mathewhe/aqua_rat huggingface dataset:
Question: Distance between A and B is 48 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 3 mph. While walking, the other man travels uniformly at 4 mph, but takes a 30-minute rest every other hour. When will they meet each other?
(A)  18 miles away from A
(B)  18 miles away from B
(C)  after 6 hours from start
(D)  after 8 hours from start
(E)  after 12 hours from start
Rationale: Since the question is asking when A and B will meet each other, the answer will be one involving time elapsed.
In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 3 mph and distance is 48 miles. So this means that A would take a total of 48/3 = 16 hours to cover the distance from A to B. So, if B's speed were also 3, both A and B would travel for 8 hours to meet in the middle.
Meanwhile, B will start at 4 mph, but during the next hour (because of his break) he will only travel 2 miles. This pattern will continue: 4, 2, 4, 2... meaning B will end up with an average speed of 3 mph for every two-hour period. Since 8 is even, then B will be traveling at the same average speed as A after 8 hours, and the two men will meet in the middle of A and B.
The correct answer is (D): after 8 hours from start.
Answer: (D)  after 8 hours from start
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
(A) 145
(B) 5617
(C) 15
(D) 20
(E) 12
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
Answer: D
Answer: (D) 20
Question: Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
(A) 11/P + 6
(B) P/11 +6
(C) 17 - P/6
(D) 17/P
(E) None of these
Rationale: Explanation:
Let Ben’s age now be B
Anita’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B. Answer: A
Answer: (A) 11/P + 6
Question: An article is bought for Rs.675 and sold for Rs.675, find the gain percent?
(A) 33 1/9%
(B) 33 8/3%
(C) 100%
(D) 33 2/3%
(E) 33 1/2%
Rationale: 675 ---- 675
100 ---- ? => 100%
Answer: C
Answer: (C) 100%
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 225.01
(A) 884.65
(B) 88.6
(C) 488.65
(D) 483.65
(E) 88.61
Rationale: Explanation:
a - 796.21 + 498.05 = 215.50 - 225.01
a = 488.65
ANSWER: C
Answer: (C) 488.65
Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 5 kmph
(B) 7 kmph
(C) 9 kmph
(D) 8 kmph
(E) 10 kmph
Rationale: Speed downstream = d/t = 95/(2 1/2) = 38 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (38 - 18)/2 = 10 kmph
Answer:E
Answer: (E) 10 kmph
Question: An alloy weighing 20 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 70 percent gold?
(A) 6
(B) 9
(C) 12
(D) 24
(E) 48
Rationale: In 24 ounces, gold is 20 * (70/100) = 14 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 14 + x = (24 + x)* 70/100 => x =9.
Answer is B.
Answer: (B) 9
Question: Riley had 21 green marbles. Then she bought 5 bags of blue marbles. There were 9 marbles in each bag. How many marbles does Riley have now?
(A) 23
(B) 49
(C) 60
(D) 41
(E) 66
Rationale: Step 1: Find the number of blue marbles.
5 × 9 = 45
Step 2: Find the total number of green and blue marbles.
21 + 45 = 66
Riley has 66 marbles.
Answer is E.
Answer: (E) 66
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 2 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
(A) d = (p-0.02)/1.18
(B) d = p/1.20
(C) d = p/1.02 - 0.18
(D) d= (p-0.18)/1.02
(E) d = p-0.20
Rationale: Let dealers price (d) be 1. so adding 2% to dealers price is d+ 2% of d. i.e. 1 + 2% of 1 which is1 + 0.02. then add 0.18 to the value.
Now 1.02 + 0.18. this is now 1.20. you have the gasoline stations price (p) as 1.20 dollars.
Now sub 1.20 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : D
Answer: (D) d= (p-0.18)/1.02
Question: Given 2x + y + z = 3 and 5x + 3y + z = 10, what is the value of x + y - z?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: (1) 5x + 3y + z = 10
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 4
The answer is B.
Answer: (B) 4
Question: If x^2+(1/x^2)=8, x^4+(1/x^4)=?
(A) 10
(B) 11
(C) 62
(D) 14
(E) 15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=8^2-2=62.
Thus, the answer is C.
Answer: (C) 62
Question: Last year 30 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
(A) 52
(B) 67
(C) 71
(D) 73
(E) 79
Rationale: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 30 + 26 + 32 - 0 - 11 - 6 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.
n(E or F or I) = 71
Answer (C)
Answer: (C) 71
Question: A man sells a car to his friend at 10% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
(A) Rs.25000
(B) Rs.37500
(C) Rs.50000
(D) Rs.60000
(E) None of these
Rationale: Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120×54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 10%.
Now S.P = Rs.45000 and loss = 10%
C.P. Rs.[10090×45000]= Rs.50000.
Correct Option : C
Answer: (C) Rs.50000
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is
(A) 15
(B) 20
(C) 25
(D) 35
(E) 45
Rationale: Explanation:
Let the numbers be a, b and c.
Then,
a2+b2+c2=138
and (ab + bc + ca) = 131
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
= 138 + 2 x 131 = 400
=>(a+b+c)=400−−−√=20.
Option B
Answer: (B) 20
Question: A customer asks for the production of x number of goods. The company produces y number of goods daily. Out of which z% are units for sale. The order will be completed in :
(A) [ x /{100y *(1 -z)}] days
(B) [(100yz) /x] days
(C) [100x /{y(100 -z)}] days
(D) 100 / {y*(z -1)} days
(E) Cannot determined
Rationale: Solution: Daily supply,
= (100-z)% of y
= {(100-z)y}/100
Thus, required number of days,
= [(100x)/(100-z)y].
Answer: Option C
Answer: (C) [100x /{y(100 -z)}] days
Question: Two trains of length 100 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 32 sec
(C) 82 sec
(D) 20 sec
(E) 19 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 100 + 280 = 380m.
The time required = d/s = 380/20 = 19 sec.
Answer:E
Answer: (E) 19 sec
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 78. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
(A) 87
(B) 89
(C) 86
(D) 93
(E) 95
Rationale: Total score on 3 tests = 78*3 = 234
Jerry wants the average to be = 80
Hence total score on 4 tests should be = 80*4 = 320
Score required on the fourth test = 320 - 234 = 86
Option C
Answer: (C) 86
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 4
(B) 6
(C) 8
(D) 2
(E) 5
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5 : 16Answer: E
Answer: (E) 5
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 60 mph. What is his average speed of travel for the entire journey?
(A) 52 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles.
Distance covered in the next 3 hours = speed * time = 60 * 3 = 180 miles.
Therefore, total distance covered = 80 + 180 = 260 miles.
Total time taken = 2 + 3 = 5 hours.
Hence, average speed = Total distance travelled/Total time taken=260/5 = 52 miles per hour.
Choice A
Answer: (A) 52 mph
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 700
(B) 720
(C) 740
(D) 780
(E) 800
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A)
Answer: (A) 700
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 25 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
(A) 20%
(B) 40%
(C) 56.25%
(D) 60%
(E) 75%
Rationale: original SP = X
Cost =C
current selling price = .8x ( 20% discount)
.8x = 1.5C (25% profit)
x= 1.25/.8 *C
x= 12.5/8 C
Original selling price is 1.5625C which is 56.25% profit
Answer C
Answer: (C) 56.25%
Question: A committee of 4 is to be selected from among 5 boys and 6 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
(A) 105
(B) 225
(C) 230
(D) 310
(E) 455
Rationale: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
6C1*5C3 + 6C2*5C2 + 6C3*5C1
6*10 + 15*10 + 20*5
60 + 150 + 100
310
D
Answer: (D) 310
Question: A family made a down payment of $50
and borrowed the balance on a set of
encyclopedias that cost $550. The
balance with interest was paid in 20
monthly payments of $30 each and a
final payment of $19. The amount of
interest paid was what percent of the
amount borrowed?
(A)  6%
(B)  12%
(C)  14%
(D)  16%
(E)  23.8%
Rationale: interest paid = 30*20+19 - 500 = 119
% off the balance = (119/500) * 100 = 23.8%
Answer is E.
Answer: (E)  23.8%
Question: Which is the middle even number between 6 and 14?
(A) 10
(B) 6
(C) 8
(D) 14
(E) 26
Rationale: 6+x = 14-x
2 x = 8
X = 4
Now 6+x = 10
ANSWER:A
Answer: (A) 10
Question: A bag consists of 20 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
(A) 3/4
(B) 2/4
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: Bag consists of 20 marbles, of which 5 are blue, 9 are red
remainder are white. So, white = 20 - 5 - 9 = 6.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/20+6/20 = 15/20 = 3/4
Hence, answer will be A.
Answer: (A) 3/4
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age four years back was?
(A) 14yr
(B) 15yr
(C) 20yr
(D) 25yr
(E) 30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 4 years back = 19-4 = 15 years
Answer is B
Answer: (B) 15yr
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 8 questions. If each question has 3 answer choices, and Kim answers every question, in how many different ways can she complete the test?
(A) a 40
(B) b 3^8
(C) c 5^8
(D) d 8^5
(E) e 40^40
Rationale: different ways to solve each question is 3.
So, 3*3*3*3.. 8 times ----> 3^8
Answer will be B
Answer: (B) b 3^8
Question: Exactly four sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?
(A) 0.3
(B) 0.2
(C) 0.01
(D) 0.148
(E) 0.144
Rationale: Total no. of sides = 10
Sides that are red = 4
Probability that the die lands with red side up = 4/10
Therefore, Probability that the die does not land with red side up = 1 - 4/10 = 6/10
Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll
= (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)
= (6/10) X (6/10) X (4/10)
= 144/1000
= 0.144
E
Answer: (E) 0.144
Question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
(A) 7
(B) 8
(C) 9
(D) 0
(E) 1
Rationale: 39 + 20 = 59/13 = 7 (Remainder)
ANSWER:A
Answer: (A) 7
Question: Two numbers are in the ratio of 5:7. If 12 is subtracted from each number, they are in the ratio of 11:17. What are the two numbers?
(A) 45, 63
(B) 50, 70
(C) 55, 77
(D) 60, 84
(E) 65, 91
Rationale: (5x-12):(7x-12) = 11y:17y
5x - 12 = 11y
7x - 12 = 17y
84-60 = 85y - 77y
24 = 8y
y = 3
5x-12 = 33
x = 9
The two numbers are 5x and 7x which are 45 and 63.
The answer is A.
Answer: (A) 45, 63
Question: A space shuttle orbits the earth at about 12 kilometers per second. This speed is equal to how many kilometers per hour?
(A)  480
(B)  2,880
(C)  4,800
(D)  28,800
(E)  43,200
Rationale: Seconds in 1 hours:
60s in 1 min
60 min in 1 hr
60*60=3600 sec in 1 hr
12*3600=43,200
Answer: E
Answer: (E)  43,200
Question: The price of a car is marked at $12,000. If the car has successive discounts of 20%, 10% and 5%, then at what price does a customer buy the car?
(A) $8208
(B) $8312
(C) $8424
(D) $8536
(E) $8610
Rationale: 0.95*0.9*0.8*12000 = $8208
The answer is A.
Answer: (A) $8208
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 100/3% loss
(C) 50/3% profit
(D) 100/3% loss
(E) None of these
Rationale: Explanation:
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
ANSWER IS A
Answer: (A) 16 2/3% loss
Question: During a sale, the price of a pair of shoes is marked down 20% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
(A) 9%
(B) 10%
(C) 11%
(D) 15%
(E) 25%
Rationale: Assume the price = 100
Price during sale = 80
Price after sale = 100
Percent increase = 20/80*100 = 25% approx.
Correct Option:E
Answer: (E) 25%
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 252° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 70%
Rationale: ANSWER: E
252° divided by 360° equals 0.7, therefore the sector is equal to 70% of the total
Answer: (E) 70%
Question: A train 990 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 2898
(B) 277
(C) 310
(D) 297
(E) 435
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (990 + x)/60 = 65/3
x = 310 m.
Answer: C
Answer: (C) 310
Question: On a Rs 10000 payment order, a person has a choice between 3	successive discounts of 10%, 10% and 30% and 3 successive discounts of 40%, 5% and 5%. By choosing the better offer, he can save :
(A) Rs 200
(B) Rs 255
(C) Rs 400
(D) Rs 433
(E) Rs 533
Rationale: 1st choice -> 3 discounts of 10%, 10% & 30%
10,000* 10%= 1000 (remaining amt after deducting discount = 9000)
9000*10% = 900 (remaining amt after deducting discount 8100)
8100*30% = 2430.
So total discount amt = 4330 (1000+900+2430)
2nd choice -> 3 discounts of 40%, 5% & 5%
10,000*40% = 4000 (remaining amt after deducting discount = 6000)
6000*5% = 300 (remaining amt after deducting discount = 5700)
5700*5% = 285
So total discount amt = 4585 (4000+300+285)
Savings = 4585-4330 = 255.
ANSWER:B
Answer: (B) Rs 255
Question: Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 900 miles?
(A) Six hours and 30 minutes.
(B) Seven hours and 30 minutes.
(C) Eight hours and 20 minutes.
(D) Nine hours and 15 minutes.
(E) Ten hours and 20 minutes.
Rationale: Speed of second train= 50*88/100= 44
Time= toral distance /total speed
900/ (50+44)= 900/94= 9.___
D is the answer
Answer: (D) Nine hours and 15 minutes.
Question: If 18 persons can build a wall 140 m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is?
(A) 28
(B) 18
(C) 24
(D) 21
(E) 16
Rationale: Explanation :
(Length 140:100) : (Persons 30:18) :: 42 : x140 x 30 x X = 100 x 18 x 42 or X = 18
Answer : B
Answer: (B) 18
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) Rs. 30
(B) Rs. 34
(C) Rs. 42
(D) Rs. 45
(E) Rs. 49
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: (C) Rs. 42
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
(A) 36
(B) 87
(C) 31
(D) 65
(E) 34
Rationale: (3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer: A
Answer: (A) 36
Question: Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
(A) 381
(B) 36
(C) 84
(D) 180
(E) 190
Rationale: Let the three people be A, B, and C.
If 1 person gets no objects, the 7 objects must be distributed such that each of the other two get 1 object at least.
This can be done as 6 & 1, 5 & 2, 4 & 3 and their rearrangements.
The answer would be ( 7C6 + 7C5 + 7C4 ) x 3! = 378
Also, two people getting no objects can be done in 3 ways.
Thus, the answer is 378 + 3 = 381
ANSWER:A
Answer: (A) 381
Question: 4, 6, 12, 14, 28, 30, ?
(A) 32
(B) 64
(C) 62
(D) 60
(E) 52
Rationale: The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer : D.
Answer: (D) 60
Question: If a and b are positive integers of I such that a/b=2.86, which of the following must be a divisor of a?
(A) 10
(B) B.13
(C) 18
(D) 26
(E) 50
Rationale: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Answer: (B) B.13
Question: A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
(A) 15 cents
(B) 10 cents
(C) 5 cents
(D) 2 cents
(E) 4 cents
Rationale: But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.
Option C is correct.
Answer: (C) 5 cents
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
(A) 50 km
(B) 56 km
(C) 70 km
(D) 80 km
(E) 46 km
Rationale: Let the actual distance travelled be x km.
Then,x/10	= (x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
Answer:A
Answer: (A) 50 km
Question: 50 is what percent of 125?
(A) 35%
(B) 40%
(C) 45%
(D) 50%
(E) 55%
Rationale: 50/125×100=50% ANSWER : B
Answer: (B) 40%
Question: There are 202 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
(A) 93
(B) 94
(C) 92
(D) 96
(E) 95
Rationale: Editing my solution:
Number of switches = 202
Number of switches turned on by A: 3, 6, ... 201 = 67
Number of switches turned on by B: 5, 10, ....200 = 40
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (67- 6) + (40 - 6) = 95
Answer: E
Answer: (E) 95
Question: A dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 5:1
(B) 10:1
(C) 15:1
(D) 20:1
(E) 25:1
Rationale: Explanation:
Dog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2.
Answer: B) 10:1
Answer: (B) 10:1
Question: A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%
(A) 4 kg
(B) 5 kg
(C) 8 kg
(D) 30 kg
(E) 35 kg
Rationale: Exp. Water in the given mixture = 10*20/100 =2 kg,
And spirit = (20-2) = 18 kg
Let x kg of water added, Then, x+2/20+x *100 ==25
4x+8 =20+x, or x =4 kg
Answer:A
Answer: (A) 4 kg
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 3
(B) 9
(C) 7
(D) 5
(E) 43
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Answer: (D) 5
Question: what will be the next for this series 9,19,40,69,149........
(A) 344
(B) 345
(C) 346
(D) 347
(E) 348
Rationale: 9 19 40 69 149 X
10 21 29 77 x-149
11 8 48 x-223
3 40 x-271
37 x-311
x-348
x-348=0
x=348
ANSWER:E
Answer: (E) 348