RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the biology club and 3/4 attend the chemistry club. 1/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
A.300
B.200
C.250
D.150
Answer: C.250
Explanation: Basically, this question is asking you to figure out how many students are being double-counted.
A-Club has 200 members (1/2 of 400)
B-Club has 250 members (5/8 of 400)
C-Club has 300 members (3/4 of 400)
We can create an equation to solve this:
200+250+300 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (50).
750 = 400 + x + 100
x =250
C
Question: Worker A takes 5 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
A.15/4
B.40/9
C.50/9
D.60/9
Answer: A.15/4
Explanation: one day work of A = 1/5
one day work of B = 1/15
so one day work of A and B together = 1/5 + 1/15 = 4/15
so total days required = 15/4
ANSWER:A
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference Z between the highest and the lowest incentive received by the 5 salesmen in the month?
A.$4000
B.$5000
C.$9000
D.$11,000
Answer: D.$11,000
Explanation: Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000
Step #4: What is the difference Z between the highest and the lowest incentive:
- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.
- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.
- Therefore the first two numbers( ab) must equal 4, 000
- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b
if a = 1,000 b = 3,000 --> difference between the highest and the lowest incentive = 12,000 - 1,000 =11, 000
no other options for a or b to fit the criteria
Final List:1,0003,0007,00012,00012,000
Answer D
Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
A.30 m2
B.40 m2
C.60 m2
D.80 m2
Answer: C.60 m2
Explanation: l = 10 m,
h = 8 m.
So, r = l2 - h2 = (10)2 - 82 = 6 m.
Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.
Answer: Option C
Question: A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.53 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
A.|k + 0.03| > 2.5
B.|k — 0.03| <= 2.5
C.|k — 2.5| > 0.03
D.|2k — 5| <= 0.06
Answer: D.|2k — 5| <= 0.06
Explanation: So, let's go through this step by step:
rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters.
In other words, any screw that is less than: 2.50 - 0.03 =2.47or greater than 2.53 will be rejected.
If k represents the length of a screw
In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53
You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.
Let's look at (D): |2k — 5| <= 0.06 or dividing by 2
|k — 2.5| <= 0.03
For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47
2.47 ≤ k ≤ 2.53
(D)
Question: A letter lock consists of three rings each marked with seven different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
A.177
B.199
C.342
D.168
Answer: C.342
Explanation: Since each ring consists of seven different letters, the total number of attempts possible with the three rings is
= 7 * 7 * 7 = 343. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 343 - 1
= 342
Answer: C
Question: Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?
A.12
B.14
C.16
D.18
Answer: D.18
Explanation: assume x is number of theft per year
24*100=120*1.1*x -> x = ~18
ANSWER:D
Question: There has been successive increases of 25% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
A.23%
B.27%
C.31%
D.35%
Answer: B.27%
Explanation: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.25*P = x*P
y = x / (1.1*1.25) which is about 0.73x which is a decrease of about 27%.
The answer is B.
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) – (3#3) is equal to
A.-656
B.82
C.128
D.512
Answer: A.-656
Explanation: Answer:
2^6 + 3^2 - 3^6 = -656
ANs A
Question: If the simple interest on a sum of money for 5 years at 18% per annum is Rs. 900, what is the compound interest on the same sum at the rate and for the same time?
A.Rs. 1287.76
B.Rs. 1284.76
C.Rs. 1587.76
D.Rs. 1266.76
Answer: A.Rs. 1287.76
Explanation: Sum = (900 * 100) / (5 * 18) = Rs. 1,000.00
C.I. on Rs. Rs. 1,000.00 for 5 years at 18% = Rs. 2,287.76.
= Rs. 2,287.76 - 1,000.00 = Rs. 1287.76
ANSWER:A
Question: If x = -12/5 and y = -6/7, what is the value of the expression -2x – y^2?
A.741/357
B.456/789
C.636/735
D.564/263
Answer: C.636/735
Explanation: x = -12/15 and y = -6/7
==> -2(-12/15) - (-6/7)^2 = 24/15 - 36/49 = 636/735
Ans: C
Question: What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?
A.272
B.120
C.277
D.2898
Answer: B.120
Explanation: When compounded annually, interest
= 12000[1 + 20/100]1 - 12000 = Rs.2400
When compounded semi-annually, interest
= 12000[1 + 10/100]2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120.Answer: B
Question: If grapes are 92% water and raisins are 20% water, then how many kilograms did a quantity of raisins, which currently weighs 5 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
A.50
B.54
C.55
D.56
Answer: A.50
Explanation: Let x be the original weight.
The weight of the grape pulp was 0.08x.
Since the grape pulp is 80% of the raisins, 0.08x = 0.8(5).
Then x = 50 kg.
The answer is A.
Question: In a vehicle's repair shed, 3 men and 8 boys can do a piece of work in 15 days; 4 men and 9 boys can do the same work in 12 days. Then, 5 men and 5 boys can do double the amount of this work in :
A.20 days
B.33 days
C.24 days
D.28 days
Answer: C.24 days
Explanation: Explanation :
Solution: (3*15) men + (8*15) boys= (4*12) men + (9*12) boys
45 M + 120 B = 48 M+ 108 B <=> 3 M = 12 B => 1 M = 4 B.
.'. 3 M + 8 B = (3*4) B+ 8 B = 20 B.
5 M + 5 B = (5*4) B + 5 B = 25 B.
Let the required number of days be x.
now, more boys, less days (IP)
more work, more days (DP)
boys 25 : 20
} : :15: x
work 1 : 2
.'. (25*1*x) = (20*2*15)
=> x = 40*15/25 = 24.
Answer : C
Question: consider a sequence of numbers is such that a1 = 11, a2 =16, and each subsequent an = an-2 + 9. Which of the following numbers is a member of the sequence?
A.216
B.246
C.289
D.299
Answer: D.299
Explanation: each odd term(1st , 3rd, 5th,...) of the sequence is given by 11 + 9*(something)
each even term(2nd, 4th, 6th...) of the sequence is given by 16 + 9*(something)
So if you subtract the numbers by 11 or 16 then it should be divisible by 9
216-11(=205) or 216-16(=200) are not divisible by 9
246-11(=235) or 246-16(=240) are not divisible by 9
289-11(=278) or 289-16(=273) are not divisible by 9
299-11(=288) is divisible by 9ANSWER, 299-16(=283) are not divisible by 9
368-11(=357) or 368-16(=352) are not divisible by 9
So, Answer is D
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
A.76 days
B.68 days
C.24 days
D.97 days
Answer: C.24 days
Explanation: B = 1/8 – 1/2 = 1/24
=> 24 days
Answer: C
Question: The cost of an item was reduced from its usual selling price of $23.99 to $19.99. Which of the following is closest to the percent decrease in the price of the item?
A.17%
B.21%
C.24%
D.25%
Answer: A.17%
Explanation: The price decreased by 23.99 - 19.99 = $4.
$4 is a bit more than 17% of original price of $24.
Answer: A.
Question: In how many different number of ways 1 boy and 4 girls can sit on a bench?
A.120
B.140
C.160
D.180
Answer: A.120
Explanation: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
A)
Question: What is the difference between the local values of 6 in the number 56406?
A.2992
B.2997
C.5994
D.2077
Answer: C.5994
Explanation: Explanation:
6000 â€“ 6 = 5994
Answer:C
Question: A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. The rate per annum is?
A.5 5/9 %
B.5 5/6 %
C.5 8/9 %
D.1 5/9 %
Answer: A.5 5/9 %
Explanation: Let sum = x. Then, amount
= 7x/6
S.I. = 7x/6 - x = x/6; Time
= 3 years.
Rate = (100 * x) / (x * 6 * 3)
= 5 5/9 %.
Answer: A
Question: A bucket contains 2 mixtures A and B in the ratio 7:5. If 9 liters of the mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7:9. How much of the liquid A was there in the bucket?
A.15liters
B.21liters
C.12liters
D.18liters
Answer: B.21liters
Explanation: 1st ratio = 7:5
2nd ratio = 7:9
Difference of cross products ratio = 7*9-7*5 = 28
common factor of the 1st ratio
= (quantity replaced/sum of terms in 1st ratio) + (Quantity replaced*term A in 2nd ratio/Difference)
= (9/7+5) + (9*7/28) = 3
Quantity of A = 7*3 = 21liters
Answer is B
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
A.15 1/3 days
B.13 1/3 days
C.19 1/3 days
D.11 1/3 days
Answer: B.13 1/3 days
Explanation: B
13 1/3 days
5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Question: The largest number that exactly divides each number of the sequence
(15 - 1), (25 - 2), (35 - 3), ...., (n5 - n), ...... is
A.1
B.15
C.30
D.120
Answer: C.30
Explanation: Sol.
Required number = (25 - 2)
= (32 - 2) = 30.
Answer C
Question: f two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
A.1/9
B.1/2
C.1/1
D.1/5
Answer: B.1/2
Explanation: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Question: Amithab's average expenditure for the January to June is Rs. 4200 and he spends Rs.1200 in January and Rs.1500 in july.The average expenditure for the months of febraury to July is:
A.Rs.4250
B.Rs.4288
C.Rs.4227
D.Rs.4218
Answer: A.Rs.4250
Explanation: Explanation:
Amithab's total expenditure for Jan - June = 4200 x 6 = 25200
Expenditure for Feb - June = 25200-1200 = 24000
Expenditure for the months of Feb - July = 24000 + 1500 =25500
The average expenditure = {25500}{6}=4250
Answer: A
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A.5
B.6
C.7
D.4
Answer: A.5
Explanation: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3/5 of its present?
A.41.66667
B.60.5
C.63.5
D.62.5
Answer: A.41.66667
Explanation: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 3x/5
Hence, number of buckets needed = 25x/(3x/5)=(25×5)/3=41.66667
Answer is A.
Question: The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
A.Rs. 960
B.Rs. 760
C.Rs. 840
D.Rs. 1020
Answer: D.Rs. 1020
Explanation: T.D = (B.Gx100)/(R/T) = (270X100)/(12X3) = Rs. 750
B.D. = Rs.(750 + 270) = Rs. 1020.
answer :D
Question: The ratio of the volumes of two cubes is 27 : 64. What is the ratio of their total surface areas?
A.9:12
B.12:18
C.9:16
D.8:2
Answer: C.9:16
Explanation: Ratio of the sides = Â³âˆš27 : Â³âˆš64
= 3 : 4
Ratio of surface areas =9:16
Answer: C
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A.57%
B.58%
C.60%
D.65%
Answer: A.57%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required % =(11628/20400)*100% = 57%
answer :A
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
A.221
B.287
C.400
D.288
Answer: C.400
Explanation: Explanation:
441 = P(21/20)2
P = 400
Answer:C
Question: A bag contains 5 red, 4 blue and 3 green balls. If 2 ballsare picked at random, what is the probability that both are red?
A.2/15
B.2/21
C.5/33
D.3/29
Answer: C.5/33
Explanation: P(Both are red),
=5C212C2=5C2/12C2
=10/66=5/33
C
Question: The average of first 10 prime numbers is?
A.12.7
B.12.2
C.12.9
D.12.1
Answer: C.12.9
Explanation: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer: C
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab is even
III. ab > 0
A.I only
B.II only
C.I and II
D.I and III
Answer: B.II only
Explanation: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
II only.letter B
Question: What is 15 percent of 54?
A.7.3
B.8.1
C.9.5
D.10.2
Answer: B.8.1
Explanation: (15/100) * 54 = 8.1
The answer is B.
Question: Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/4 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
A.7/12
B.29/60
C.17/30
D.19/30
Answer: A.7/12
Explanation: Let s assume the platinum card spending limit =x
Gold card spending limit will be =x/2
balance on gold card is =x/2*1/3=x/6
Platinum card unspent limit is= x-1/4x=3/4x
So if gold card balance is transferred then the rest unspent will be
3/4x-x/6=7/12x
So the ans is A
Question: A company selects an employee at his 25th age and offers salary as Rs.40000 per
annum for first 2 years. Afterwards, every year he gets increment of Rs.4000 for
next 15 years and his salary become constant till his retirement. If Rs.80,000 is
his average salary (throughout his career) then at what age he retires?
A.48
B.49
C.50
D.52
Answer: D.52
Explanation: For 1st 2 yrs salary=40,000
After 2 years he get increment of 4000 every year for 15 years
So 15th year salary =44000+14*4000=100000
Now by using arithmetic progression
S15=n/2(a+l)=15/2(44000+100000)=1080000
Now avg salary=80000
80000+10,80000+10,0000x/17+x=80000
By solving
x=10
now 27+15+10=52
so 52 is the age
ANSWER:D
Question: In a certain sequence, the first term is 1, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term of the sequence?
A. 3/5
B. 5/8
C. 8/5
D. 5/3
Answer: C. 8/5
Explanation: First term = 1
Second term = (1/1)+1 = 2
Third Term = (1/2)+1 = 3/2
Forth Term = [1/(3/2)]+1 = 5/3
Fifth Term = [1/(5/3)]+1 = 8/5
Answer: Option C
Question: A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty?
A.1//3
B.2/3
C.4/9
D.4/7
Answer: C.4/9
Explanation: 2/3 ---- 12
? ----- 8 ==> 4/9
C
Question: Nr Books bought Nr of People
1 5
3 2
4 7
6 3
What is the median of books bought per person?
A.a) 2
B.b) 4
C.c) 6
D.d) 8
Answer: B.b) 4
Explanation: 1,1,1,1,1,3,3,4,4,4,4,4,4,4,6,6,6
so you will observer that the median of the list is 4.
Ans B
Question: The averageincome of M and N is Rs. 5050. The average monthly income of N and O is Rs. 6250 and the average monthly income of M and Ois Rs. 5200. The income of M is?
A.Rs. 2000
B.Rs. 3000
C.Rs. 4000
D.Rs. 4500
Answer: C.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)
M + O = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(M + N + O) = 33000 or M + N + O = 16500 .... (iv)
Subtracting (ii) from (iv), we get M = 4000.
M's monthly income = Rs. 4000
C
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
A.Rs529
B.Rs527
C.Rs598
D.Rs540
Answer: D.Rs540
Explanation: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 =Rs540
Answer:D
Question: Find the average of all the numbers between 17 and 32 which are divisible by 3.
A.15
B.18
C.20
D.26
Answer: D.26
Explanation: Sol.
Average = (21+ 24+ 27+ 30/ 4) = 102 / 4 = 25.5
Answer D
Question: In a barrel of juice there is 40 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
A.3:2.
B.2:1.
C.3:1.
D.4:3.
Answer: A.3:2.
Explanation: Juice barrel : beer Barrel = 40:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 4/8 costs 3/4, ie 4J / 8B = 3/4.
Solving for J/B, we get 3:2
Answer A.
Question: The average weight of 8 person's increases by 6 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person?
A.80 kg
B.85 kg
C.90 kg
D.88 kg
Answer: D.88 kg
Explanation: Total weight increased = (8 x 6) kg = 48 kg.
Weight of new person = (40 + 48) kg = 88 kg.
Answer : D
Question: In a company the manager wants to give some gifts to all of the workers. In each block there are about 100 workers are there. The total amount for giving the gifts for all the workers is $4000. The worth of the gift is $4. How many blocks are there in the company?
A.12
B.10
C.15
D.17
Answer: B.10
Explanation: Each employee will get a gift worth of = $4
total employees = 4000/4 = 1000
total blocks = 1000/100 = 10
correct option is B
Question: Mary can do a piece of work in 28 days. Rosy is 40% more efficient than Mary. The number of days taken by Rosy to do the same piece of work is?
A.22
B.24
C.20
D.25
Answer: C.20
Explanation: Ratio of times taken by Mary and Rosy = 140:100 = 14:10
Suppose Rosy takes x days to do the work.
14:10 :: 28:x => x= 20 days.
Hence, Rosy takes 20 days to complete the work.
Answer: C
Question: A certain restaurant offers 6 different salads, 4 different main courses, and 7 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
A.260
B.388
C.436
D.504
Answer: D.504
Explanation: The number of possible choices for desserts is 7C2 = 21
The number of possible meals is 6*4*21 = 504
The answer is D.
Question: In how many ways can Nicole distribute 20 chocolates among Ben, Kate, Mark and Tom so that each receives at least one?
A.20C4
B.19C3
C.21C4
D.21C3
Answer: B.19C3
Explanation: The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is n−1Cr−1
Thus the answer is 19C3.
Answer: B.
Question: 8k8
+ k88
--------
1,6r6
If k and r represent non-zero digits within the integers above, what is r?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: 8k8
k88
--------
16r6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and r=6.
Answer: A.
Question: A and B started a partnership business investing some amount in the ratio of 2 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
A.4 : 10 : 5
B.5 : 7 : 4
C.6 : 10 : 5
D.7 : 9: 4
Answer: A.4 : 10 : 5
Explanation: Let the initial investments of A and B be 2x and 5x.
A : B : C = (2x x 12) : (5x x 12) : (5x x 6) = 24 : 60 : 30
= 4 : 10 : 5.
ANSWER :A
Question: It was raining and a water drop accumulated itself over a leaf. It fell down to another leaf and lost 1/4th of its volume. It then fell off to another leaf losing 1/5th of its volume. After that it fell to another leaf losing 1/6th of its volume. This was process was repeated again and again till the water drop reached the last leaf and lost 1/75th of its volume.
Seeking the facts given in the question, will you be able to determine the accurate percentage of loss in the volume of the water drop when it is on the last leaf from its initial volume?
A.5%
B.3%
C.8%
D.4%
Answer: D.4%
Explanation: D
4%
Suppose that the initial volume of the water drop was p.
p - (1/4) p = (3/4) p
(3/4) p - (1/5) [(3/4) p] = (3/4) p * [1 - (1/5)] = (3/4) p * (4/5) = (3/5) p
(3/75) p = (1/25) p
1/25 = 4%
Therefore, the required percentage is four percent.
Question: Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?
A.The average speed is 1/5 miles per hour.
B.The average speed is 1/3 miles per hour.
C.The average speed is 2/5 miles per hour.
D.The average speed is 2/3 miles per hour.
Answer: B.The average speed is 1/3 miles per hour.
Explanation: We know the average speed and must find the fraction of time taken at a particular speed.
t1/t2 = (A2 – Aavg)/(Aavg – A1)
t1/t2 = (60 – 50)/(50 – 30) = 1/2
So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3.
ANSWER (B)
Question: A quiz has one mcq question with a,b and c as options. and two questions with true/false answers. what is the probability of giving all 3 answers correct?
A.1/12
B.1/3
C.1/4
D.1/2
Answer: A.1/12
Explanation: probability of getting mcq answer correct = 1/3
probability of getting one true/false answer correct = 1/2
probability of getting all 3 answers correct = 1/3 * 1/2 *1/2
=1/12
ANSWER:A
Question: If -6 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
A.-42 < xy < 21
B.-42 < xy < 24
C.-28 < xy < 18
D.-42 < xy < 36
Answer: D.-42 < xy < 36
Explanation: The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-6)*(-6)=36.
Therefore -42 < xy < 36.
Answer: D.
Question: Convert 0.34 in to a vulgar fraction ?
A.18/50
B.16/50
C.17/50
D.19/50
Answer: C.17/50
Explanation: Answer
0.34 = 34/100 = 17/50
Correct Option: C