mathewhe/aqua_rat huggingface dataset:
Question: A certain class of students is being divided into teams. The class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
(A) 24
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: Let total no of students in the class be N
So, we are told that N is divisible by both 12 24
So, Lets find the least common multiple of 12 24 , ie 24
So our answer is (A) 24
Answer: (A) 24
Question: Find all rational zeros of P(x) = x3 - 7x + 6.
(A) x=1,2,-3
(B) x=2,2,-5
(C) x=7,4,-8
(D) x=6,6,-9
(E) x=2,1,-3
Rationale: P(x) = x3 - 7x + 6 : given
leading coefficient 1 and its factors are : +1,-1
constant term is 6 and its factors are : +1,-1,+2,-2,+3,-3,+6,-6
possible rational zeros : +1,-1,+2,-2,+3,-3,+6,-6
test : P(1) = 0, P(2) = 0 and P(-3) = 0
x = 1, x = 2 and x = -3 are the zeros of P(x).
correct answer A
Answer: (A) x=1,2,-3
Question: What is the remainder when 3^29 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
29 has the form 4k+1, so the units digit of 3^29 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Answer: (D) 3
Question: Find out the square of a number which when doubled exceeds its one nineth by 17 ?
(A) 16
(B) 25
(C) 81
(D) 26
(E) 17
Rationale: Let the number be p, then the square will be p^2
According to question:
2p = (p/9) + 17
=> 18p = p + 153
=> p = 9
p^2 =9^2 = 81
Answer : C
Answer: (C) 81
Question: The probability of Sam passing the exam is 1/2. The probability of Sam passing the exam and Michael passing the driving test is 1/6. What is the probability of Michael passing his driving test?
(A) 1/24.
(B) 1/2.
(C) 1/3.
(D) 2/3.
(E) 2/5
Rationale: 1/2 *1/m= 1/6 , 1/m = 1/3
Answer C
Answer: (C) 1/3.
Question: Mr. Wayne bungee jumps from the top of a building straight to the ground at a constant speed. 3 seconds after he starts plummeting he passes the 20th floor. 15 seconds after he starts plummeting he passes the 5th floor. Each floor is 3.8 meters high. What is Mr. Wayne's speed in meters per second?
(A) 3
(B) 4.75
(C) 4
(D) 4.25
(E) 5
Rationale: IMO: B
15 Floors * 3.8 Meter/Floor = 57 Meters
Time= 12 sec
Rate * 12 = 57
Rate= 57/12
=4.75
Answer B
Answer: (B) 4.75
Question: Manie spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?
(A) $30
(B) $35
(C) $70
(D) $105
(E) $210
Rationale: Manie spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
Answer: (C) $70
Question: If John takes 5 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
(A) 5z/x
(B) 300z/x
(C) 300xz
(D) 300x/z
(E) 5x/z
Rationale: It will take (z/x)(5) minutes which is (z/x)(5)(60) seconds = 300z/x seconds.
The answer is B.
Answer: (B) 300z/x
Question: If there are 35 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:4, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
(A) 1/25
(B) 2/25
(C) 3/25
(D) 4/25
(E) 6/49
Rationale: 35 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:4
So, 7x=35 ---> x=5
Red marbles = 3*x = 3*5 = 15
Blue marbles = 4*x = 4*5 = 20
Prob to select a red marble = 15/35 = 3/7
Prob to select 2 red marbles with replacement = 3/7*2*7 = 6/49
Hence, answer will be E.
Answer: (E) 6/49
Question: A firm has 5 senior partners and 7 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
(A) 145
(B) 155
(C) 165
(D) 175
(E) 185
Rationale: The number of ways to form a group of 3 is 12C3 = 220
The number of groups with no senior partner is 7C3 = 35
The number of groups with at least one senior partner is 220-35 = 185
The answer is E.
Answer: (E) 185
Question: If the sum of two numbers is 45 and the H.C.F and L.C.M of these numbers are 3 and 100 respectively, then the sum of the reciprocal of the numbers is equal to:
(A) 103/300
(B) 103/200
(C) 112/300
(D) 154/140
(E) 100/300
Rationale: Let the numbers be a and b.
Then, a + b = 45 and ab = 3*100 = 300.
Required sum = 1/a + 1/b = (a + b)/ab = 103/300
ANSWER:A
Answer: (A) 103/300
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 6?
(A) y = -1/2*x + 3
(B) y = 1/2*x - 6
(C) y = 1/2*x + 3
(D) y = 2x + 3
(E) y = 2x − 3
Rationale: Since our line has to perpendicular to y = − 2x + 3
Slope of this line , m = -2
Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)
y-intercept of line L is same as y intercept of line y = 2x − 6
y - intercept of line L = -6
Required line = 1/2* x - 6
Answer B
Answer: (B) y = 1/2*x - 6
Question: Which of the following could be the value of x, if |4x – 2| = 10?
(A) –3
(B) –2
(C) 1
(D) 2
(E) 4
Rationale: |4x – 2| = 10
=> 4x - 2 = 10
or 4x - 2 = -10
=> 4x = 12 or 4x = -8
=> x = 3 or x = -2
Answer B
Answer: (B) –2
Question: In a hotel we can order two types of varieties, but we can make 4 more varieties in home. One can choose the four varieties with two from hotel as must. Find how many ways one can order.
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: 2c2*4c2=6ways
ANSWER:C
Answer: (C) 6
Question: Calculate the fourth proportional to 5.2, 6.6 and 9.1?
(A) 19.55
(B) 10.55
(C) 11.55
(D) 10.2
(E) 12.5
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 5.2 , B = 6.6 and C = 9.1
(6.6 × 9.1)/5.2 = 11.55
Answer: Option C
Answer: (C) 11.55
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than seven people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
(A) x/4
(B) x/7
(C) x/11
(D) x/28
(E) 3x/28
Rationale: If 7 people share the rent, each person would pay x/7.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/7 = 7x/28 - 4x/28 = 3x/28
The answer is E.
Answer: (E) 3x/28
Question: A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 200
(B) 220
(C) 180
(D) 250
(E) 260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 32 = 15
x + 300 = 480
x = 180 m.
Answer: Option C
Answer: (C) 180
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is?
(A) 109
(B) 106
(C) 104
(D) 108
(E) 101
Rationale: Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.Answer: D
Answer: (D) 108
Question: In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.35 sec
(B) 2.85 sec
(C) 7.5 sec
(D) 2.75 sec
(E) 1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 110/40
= 2.75 sec.
Answer:D
Answer: (D) 2.75 sec
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 6
(B) 5
(C) 4
(D) 78
(E) 2
Rationale: 150 = (750*5*R)/100
R = 4%.Answer: C
Answer: (C) 4
Question: Find out the wrong number in the series.
6, 12, 48, 102, 384, 768, 3072
(A) 768
(B) 384
(C) 102
(D) 488
(E) 12
Rationale: Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 102.
ANSWER:C
Answer: (C) 102
Question: Manet has to pay back her bank loan over 9 months following the below sequence.
$50, $55, $65, $80, $85, $95, $110, $115, ?
How much will she pay back on the ninth month?
(A) $155
(B) $145
(C) $135
(D) $125
(E) $130
Rationale: The sequence progresses +5, +10, +15 repeated; The amount to pay back on the 9th Month is $125
Ans D
Answer: (D) $125
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is
(A) 69990
(B) 69993
(C) 70000
(D) 77000
(E) 78000
Rationale: Explanation:
(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
B)
Answer: (B) 69993
Question: In a workshop there are 4 kinds of beds, 2 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) 72.
(B) 80.
(C) 56.
(D) 48.
(E) 16.
Rationale: Bed = Select 1 out of 4 = 4C1 = 4
Shelf = Select 1 out of 2 = 2C1= 2
Chair (7)+ Closet (2) = Total 9 = Select 1 out of 9 = 9C1
Possible combinations to chooseBED*SHELF*(CHAIR+CLOSET)=4*2*9=72 ways
ANSWER IS A
Answer: (A) 72.
Question: Find the largest number of four digits exactly divisible by 12,15,18 and 27.
(A) 9770
(B) 9740
(C) 9780
(D) 9750
(E) 9720
Rationale: The Largest number of four digits is 9999.
Required number must be divisible by L.C.M. of 12,15,18,27 i.e. 540.
On dividing 9999 by 540,we get 279 as remainder .
Therefore, Required number = (9999-279) = 9720.
Answer is E.
Answer: (E) 9720
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
(A) 2888
(B) 24000
(C) 27777
(D) 29997
(E) 27712
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer: B
Answer: (B) 24000
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 299
(B) 277
(C) 112
(D) 750
(E) 123
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time
= 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x
= 25 * 60 / 2
= 750
Answer: D
Answer: (D) 750
Question: The perimeters of two squares are 40 cm and 24 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 22 cm
(B) 24 cm
(C) 32 cm
(D) 28 cm
(E) 29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 24/4 = 6 cm
Area of third Square = 10*10 - 6*6
= 64 cm
So side of third square = 8 [because area of square = side*side]
Perimeter = 4*Side = 4*8 = 32 cm
Answer: Option C
Answer: (C) 32 cm
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/3% profit
(B) 50/6% profit
(C) 16 2/3% loss
(D) 100/3% loss
(E) 120/3% loss
Rationale: Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
ANSWER IS C
Answer: (C) 16 2/3% loss
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/35
(C) 31/31
(D) 31/36
(E) 31/37
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
Answer: (A) 31/32
Question: A man can row a boat at 18 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/16 hours
(B) 80/13 hours
(C) 15/6 hours
(D) 30/13 hours
(E) 50/13 hours
Rationale: Speed downstream = 18 + 6 = 24 kmph.
Time required to cover 60 km downstream
= d/s = 60/24
= 15/6 hours.
Answer:C
Answer: (C) 15/6 hours
Question: The ratio of the first and second class fares between two stations is 3 : 1 and that of the number of passengers travelling between the two stations by the first and the second class is 1 : 50. If in a day, Rs. 1, 325 are collected from the passengers travelling between the two stations, then the amount collected from the second class from the second class passengers is
(A) 1,250
(B) 1,000
(C) 850
(D) 750
(E) 350
Rationale: Explanation:
Let the fares be 3 x and x respectively for the first and second class.
Suppose in a day passengers travelling between the two stations be 1 and 50.
Then by given condition, 3 x × 1+x × 50=1,325 => x=25
The amount collected from second class = 25×50 = Rs. 1250
Answer: A
Answer: (A) 1,250
Question: In a class, 5 people like baseball and football, 2 people only like baseball, 3 people only like football, and 6 people like neither. How many people are in the class?
(A) 10
(B) 14
(C) 16
(D) 20
(E) 22
Rationale: 16.
To get the answer, you can simply add the different types of students, as there are no overlaps in the categories: 5+2+3+6=16. As such, the correct answer is C: 16.
Answer: (C) 16
Question: Mr. Sam's car gets him 50 miles per gallons of gas. If Mr Sam get a full tank with 14 gallons of gas, How far can Mr Sam go?
(A) 52 miles
(B) 1400 miles
(C) 700 miles
(D) 1000 miles
(E) 100 miles
Rationale: Solution
Number of miles per gallon = 50 miles
Number of miles 14 gallons = x
x = 50 Ã— 14 = 700 miles.
So, Number of miles Sam gets with 14 gallons = 700 miles.
Option C
Answer: (C) 700 miles
Question: The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21, is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Let x is subtracted.
Then,
(6−x)/(7−x)< 16/21
21(6—x)<16(7—x)
=>5x>14=x>2.8
Least such number is 3
Option A
Answer: (A) 3
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 50 sec
(B) 190 sec
(C) 287 sec
(D) 74 sec
(E) 697 sec
Rationale: Explanation:
Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
ANSWER B
Answer: (B) 190 sec
Question: The length of a rectangle is increased by 35% and its breadth is decreased by 20%. What is the effect on its area?
(A) 10800
(B) 1299
(C) 1000
(D) 10000
(E) 2887
Rationale: 100 * 100 = 10000
135 * 80 = 10800
Answer: A
Answer: (A) 10800
Question: If the average cost of a house was $50,000 in 1965 and was x in 2000, what was the average increase in home prices per year over this period?
(A) A)(x+50,000)/40
(B) B)(x-50,000)/35
(C) C)(50,000/40)+x
(D) D)(50,000-x)/40
(E) E)x/40
Rationale: Average house price in 2000: x
Average house price in 1965: 50,000
2000-1965=35
Average increase per year: (x-50,000)/35
Answer is B
Answer: (B) B)(x-50,000)/35
Question: To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 5 pounds and 10 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 10 cents
(B) Combined, with a saving of 15 cents
(C) Separately, with a saving of 5 cents
(D) Combined, with a saving of 5 cents
(E) Separately, with a saving of 15 cents
Rationale: 5 pounds = 1*10+4*5 = 30
10 pounds = 1*10+9*5 =55
total = 85
15 pound = 1*10+14*5 = 80
dif. 5
Answer : D
Answer: (D) Combined, with a saving of 5 cents
Question: A department of eight people - four men and four women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?
(A) 36
(B) 48
(C) 60
(D) 72
(E) 90
Rationale: They can make a team of 3 men and 2 women.
The number of ways to do this is 4C3*4C2=4*6 = 24
They can make a team of 2 men and 3 women.
The number of ways to do this is 4C2*4C3=6*4 = 24
The total number of distinct groups is 48.
The answer is B.
Answer: (B) 48
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
(A) 720
(B) 730
(C) 740
(D) 780
(E) 790
Rationale: 720
Option 'A'
Answer: (A) 720
Question: A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got! How many students were there in the class?
(A) 30
(B) 26
(C) 11
(D) 31
(E) 32
Rationale: DETAILED SOLUTION
Let the total students be (n + 1)
Let total badges be x
Let the average of ‘n’ students be y
The student who got 1/6th of x = 5y
Or y = x/30
Therefore ‘n’ students got 1/30th of total share each
Or n * x/30 + 1 * x/6 = x
nx + 5x = 30x
n + 5 = 30
Or n = 25
Total = n + 1 = 26
Correct Answer: B
Answer: (B) 26
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 5 employees to 3 different offices?
(A) 243
(B) 245
(C) 45
(D) 121
(E) 11
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 3*3*3*3*3=3^5=243.
Answer: A.
Answer: (A) 243
Question: Matt gets a $1,600 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?
(A) 9
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let, Average Commission = x
No. of items sold = y
Total Commission = xy
New Commission = xy+1600
New Average = (xy+1600) / (y+1) = 150+x
i.e. (xy+1600) = (y+1)* (150+x)
i.e. (xy+1600) = (xy+x+150y+150)
i.e. (1450) = (x+150y)
New Commission = 400 = 150+x
i.e. x=250
i.e. y = 8
New Sales = y+1 = 9
Answer: option A
Answer: (A) 9
Question: Samantha's investment portfolio consists of three stocks: a railway, a bank, and a computer company. In the month of February, the price of the railway's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 15%, but the overall value of her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order railways, bank, and computer company respectively?
(A) $55, $85, $40
(B) $65, $60, $60
(C) $65, $55, $90
(D) $25, $60, $70
(E) $85, $25, $20
Rationale: Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B and E, E is obviously the safer bet and is the right answer.
Answer is E.
Answer: (E) $85, $25, $20
Question: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in (10+10) hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
(A) -$56
(B) -$6
(C) $0
(D) $6
(E) $8
Rationale: A professional janitor can clean a certain high school in 8 hours
So (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR
A student sentenced to detention can clean that same high school in 20 hours
So (applying rule #1), the student can clean 1/(10+10) or 1/20 of the school in ONE HOUR
So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR
1/8 + 1/20 = 5/40 + 2/40 = 7/40
So, in ONE HOUR they can clean 7/40 of the school.
Applying rule #2, it will takethem40/7 hoursto clean the ENTIRE school.
The janitor earns $21/hour and the student earns $7/hour, so their combined rate is$28/hour.
Theircombined wages= (pay rate)(time) = ($28/hour)(40/7 hours) =$160
Working ALONE, the janitor takes 8 hours and earns $21/hour
So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) =$168
$168-$160= $8, so the answer is E
Answer: (E) $8
Question: When m is divided by 9, the remainder is 8. When m is divided by 13, the remainder is 1. If 1 < m < 200, what is the greatest possible value of m?
(A) 47
(B) 65
(C) 103
(D) 117
(E) 170
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
170 = 162 + 8 (162 divisible by 9)
170 = 169 + 1 (169 divisible by 13)
it fits the result
Answer = E
Answer: (E) 170
Question: a coffee seller has two types of coffee Brand A costing 5 bits per pound and Brand B costing 3 bits
per pound. he mixes two brands to get a 40 pound mixture. he sold this at 6 bits per pound. the seller gets a profit of 33 1/2 percent. how much he has used Brand A in the mixture?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: cost price of mixture=(100*selling price of mixture)/(100+profit)=(100*6)/(100+33.5) =600/133.5=Rs 4.50(approximately),
Then ratio of A and B = (4.50-3):(5-4.50)=3:1,
Therefore Brand A in 40 pound mixture=40*3/4=30
ANSWER:C
Answer: (C) 30
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections R of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
R=3*20=60
E. 60
Answer: (E) 60
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.00 a.m. ?
(A) 7
(B) 6
(C) 5
(D) 2
(E) 8
Rationale: C
5
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 5 times before 9.00 a.m.
Answer: (C) 5
Question: The compound interest earned on a sum for the second and the third years are $1200 and $1260 respectively. What is the rate of interest?
(A) 5%
(B) 8%
(C) 11%
(D) 14%
(E) 18%
Rationale: 1260 - 1200 = 60 is the rate of interest on $1200 for one year.
The rate of interest = (100 * 60) / (1200) = 5%
The answer is A.
Answer: (A) 5%
Question: A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 6 p.m.?
(A) 30 min
(B) 35 min
(C) 45 min
(D) 50 min
(E) 55 min
Rationale: there are 9 hours in between 9 a.m. to 6 p.m.
9*5=45 minutes.
ANSWER:C
Answer: (C) 45 min
Question: A coin is tossed 7 times. Find the probability of getting more heads than tails in all 7 tosses?
(A) 1/2
(B) 63/128
(C) 4/7
(D) 61/256
(E) 63/64
Rationale: Assuming the coin is fair - P(H)=P(T)=1/2
We can do as proposed by the explanation in your initial post:
Total outcomes: 2^7
Favorable outcomes:
4 heads --> combination of HHHHTTT --> 7!/(4!*3!)=35 (# of permutation of 7 letters out of which 4 H's and 3 T's are identical);
5 heads --> combination of HHHHHTT --> 7!/(5!*2!)=21;
6 heads --> combination of HHHHHHT --> 7!/(6!*1!)=7;
7 heads --> combination of HHHHHHH --> 1;
P(H>T)=Favorable outcomes/Total outcomes=(35+21+7+1)/2^7=1/2.
Answer:A
Answer: (A) 1/2
Question: Working together at their respective constant rates, Machine A and Machine B can produce 900 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 900 unit total would it produce?
(A) 30
(B) 33
(C) 50
(D) 67
(E) 75
Rationale: 1/A+1/B= 1/T
1/A +1/12= 1/8 (50% more of 8 is 12)
1/A= 1/24
Machine A can produce 900 units in 24 hrs, so it can produce 900*8/24= 300 units is 8 hrs.
300 is 30% of 900.
A is the answer
Answer: (A) 30