RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.10 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
A.12
B.15
C.16
D.28
Answer: A.12
Explanation: Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: A
Question: Find the value for x from below equation: x/3=-2?
A.-6
B.1
C.-2
D.-3
Answer: A.-6
Explanation: 1. Multiply both sides by 3:
x*3/3= -2/3
2. Simplify both sides:
x = -6
A
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
A.299
B.277
C.800
D.289
Answer: C.800
Explanation: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer:C
Question: The units digit of (35)^(87) + (93)^(49) is:
A.2
B.4
C.6
D.8
Answer: D.8
Explanation: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
49 has the form 4k+1, so the units digit of 93^49 is 3.
The units digit of powers of 5 is always 5.
3+5 = 8, so the units digit is 8.
The answer is D.
Question: There are 9 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
A.90
B.120
C.540
D.180
Answer: C.540
Explanation: Number of ways of selecting 2 fiction books = 9C2
Number of ways of selecting 2 non fiction books = 6C2
9C2 * 6C2 = 36 * 15 = 540
Answer: C
Question: A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate.
A.276.25
B.256.25
C.256.29
D.236.25
Answer: B.256.25
Explanation: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.500
(P)(8)(5)/100 = 500
P = 1250
C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years
=2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}
= 2500/400(441 - 400)
= 25/4(41) = 1025/4 = Rs.256.25.Answer:B
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when No boy gets more than one prize?
A.112
B.114
C.117
D.210
Answer: D.210
Explanation: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 7 ways. The second in 6 ways and the third in 5 ways. But fundamental principle, (7 x 6 x 5) ways = 210 ways
D
Question: An estate pay would be divided among five sons with the remainder donated to charity. One stipulation in the estate is that no one among the sons can receive an amount within 15% of another's amount. If one of the sons received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five sons?
A.$4096
B.$4804
C.$7892
D.$6736
Answer: B.$4804
Explanation: 1st - 10,000.
2nd - 0.85*10,000 = 8500
3rd - 0.85*8,500 = 7,225
4th - 0.85*7,225 = ~6,141.25
5th - 0.85*6,141.25 = ~5,220.0625
Range = 10,000 - 5,220 = 4,780
Answer: B.
Question: Ms. Feldman invested $10,000 for 1 year, part at 7% and part at 6.25%.
If she earned a total interest of $656.50, how much was invested at each rate?
A.4200 & 5800
B.4600 & 5400
C.9000 & 1000
D.7000 & 3000
Answer: A.4200 & 5800
Explanation: Interest rate of 4200/- =294
Interest rate of 5800/- =362.50
Answer is A
Question: If x > y^4 > z^7, which of the following statements could be true? I.x>y>z II.z=x III.x<z
A.I,III only
B.I only
C.II only
D.III only
Answer: B.I only
Explanation: Answer : B
Question: A focus group is currently made up of x red balls and y green balls. If 5 red balls and 4 green balls are added to the group, and if one ball is selected at random from the larger focus group, then what is the probability that a red ball is selected?
A.x/(x + 4)
B.y/(x + 5)
C.(x + 5)/(x + y + 9)
D.(y + 4)/(x + y + 9)
Answer: C.(x + 5)/(x + y + 9)
Explanation: x red balls
y green balls
x+4+y+5 is the total
=x+y+9
x+5 is the number of red balls
so (x + 5)/(x + y + 9)
the answer is C
Question: A train 275 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.8
B.6
C.5
D.15
Answer: D.15
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 275 * 3/55 = 15 sec.
Answer: D
Question: Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?
A.10 minutes
B.15 minutes
C.12 minutes
D.9 minutes
Answer: D.9 minutes
Explanation: Explanation:
Let B be turned off after X minutes.
Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1
=> x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1
=> x(2/75 + 1/45) + (30-x)2/75 = 1
=> 11x + 180 – 6x = 225
Therefore, x = 9 minutes
ANSWER: D
Question: Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
A.75
B.150
C.300
D.1200
Answer: D.1200
Explanation: I'd use backsolving for this question. Check option C first:
300 lenses = 150 usable lenses = 75 tubes = 75 eyepieces. We cannot buy 75 tubes or 75 eyepieces, so that not to have leftovers.
A and B are automatically out. Check D:
1200 lenses = 600 usable lenses = 300 tubes = 300 eyepieces. We CAN buy 300 tubes and 300 eyepieces, so that not to have leftovers.
Answer: D.
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.26 km/hr
B.17 km/hr
C.60 km/hr
D.77 km/hr
Answer: C.60 km/hr
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C
Question: J is 25% less than P and 20% less than T. T is x% less than P. What is the value of x?
A.93.5
B.90
C.6.75
D.6.25
Answer: D.6.25
Explanation: Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(x/100)]*P
i.e. 100-x = 100*T/P = 100*375/400 = 93.75
i.e. x = 6.25
Answer: Option D
Question: The monthly rent of a shop of dimension 10feet × 8feet is Rs.2400. What is the annual rent per square foot of the shop?
A.43
B.56
C.68
D.360
Answer: D.360
Explanation: Sol. Monthly rent per square feet = 2400/(10*8) = 30
& Annual rent per square feet
=12*30=360
Answer : D
Question: Tomy's age 18 years hence will be thrice his age four years ago. Find Tomy's present age?
A.12 years
B.13 years
C.15 years
D.17 years
Answer: C.15 years
Explanation: Let MTomy's present age be 'x' years.
x+ 18 = 3(x- 4)
=> 2x = 30 => x = 15 years.
C
Question: Sum of 42 odd numbers is?
A.1764
B.1774
C.1784
D.1794
Answer: A.1764
Explanation: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 42 odd numbers = 42^2 = 1764
ANSWER:A
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.196 where as B does not. In what ratio should they divide the second year's profit?
A.39:40
B.39:49
C.24:25
D.39:47
Answer: C.24:25
Explanation: Explanation:
3: 4
A = 3/7*196 = 84
384: 400
24:25
Answer:C
Question: A certain no. when divided by 35leaves a remainder 25, what is the remainder if the same no.be divided by 15?
A.2
B.4
C.7
D.8
Answer: B.4
Explanation: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
B
Question: The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?
A.0.05
B.0.15
C.0.45
D.0.5
Answer: C.0.45
Explanation: P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45
ANSWER:C
Question: A right triangle ARC has to be constructed in the xy-plane so that the right angle is at A and AR is parallel to x axis. The coordinates of A, R and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
A.63
B.336
C.567
D.3024
Answer: D.3024
Explanation: All the cordinates are integer hence,
possible AR values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee
A.36
B.46
C.50
D.52
Answer: B.46
Explanation: 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
At least one women = total - with out women
At least one women = 56 - 10 = 46
B)
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
A.4%
B.4.04%
C.4.23%
D.4.56%
Answer: B.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.240
B.377
C.2908
D.287
Answer: A.240
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: A
Question: he speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.25 kmph
B.15 kmph
C.17 kmph
D.95 kmph
Answer: B.15 kmph
Explanation: 90 * 10/60 = 15 kmph
Answer:B
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 66 days after his birthday?
A.Thursday
B.Friday
C.Saturday
D.Sunday
Answer: D.Sunday
Explanation: Day of week after 66 days after Arman's birthday = 7*9 + 3
Saturday as the period will have 9 weeks and 3 days .
The 3 days in the end will be Friday - Saturday and Sunday
Answer D
Question: What is the 9th term in this sequence?
1,3,4,11,19,30,53,87
A.120
B.129
C.140
D.180
Answer: C.140
Explanation: 1+3 =4 +0 =4
4+3 =7+4 =11
11+4 =15+4 =19
19+11=30+0 =30
30+19=49+4 =53
53+30=83+4 =87
87+53=140+0=140
so 9th term is 140
ANSWER:C
Question: Find the fraction which has the same ratio to 1/2 that 2/5 has to 3/7
A.1/2
B.2/12
C.14/30
D.3/8
Answer: C.14/30
Explanation: A : 1/2 = 2/5 : 3/7
As the product of the means is equal to the product of the extremes.
A*3/7 = 1/2 * 2/5
A*3/7 = 2/10
A = 14/30 => A = 14/30
ANSWER:C
Question: The ratio of the ages of Maala and Kala is 3 : 5. The total of their ages is 3.2 decades. The proportion of their ages after 0.8 decades will be
[1 Decade = 10 years]
A.6:5
B.5:7
C.4:5
D.7:9
Answer: B.5:7
Explanation: Let, Maala’s age = 3A and Kala’s age = 5A
Then 3A + 5A = 32
A = 4
Maala’s age = 12 years
and Kala’s age = 20 years
Proportion of their ages after 8 is = (12 + 8) : (20 + 8)
= 20 : 28
= 5 : 7
Answer : B
Question: The smallest 3 digit prime number is
A.A)103
B.B)101
C.C)109
D.D)113
Answer: B.B)101
Explanation: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
B)
Question: John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
A.95/8
B.93/8
C.90/8
D.12
Answer: A.95/8
Explanation: In such questions, you need to start from the end. Last 4 days John works alone and completes 5 * (1/20) = 1/4 of the work.
So 3/4 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/20 + 1/12 = 8/60
Time taken to complete 3/4 of the work = (3/4)/(8/60) = 45/8 days.
So total number of days taken to complete the work = 45/8 + 5 = 95/8 days.
A
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
A.Rs.5000
B.Rs.25000
C.Rs.7500
D.Rs.8500
Answer: A.Rs.5000
Explanation: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
ANSWER:A
Question: There is a 20% chance that Lions will not win at all during the whole season. There is a 30% chance that Tigers will not play at all in the whole season. What is the greatest possible probability that the Lions will win and Tigers will play during the season?
A. 55%
B. 60%
C. 70%
D. 72%
Answer: C. 70%
Explanation: There is a 20% chance that Lions will not win at all during the whole season
We can infer that there is 80% chance Lions will win .
Similarly There is a 30% chance that Tigers will not play at all in the whole season
We can also infer that there is 70% chance that Tigers will play.
Answer C
Question: If A and B are two events such that P (A) = 1/2, P (B) = 3/4 and P (A n B) = 3/8,
find P (not A and not B).
A.A)1/7
B.B)1/8
C.C)1/9
D.D)1/10
Answer: B.B)1/8
Explanation: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (1/2 + 3/4 - 3/8)
P(not A and not B) = 1 - (7/8)
P(not A and not B) = 1/8.
B
Question: If b= (a-1)(a+2), then what is the least possible value of b?
A.-9/4
B.3
C.2
D.1
Answer: A.-9/4
Explanation: Answer : A
Question: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
A.36
B.45
C.50
D.55
Answer: A.36
Explanation: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36.
A
Question: If a and y are integers and (15^a + 15^(a+1))/4^y = 15^y what is the value of a?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: \frac{15^a( 1+ 15)}{4^y} = 15^y
(15^a . 4^2 ) / 4^y = 15^y. 4^0
15^a . 4^(2-y) = 15^y. 4^0
Equating the powers, a = y; 2-y = 0; So a = y = 2=A
Question: 6 points are marked on a straight line and another 7 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
A.9
B.105
C.196
D.21
Answer: A.9
Explanation: assuming that the top line can have either 2 points or 1 point...
6! / 1!5! - 6! / 2! 4! yields 9.
A
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
A.200m
B.225m
C.245m
D.250m
Answer: C.245m
Explanation: Speed = 45/18 x	5	m/sec	= 25/2	m/sec.
Time = 30 sec.
Let the length of bridge be x metres.
Then,	130 + x/ 30	=	25/2
2(130 + x) = 750
x = 245 m.
ANSWER IS C
Question: Express 25 mps in kmph?
A.23
B.88
C.90
D.27
Answer: C.90
Explanation: 25 * 18/5 = 90 kmph
Answer:C
Question: Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?
A.77km
B.56km
C.25.9km
D.48.72km
Answer: D.48.72km
Explanation: 1 day=2 trips,
3 days=2*3=6 trips
6*8.12= 48.72km.
Answer is D.
Question: If the number of 53,n87, where n represents the hundreds digit, is a multiple of 3, then the value of n could be which of the following?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 5+3+n+8+7 = multiple of three
or, 23 + n = multiple of 3.
If n=1, 23 + n =24,which is a multiple of 3.
Hence answer is B.
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is
A.7/19
B.6/19
C.5/19
D.4/19
Answer: A.7/19
Explanation: Explanation:
Please remember that Maximum portability is 1.
So we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs.
So here we go,
Total cases of non defective bulbs
16C2=16∗15/2∗1=120
total cases = 20C2=20∗19/2∗1=190
probability = 120/190=12/19
P of at least one defective = 1−12/19=7/19
Option A
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
A.Rs. 3000
B.Rs. 4000
C.Rs. 5000
D.Rs. 6000
Answer: B.Rs. 4000
Explanation: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
B)
Question: The mean of 50 observations is 200. But later he found that there is decrements of 34 from each observations. what is the the updated mean is ?
A.165
B.166
C.190
D.198
Answer: B.166
Explanation: 166
Answer is B
Question: X and Y run a 50 m race,where X beats Y by 5 m. To do a favor to Y, X starts 5 m behind the starting line in a second 50 m race. Both run at the same previous speed. Which of the following is true?
A.X Beats Y by 2m
B.X Beats Y by 0.5 m
C.Y Beats X by 10m
D.Y Beats X by 11m
Answer: B.X Beats Y by 0.5 m
Explanation: Let's suppose that the speed of X is 5m/s and that the speed of Y is 4.5m/s.
So, in the first race, the results are the following:
X crosses the finish line in 10s. In other words, X has run 50 m in 10 s.
In 10s, Y has run 45 meters.
Therefore, there is the difference of 5 meters mentioned in the question.
Now, let's review the second race.
In 11 seconds, X can complete the 50 meters race. We have to remember that X is 5 meters behind the starting line.
But in 11 seconds, Y has covered (45+4.5 ) =49.5 meters. Also, it is important to notice that in 11 seconds Y cannot arrive to the finish line.
So, 50- 49.5 = 0.5 meter
Answer: B
Question: 78, 64, 48, 30 10, (...)
A.-12 number
B.-14
C.2
D.8
Answer: A.-12 number
Explanation: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Question: Working together, John and Jack can type 10 pages in one hour. If they would be able to type 12 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
A.3/1
B.1/3
C.4/1
D.1/4
Answer: C.4/1
Explanation: Lets say John types x pages an hour and Jack types y pages an hour.
We know that x+y=10
Jack increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=12
We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=2 so y=8 ... so x=2
(y/x)=8/2 =4/1
Answer is (C)
Question: 3^x + 9*3^-x = 6 What is the value of x?
A.-1
B.1
C.0
D.1/2
Answer: B.1
Explanation: let 3^x = t
t+9/t =6
t^2 -6t +9 =0
(t-3)^2=0
t-3=0
t=3
3^x=3
x=1
Ans: B
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
A.25
B.23
C.19
D.18
Answer: C.19
Explanation: Explanation:
Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years. Answer: C
Question: The sum of money will be double itself in 10years and simple interest find rate of interest?
A.10%
B.15%
C.20%
D.25%
Answer: A.10%
Explanation: T = 10 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/10x =10%
Answer is A
Question: Chocolate bars are sold in packages of four or nine only. If Mark bought 97 chocolate bars exactly, what could be the number of large packs Mark bought?
A.3
B.4
C.8
D.9
Answer: D.9
Explanation: Let number of packs of four = f
let number of packs of nine = n
4f + 9n = 97
Now , we need to test for values of n.
Since sum 97 is odd and 4f will always be even , n can't be even .
Now , we can test for values e = 2 , 4 and 6
4*4 + 9*9 = 16 + 81 = 97
Answer D
Question: For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
A.1/9
B.4/9
C.5/9
D.2/3
Answer: C.5/9
Explanation: Paul picks A with the same probability as A’schances of winning
So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning
= 2/3 * 2/3 + 1/3 * 1/3
= 5/9
ANSWER:C
Question: If Susan takes 8 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
A.xy/8
B.8x/(60y)
C.60xy/8
D.xy/480
Answer: B.8x/(60y)
Explanation: The answer is B.
She runs x yards in 8x/y seconds =8x/60y minutes.
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
A.Rs. 10,500, Rs. 13,500, Rs. 16,500
B.Rs. 10,600, Rs. 13,500, Rs. 96,500
C.Rs. 10,500, Rs. 73,500, Rs. 16,500
D.Rs. 10,500, Rs. 18,500, Rs. 16,500
Answer: A.Rs. 10,500, Rs. 13,500, Rs. 16,500
Explanation: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer:A
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
A.44
B.73
C.53
D.32
Answer: A.44
Explanation: A
44
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Question: Two taps can separately fill a cistern 5 minutes and 10 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in?
A.7
B.8
C.6
D.4.2
Answer: D.4.2
Explanation: 1/5 + 1/10 - 1/x = 1/15
x = 30/7 = 4.2
Answer: D