divelab/Sys2Bench huggingface dataset:
Question: Two cars are driving toward each other. The first car is traveling at a speed of 90 km/h, which is 50% faster than the second car's speed. If the distance between the cars is 975 km, how many hours will it take until the two cars meet?
Options:
A)6
B)6.5
C)7
D)7.5
E)8
Rationale: The speed of the first car is 90 km/h.
The speed of the second car is 90 / 1.5 = 60 km/h.
The two cars complete a total of 150 km each hour.
The time it takes the cars to meet is 975 / 150 = 6.5 hours.
The answer is B.
Answer: B
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
Options:
A)20
B)10
C)50
D)40
E)60
Rationale: D
40
We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer: D
Question: If a + b > 0 and a * b < 0, which of the following must be true?
I. a > 0 or b > 0
II. a < 0 or b < 0
III. a and b have the same sign
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: I. True, for the sum to be greater than 0, at least one of a or b has to be positive
II. True, for the product to be less than 0, one of a or b has to be negative
III. Not true, by the previous two, one of a or b has to be positive and the other has to be negative
D
Answer: D
Question: Three printing presses, P, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take P, working alone at its constant rate, to do the same job?
Options:
A)8
B)10
C)12
D)15
E)20
Rationale: =1/4-1/5=1/20
P can do 1/20 job in 1 hour
P can do the whole job in 20 hours=E
Answer: E
Question: what is the value of y if the greatest common divisor of (e+5)!,(e-2)!, and (e+2)! is 24.
Options:
A)5
B)7
C)4
D)66
E)6
Rationale: GCD of (e+4)!,(e-2)!, and (e+2)! is 24. Find x.
Best way to find n is substitute each of the answer and find out the correct one.
Only option E gave the correct answer.
Try 6 and find GCD or 10!, 4! and 8!. 4! itself is 24 and 4! which is contained in the other two factorials. This satisfies the condition, hence answer is 6.
Answer is E.
Answer: E
Question: What is the sum of the different positive prime factors of 640?
Options:
A)5
B)7
C)10
D)15
E)17
Rationale: The prime factorization of 640
= 64 * 10
= 2^6 * 2*5
The sum of the different positive prime factors = 2+5 = 7
The answer is B.
Answer: B
Question: If two painters can complete two rooms in two hours, how many rooms painted if 10 painters work for 6 hours?
Options:
A)35
B)25
C)20
D)30
E)15
Rationale: Explanation:
Two painters can complete two rooms in two hours.So 30 rooms can be painted in 6 hrs by 10 painters
Answer: D) 10 painters
Answer: D
Question: A person travels equal distances with speeds of 3km/hr, 6km/hr, 9km/hr. and takes a total time of 11minutes. Find the total distance ?
Options:
A)1km
B)500mts
C)900mts
D)2km
E)250mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/3)+(x/6)+(x/9) = 11/60
x=0.3
total distance = 3*0.3 = 0.9km = 900meters
correct option is C
Answer: C
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.45 only. Menâ€™s wages are?
Options:
A)6Rs
B)7Rs
C)8Rs
D)4Rs
E)3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 45 Rs.
5M + 5M + 5M ----- 45 Rs.
15M ------ 45 Rs. => 1M = 3Rs.
Answer:E
Answer: E
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 7.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
Options:
A)$0.50
B)$1.00
C)$1.25
D)$1.50
E)$1.75
Rationale: OA is definitely wrong. The answer should be C.
Answer: C
Question: A student gets 50% in one subject, 70% in the other. To get an overall of 70% how much should get in third subject.
Options:
A)90%
B)25%
C)45%
D)55%
E)65%
Rationale: Let the 3rd subject % = x
50+70+x = 3*70
120+x =210
x = 210-120 = 90
Answer : A
Answer: A
Question: A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
Options:
A)4.8 cm
B)4.4 cm
C)4.9 cm
D)5.0 cm
E)5.2 cm
Rationale: Area of triangle is 1/2 * 12 * 8 = 48
Side of square = x
The entire triangle split into two right angled triangle and one square with dimensions as follows
i) square with side x
ii) Right angled triangle with perpendicular sides x and 12-x
iii) Right angled triangle with perpendicular sides 8-x and x
Sum of area of all three = 48
= x2 + 1/2*x*(12-x) + 1/2*x*(8-x) = 48
= x = 4.8 cm
answer : A
Answer: A
Question: If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
Options:
A)-10.0
B)-0.5,
C)-0.4
D)-0.2,
E)10.0
Rationale: Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: C
Answer: C
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
Options:
A)11.1%
B)20%
C)45.8%
D)10.5%
E)31.6%
Rationale: Option E
Explanation:
100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: E
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)7 days
Rationale: Answer: Option 'A'
That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
Answer: A
Question: On the number line, if x is halfway between -8 and 4, and if y is halfway between -2 and 6, what number is halfway between x and y?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: x= -2 and y = 2.
The answer is C.
Answer: C
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x
Options:
A)2980
B)2990
C)3000
D)3100
E)3158
Rationale: 12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
E
Answer: E
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Options:
A)104
B)376
C)1267
D)198
E)621
Rationale: 624/6 = 104 kmph
Answer: A
Answer: A
Question: The ratio 5:20 expressed as percent equals to
Options:
A)50 %
B)125 %
C)25 %
D)None of above
E)30%
Rationale: Explanation:
Actually it means 5 is what percent of 20, which can be calculated as,
(5/20)*100 = 5 * 5 = 25
Option C
Answer: C
Question: A woman on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options:
A)71.11 km/hr.
B)68.11 km/hr.
C)44.11 km/hr.
D)88.11 km/hr.
E)31.11 km/hr.
Rationale: A
71.11 km/hr.
Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 320 x 2/9 = 71.11 km/hr.
Answer: A
Question: The average (arithmetic mean) of the even integers from 24 to 48 inclusive is how much greater than the average (arithmetic mean) of the even integers from 12 to 24 inclusive?
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: So, according to A mean of a set of even numbers from 24 to 48 =(24+48)/2=36 and mean of a set of even numbers from 12 to 24 =(12+24)/2=18
Difference=36-18=18
Answer: C.
Answer: C
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {7, 8, 9, 11, 12, 13}, standard deviation = A
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = B
Set III = {6, 6, 6, 14, 14, 14}, standard deviation = C
Rank these three standard deviations from least to greatest.
Options:
A)A, B, C
B)A, C, B
C)B, A, C
D)B, C, A
E)C, B, A
Rationale: SD is minimum when the terms are closer to the mean.
In set 2, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 1 and Set 3, Set 1 has terms more closer to mean than set 3. hence, Set 3 Sd is the highest.
So, Answer is C
Answer: C
Question: There are 200 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of managers to 98%?
Options:
A)150
B)100
C)99
D)50
E)25
Rationale: There are 198 managers and 2 others. The 2 others would compose 2% of the total number of people if there were 100 people in the room. Thus 100 managers must leave.
The answer is B.
Answer: B
Question: welve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. Sixteen adults left and four children joined them. How many days will they take to complete the remaining work?
Options:
A)3 days
B)4 days
C)6 days
D)8 days
E)10 days
Rationale: One child’s one day work = 1/192.
One adult’s one day’s work = 1/96.
Work done in 3 days = ((1/96) x 16 x 3) = 1/2
Remaining work = 1 – 1/2 = 1/2
(6 adults+ 4 children)’s 1 day’s work = 6/96 + 4/192 = 1/12
1/12 work is done by them in 1 day.
1/2 work is done by them in 12 x (1/2) = 6 days
ANSWER:C
Answer: C
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 five years back was:
Options:
A)76 years.
B)14 years.
C)55 years.
D)45 years.
E)61 years.
Rationale: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
Answer: B
Answer: B
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $5 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)8n + 2
B)8n + 4
C)9n + 2
D)9n + 3
E)9n + 4
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [5+ (n-1)]
= $ n+4
total cost
8n+n+4 = 9n+4
E
Answer: E
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability T that their product will be of the form of x^2-(by)^2, where b is an integer?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)T=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability T= 1/12 * 2 = 1/6
Ans E
Answer: E
Question: If x = y+3+4.5x and y = x+17, what is the value of x/y ?
Options:
A)-6/5.
B)-40/113.
C)1/4.
D)5/6.
E)1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 17 (Eq. we are given)
x = x + 17 + 3 + 4.5x
Combine like terms
x = 5.5x + 20 --> -4.5x = 20 --> x = -40/9
(2) y = x + 17
Substitute x for x = -40/9
y = (-40/9) + 17 = 113/9
(3) x/y = ?
Substitute x and y we found above
x/y = (-40/9) / (113/9) = (-40/9) * (9/113) = -40/113
My answer: B
Answer: B
Question: The greatest number of four digits which is divisible by 15, 24, 40 and 75 is :
Options:
A)9000
B)9400
C)9600
D)9800
E)None of these
Rationale: Solution
Greatest number of 4 digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
∴ Required number =(9999 - 399) = 9600. Answer C
Answer: C
Question: Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks?
Options:
A)6.
B)16.
C)18
D)21
E)26
Rationale: 5 = 1P + 1 N
93 = XP + 15N, where X is the number of pencils
Possible prices for 1P & 1N (integers):
N = 1 P = 4 then 15N = 15, 4X = 93 - 15 = 78, X = 19.5 (not an integer)
N = 2 P = 3 then 15N = 30, 3X = 93 - 30 = 63, X = 21 (the answer we were looking for, no need to continue calculations)
N = 3 P = 2
N = 4 P =1
Answer: D
Answer: D
Question: The number of female students in a college in the previous year was 480. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
Options:
A)1680
B)1760
C)1840
D)1920
E)2000
Rationale: Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/480 = 2(2x/y)
y = 1920
The answer is D.
Answer: D
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
Options:
A)r / (r + b + w)
B)r
C)(r + b + w)
D)r / (r + b)
E)(r + b + w)*e
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
A
Answer: A
Question: A, B and C invest in a partnership in the ratio: 7/2,4/3,6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year is Rs.21,600, then what is B's share in the profit?
Options:
A)1000
B)2000
C)3000
D)4000
E)5000
Rationale: Ratio of the initial investment
=7/2:4/3:6/5=105:40:36
Therefore, let the initial investments of A, B and C be 105x,40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments
=(105x×4)+(105x×150/100×8) :40x×12:36x×12
=105+(105×3/2×2) :40×3:36×3
=105×4:40×3:36×3
=35×4:40:36
=35:10:9
B's share = total profit × 10/54
=21600×10/54=4000
Answer is D.
Answer: D
Question: Each student at a certain business school is assigned a 5-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
Options:
A)9,000
B)36,000
C)2,700
D)2,592
E)1,944
Rationale: The identification number is of the form _ _ _ _
1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7
We can have the following number of possibilities for each space
__ __ __ __
9 10 10 10 4
Total cases = 36000
Option C
Answer: C
Question: A person borrows Rs. 7000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
Options:
A)100 rs
B)150 rs
C)140 rs
D)180 rs
E)200 rs
Rationale: Gain in 2 years =
[(7000*6*2)/100]-[(7000*4*2)/100]
840-560=280
Gain in 1 year =(280/2)=140 rs
ANSWER:C
Answer: C
Question: If 13 = 13w/(1-w) ,then (6w)2 =
Options:
A)1/4
B)1/2
C)1
D)2
E)6
Rationale: 13-13w=13w
26w=13
w=1/2
6w=3
6w*2=3*2=6
ANSWER:E
Answer: E
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?
Options:
A)1.1G
B)1.2G
C)1.3G
D)1.4G
E)1.5G
Rationale: After 3 weeks, the price was 1.3*0.8*1.25*G=1.3G
The answer is C.
Answer: C
Question: 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
Options:
A)Sunday
B)Tuesday
C)Friday
D)Tuesday
E)Thursday
Rationale: Explanation:
Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday
Answer: Option C
Answer: C
Question: The captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Let the average age of the whole team be x years.
11x - (27 + 30) = 9 (x - 1)
11x - 9x = 48
2x = 48
x = 24.
The average age of the team is 24 years.
The answer is D.
Answer: D
Question: If the operation x is defined by a x b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then − 1 x (1 x − 1) =
Options:
A)−1
B)0
C)1
D)25
E)29
Rationale: On solving the inner bracket we get 4.
then we get equation as -1 x 4 where b=4 and a=-1
Answer D
Answer: D
Question: A bus leaves the stop 30 minutes before the scheduled time. The driver decreases its speed by 30km/hr. At the next bus stop 180 km away, the bus reached on time. Find the original speed of the bus?
Options:
A)110 kms/hr
B)120 kms/hr
C)130 kms/hr
D)140 kms/hr
E)None of above
Rationale: actual time = t180 = x*t180 = (x – 30)*(t +1/2)Solve both equation, we will get x = 120km/hr Answer : B
Answer: B
Question: The inverse ratio of 3: 2: 1 is?
Options:
A)1:2:3
B)2:3:1
C)3:1:2
D)2:3:6
E)None of these
Rationale: Explanation:
1/3: 1/2: 1/1 = 2:3:6
Answer is D
Answer: D
Question: Look at this series: 4, 2, 1, (1/2), (1/4), ... What number should come next?
Options:
A)1/8
B)1/3
C)1/4
D)1/2
E)1/5
Rationale: A
Answer: A
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 3 runs. His new average is:
Options:
A)60 runs
B)65 runs
C)70 runs
D)75 runs
E)78 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 3
= 11x + 33 = 10x + 108
= x = 75.
New average = (x + 3) = 78 runs.
Answer:E
Answer: E
Question: A car is purchased on hire-purchase. The cash price is $21 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly instalments. Interest is charged at 12% p.a. What is the monthly instalment?
Options:
A)$503
B)$504
C)$505
D)$506
E)$507
Rationale: Explanation:
Cash price = $21 000
Deposit = 10% × $21 000 = $2100
Loan amount = $21000 − $2100
= $18900
I=p*r*t/100
I=11340
Total amount = 18900 + 11340 = $30240
Regular payment = total amount /number of payments
Answer: B
Answer: B
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)10/3 sec
B)20/4 sec
C)20/7 sec
D)22/7 sec
E)60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 72)*5/18 = 6*5 = 30 mps.
The time required = d/s = 100/30 = 10/3 sec.Answer:A
Answer: A
Question: If 21/22 = 0.95.45, what is the 57th digit to the right of the decimal point of the fraction?
Options:
A)1
B)4
C)5
D)7
E)9
Rationale: we are not concerned what 21/22 means..
we have to look at the decimal..
0.9544 means 0.95454545....
so leaving first digit to the right of decimal, all ODD numbered digits are 4 and all EVEn numbered are 5..
here 57 is odd, so ans is 4
Answer is B
Answer: B
Question: 16 men can complete a piece of work in 28 days. In how many days can 20 men complete that piece of work?
Options:
A)55 days
B)77 days
C)22.4 days
D)88 days
E)44 days
Rationale: 16 * 28 = 20 * x => x
= 22.4 days
Answer: C
Answer: C
Question: John left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change?
Options:
A)40
B)200
C)266
D)267
E)600
Rationale: In order not to lose money because of the change John's total commission must beat least$75,000-$45,000=$30,000, so total sales must beat least$30,000/0.15=$200,000. Which means that he must makeat least$200,000/750=800/3=266.6 sales, so 267 sales.
Answer: D.
Answer: D
Question: The diagonals of a rhombus are 14 cm and 20 cm. Find its area?
Options:
A)176
B)190
C)140
D)278
E)292
Rationale: 1/2 * 14 * 20
= 140
Answer:C
Answer: C
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability Q that exactly two visitors will buy a pack of candy?
Options:
A)0.343
B)0.147
C)0.189
D)0.063
E)0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=Q
Answer - C
Answer: C
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)150 m
B)240 m
C)589 m
D)600 m
E)200m
Rationale: Explanation:
Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: B
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent Q above the cost price were his articles marked?
Options:
A)100%
B)80%
C)75%
D)66+2/3%
E)50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 Q= 200%
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: A
Question: Three pipes A, B and C can fill a tank from empty to full in 20 minutes, 20 minutes and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
A)1/2
B)1/5
C)1/3
D)1/4
E)1/6
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/20 + 1/20 + 1/30) = 6/15
Part filled by C in 3 minutes = 3/30
Required ratio = 3/30 * 15/6 = 1/4
Answer:D
Answer: D
Question: Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 6 days?
Options:
A)24
B)18
C)16
D)12
E)8
Rationale: 4 machines do x units in 6 days
we have x/6 => rate of the 4 machines
we know that we need to have 4x units in 6 days
therefore, we need to get to 4x/6 rate of the machines.
rate of one machine is x/6*1/4 = x/24.
now, we need to know how many machines need to work simultaneously, to get 3x done in 6 days.
3x/6 work needs to be done by machines that work at x/24 rate.
let's assign a constant Y for the number of machines:
(x/24)*y = 3x/6
y = 3x/6 * 24/x
cancel 6 with 24, and x with x and get -> 12. Answer choice D
Answer: D
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
Options:
A)17/65
B)17/25
C)17/28
D)17/65
E)17/39
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability
= 34/50
= 17/25.
Answer: B
Answer: B
Question: A man's speed with the current is 21 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
Options:
A)10
B)20
C)16
D)30
E)40
Rationale: Man's speed with the current = 21 km/hr
=> speed of the man + speed of the current = 21 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 21 - 2.5 = 18.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 18.5 - 2.5 = 16 km/hr
Answer is C.
Answer: C
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)28
B)27
C)30
D)29
E)12
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: C
Question: After 6 games, team B had an average of 70 points per game. If it got only 47 points in game 7, how many more points does it need to score to get its total above 500?
Options:
A)85
B)74
C)67
D)33
E)28
Rationale: (6*70) + 47 +x >500
420+47+x > 500
467+x >500
=> x>33
Option D
Answer: D
Question: 18 balls are numbered 1 to 18. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
Options:
A)2/9
B)4/17
C)6/29
D)8/35
E)10/43
Rationale: P(1st ball is even) = 9/18
P(2nd ball is also even) = 8/17
P(both balls are even) = 9/18 * 8/17 = 4/17
The answer is B.
Answer: B