RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples?
A.1:7
B.1:5
C.1:4
D.1:2
Answer: C.1:4
Explanation: To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars.
To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.
45 split in the ratio 1:4 gives 9 and 36.
9 apples split into 3 apples each will give $3.
36 apples split into 6 apples each will give $6.
They add up to $9 so we have hit the right answer.
Answer (C)
Question: Milton has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
A.52
B.56
C.50
D.48
Answer: C.50
Explanation: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 50 that is c is the option which is divisible by 5.
so answer is C
Question: 70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 90 percent have washing machines. At least what percentage of employees has all four gadgets?
A.(a) 15%
B.(b) 5%
C.(c) 10%
D.(d) 20%
Answer: A.(a) 15%
Explanation: so 30% employees don't have VCD devices.
25% employees don't have MO
20% employees don't have ACs
10% employees don't have WM
Summ of employees that don't have some device = 30%+25%+20%+10% = 85% < 100%
So definitely at least 15% employees have 4 devices.
ans: A
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 8, what is the greatest number of four-digit extensions that the company can have?
A.4
B.6
C.12
D.16
Answer: C.12
Explanation: Since the phone number must be even, the unit's digit can be either 2 or 8.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 8 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:C
Question: If 4/(1 + 3/x) = 1, then x =
A.3
B.1
C.1/3
D.-1/3
Answer: B.1
Explanation: The expression 4/(1 + 3/x) = 1 should have been equal to something .
If 4/(1 + 3/x) = 1
=> 4x/(x+3)=1
=> 4x=x+3
=>3x = 3
=>x = 1
Correct Option: B
Question: A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than six times?
A.37/256
B.56/256
C.65/256
D.9/256
Answer: D.9/256
Explanation: More than 5 times tails = 7times+8times = 8C7 + 8C8 = 9
2 2 2 2 2 2 2 2
2^8 times total events and 9 events where tails side up .
So probability = 9/2^8 = 9/256 (Answer D)
Question: There are two alloys madeup of copper and aluminium. In the first alloy copper is half as much as aluminium and in the second alloy copper is thrice as much as aluminium. How many times the second alloy must be mixed with first alloy to get the new alloy in which
copper is twice as much as aluminium?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: first alloy second alloy
C Al C Al
Required alloy
C Al
2 1
Thus, Copper in first alloy = 1/3
copper in second alloy = 3/4
copper in required alloy =2/3
ANSWER:C
Question: Find the odd man out: 8, 12, 16, 21, 24, 28, 32
A.21
B.24
C.28
D.32
Answer: A.21
Explanation: Each number is a multiple of 4, except 21.
2*4=8
3*4=12
4*4=16
5*4=20
6*4=24
7*4=28
8*4=32
ANSWER: A
Question: If P is a prime number greater than 3, what is the remainder when P^2 is divided by 4.
A.1
B.3
C.2
D.4
Answer: A.1
Explanation: take square of any prime number
remainder will be 1
Ans A
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 420 m, its area is?
A.150
B.882
C.277
D.210
Answer: D.210
Explanation: 5x + 12x + 13x = 420 => x = 14
a = 70, b = 168, c = 182
S = (70 + 168 + 182)/2 = 210
Answer: D
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 5 meters apart,then at what speed is the train traveling?
A.100km/hr
B.110km/hr
C.50km/hr
D.150km/hr
Answer: D.150km/hr
Explanation: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*50 = 2500m = 2.5km
Speed = 60*2.5=150km/hr
Answer is D
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage?
A.7
B.1
C.5
D.3
Answer: C.5
Explanation: The difference of two successive amounts must be the simple interest in 1 year on
the lower amount of money.
S.I = 18522/- - 17640/- = Rs. 882/-
Rate of interest = (882/17640) × (100/1) => 8820/1764 = 5%
Principal = Amount/(1 + R/100)n
= 17640/(1 + 5/100)2
= 17640/(21/20 × 21/20)
= 17640/(1.05 × 1.05)
= 17640/1.1025
= 16000
Thus the principal is Rs.16000/- and the rate of interest is 5%
Answer is C.
Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, four orange ice pops, and four lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
A.3/5
B.5/7
C.8/11
D.11/15
Answer: C.8/11
Explanation: P(2 cherry) = 3/11 * 2/10 = 6/110
P(2 orange) = 4/11 * 3/10 = 12/110
P(2 lemon) = 4/11 * 3/10 = 12/110
P(2 of the same flavor) = 30/110
P(2 different flavors) = 1 - 30/110 = 80/110 = 8/11
The answer is C.
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings are divisible by 11?
A.4x + 6y
B.4x - 9y
C.4x + 6y
D.9x + 4y
Answer: B.4x - 9y
Explanation: By hit and trial method, we get x=5 and y=1 such that 3x + 7y = 15 + 7 = 22 is a multiple of 11.
Then
(4x + 6y) = (4 × 5 + 6 × 1) = 26 which is not divisible by 11
(x + y + 4) = (5 + 1 + 4) = 10 which is not divisible by 11
(9x + 4y) = (9 × 5 + 4 × 1) = 49 which is not divisible by 11
(4x - 9y) = (4 × 5 - 9 × 1) = 20 - 9 = 11 which is divisible by 11
Answer is B
Question: If the sum of a number and its square is 272, What is the number?
A.16
B.77
C.25
D.87
Answer: A.16
Explanation: Explanation:
Let the integer be x.
Then, x + x2 = 272
x2 + x - 272 = 0
(x + 17) (x – 16) = 0
x = 16
ANSWER: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
A.1/455
B.1/452
C.1/459
D.1/455
Answer: A.1/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Question: The compound ratio of 2/3, 6/7, 1/5 and 1/8 is given by?
A.7/98
B.1/48
C.1/98
D.3/350
Answer: D.3/350
Explanation: 2/3 * 6/7 * 1/5 * 1/8 = 12/1400 = 3/350
ANSWER:D
Question: The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80% capacity, how long will it take to drain the pool?
A.1000
B.1400
C.1200
D.800
Answer: D.800
Explanation: volume of pool = 60*100*10 cu.ft , 80% full = 60*100*10*0.8 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 60*100*10*0.8/ 60 min= 800 min
D
Question: Rs.1210 were divided among 3 person P, Q, R so that P:Q=5:4 and Q: R=9:10. Then R gets the amount?
A.Rs.300
B.Rs.400
C.Rs.480
D.Rs.500
Answer: B.Rs.400
Explanation: P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.
So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is = ( 45 + 36 + 40 ) =121.
R share of amount is Rs (1210 x 40 / 121) = Rs.400.
B
Question: If 40 men can make 30 boxes in 20 days, How many more men are needed to make 60 boxes in 25 days?
A.28
B.24
C.22
D.26
Answer: B.24
Explanation: Explanation :
Given that 40 men can make 30 boxes in 20 days
Let x more men are needed to make 60 boxes in 25 days
Then (40 + x) men can make 60 boxes in 25 days
More boxes, more men(direct proportion)
More days, less men(indirect proportion)
Hence we can write as
⇒ 30 × 25 × (40 + x) = 60 × 20 × 40
⇒ 25 × (40 + x) = 2 × 20 × 40
⇒ 5 × (40 + x) = 2 × 4 × 40
⇒ (40 + x) = 2 × 4 × 8 = 64
⇒ x = 64 − 40 = 24. Answer : Option B
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
A.4:8
B.1:4
C.6:2
D.3:1
Answer: B.1:4
Explanation: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
ANSWER:B
Question: 10 play kabadi, 30 play kho kho only, 5 play both gmaes. Then how many in total?
A.30
B.35
C.38
D.40
Answer: D.40
Explanation: 10 play kabadi =>n(A)=10,
5 play both gmaes.=> n(AnB)=5
30 play kho kho only,=>n(B)=n(B only)+n(AnB)=30+5=35
Total => n(AUB)= n(A)+n(B)-n(AnB)
= 10+35-5
= 40
ANSWER:D
Question: A train running at the speed of 300 km/hr crosses a pole in 15 seconds. What is the length of the train?
A.1200 m
B.1250 m
C.1300 m
D.1350 m
Answer: B.1250 m
Explanation: Speed=(300 * 5/18) m/sec
= (250/3) m/sec Length of the train
= (Speed x Time)
= (250/3 * 15) m = 1250 m.
Answer:B
Question: A superhero flies at an incredible rate of 1000 kilometers per minute. What is her speed in miles per hour? [1km = 0.6 miles]
A.6000
B.36000
C.60000
D.600
Answer: B.36000
Explanation: To calculate the equivalent of miles in a kilometer
0.6 kilometers= 1 mile
1000 kilometers = (0.6)*1000 = 600 miles
Speed in miles per minute = 600 = 600
1 hour = 60 minutes
Speed in miles per hour = 600 * 60 = 36,000
Correct Answer - B
Question: Tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A.2/15
B.7/15
C.10/30
D.7/30
Answer: B.7/15
Explanation: Here, the sample space S = (1, 2, 3, 4, 5, ...,29, 30).
Let E = the event of getting a multiple of 3 or 5.
E = (3, 6, 9, 12, 15, 18, 5, 10, 20, 21, 24, 25, 27, 30)
P(E) = n(E) / n(S) = 14/30 = 7/15
ANSWER:B
Question: A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
A.60 km/hr
B.50 km/hr
C.36 km/hr
D.26 km/hr
Answer: A.60 km/hr
Explanation: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 15 = 45 => x = 60 km/hr.
Answer:A
Question: In Jonathan's pen there are 300 sheep's. 5/6 of the sheep's are white, 2/3 of the sheep's have soft wool. What can't be the number of white sheep's that also have soft wool in the pen?
A.100
B.200.
C.190.
D.180.
Answer: A.100
Explanation: ..................................White Sheep...........not- white sheep
Softwool............................................................................ 2/3×300 =200
Not soft wool ......................................................................300-200=100
................................5/6 ×300= 250...........300-250=50..........Total = 300
As per the matrix it's obvious that the number of white sheep with Soft Wool cannot be 100. As this would lead to a value of 100 for black sheep with soft wool, an impossible consequence as per the matrix.
Therefore A is the correct answer.
Question: The initial price of an article is Rs.2000 which increases 30% increse in its price in the first year,a 20% decrease in the second year and a 10% increase in the next year. What is the final price of the article ?
A.Rs.1748
B.Rs.1948
C.Rs.1848
D.Rs.2048
Answer: C.Rs.1848
Explanation: The initial price of the article, four years age is Rs. 2000 in the 1st year, price of the article = 2000 + 600 = Rs. 2600. In the 2nd year, price = 2600 - 20% of 2600 = 2200- 520 = Rs. 1680.
In the 3rd year, price = 1680+ 10% of 1680 = 1680 + 168= Rs.1848.
Required price = Rs.1848
Answer:C
Question: A certain truck uses 18 gallons of diesel fuel in traveling 240 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
A.8
B.9
C.12
D.15
Answer: B.9
Explanation: There are two sets 18G1 gallons and 10G2 gallons details given.
18 gallons covering 240 miles
Then 1 G1 is used to cover 15 miles.
Now for 10 G2 covering 240 miles.
then 1 G2 is used to cover 24 miles.
There must 24 - 15 = 9 miles per gallon increment is needed for 10 gallons to improve the mileage to cover 240 miles.
IMO B is correct answer.
Question: A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.
A.48
B.288
C.495
D.990
Answer: C.495
Explanation: The number of ways of choosing 4 sites out of 12 are counted by = 12C4 ways = 495
Answer: Option C
Question: The average mark of a class of twenty students is 64. If three students whose marks are 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.
A.71
B.74
C.57
D.70
Answer: D.70
Explanation: Exp. Total mark of 20 students = 64*20 = 1280,
Total mark after the removal of 3 students = 1280 –(32 +28+34 )
= 1280 – 94 = 1186
Approximate average mark = 1186/(20-3) = 1186/ 17 = 70
Answer: D
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 8% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
A. 0.25
B. .05^10
C. 1-0.92^10
D. 1-0.05^10
Answer: C. 1-0.92^10
Explanation: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.92^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.92^10.
Answer: C.
Question: {(481 + 426)2 - 4 x 481 x 426} = ?
A.3025
B.4200
C.3060
D.3210
Answer: A.3025
Explanation: Explanation :
Here, the given statement is like (a + b)2 - 4ab where a= 481 and b = 426
(a + b)2 - 4ab = (a2 + 2ab + b2) - 4ab = a2 - 2ab + b2 = (a - b)2
Hence {(481 + 426)2 - 4 x 481 x 426} = (481 - 426)2 = 552 = 3025. Answer : Option A
Question: Indu gave Bindu Rs.625 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.1
B.2
C.7
D.4
Answer: A.1
Explanation: 625 = D(100/4)2
D = 1
Answer:A
Question: in how many ways u can form a group of 11 members from 5 men and 11 women if the men member not more than 3?
A.2256 ways
B.2356
C.3456
D.4456
Answer: A.2256 ways
Explanation: we need team members=11 such that there should not be more than 3 men
so the conditions are (3M,8W),(2M,9W),(1M,10W)
Now, no. of ways=11c11+5c3*11c8+5c2*11c9+5c1*11c10=2256
ANSWER:A
Question: A person was fined for exceeding the speed limit by 10 km/hr.Another person was also fined for exceeding the same speed limit by twice the same.If the second person was traveling at a speed of 35 km/hr,find the speed limit.
A.487
B.15
C.76
D.29
Answer: B.15
Explanation: If x is speed limit,
Speed of first person = x + 10
Speed of 2nd person = x + 20
But speed of 2nd person = 35 kmph
x + 20 = 35
x = 15 kmph.
so speed limit is 15 kmph option D
Answer:	B
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A
A.11
B.12
C.13
D.14
Answer: A.11
Explanation: Explanation:
Given that A+B = 11 + B + C
=> A ? C = 11 + B ? B = 11
=> C is younger than A by 11 years
Answer: Option A
Question: 3-3*5+2=
A.A)2
B.B)-10
C.C)-18
D.D)-17
Answer: B.B)-10
Explanation: 3-3*5+2 = 5-15 = -10...
so the answer is -10... B
Question: In the Hillside summer camp there are 60 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
A.50.
B.45.
C.40.
D.60.
Answer: D.60.
Explanation: Given there are 60 students , 90% of 60 = 54 boys and remaining 6 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 60 to existing 54 then the count will be 114and the girls number will be 6 as it.
Now boys are 95% and girls are 5%. ( out of 120 students = 114 boys + 6 girls ).
IMO option D is correct.
Question: If n is a positive integer, what is the remainder when (7^(4n+3))(3^n) is divided by 10?
A.1
B.2
C.4
D.6
Answer: B.2
Explanation: This one took me bout 3 1/2 min. Just testin numbers and what not.
First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.
1-7 stands for ^1 thru 7
1: 7*1=7
2: 7*7=9
3: 7*9=3
4: 7*3=1
5: 7*1=7
6: 7*7=9
7: 7*9=3
Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.
so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8
Now from here if id double check just to make sure.
7^4(2)+3*6^2 ---> 7^11*36 or we can just say again 7^11*6 (b/c we are only interested in the units digit).
Since ^12 is going to be 1 that means ^11 is going to be 3 (as taken from our pattern)
so again 3*6=18/10 ---> R =2
B or J in this problem.
Question: When 6 + 2 = 85, 8 + 3 = 115, 7 + 5 = 125, then 5 + 8 = ?
A.145
B.185
C.245
D.135
Answer: D.135
Explanation: 6 + 2 => 6 + 2 = 8 => 8 Ã— 10 + 5 = 85
8 + 3 => 8 + 3 = 11 => 11 Ã— 10 + 5 = 115
7 + 5 => 7 + 5 = 12 => 12 Ã— 10 + 5 = 125
Then 5 + 8 => 5 + 8 = 13 => 13 Ã— 10 + 5 = 135
Answer : D
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 8 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
A.2.6
B.5.6
C.6.3
D.8
Answer: A.2.6
Explanation: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+8)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=2.6 m/s
A
Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
A.5
B.6
C.7
D.8
Answer: B.6
Explanation: Explanation:
Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 -> 9 (X)
2343 -> 12 (/)
3474 -> 18 (X)
4131 -> 9 (X)
5286 ->21 (/)
5340 -> 12 (/)
6336 -> 18 (X)
7347 -> 21 (/)
8115 -> 15 (/)
9276 -> 24 (/)
Required number of numbers = 6.
ANSWER IS B
Question: For all numbers c and d, the operation @ is defined by c@d = c^2 - cd. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
A.II
B.I and II
C.I and III
D.II and III
Answer: B.I and II
Explanation: c@d = c^2 - cd=c(c-d).... so c@d will be zero if c=d or c=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B
Question: Have a look at the formula P = nRT/V.
if R is doubled, T is doubled and V is quadrupled, by what factor does P change.
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: Given,
P = nRT/V
Here, R and T are doubled and V is quadrupled. Applying these conditions we have,
P = n*(2R)*(2T)/(4V)
P = 4nRT/4V
P = nRT/V
Intially, P = nRT/V. After changing R, T & V, P = nRT/V.
Therefore, P changes by a factor of 1.
Answer = A =1
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 7 minutes earlier. How far is the office from his house?
A.3 Km
B.3 1/5 Km
C.4 1/5 Km
D.5 1/5 Km
Answer: A.3 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 15/6
= 24/2 * 15/60
= 15/5 = 3 Km
A
Question: One fill pipe A is 3 times faster than second fill pipe B and takes 10 minutes less time to fill a cistern than B takes. Find when the cistern will be full if fill pipe B is only opened.
A.20 min
B.18 min
C.15 min
D.10 min
Answer: C.15 min
Explanation: Let B can fill the cistern in x min. Then,
then A can fill the cistern in x⁄3 min
Given x - x⁄3 = 10 ⇒ x = 15 min
Answer C
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 40 phone numbers by using the readable digits followed by 40 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
A.1/9
B.10/243
C.4/27
D.10/271
Answer: C.4/27
Explanation: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 40/(9*9*3+9*3) = 4/27.
Answer: C.
Question: What is the least integer greater than 0+0.5?
A.–2
B.–1
C.0
D.1
Answer: D.1
Explanation: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(0) + (0.5) = 0.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from 0 to 0.5).
Next, the question asks for the LEAST integer that is GREATER than 0.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of 0.5 is 1.
Final Answer:
D