mathewhe/aqua_rat huggingface dataset:
Question: In a renowned city, the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A) 32,300
(B) 172,800
(C) 345,600
(D) 338,200
(E) 259,200
Rationale: Every 2 seconds, 8 persons are added (10-2). Every second 4 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 4 = 345600
Option C
Answer: (C) 345,600
Question: A man can row his boat with the stream at 6 km/h and against the stream in 3 km/h. The man's rate is?
(A) 1.5 kmph
(B) 3 kmph
(C) 8 kmph
(D) 7 kmph
(E) 5 kmph
Rationale: DS = 6
US = 3
S = ?
S = (6 - 3)/2 = 1.5 kmph
Answer: A
Answer: (A) 1.5 kmph
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The sum of the first 53 positive even integers is 2550. What is the sum of the even integers from 96 to 200 inclusive?
(A) 5,100
(B) 7,844
(C) 10,100
(D) 15,500
(E) 20,100
Rationale: even numbers from 96 to 200=104/2+1=53
Sum= (200+96)x53/2=7844
So B is the ans.
Answer: (B) 7,844
Question: Carmelo and LeBron participate in a five-person footrace on the basketball court during All-Star Weekend. If all five contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?
(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 60
Rationale: 5! = 120
120/2=60 half the time carmelo is in front, vice versa
Answer:
(E) 60
Answer: (E) 60
Question: Given the equation 7^p-3^(-p)=6.7, which of the following options is the correct value of p?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 0
Rationale: Plugging in the various option into the equation to find out which is correct:
7^p-3^(-p)=6.7
7^1-3^(-1)=6.7 Ans. A
Answer: (A) 1
Question: There is a 50 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 50 cm, how many insects were still left after the race was over?
(A) 0
(B) 4
(C) 6
(D) 8
(E) 11
Rationale: Only the prime numbers greater than 10 and less than 50 were left.
That is 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
The total is 11.
The answer is E.
Answer: (E) 11
Question: If each digit in the set A = {1, 2, 3, 4, 5, 6} is used exactly once, in how many ways can the digits be arranged?
(A) 720
(B) 830
(C) 940
(D) 1050
(E) 1160
Rationale: 6! = 720
The answer is A.
Answer: (A) 720
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
(A) 7
(B) 9
(C) 11
(D) 12
(E) 15
Rationale: Explanation:
x/2 – x/3 = 6 => x =6
3 + 6 = 9
B)
Answer: (B) 9
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a, |b-3| + |ab-b| =
(A) ab-4+b
(B) 2b-ab-4
(C) ab+4
(D) ab-2b+5
(E) 4-ab
Rationale: Given: |ab| = ab and |a| = -a
Question: |b-3| + |ab-b| = ?
**** Looking at |ab| = ab tells us that a and b are either both positive or negative
**** Looking at |a| = -a tells us that a must be negative
**** Combine two observations: a and b are both negative values
Let a=-1 and b=-1
|b-4| + |ab-b| = |-1-3| + |1-(-1)| = 5
Test a) ab-4 = (-1)(-1)-4 = -5
Test b) 2b-ab-4 = (2)(-1) - (1) - 4 = -7
Test c) ab+4 = 1 + 4 = 5
Answer: C
Answer: (C) ab+4
Question: There are 9 cities numbered 1 to 9.From how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Start from 1: 1368, Start from 2: 2358, Start from 3: 378, Start from 4: 48, Start from 5: 528, Start from 6: 678, Start from 7: 78, Why start from 8???, Start from 9: 918. So flights can start from all 8 other cities.
ANSWER:B
Answer: (B) 8
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in
(A) 144 mins
(B) 140 mins
(C) 136 mins
(D) 132 mins
(E) None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/36
=>4/x=1/36
x=36∗4=144mins
Answer: Option A
Answer: (A) 144 mins
Question: A bag contains 18 purple jellybeans, 14 green jellybeans, and 12 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
(A) 15%
(B) 20%
(C) 32%
(D) 30%
(E) 35%
Rationale: Probability of green beans = 14 / (18 + 14 + 12) = 14/44 = 32%
Answer is C
Answer: (C) 32%
Question: In what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way?
(A) 3 sec
(B) 4 sec
(C) 8 sec
(D) 6 sec
(E) 7 sec
Rationale: T = 52/24 * 18/5 = 8 sec
ANSWER:C
Answer: (C) 8 sec
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?
(A) 87 kg
(B) 36 kg
(C) 98 kg
(D) 65 kg
(E) 87 kg
Rationale: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 45
=> 5k = 45 => k = 9
Therefore the weight of the lightest boy
= 4k = 4(9) = 36 kg.
Answer:B
Answer: (B) 36 kg
Question: A club with a total membership of 25 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: As no member of committee M is on either of the other 2 committees then 25-M=25-8=17 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 17-12=5 is the greatest possible number of members in the club who are on none of the committees.
Answer: A.
Answer: (A) 5
Question: Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21
(A) 1
(B) 2
(C) -1
(D) -3
(E) -4
Rationale: C
-1
19x + 19y + 17 = -19x + 19y - 21
38x = -38 => x = -1
Answer: (C) -1
Question: A is half good a work man as B and together they finish a job in 13 days. In how many days working alone B finish the job?
(A) 23
(B) 22
(C) 39/2
(D) 36
(E) 48
Rationale: C
39/2
WC = 1:2
2x + x = 1/13 => x = 1/39
2x = 2/39 => 39/2 days
Answer: (C) 39/2
Question: How many diagonals does a 58-sided convex polygon have?
(A) 870
(B) 1125
(C) 1595
(D) 2560
(E) 3190
Rationale: A 58-sided convex polygon has 58 vertices.
If we examine a single vertex, we can see that we can connect it with 55 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be (58)(55) = 3190
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3190 by 2 to get 1595.
The answer is C.
Answer: (C) 1595
Question: If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(C) 11 × 10
(D) 55
(E) 45
Rationale: If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
1st person will have 9 handshakes, 2nd will have 8, ....9th will have 1 and 10th will have 0
= 9+8+7+6+5+4+3+2+1 = 45
if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.
Ans.E) 45
Answer: (E) 45
Question: The sum of two numbers is 72, and one of them is 12 more than the other. What are the two numbers?
(A) 36-48
(B) 50-34
(C) 60-24
(D) 30-42
(E) 21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 72:
word problem = 72
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 72 âˆ’ 12
= 60.
x = 60/2
= 30.
This is the first number. Therefore the other number is
x + 12 = 30 + 12 = 42.
The sum of 30 + 42 is 72.
D
Answer: (D) 30-42
Question: The ratio of the volumes of two cubes is 9261: 12167. What is the ratio of their total surface areas?
(A) 1:12
(B) 85:31
(C) 51:45
(D) 58:67
(E) 53:58
Rationale: Ratio of the sides
= ³√9261 : ³√12167= 21 : 23
Ratio of surface areas
= 212 : 232 = 53:58
Answer:E
Answer: (E) 53:58
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000?
(A) 6620
(B) 3277
(C) 2688
(D) 2998
(E) 9930
Rationale: A = 30000(11/10)3
= 39930
= 30000
----------
9930
Answer:E
Answer: (E) 9930
Question: How much interest will $2,400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months?
(A) $141
(B) $150
(C) $197
(D) $234
(E) $312
Rationale: Rate 8% compounded every 4 months = 8/3 %. Interest for the first 4 months = 8/3 % of 2400 = 8/3 * 2400 * 1/100 = 64.
Now in this particular scenario, the next 4 months will earn an interest on 2400, and an interest on 64.
For approximation, let's calculate total interest without considering interest on the interest earned. Thus total interest earned will be 64*3 = 192
Now, we will earn some interest on this interest as well. So the total will be a little more than 192. And the only option that satisfies that is $197
. So the answer is option C
Answer: (C) $197
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 5%. What is the cost price?
(A) s.933.33
(B) s.1009
(C) s.1007
(D) s.1006
(E) s.1002
Rationale: Explanation:
90%
105%
--------
15% ---- 140
100% ---- ? => Rs.933.33
Answer:A
Answer: (A) s.933.33
Question: Tough and Tricky questions: Number Properties.
If (z + 3)/9 is an integer, what is remainder when z is divided by 9?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Assume the answer choices as the value of z
9/9=1
Ans E
Answer: (E) 6
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
(A) Rs.2166.67
(B) Rs.3210
(C) Rs.3210.14
(D) Rs.3344.24
(E) Rs.4500.12
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20	× x –	10	× (5000 – x) =	3	× 5000
100	100	100
x	–	(5000 – x)	= 150
5	10
10x	–	(5000 – x) × 10	= 150 × 10
5	10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: (A) Rs.2166.67
Question: The length of a rectangle ishalved, while its breadth is tripled. Watis the % change in area?
(A) 25%
(B) 30%
(C) 50%
(D) 65%
(E) 70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: Stacy and Heather are 25 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour fast than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?.
(A) 9.0mile
(B) 13.0mile
(C) 11.0mile
(D) 10.2 mile
(E) 12 mile
Rationale: Ss - Stacy's speed = 6m/hr
Sh - Heather's speed = 5m/hr
In 24 minutes Stacy will cover = (24/60)*6 = 2.4miles
Now since both are walking in opposite directions, add their speeds - 6+5 =11m/hr and distance to cover is 25 -2.4 = 22.6
Time taken = Distance/ Speed = 22.6/11 = 2.05 hrs
Heather will cover = 5*2.4 = 10.2 miles.
Answer D
Answer: (D) 10.2 mile
Question: The radius of a semi circle is 14 cm then its perimeter is?
(A) 32.8
(B) 32.4
(C) 72
(D) 32.2
(E) 32.9
Rationale: Diameter = 28 cm
1/2*22/7*28+28 = 72
Answer : C
Answer: (C) 72
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
(A) 277
(B) 269
(C) 215
(D) 177
(E) 123
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is
= 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1
= 215.
Answer:C
Answer: (C) 215
Question: O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–3.3) + e(4.7) is:
(A) -3
(B) -1
(C) 0
(D) 1
(E) 3
Rationale: O(5.3) + E(–6.7) + o(–3.3) + e(4.7) = 7 + (-6) + (-5) + 4 = 0
The answer is C.
Answer: (C) 0
Question: One woman and one man can build a wall together in five hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them nine hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 55/7
(B) 1
(C) 135/32
(D) 222/37
(E) 252/58
Rationale: Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/5-->(1) , w + 2g = 1/5-->(2) and m + g =1/9-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/27,m=2/27 and w=17/135.
So, n = 1/(32/135) = 135/32
Option, C
Answer: (C) 135/32
Question: Which of the following is not a leap year?
(A) 700
(B) 800
(C) 1000
(D) 1200
(E) 2000
Rationale: The century divisible by 400 is a leap year.
The year 700 is not a leap year.
Answer: Option A
Answer: (A) 700
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 30 kmph. Of how many minutes does the train stop per hour?
(A) A)5
(B) B)10
(C) C)20
(D) D)30
(E) E)40
Rationale: Explanation:
T = 15/45 * 60 = 20
Answer: Option C
Answer: (C) C)20
Question: Find the area of a parallelogram with base 20 cm and height 40 cm?
(A) 100 cm2
(B) 250 cm2
(C) 800 cm2
(D) 296 cm2
(E) 456 cm2
Rationale: Area of a parallelogram
= base * height
= 20 * 40
= 800 cm2
Answer: C
Answer: (C) 800 cm2
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
(A) ²²C₉
(B) ²²C₁₀
(C) ²²C₉ + ¹⁰C₁
(D) ²²C₁₀ - 1
(E) ¹⁰C₁
Rationale: The total number of ways of forming the group of ten representatives is ²²C₁₀.
The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way
The required number of ways
= ²²C₁₀ - 1
Answer:D
Answer: (D) ²²C₁₀ - 1
Question: A bucket full of nuts was discovered by the crow living in the basement. The crow eats a sixth of the total number of nuts in 8 hours. How many hours in total will it take the crow to finish a quarter of the nuts?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: In one hour, the crow eats 1/48 of the nuts.
(1/4) / (1/48) = 12 hours
The answer is B.
Answer: (B) 12
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 15 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
(A) 10.5
(B) 15
(C) 25.5
(D) 30
(E) 60
Rationale: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 15
x=10.5 minutes
Answer: A
Answer: (A) 10.5
Question: Mr Jacobs placed his folders on three chairs in a conference room comprising of 12 chairs, if Mrs Roberts walked in and also placed her folders on 3 chairs, what is the probability that she did no place any of her folders on a chair already containing Mr Jacobs folder?.
(A) 3/9
(B) 3/55
(C) 9/12
(D) 21/55
(E) 3/12
Rationale: Since Mr Jacob's folders are already on 3 chairs, the subset from which the 3 chairs on which Mrs Roberts placed her folders should be chosen are the 9 chairs not occupied by Mr Jacob's folders from the universe of 12.
The first chair can be one of the 9 from the 12 with probability 9/12.
The second chair can be one of the 8 from the 11 remaining with probability 8/11.
The third chair can be one of the 7 from the 10 remaining with probability 7/10.
The total probability will be 9/12 × 8/11 × 7/10. On cancellation, this comes to 21/55.
Thus, the answer is D - 21/55
Answer: (D) 21/55
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 189 m
(B) 178 m
(C) 172 m
(D) 600 m
(E) 186 m
Rationale: Distance covered by Amar
= 18/4.8 (1.6km)
= 3/8(1600) = 600 m
Answer:D
Answer: (D) 600 m
Question: A 110 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 35
(B) 20
(C) 47
(D) 36
(E) 31
Rationale: 1: 2/5 = 5: 2
2/7 * 110 =31
Answer:E
Answer: (E) 31
Question: A couple decides to have 6 children. If they succeed in having 6 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 3 girls and 3 boys?
(A) 1
(B) 9/64
(C) 1/8
(D) 3/16
(E) 9/32
Rationale: Sample space = 2^6 = 64.
Favourable events = {bbbggg}, {bgbgbg}, {bgbggb}, {bggbbg} {gggbbb}, {gbgbgb}, {gbbggb}.{gbgbbg}{gbbgbg}
Probability = 9/64 = 9/64
Ans (B).
Answer: (B) 9/64
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 80
(B) 90
(C) 120
(D) 140
(E) 160
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: (C) 120
Question: 3648,3648,1216.243.2,34.74,?
(A) 1.24
(B) 2.68
(C) 3.98
(D) 5.68
(E) 3.86
Rationale: Explanation :
Terms are continuously divided by 1,3,5 ,7, and so on
3648
3648 Ã· 1 = 3648
3648 Ã· 3 = 1216
1216 Ã· 5 = 243.2
243.2 Ã· 7= 34.74
34.74Ã·9=3.86
Answer : Option E
Answer: (E) 3.86
Question: A man has some hens and cows. If the number of heads be 100 and the number of feet equals 240, then the number of cows will be:
(A) 22
(B) 23
(C) 24
(D) 20
(E) 28
Rationale: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 100 .... (i)
and 2x + 4y = 240 x + 2y = 120 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 20.
The required answer = 20.
Answer: D
Answer: (D) 20
Question: If I walk at 2 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
(A) 4/13 km
(B) 4/15 km
(C) 4/17 km
(D) 1/15 km
(E) 2/15 km
Rationale: x/2 – x/4 = 4/60
x = 4/15 km
ANSWER:B
Answer: (B) 4/15 km
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 27
(C) 45
(D) 99
(E) 12
Rationale: Relative speed = 50 + 30 = 80 km/hr.
80 * 5/18 = 200/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000*9/200= 45 sec.
Answer: C
Answer: (C) 45
Question: 6/9 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
(A) 64%
(B) 41%
(C) 45%
(D) 72%
(E) 78%
Rationale: Total population = 90 (assume).
6/9*90=60 people from Montague.
3/9*90=30 people from Capulet.
0.2*60=12 people from Montague support Juliet.
0.7*30=21 people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 21/(12+21)=~64.
Answer: A
Answer: (A) 64%
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 250 inclusive?
(A) 90
(B) 95
(C) 100
(D) 130
(E) 170
Rationale: The multiples of ten from 10 to 250 inclusive would be an evenly spaced set with 25 terms - 10, 20, 30,.......250
So average = (First term + Last Term)/2 = (10 + 250)/2 = 260/2 = 130
Hence, the correct answer is D.
Answer: (D) 130
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds?
(A) 180
(B) 184
(C) 188
(D) 192
(E) 196
Rationale: J + K = 290 and so K = 290 - J
J - 8 = 2K
J - 8 = 2(290-J)
3J = 588
J = 196
The answer is E.
Answer: (E) 196
Question: Two numbers A and B are such that the sum of 6% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 3
(B) 1 : 2
(C) 4 : 3
(D) 1 : 1
(E) 3 : 2
Rationale: Explanation:
6% of A + 4% of B = 2/3(6% of A + 8% of B)
6A/100 + 4B/100 = 2/3(6A/100+8B/100)
⇒6A + 4B = 2/3(6A + 8B)
⇒18A + 12B = 12A + 16B
⇒ 6A = 4B
⇒ AB = 4/6=2/3
⇒ A:B=2:3
Answer: Option A
Answer: (A) 2 : 3
Question: Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1 sensor between the black and white border on the edge of disk
1 is enough to determine the drection
ANSWER:A
Answer: (A) 1
Question: Sum of two number is 1000 and the sum of their recipocal is 2/255.Let the smallest of 2 number be L, so which of the following is correct value range for L?
(A) 100
(B) 150
(C) 180
(D) 200
(E) 220
Rationale: As per the question , let the smaller number be L and larger number be H.
So, L+H = 1000..........eqn 1
And
1/L+1/H= 2/255
(L+H)/LH = 2/255
LH = (L+H)*255/2
LH= 127500.................eqn 2
Now,
(H-L)^2 =(H+L)^2 - 4HL
(H-L)^2 = 1000000-4*127500
= 1000000-510000
=490000
Now,
(H-L) =sqrt(490000)
= 700
H-L=700...............................eqn 3
From eqn 1 and 3
L=150
ANSWER:B
Answer: (B) 150