.125 cm2
D.115 cm2
Answer: B.105 cm2
Explanation: The triangle with sides 30 cm, 21 cm and 10 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle = 1/2 * 21 * 10 = 105 cm2
Answer: B
Question: A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 10% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?
A.$3996
B.$3395
C.$2892
D.$3736
Answer: B.$3395
Explanation: 1st - 10,000.
2nd - 0.9*10,000 = 9000
3rd - 0.9*9,000 = 8,100
4th - 0.9*8,100 = ~7,290
5th - 0.9*7,290 = ~6,561
Range = 10,000 - 6,561 = 3,439.
Answer: B.
Question: Find the average of all prime numbers between 30 and 50?
A.39.8
B.31.2
C.12.4
D.17.9
Answer: A.39.8
Explanation: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 =199/5 =39.8.
Option A
Question: a pizza which is thin is cut into 'x' pieces by 4 straight lines then the lowest possible value of x is?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: 4 parallel lines will give minimum number of pieces.
5 pieces.
ANSWER:C
Question: A person takes 5hrs 45 min in walking to a place and riding back. He would have gained 3hrs by riding both ways. The time he would take to walk both ways is?
A.5 hours 45 min
B.5 hours 55 min
C.6 hours 45 min
D.8 hours 45 min
Answer: D.8 hours 45 min
Explanation: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 3 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 3 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 3 hours = 8 hours 45 min
D
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
A.1261
B.1228
C.2773
D.288
Answer: A.1261
Explanation: A = 8000(21/20)3
= 9261
= 8000
---------
1261.Answer: A
Question: A survey was sent to 70 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
A.2%
B.6%
C.4%
D.28%
Answer: C.4%
Explanation: case 1: (7/70)=x/100
x=10%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-10)%=4%
Answer is C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
A.125/167
B.125/186
C.125/126
D.125/186
Answer: C.125/126
Explanation: Required probability
= 1 - 1/126
= 125/126
Answer: C
Question: S is a set containing 8 different positive odd primes. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
A. The median of S is prime.
B. The median of T is prime
C. The median of S is equal to the median of T.
D. The sum of the terms in S is prime.
Answer: D. The sum of the terms in S is prime.
Explanation: Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The median of S is prime.
Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.
(B) The median of T is prime.
Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.
(D) The sum of the terms in S is prime.
Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.
(E) The sum of the terms in T is prime.
Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.
D
Question: Total number of students in a class is 95. if the total number of girls in the class is 45, then the ratio of total number if boys to total number girls is
A.9:10
B.7:8
C.10:9
D.9:11
Answer: C.10:9
Explanation: Let the total number of boys in the class be x.
Then, according to the question,
x + 45 = 95
x = 95 - 45 = 50
Hence, the required ratio of total number of boys to total number of girls = B:G = 50:45 = 10:9
ANSWER :C
Question: If there are 210 workers in a factory, and on a certain day, 198 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
A.94.3%
B.95.3%
C.93.3%
D.92.3%
Answer: A.94.3%
Explanation: 198/210*100=94.28
94.3%
correct answer A
Question: A Pentagon marked P,Q,R,S and T on its five sides. five colors, black, brown,blue,violet and white are used to paint the five sides of the pentagon. If the adjacent faces are painted with the different colors, in how many ways can the pentagon be painted?
A.5
B.9
C.12
D.6
Answer: A.5
Explanation: If the base of the pentagon is Black, then in order the adjacent faces to be painted with the different colors. 4 side faces can be painted in Brown-White-Violet-Blue Brown-White-Violet-Blue OR White-Blue-Violet-Brown White-Blue-Violet-Brown .
But we can have the base painted in either of the four colors, thus the total number of ways to paint the Pentagon is 5*1=5.
Answer: A.
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A.733 1/3%
B.163 1/3%
C.33 1/3%
D.213 1/3%
Answer: C.33 1/3%
Explanation: Explanation:
1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Question: Convert the 13/36 m/s into kilometers per hour?
A.1.6kmph
B.2.3 kmph
C.1.3 kmph
D.1.7 kmph
Answer: C.1.3 kmph
Explanation: 13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.Answer: C
Question: In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 12,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: this is equivalent to :-
2x * 4y * 5z = 12000
y = z (given)
2x * 4y * 5y = 12000
2x * y^2 = 12000/20
2x * y^2 = 600
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 3 as
2* 3 * y^2 =600
y^2 = 100
y =10
Number of red chips = 3 hence C
Question: A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours.
What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
A.1
B.3
C.2
D.5
Answer: A.1
Explanation: A
In one hour,
Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Soln 2:
Let V be the total volume of the tank. From equation (1),
Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.
Substituting in equation (2),
Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).
Using the above result in equation (1),
Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].
Note that V cancels out on simplifying the above expression.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Question: A train passes a station platform in 36 sec and a man standing on the platform in 24 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.288
B.180
C.881
D.1277
Answer: B.180
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 24 = 360 m.
Let the length of the platform be x m . Then,
(x + 360)/36 = 15 => x = 180 m.
Answer: B
Question: Find the value of (950+ 220/900) × 900
A.854542
B.856945
C.758965
D.855220
Answer: D.855220
Explanation: (855000+220)/900 * 900 = 855000+220 = 855220
Answer : D
Question: Find the greatest number that will divided 43,91 and 183 so as to leave the same remainder in each case
A.4
B.7
C.9
D.13
Answer: A.4
Explanation: Solution
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4. Answer A
Question: The ratio Q , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
A.79 litres
B.78 litres
C.77 litres
D.152 liters
Answer: C.77 litres
Explanation: I guess it should be
the ratio Q, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.76
B.15
C.18
D.16
Answer: C.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: C
Question: A child must place 4 different toys in 5 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
A.5^4
B.6^4
C.4^6
D.4^4
Answer: A.5^4
Explanation: there are 4 different bins and each of the toy can go to any of these bins..
so answer 5âˆ—5âˆ—5âˆ—5=5^4
ANSWER:A
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.48%
B.24%
C.44%
D.46%
Answer: C.44%
Explanation: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2000. then his monthly salary is
A.Rs. 10000
B.Rs. 6000
C.Rs. 8000
D.Rs. 4000
Answer: A.Rs. 10000
Explanation: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 2000
â‡” 20 / 100x = 2000
â‡” x = 2000 Ã— 5 = 10000.
Answer A
Question: The radius of the two circular fields is in the ratio 4: 5 the area of the first field is what percent less than the area of the second?
A.42%
B.39%
C.38%
D.36%
Answer: D.36%
Explanation: r = 4 Ï€r2 =16
r = 5 Ï€r2 = 25
25Ï€ â€“ 9Ï€
100 ---- ? => 36%.Answer:D
Question: The operation is defined for all integers a and b by the equation ab = (a - 1)(b - 1). If x20 = 190, what is the value of x ?
A.10
B.12
C.11
D.13
Answer: C.11
Explanation: ab = (a - 1)(b - 1)
x20 = (x-1)(20-1) = 190 --> x-1=10 --> x=11
Answer: C
Question: An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 15% profit, offers a discount of 15% on the marked price. What is his actual profit on the sales?
A.12.50 %
B.27.50 %
C.14 %
D.14.50 %
Answer: B.27.50 %
Explanation: Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 150.
S.P. = 85% of Rs. 150 = Rs. 127.5.
∴ Gain% = 27.50%.
Answer B
Question: John bought Bicycles at 6 for Rs 10000.What is the profit or loss Percentage after selling Bicycles at 5 for Rs 10000.
A.30%
B.50%
C.20%
D.60%
Answer: C.20%
Explanation: C.P. of 6 Bicycles = Rs10000
C.P. of 1 Bicycle = Rs10000/6=Rs 5000/3
S.P. of 5 Bicycles = Rs10000
S.P of 1 Bicycle= Rs 2000
Therefore, Profit Percentage={(2000-5000/3)/(5000/3)}100=20%
Answer: Option C
Question: Look at this series: 70, 71, 76, __, 81, 86, 90, 91, ... What number should fill the blank?
A.70
B.71
C.80
D.96
Answer: C.80
Explanation: 70,71,76
80,81,86
90,91,96
ANSWER:C
Question: A container contains 40lit of milk. From this container
4 lit of milk was taken out and replaced by water.
This process was repeated further two times.
How much milk is now contained by the container?
A.19.16 lit
B.29.16 lit
C.9.16 lit
D.26.16 lit
Answer: B.29.16 lit
Explanation: Amount of milk left after 3 operations = 40(1-4/40)3lit
=(40*9/10*9/10*9/10)
= 29.16 lit
ANSWER : B 29.16 lit
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
A.3000
B.3300
C.3400
D.3700
Answer: A.3000
Explanation: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
A)
Question: If s,u, and v are positive integers and 2s=u+2v, which of the following must be true?
i. u>v
ii. u is not equal to v
iii. s=u
A.None
B.I only
C.II only
D.III only
Answer: B.I only
Explanation: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.
Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option I must be true.
Answer: B
Question: If x% of y is 100 and y% of z is 200, then find the relation between x and z.
A.z = x
B.2z = x
C.z = 2x
D.None of above
Answer: C.z = 2x
Explanation: Explanation:
It is , y% of z = 2(x% of y)
=> yz/100 = 2xy/100
=> z = 2x
Option C
Question: A trader bought a car at 10% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A.118
B.110
C.112
D.126
Answer: D.126
Explanation: Original price = 100
CP = 80
S = 80*(140/100) = 126
100 - 126 = 26%
Answer: D
Question: A certain roller coaster ride has between 80 and 110 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster. How many riders are in the line?
A.82
B.87
C.90
D.102
Answer: D.102
Explanation: let 'x' be the number of riders. Given
x=5k+2 and x=6q also x is between 80-110
so multiples of 5= 80, 85, 90, 95, 100, 105, 110
multiples of 6= 84, 90, 96, 102, 108
Condition: If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on the roller coaster.
only value satisfying this condition within a group of 80-110 riders is 102.
ANSWER:D
Question: If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 8 € (4 € 5) =
A.80
B.120
C.160
D.640
Answer: D.640
Explanation: working inside out,
(4 € 5) = 2*4*5 = 40
8 € 40 = 2*8*40 = 640
Hence, answer is D
Question: The ratio of the volumes of two cubes is 729 : 343. What is the ratio of their total surface areas?
A.81 : 49
B.81 : 122
C.81 : 124
D.81 : 126
Answer: A.81 : 49
Explanation: Ratio of the sides = 3√729 : 3√343 = 9 : 7
Ratio of surface areas = 9^2 : 7^2 = 81 : 49
Answer: Option A
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.39 sec
B.87 sec
C.36 sec
D.16 sec
Answer: A.39 sec
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 150 = 390 m.
Time taken = 390/10 = 39 sec.
Answer: A