divelab/Sys2Bench huggingface dataset:
Question: 10 different letters of English alphabet are given. A word is formed using 5 letters ( with replacement ) out of these. Find the probability that at least one letter is repeated in the word.
Options:
A)(10^5 - 10P5 ) / 10^5
B)(10P5 ) / 10^5
C)(10^5 - 10P5 ) / 10
D)None of these
E)Cannot be determined
Rationale: Explanation :
Without restriction,
No. of arrangements of 5 letter out of 10 different letters = 10(5).
To find at least one, it is better to find the probability of the complement of the event (no letter is repeated).
No. of arrangements of 5 letters ( out of 10) without repetition = 10P5.
=> P (no letter is repeated)
= 10P5 / 10(5) .
=> P ( at least one letter is repeated )
= 1 - ( 10P5 / 10(5) ).
Hence, the required probability is (105 - 10P5 ) / 10(5)
Answer : A
Answer: A
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 279 metres long in 20 seconds. The length of the train (in metres) is:
Options:
A)186
B)176
C)175
D)96
E)None of these
Rationale: Explanation:
Let the length of train be L m.
Acc. to question
(279+L)/20 = L/8
2232+8L=20L
L= 2232/12 = 186 m
Answer A
Answer: A
Question: x3−ax2+3x−b=0x3−ax2+3x−b=0 has one factor as (x - 2). When the equation is divided by (x + 1), it leaves a remainder -12. What are the values of ‘a’ and ‘b’?
Options:
A)2,2
B)2,6
C)2,1
D)2,9
E)2,7
Rationale: x3−ax2+3x−b=0x3−ax2+3x−b=0 has one factor as (x - 2). So for x = 2 the equation will satisfy or we can say if we substitute the value of x in the equation as 2 it will result into 0.
8 - 4a + 6 - b = 0 or 4a + b = 14 ....(i)
Now if we say that by dividing the equation by (x + 1) we get the remainder as -12 then if we put x = -1 in the equation then it will result in -12.
-1 - a - 3 - b = -12 or a + b = 8 ....(ii)
By solving (I) and (II) a = 2 and b = 6.
Answer:B
Answer: B
Question: present ages of sam and john are in the ratio of 4:3 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what john's present age in years
Options:
A)6
B)12
C)20
D)8
E)15
Rationale: sam and john be 4x years and 3x years respectively
(4x+3)/(3x+3)=11/9
9(4x+3)= 11(3x+3), 36x+27=33x+33
36x-33x=33-27
x=2, therefore john's present age : 3x=6 years
correct answer(A)
Answer: A
Question: Machine A can do a certain job in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All three machines start the job at 9:00 a.m. Machine A breaks down at 11:00 a.m., and the other two machines finish the job. Approximately what time E will the job be finished?
Options:
A)Noon
B)12:30 p.m.
C)1:00 p.m.
D)1:30 p.m.
E)2:00 p.m.
Rationale: Ans: C (1:00pm)
From 9:00-11:00c(2 hrs)
A can do 1/8 Job/hr. so in 2 hours he can do 1/4 job.
B can do 1/10 job/hr so in 2 hrs. he can do 1/5 Job.
C can do 1/12 job/hr so in 2 hours he can do 1/6 job.
Total = 1/4+1/5+1/6 = 37/60 Job
Now balance work needs to be done by B and C.
Balance Work= 23/60 Job
Combined rate of B and C = 1/10+1/12 = 11/60 job/hr.
So they will do 22/60 work in 2 hrs (approx. to the balance work of 23/60)
Hence the Job will be completed 2hrs. after 11:00 i.e. @ 1:00pm=E
Ans: C (1:00pm)
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 24km/h, what is the circumference of the tire?
Options:
A)1 meters
B)6 meters
C)5 meters
D)3 meters
E)7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 24,000 m : C is the circumference
C = 1 meters
correct answer A
Answer: A
Question: 25.25/2000 is equal to:
Options:
A)1.012526
B)0.012625
C)0.12526
D)0.12625
E)0.12725
Rationale: 25.25/2000 = 2525/200000
= 0.012625
ANSWER:B
Answer: B
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/3:1/5 . What is the minimum no. of pencils that the person should have?
Options:
A)41
B)65
C)70
D)77
E)98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,3 and 5 is 30.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 30 ) = 15.
Rahul = ( 1 / 3 x 30 ) = 10.
Ranjan = ( 1 / 3 x 30 ) = 10.
Rohit = ( 1 / 5 x 30 ) = 6.
Step 3: Total number of pencils are ( 15 x + 10 x + 10 x + 6 x) = 41 x.
For minimum number of pencils x = 1 .
The person should have at least 41 pencils.
A)
Answer: A
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)23
C)29
D)26
E)13
Rationale: Sum of the marks for the 12 students
= 12 * 36 = 432.
The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average
= 864/12 = 72.
Answer: A
Answer: A
Question: Linda spent 5/6 of her savings on furniture and the rest on a TV. If the TV cost her $500, what were her original savings?
Options:
A)$9000
B)$3000
C)$6000
D)$7000
E)$8000
Rationale: If Linda spent 5/6 of her savings on furniture, the rest
6 / 6 - 5 / 6 = 1 / 6 on a TV
But the TV cost her $500. So 1 / 6 of her savings is $500. So her original savings are 6 times $500 = $3000
correct answer B
Answer: B
Question: A and B together can complete a piece of work in 10days. If A alone can complete the same work in 15days, in how many days, in how many days can B alone complete that work?
Options:
A)10
B)30
C)25
D)15
E)45
Rationale: (A+B)'s 1day's work = 1/10
A's 1day's work = 1/15
B's 1days's work = (1/10)-(1/15) = 1/30
Hence, B alone can complete the work in 30days.
Answer is B
Answer: B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is $50, what is the compound interest on the same at the same rate and for the same time?
Options:
A)$50
B)$51.5
C)$52
D)$52.5
E)$51.25
Rationale: Sum = 50 x 100 /(2 x 5) = 500
= 500 x (1 +	5/100)^2
= 500 x 21/20 x 21/20
= 551.25.
C.I = 551.25 - 500 = 51.25.
Answer E)$51.25
Answer: E
Question: If ratio of profit of A and B is 4:5 and they together invested Rs.90,000 then money invested by B is
Options:
A)Rs.48,000
B)Rs.45,000
C)Rs.30,000
D)Rs.50,000
E)None of the above
Rationale: investment by B=(5*90000)/(4+5)
=50000
ANSWER:D
Answer: D
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 8 years?
Options:
A)3 : 2
B)1 : 3
C)2 : 3
D)3 : 1
E)1 : 4
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 8 years
=T1/T2
=2/8
=1/4
=1:4
Answer : Option E
Answer: E
Question: (0.03)*(0.04)/(0.05)*(0.11)=?
Options:
A)0.2
B)0.22
C)0.5
D)0.005
E)0.022
Rationale: With questions like this, take a look at the answers first. Notice the only distinction between the answers is the factor of ten; thus, an exact calculation is not necessary to solve the problem, just a quick approximation.
.03*.04~.0012, which can be approximated to .0012.
.05*.11~=.0055
Thus we have 0.0012/0.055 give us 0.218
So the answer is 0.22(approximately)
The option is B
Answer: B
Question: Before a salary increase, the weekly salary of a worker for 26 hours in a week was as much as the worker is paid now for 20 hours of work in a week. What is the percent increase in the worker's salary per hour?
Options:
A)28
B)30
C)32
D)34
E)36
Rationale: Let x be the original salary per hour.
Let y be the salary per hour after the increase.
20y=26x
y=(26/20)x=1.3x
The salary increased 30%.
The answer is B.
Answer: B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/96
B)33/91
C)33/78
D)33/92
E)33/21
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:B
Answer: B
Question: When average age of 24 members are 0, how many members greater than 0?
Options:
A)17
B)23
C)21
D)24
E)25
Rationale: Average of 24 numbers = 0.
Sum of 24 numbers (0 x 24) = 0.
It is quite possible that 23 of these numbers may be positive and if their sum is a then 24th number is (-a)
Answer is 23 (B)
Answer: B
Question: A car runs at the speed of 25 km per hour when not serviced and runs at 75 kmph when serviced. After servicing the car covers a certain distance in 5 hours. How much time will the car take to cover the same distance when not serviced?
Options:
A)8 hours
B)16 hours
C)15 hours
D)7 hours
E)None
Rationale: Explanation :
Time = 75*5 / 25 = 15 hours
Answer â€“ D
Answer: D
Question: Billy's farm is in the shape of a rectangle. It's width is 45 yards less than its length. The area of the farm is 11,704 square yards. What is the perimeter of the farm?
Options:
A)88 yards
B)133 yards
C)260 yards
D)442 yards
E)None of the above
Rationale: l-w=45
lxw=11,704
Solving the 2 equations, you get l=133 yards and w=88 yards
So 2(l+w)= 442 yards
Correct answer: D
Answer: D
Question: In how many different ways can 10 people be seated in a room with 12 chairs?
Options:
A)40,320
B)181,440
C)403,200
D)1,814,400
E)239,500,800
Rationale: Order doesn't matter
With 12 chairs and only 10 to seat
10!- Number of ways the 10 can seat on the chair
12C2 - Number of ways the 2 empty sits can be vary with the 10 seated
10! * 12C2 = 239,500,800 Answer - E
Answer: E
Question: The interest on a certain deposit at 4.5% p.a. is Rs. 405 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?
Options:
A)Rs.50
B)Rs. 45
C)Rs.40.5
D)Rs. 48.5
E)Rs. 49.5
Rationale: S.I. = Rs. 405 R = 4.5% T = 1 year
Principal = (100 *405)/(4.5*1) = Rs.9000
S.I at 5% interest = (9000*5*1)/100 = Rs.450
Difference in interest = 450 – 405 = Rs.45
ANSWER:B
Answer: B
Question: In a certain lottery drawing, two balls are selected at random from a container with 300 balls, numbered from 1 to 300, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?
Options:
A)$9.85 x 10^6
B)$9.90 x 10^6
C)$1.00 x 10^7
D)$8.97 x 10^7
E)$9.90 x 10^7
Rationale: The max product of any two balls can be 299 * 300 = 9900 = 8.97 * 10^4
If you multiply it by $1000 the max amount will be 8.97* 10^7.
Answer: D
Answer: D
Question: What will be remainder when (67^67 + 67) is divided by 68 ?
Options:
A)1
B)63
C)66
D)67
E)69
Rationale: (x^n + 1) will be divisible by (x + 1) only when n is odd.
(67^67 + 1) will be divisible by (67 + 1)
(67^67 + 1) + 66, when divided by 68 will give 66 as remainder.
Answer:C
Answer: C
Question: A boat having a length 8 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options:
A)100 kg
B)120 kg
C)89 Kg
D)80 Kg
E)240 Kg
Rationale: Volume of water displaced	= (8 x 3 x 0.01) m3
= 0.24 m3.
Mass of man = Volume of water displaced x Density of water
= (0.24 x 1000) kg
= 240 kg.
Answer: E
Answer: E
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
7 – 9 + 8 × 3 ÷ 20 =
Options:
A)11
B)10
C)12
D)-2
E)8
Rationale: A 11
Answer: A
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Options:
A)2 hour
B)5 hour
C)1 hour
D)3 hour
E)2 hour
Rationale: C
1 hour
Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? 1 hour
Answer: C
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
Options:
A) 22.5%
B) 24%
C) 30%
D) 33%
E) 20%
Rationale: Say Morks income is - 100
So tax paid will be 40
Say Mindys income is 4*100 = 400
So tax paid is 20% * 400 = 80
Total tax paid = 40+80 = 120.
Combined tax % will be 120/100+400 = 24%
Answer: B
Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
Options:
A)190 metres
B)160 metres
C)200 metres
D)120 metres
E)250 metres
Rationale: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the train = 200 m
Correct answer is 200 metres
Answer: C
Question: A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?
Options:
A)240 mts
B)270 mts
C)260 mts
D)250 mts
E)None of these
Rationale: Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 x 5/18 = 500/9 m/sec.
Let the length of the other train be L mts.
Then, (L + 260)/9 = 500/9 => L = 240 mts.
ANSWER IS A
Answer: A
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.36, the number of 25 paisa coins is?
Options:
A)30
B)36
C)32
D)34
E)38
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3600
600x = 3600
x = 6 => 6x = 36
ANSWER:B
Answer: B
Question: Bob bikes to school every day at a steady rate of c miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
Options:
A)(c + y) / t
B)2(c + t) / cy
C)2cyt / (c + y)
D)2(x + y + t) / xy
E)x(y + t) + y(x + t)
Rationale: If we choose for d (distance): 10 miles, for c 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.
Answer: C
Question: A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone?
Options:
A)1 1/9 days
B)1 1/2 days
C)1 2/2 days
D)2 1/2 days
E)1 5/2 days
Rationale: 3/20 * 2 + (2 + x)/5 = 1
x = 1 1/2 days
Answer:B
Answer: B
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/4th of the other, how many centimeters will the shorter piece be?
Options:
A)A)73
B)B)20
C)C)83
D)D)21
E)E)52
Rationale: Explanation:
1: 2/4 = 4: 2
2/6* 60 = 20
Answer: Option B
Answer: B
Question: The GDP of a country is $13.8 billion, and the total production of one of its industries is $3.3 billion. If the GDP were to grow by 5% per year in the future, which of the following would be the MINIMUM required annual growth in this industry that would it represent more than half of the GDP in ten years?
Options:
A)10%
B)15%
C)20%
D)25%
E)35%
Rationale: GDP in 10 years with this rate would be - 13.8 (1+0.05)^10
Half of the above value - 6.9 (1.05)^10
Industry's annual growth (say x is the rate of growth of the industry annually) = 3.3 (1+(x/100))^10
Now, the minimum of above value has to be greater than the half of the value of GDP.
3.3 (1+(x/100))^10 > 6.9 (1.05)^10
((1+(x/100))/1.05)^10 > 2 (approx)
Minimum value of x to satisfy this equation is 15
Hence B
Answer: B
Question: If Scott has earned 924 dollars by working 6 hrs/day a week at a constant daily rate for 2 weeks, which of the following represents his daily wage?
Options:
A)13
B)12
C)11
D)17
E)14
Rationale: Scott total earning = 924
No days he worked = 6 * 7 = 42
Rate = 2 week
Daily wage = total / (Rate * days)
= 924/(6*7*2)
= 11
C is correct answer...
Answer: C
Question: A speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: P( A)=75/100, P(B)=80/100
P( A’)=1/4
P(B’)=1/5
P( A and B contradict each other)=P(A).P(B’)+P(A’).P(B)
=35%
ANSWER D 35%
Answer: D
Question: Three unbiased coin are tossed. What is the probability of getting atmost
one head?
Options:
A)1/2
B)1/4
C)7/8
D)3/5
E)1/6
Rationale: Here n(S)= 2^3
Let E=event of getting atmost one head =
n(E)= 7
P(E)=n(E)/n(S)=7/8
Answer option C)
Answer: C
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 1 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)15
B)30
C)45
D)60
E)90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 1.
So, x =65 / 4 ounces.
Water = (60 / 65) * (65 / 4) = 15 ounces.
Ans A
Answer: A
Question: A box contains four dimes, of which two dimes have heads on both their faces, one dime has tail on both its faces and the fourth dime is a normal one. A dime is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the dime tossed is also a head.
Options:
A)3/5
B)4/5
C)2/5
D)3/4
E)1/2
Rationale: There are four ways (2 heads in one two-headed dime and 2 heads in the other two-headed dime)
How many ways can you get heads from this entire set of dimes? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option B
Answer: B
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: B
Question: A shoe merchant has declared a 10% rebate in prices. How much rebate would one get if he purchases 5 pairs of shoes at Rs.28 each?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation:
5 shirts * Rs.28 = Rs.140
Rebate = 10% * 140 = 14
Correct Option : D
Answer: D
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=16, what is the maximum value of y for which f(x,y)=0?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: The question is finding y such that (16-y)! is a multiple of 16. That means we need to have 2^4 in (16-y)!
6! is the smallest factorial number with 2^4 as a factor.
16-y = 6
y = 10
The answer is B.
Answer: B
Question: Obra drove 180π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
Options:
A)37.5%
B)12.5%
C)18.75%
D)25%
E)33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 180π/480π =37.5%
Hence, answer is A.
Answer: A
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 28 cm.
Options:
A)200cm2
B)300cm2
C)400cm2
D)448cm2
E)100cm2
Rationale: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 28 x 32) cm2 = 448 cm2
Answer: Option D
Answer: D
Question: The period of 2 sin x cos x is
Options:
A)4 pi 2
B)2 pi
C)4 pi
D)pi
E)None
Rationale: Solution
According to trigonometric identities, 2 sin x cos x = sin(2x) and the period is given by.
2 pi / 2 = pi
Answer D
Answer: D
Question: Integer X represents the product of all integers between 1 to 27 (inclusive). The smallest prime factor of (x+1) must be
Options:
A)Between 1 to 10
B)Between 11 to 15
C)Between 15 to 20
D)Between 20 to 27
E)Greater than 27
Rationale: Answer = E = Greater than 27
This problem is asking smallest prime factor of (25!+1)
25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)
Just adding 1 to 27! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 27
Answer = E
Answer: E
Question: Score Interval Number of Scores
50-59 2
60-69 10
70-79 16
80-89 27
90-99 17
The table shows a distribution of test scores. Which score interval contains the median of the 72 scores?
Options:
A)a) 60-69
B)b) 70-79
C)c) 80-89
D)d) 90-99
E)e) Cannot determine.
Rationale: 36th person
80-89 C
Answer: C
Question: Find the least number when successively divided by 2, 3 and 7 leaves remainders 1, 2 and 3 respectively?
Options:
A)67
B)65
C)75
D)61
E)60
Rationale: 2) 65 (32 3) 32 (10 7) 10 (1
64 30 7
-------- -------- - -----
1 2 3
=> 65
ANSWER:B
Answer: B
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,600 nuts and 1,600 bolts?
Options:
A)1,250 seconds
B)1,500 seconds
C)1,750 seconds
D)2,400 seconds
E)3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 1,600*1 seconds to produce 1,600 bolts, so 2 need half of that, so 1,600/2 seconds.=800
1 machine needs 1,600*2 seconds to produce 1,600 nuts, so 2 need half of that, so 1,600*2/2 seconds.=1600
total = 2400
D
Answer: D
Question: At a certain store, the price of a pair of shoes is twenty dollars more than three times the price of a pair of jeans and the price of a sweater is seventy percent more than the price of a pair of shoes. If the price of a pair of jeans is j dollars at this store, then what is the price, in dollars, of a pair of shoes, a sweater and a pair of jeans, in terms of j ?
Options:
A)9.1j + 54
B)3j + 20
C)4.5j + 30
D)5.5j + 30
E)8.5j + 50
Rationale: Ans A
Given
Price of Jeans = J
Price of shoes = 20+3J
Price of Sweater = 1.7(20+3J)
Total Price of all three items = J+20+3J+1.7(20+3J) = 54+9.1J
Answer: A
Question: A certain rectangular crate measures 8 feet by 14 feet by 16 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
Options:
A)4
B)5
C)6
D)8
E)10
Rationale: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 14x20 i.e. of radius 12/2 = 6
C
Answer: C
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 3?
A. 48 kmph
Options:
A)33
B)480/9
C)28
D)27/8
E)16
Rationale: Let the distances between city A to B and B to C be x km and 3x km respectively.
Total time taken to cover from A to C
= (x)/40 + (3x)/60 = (3x + 6x)/120 = 9x/120 Average speed = (x + 3x)/(9x/120) = 480/9 kmph.
Answer: B
Answer: B