divelab/Sys2Bench huggingface dataset:
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)1800
B)2000
C)2200
D)2400
E)2600
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
= x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
= x + 2 x 200 = 800
= x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
answer : D
Answer: D
Question: Dany bought a total of 18 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
Options:
A)4
B)10
C)7
D)3
E)12
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 18. Hence
X + Y = 18
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 18
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 18 - X. Substitute y by 18 - x in the second equation and solve
0.25 X + 0.15 (18 - X) = 4.2
X(0.25 - 0.15) + 2.7 = 4.2
0.1 X = 1.5
X = 15 and Y = 18 - 15 = 3
correct answer D
Answer: D
Question: If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?
Options:
A)76
B)77
C)78
D)79
E)None of these
Rationale: Solution:
Suppose the start number is x Division into 3 equal groups is: x/3, and then in half is (x/3)/2 = 13
x/6 = 13
x = 13 * 6 = 78
Answer C
Answer: C
Question: A man can row a boat at 12 kmph in still water. If the speed of the stream is 4 kmph, what is the time taken to row a distance of 50 km downstream?
Options:
A)25/8
B)29/8
C)23/8
D)27/8
E)21/8
Rationale: Speed downstream = 12 + 4 = 16 kmph.
Time required to cover 50 km downstream = d/s = 50/16
= 25/8 hours.
Answer: A
Answer: A
Question: Find the greatest number which on dividing 1428 and 2206, leaves a reminder of 9 and 13 respectively
Options:
A)125
B)127
C)129
D)131
E)141
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1428 - 9) and (2206 -13)
= HCF (1419, 2193) = 129
Option C
Answer: C
Question: Which one of the given numbers is divisible by 11?
Options:
A)4823718
B)8423718
C)8432718
D)4832817
E)4852718
Rationale: Explanation:
4832817 = (4+3+8+7) – (8+2+1) = 11
So, the given number is divisible by 11
Answer:D
Answer: D
Question: (500 + 200) × 4 × (3 + 2) = ?
Options:
A)2902
B)14000
C)8402
D)16800
E)None of these
Rationale: (500 + 200) × 4 × (3 + 2) = ?
or, ? = 700 × 4 × 5 = 14000
Answer B
Answer: B
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 121 hours and 100 hours respectively. The ratio of their speeds is:
Options:
A)2 : 3
B)4 : 3
C)6 : 7
D)9 : 16
E)None of these
Rationale: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = âˆšb : âˆša = âˆš100 : âˆš121 = 10 : 11.
Answer E
Answer: E
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11, 60 and 61?
Options:
A)6.5
B)12.5
C)28
D)30.5
E)40
Rationale: Some of pyhtagron triplets we need to keep it in mind.
Like {( 2,3,5) , ( 5,12,13) ,( 7, 24,25), ( 11, 60,61).
So now we know the triangle is an right angle triangle. The circle circumscribes the triangle.
The circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5
Ans. D
Answer: D
Question: January 1, 2008 is Monday. What day of the week lies on Jan 1, 2009?
Options:
A)Saturday
B)Wednesday
C)Thursday
D)Tuesday
E)Monday
Rationale: Explanation:
Number of odd days in 2008 = 2 (since it is a leap year)
(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)
Given that January 1, 2008 is Monday.
Hence January 1, 2009 = (Monday+ 2 odd days) = Wednesday
Answer: Option B
Answer: B
Question: Which of the following points is closest to line y=x
Options:
A)(2, -1)
B)(-2, -4)
C)(-1, 1)
D)(-2, 1)
E)(-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (-2, -4) is the closest to line y=x.
Answer: B.
Answer: B
Question: Train X crosses a stationary train Y in 60 seconds and a pole in 25 seconds with the same speed. The length of the train X is 300 m. What is the length of the stationary train Y ?
Options:
A)360 m
B)420 m
C)460 m
D)320 m
E)340 m
Rationale: Explanation:
Let the length of the stationary train Y be LY
Given that length of train X, LX = 300 m
Let the speed of Train X be V.
Since the train X crosses train Y and a pole in 60 seconds and 25 seconds respectively.
=> 300/V = 25 ---> ( 1 )
(300 + LY) / V = 60 ---> ( 2 )
From (1) V = 300/25 = 12 m/sec.
From (2) (300 + LY)/12 = 60
=> 300 + LY = 60 (12) = 720
=> LY = 720 - 300 = 420 m
Length of the stationary train = 420 m
ANSWER IS B
Answer: B
Question: Two containers of equal capacity are full of a mixture of oil and water . In the first, the ratio of oil to water is 4:7 and in the second it is 7:11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water.
Options:
A)149 : 247
B)247 : 149
C)143 : 241
D)241 : 143
E)341 : 243
Rationale: Two Container C1, C2 of equal capacity x.
For C1:
Oil= 4/11 x
Water= 7/11 x
For C2
Oil= 7/18 x
Water = 7/11 x
Mix C1 and C2.
Total Oil= 4/11 x + 7/18 x = 149/198 x
Total Water= 7/11 x + 7/11 x = 247/198 x
resulting ratio of oil to water = (149/198 x) / (247/198 x)
= 149:247.
ANSWER:A
Answer: A
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)22 2/3% loss
C)88 2/3% loss
D)66 2/3% loss
E)22 2/5% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: A
Question: If log 27 = 1.431, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.965
Rationale: log 27 = 1.431
log (33 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
Answer: Option C
Answer: C
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
Options:
A)14300
B)12000
C)14500
D)14600
E)15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100 = 12000
B)
Answer: B
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 9:00 pm and not earlier, when was the drain opened?
Options:
A)at 10:00 am
B)at 11:00 am
C)at 12:00 pm
D)at 1:00 pm
E)at 2:00 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (12-x)/20 = 1
5x + 12 - x = 20
4x = 8
x = 2
The answer is 11:00 am.
The answer is B.
Answer: B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 25 seconds. The ratio of their speeds is?
Options:
A)3/7
B)3/2
C)3/5
D)8/1
E)3/3
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 25
==> 27 x + 17 y = 25 x + 25 y ==> 2x = 8 y ==> x/y
= 8/1.
Answer: D
Answer: D
Question: Rice weighing 29/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces)
Options:
A)21
B)25
C)29
D)33
E)37
Rationale: 29/4 ÷ 4 = 29/16 pounds in each container
29/16 pounds * 16 ounces / pound = 29 ounces in each container
The answer is C.
Answer: C
Question: A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:
Options:
A)1.5 kmph
B)1.75 kmph
C)2 kmph
D)3 kmph
E)None
Rationale: Sol.
Rate downstream = [32/6] kmph; Rate upstream = [14/6] kmph.
∴ Velocity of current = 1/2[32/6 - 14/6] kmph = 3/2 kmph = 1.5 kmph.
Answer A
Answer: A
Question: What day of the week was 11th January 1801
Options:
A)Monday
B)Sunday
C)Friday
D)Thursday
E)Tuesday
Rationale: Explanation:
11th Jan 1801 = (1800 years + 11th Jan 1801)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1800
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
11th Jan 1801 = 4 odd day
Total number of odd days = (0 + 3 + 4) = 7 =0
0 odd days = Sunday
Hence 11th January 1801 is Sunday.
Answer: Option B
Answer: B
Question: The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
Options:
A)40 days
B)20 days
C)30 days
D)50 days
E)45 days
Rationale: one man can consume the same food in 30*40 = 1200 days.
10 more men join, the total number of men = 40
The number of days the food will last = 1200/40 = 30 days.
ANSWER:C
Answer: C
Question: Find the value of (875 233/899) × 899
Options:
A)786858
B)786900
C)786920
D)786913
E)786960
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
A
Answer: A
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 1/5 % his yearly income diminishes by Rs.61.50. his capital is
Options:
A)22.378
B)37.78
C)76.88
D)27.888
E)12.771
Rationale: Explanation:
Capital = Rs.x , then
4/5 x =61.5
x = 76.88
Answer: C) Rs.76.88
Answer: C
Question: Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$10,464
B)$ 864
C)$ 816
D)$ 800
E)$ 480
Rationale: Approach #1:
8 percent compounded semiannually --> 4% in 6 moths.
For the first 6 moths interest was 4% of $10,000, so $400;
For the next 6 moths interest was 4% of $10,000, plus 4% earned on previous interest of $400, so $400+$16=$416;
Total interest for 1 year was $400+$416=$816.
Answer: C.
Answer: C
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 50 minutes later?
Options:
A)2(10^5)
B)5(10^5)
C)(2^5)(10^5)
D)(10^5)(10^5)
E)(10^5)^5
Rationale: Every 10 minutes, the population is double the previous population.
In 50 minutes, the population doubles 5 times.
The population then is 2^5*10^5.
The answer is C.
Answer: C
Question: Calculate the circumference of a circular field whose radius is 7 centimeters.
Options:
A)11 π cm
B)15 π cm
C)1 π cm
D)4 π cm
E)14 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*7 = 14 π cm
Answer: E
Answer: E
Question: A student chose a number, multiplied it by 2, then subtracted 140 from the result and got 102. What was the number he chose?
Options:
A)90
B)100
C)120
D)160
E)121
Rationale: Solution:
Let x be the number he chose, then
2*x*140=102
2x=242
x=121
correct answer E
Answer: E
Question: Of the 70 electronics components that a factory must manufacture, 90 percent would be most e¢ ciently manufactured by Machine A and the remaining 10 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 70 components. If 50 percent of the components were manufactured by Machine A and the remainder were manufactured by Machine B, what is thehighest possible number of components that were manufactured by the machine that would manufacture them the most efficiently?
Options:
A) 30
B) 32
C) 42
D) 35
E) 36
Rationale: A can manufacture 90 % of 70 efficiently, which is 63.
B can manufacure 10 % of 70 efficiently, which is 7.
Now 50 % of 70 are produced by A. This means 35 parts. Since A can produce 63 efficiently, all 35 are produced efficiently. Rest (35) is produced by B, which can produce max. 7 parts efficiently.
Hence parts that were produced efficiently = 7+35 = 42. (C).
Answer: C
Question: A box measuring 25 inches long by 30 inches wide by 15 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)80
B)82
C)84
D)88
E)90
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
5 is the biggest number that could divide all three, 25, 30 and 15.
Thus side of cube must be 5, and total number of cubes = 25/5 * 30/5*15/5= 90
Ans E.
Answer: E
Question: Little John had $16.10. He spent $3.25 on sweets and gave to his two friends $2.20 each. How much money was left?
Options:
A)$6.45
B)$8.35
C)$8.75
D)$8.85
E)$8.45
Rationale: John spent and gave to his two friends a total of
3.25 + 2.20 + 2.20 = $7.65
Money left
16.10 - 7.65 = $8.45
Answer :E
Answer: E
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake’s present weight, in pounds?
Options:
A)131
B)135
C)139
D)147
E)188
Rationale: Consider Sister weight Now as x
Jakes weight (2times +8) = 2x+8
(2x+8)+(x) =278
x=90
Jake's weight is ....188
Correct answer is E
Answer: E
Question: Of 70 players on a football team, 40 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)59
C)60
D)71
E)92
Rationale: Total = 70
Thrower = 40
Rest = 70 - 40 = 30
Left Handed = 30/3 = 10
Right handed = 20
If all Throwe0r are right handed then total right handed is 40 + 20 = 60
so C. 60 is the right answer
Answer: C
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product X of all the fractions that are in S?
Options:
A)1) 1/20
B)2) 1/21
C)3) 1/2
D)4) 19/40
E)5) 19/20
Rationale: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Answer: A
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 15 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)40
B)48
C)80
D)192
E)120
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =15 => 16x = 120 (2) 3x =15 => 16x = 80 (3) 5x =15 => 16x = 48 (4) 6x =15 => 16x = 40
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: In a race of 800 mtr gives Mary a start of 200 mtr and then loses the race by 20 seconds. What is the speed of Mary & Rose respectively ? If the ratio of respective speeds be 3:2?
Options:
A)10 m/s
B)12 m/s
C)16 m/s
D)20 m/s
E)30 m/s
Rationale: Let the speed of Kaushik be and speed of Piyush be and let the time taken by Piyush be t second then,
t = 20 s
Speed of Priya = 30 m/s
and Speed of Kala = 20 m/s
D
Answer: D
Question: A thief is spotted by a policeman from a distance of 200metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
Options:
A)1km
B)500m
C)650m
D)750m
E)800m
Rationale: Relative speed of the policeman = 20-16 = 4 km/hr
time taken by policeman to cover 200m = (200/1000)*(1/4) = 1/20 hr
In 1/20 hr the thief covers a distance of 16/20 km = 4/5 km = 800m
Answer is E
Answer: E
Question: There are 720 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Options:
A)320
B)345
C)450
D)380
E)400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 720. Hence
3x + 5x = 720
Solve for x
8x = 720
x = 90
Number of boys
3x = 3 × 90 = 270
Number of girls
5x = 5 × 90 = 450
C
Answer: C
Question: Find the last non-zero digit of 30^2345
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 30^2345=(3*10)^2345=3^2345*10^2345
so 30^2345 has 2345 zeroes,the last non-zero digit of 30^2345 will be same as unit digit of 3^2345
3^2345=3^(4*586+1)=> 3^1=3
last non-zero digit of 30^2345= 3
ANSWER:C
Answer: C
Question: The labelled price of a cupboard is Rs. 6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?
Options:
A)5350
B)5450
C)5500
D)5700
E)None
Rationale: Sol.
S.P. = 95% of Rs. 6500 = Rs. [95 / 100 * 6500] = Rs. 6175.
Profit = 15%.
∴ C.P. = Rs. [110 / 115 * 6175] = Rs. 5369.56 = Rs. 5350.
Answer A
Answer: A
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 196, the sum due is:
Options:
A)s. 768
B)s. 968
C)s. 896
D)s. 2400
E)s. 2800
Rationale: td=pw*r*t/100 so 196=pw*14*2/100 so pw=700
sum=pw+td..
sum=700+196=896
ANSWER:C
Answer: C
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 576 feet squared, what is the difference between the length and the width of the roof?
Options:
A)38.
B)40.
C)36.
D)44.
E)46.
Rationale: Let the width= x
x*4x=576
x^2= 144
x= 12
Length= 4*12= 48
difference= 48-12= 36
C is the answer
Answer: C
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over. What is the sum of the two smallest possible values of n?
Options:
A)54
B)58
C)62
D)66
E)70
Rationale: n = 4k+1 = 7j+3
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+3.
1, 5, 9, 13, 17 = 7(2)+ 3
The next such number is 17 + 4*7 = 45.
17+45 = 62
The answer is C.
Answer: C
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in five times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 45 minutes, then how many minutes does it take pump X alone to fill the tank?
Options:
A)27
B)30
C)33
D)36
E)39
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/45 per minute.
(R - V/45)*5T=V=RT.
(R-V/45)*5=R
4R=V/9.
R=V/36.
It takes pump X 36 minutes to fill the tank.
The answer is D.
Answer: D
Question: In what time will a railway train 30 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)6 sec
B)7 sec
C)3 sec
D)9 sec
E)2 sec
Rationale: T = 30/36 * 18/5
= 3 sec
Answer:C
Answer: C
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.25,000 earned at the end of 2years from the startingof the business?
Options:
A)Rs. 5,000
B)Rs. 5,500
C)Rs. 5,700
D)Rs. 6,500
E)Rs. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 25000 x	3/10	= Rs. 7,500.
E
Answer: E
Question: Share Rs.5400 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
Options:
A)1800
B)980
C)1200
D)1240
E)1400
Rationale: Amount received by sanjay.
4 / 12 X 5400 = 1800= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1800.
A
Answer: A
Question: For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 70 terms?
Options:
A)3/5
B)7/15
C)35/36
D)70/71
E)140/141
Rationale: a1 = 1 - 1/2
a2 = 1/2 - 1/3
a3 = 1/3 - 1/4
etc...
a70 = 1/70 - 1/71
The sum of these terms is 1-1/71 = 70/71
The answer is D.
Answer: D
Question: The diagonal of a rhombus are 80 m and 120m. Its area is:
Options:
A)4500
B)4000
C)4800
D)4600
E)4320
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 80 Ã— 120) Cm(power)2
= 80Ã— 60= 4800 Cm(power)2
Answer is C.
Answer: C
Question: The average age of a group of persons going for picnic is years. Seventeen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
Options:
A)5
B)10
C)17
D)23
E)50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 17 x 15 = 15.5(x+20)
= 0.5x = 8.5
x = 17.
Answer C
Answer: C
Question: A box contains 14 mangoes out of which 6 are spoilt. If six mangoes are chosen at random, find the probability that A number is selected at random from first fifty natural numbers. What is the chance that it is a multiple of either 5 or 12?
Options:
A)15/25
B)2/25
C)14/25
D)7/25
E)7/50
Rationale: The probability that the number is a multiple of 5 is 10/50. (Since 5*10 = 50).
Similarly the probability that the number is a multiple of 12 is 4/50. {Since 14*4 =
48).
Neither 5 nor 12 has common multiple from 1 to 50. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 5 or 12 is (10+4)/50 = 7/25.
ANSWER:D
Answer: D
Question: David has $1,800 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
Options:
A)$200
B)$500
C)$600
D)$800
E)$1,200
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-800
x+x-800 = 1800
x= 1300
Money not spend= 1300-800= 500
Answer : B
Answer: B
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits F can does Grace have available during her trip?
Options:
A) 2,520
B) 1,260
C) 620
D) 360
E) 120
Rationale: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you F=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: B
Question: The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 or 4 as its largest number?
Options:
A)3/4
B)3/8
C)3/16
D)5/16
E)3/32
Rationale: The set S has 2^5 = 32 subsets.
The number 5 is in half of these subsets.
Of the remaining 16 subsets, 4 is an element in 8 of them.
Thus 4 is the largest number in 8 subsets of S.
Of the remaining 8 subsets, 3 is an element in 4 of them.
Thus 3 is the largest number in 4 subsets of S.
The probability that 3 or 4 is the largest number is 12/32 = 3/8.
The answer is C.
Answer: B
Question: There are 60 slots around a circle,numbered 1 to 60. A man starts from the first slot and jumps to the 5th slot.From there he jumps to the 9th slot and so on. In which slot will he land in his
2200th jump?
Options:
A)1
B)5
C)41
D)45
E)46
Rationale: every 15th jump, he comes back to 1st position
so, 2200/15 = Remainder 10
Hence 10th position is 41st slot
ANSWER:C
Answer: C