divelab/Sys2Bench huggingface dataset:
Question: A bill for Rs. 3000 is drawn on 14th July at 5 months. It is discounted on 5th October at 10%. What is the Banker's Discount?
Options:
A)Rs. 60
B)Rs. 82
C)Rs. 90
D)Rs. 120
E)None of these
Rationale: Explanation :
F = Rs. 3000
R = 10%
Date on which the bill is drawn = 14th July at 5 months
Nominally Due Date = 14th December
Legally Due Date = 14th December + 3 days = 17th December
Date on which the bill is discounted = 5th October
Unexpired Time
= [6th to 31st of October] + [30 Days in November] + [1st to 17th of December] = 26 + 30 + 17
= 73 Days
=73/365 year=1/5 year
BD = Simple Interest on the face value of the bill for unexpired time
=FTR/100=[3000×(1/5)×10]/100=30×1/5×10 = Rs. 60 Answer : Option A
Answer: A
Question: A train 500m long takes 10 sec to cross a man walking at 4kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)A)174kmph
B)B)150kmph
C)C)162kmph
D)D)145kmph
E)E)100kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+4 = (x+4)*5/18 m/sec
500/[(x+4)*5/18] = 10
10(x+4) = 1800
x = 174kmph
Answer is A
Answer: A
Question: What will be the result of 2^25 - 2^14 +(2*4 /8) ?
Options:
A)12
B)18
C)15
D)30
E)22
Rationale: The multiplication(e.g. 2^14) and division(e.g. 4/8) is done first and then the sum(e.g. 22+0) and
subtraction (e.g.50-28). And the answer is 22, option E.
Answer: E
Question: If a, q, and c are consecutive even integers and a < q < c, all of the following must be divisible by 4 EXCEPT
Options:
A)a + c
B)q + c
C)ac
D)(bc)/2
E)(abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2q. 2q will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'q' already has a prime factorization of at least a '2'. Hence '2q' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - qc/2 = (a + 2)(a + 4)/2. Either q or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - aqc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'q' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - q + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)6
C)18
D)Cannot be determined
E)None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 432
=> 12R2= 432
=> R2= 36
=> R= 6
Answer B
Answer: B
Question: A train passes a station platform in 30 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
Options:
A)320
B)340
C)360
D)380
E)400
Rationale: The speed of the train is 72 * 5/18 m/s = 20 m/s
The length of the train is 20 x 12 = 240 m
platform + 240 = 20 * 30
platform = 600 - 240 = 360
The answer is C.
Answer: C
Question: What was the day of the week on 24th Feb, 2006?
Options:
A)Thursday
B)Friday
C)Saturday
D)Sunday
E)Monday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb.
(31 + 24 ) = 55 days
55 days = (7 weeks + 6 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 6) = 12 0 odd day.
Given day is Friday.
Answer: Option B
Answer: B
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 20DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Options:
A)40/3 DAYS
B)10/3 DAYS
C)20/3 DAYS
D)3/20 DAYS
E)3/10 DAYS
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/10, B'S 1 DAY'S WORK = 1/20
(A+B)'S 1 DAY'S WORK = (1/10+1/20)=3/20=20/3
SO, A AND B TOGETHER CAN FINISH THE WORK IN 20/3 DAYS.
CORRECT OPTION: C
Answer: C
Question: The length of a rectangle is 3 times its width. If the width of the rectangle is 6 inches, what is the rectangle's area, in square inches?
Options:
A)30 square inches
B)108 square inches
C)68 square inches
D)89 square inches
E)92 square inches
Rationale: If the width is 6 in and the length is 3 times the width, then the length is
3 * 6 = 18 in
The area is given by
6 * 18 = 108 square inches
correct answer B
Answer: B
Question: c, q, and r are positive integers. If c, q, and r are assembled into the six-digit number cqrcqr, which one of the following must be a factor of cqrcqr?
Options:
A) 23
B) 19
C) 17
D) 7
E) none of the above
Rationale: One short way -
cqrcqr = 1000cqr + cqr = (1000+1)cqr = 1001cqr
Therefore any factor of 1001 is a factor of cqrcqr
7 is a factor of 1001
So D
Answer: D
Question: Given two cylindrical containers--A and B. Cylinder A has a diameter of 12 meters and a height of 10 meters. Cylinder B has a radius of 2 meters and a height of 4 meters. If cylinder A is filled to capacity with water, how many cylinder B will be filled to capacity with the content of cylinder A?
Options:
A)23
B)22
C)21
D)25
E)24
Rationale: Calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder.
volume of cylinder =πr2h
Cylinder A volume=1130.97
Cylinder B volume=50.27
therefore the number of cylinders B that can be filled to capacity=1130.97/50.27=22.5
Answer is B only 22 Cylinders B can be filled to capacity.
Answer: B
Question: A container contains 30 liters of milk. From this container 5 liter of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Options:
A)18.45 liter
B)23.44 liter
C)17.36 liter
D)21.87 liter
E)None of these
Rationale: ANSWER: 17.36 liter
Option:C
Answer: C
Question: If 10 people contributed a total of $20.00 toward a gift and each of them contributed at least $1.00, then the maximum possible amount any one person could have contributed is
Options:
A) $11.00
B) $1.25
C) $5.00
D) $6.00
E) $20.00
Rationale: A for me
9 people with 1$ each -> maximum = 11
Answer: A
Question: A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?
Options:
A)9 days
B)21 days
C)24 days
D)27 days
E)28 days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 woman’s 1 day’s work = 1/3 – 2/9 = 3-2/9 = 1/9
Therefore, the woman alone can finish the work in 9 days.
Answer: Option A
Answer: A
Question: If ab - 2c = a(b - c), which of the following must be true?
Options:
A) a=2 and c=0
B) a=1/2 and b=2
C) b=1 and c=0
D) a=1 or b=0
E) a=1/2 or c=0
Rationale: ab-2c = a (b-c)
ab - 2c = ab - ac
2c= ac
ac-2c = 0
c(a-2) = 0
Either c = 0; or a = 2
A is the answer
Answer: A
Question: A number x is 8 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)87.5%
C)80%
D)11%
E)1%
Rationale: Say y=1 and x=8.
Then y=1 is less than x=8 by (8-1)/8*100=7/8*100=87.5%.
Answer: B.
Answer: B
Question: If xy > 0, 1/x + 1/y = 6, and 1/xy = 12, then (x+y)/6 = ?
Options:
A)1/12
B)1/6
C)1/5
D)5
E)6
Rationale: (1/X+1/Y)=6 canbe solved as {(x+y)/xy}=12. Substituting for 1/xy=12, we get
x+y=6/12
==> (x+y)/6= 6/(12*6)=1/12.
A
Answer: A
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 2, 3 and 5?
Options:
A)2.5
B)3
C)4
D)4.5
E)5
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 = 5 / 2 = 2.5
Ans. A
Answer: A
Question: There are 810 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)125
D)135
E)225
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 810.
Hence, we have m+f= 810
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 810/3 = 270
Solving the three equations yields the solution
f = 270,m= 540, and d= 270.
The number of female democratic participants equals half the female participants equals
270/2 = 135.
ANSWER:D
Answer: D
Question: Suppose 10 monkeys take 10 minutes to eat 10 bananas. How many monkeys would it take to eat 70 bananas in 70 minutes?
Options:
A)9
B)17
C)11
D)10
E)13
Rationale: One monkey takes 10 min to eat 1 banana , so in 70 mins 1 monkey will eat 7 bananas , so for 70 bananas in 70 min we need 70/7 =10 monkeys
ANSWER:D
Answer: D
Question: For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 80 color copies at Print Shop Y than at Print Shop X?
Options:
A)$120
B)$125
C)$130
D)$135
E)$140
Rationale: The difference in the two prices is $2.75 - $1.25 = $1.50 for each color copy.
Each color copy will cost an extra $1.50 at Print Shop Y.
80*$1.50 = $120
The answer is A.
Answer: A
Question: What is the sum of the multiples of 3 from 33 to 60, inclusive?
Options:
A)465
B)470
C)452
D)450
E)460
Rationale: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 7 and add 1.
(60/3) - (33/3) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(33 + 60)/2 * (60/3) - (33/3) + 1 = Sum
93/2 *10 = 465
A
Answer: A
Question: Car A runs at the speed of 33km/hr & reaches its destination in 7hr. Car B runs at the speed of 44 km/h & reaches its destination in 5h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)20 : 23
B)25 : 27
C)21 : 20
D)29 : 23
E)24 : 25
Rationale: Sol. Distance travelled by Car A = 33 × 7 = 231 km
Distance travelled by Car B = 44 × 5 = 220 km
Ratio = 231/220 = 21 : 20
C
Answer: C
Question: A group of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 4 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
Options:
A)x/70
B)x/35
C)3x/70
D)3x/10
E)4x/77
Rationale: cost of boat per day = x
cost per person =x/7
if three more persons afre there, cost =x/11
difference = x/7-x/11
=4x/77
Ans E
Answer: E
Question: Mahesh, Ramesh and Suresh invest Rs. 45000, Rs. 55000 and Rs. 65000 respectively for 9 months in a partnership firm. If the total profit of Rs.13200 was made at the end of 9 months. How much did Suresh get more than Mahesh?
Options:
A)Rs. 900
B)Rs. 1200
C)Rs. 800
D)Rs. 1600
E)None of these
Rationale: Explanation:
Rs. 1600
Answer: Option D
Answer: D
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 10 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
Options:
A)25
B)34
C)30
D)67
E)100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 10 oz can = 300 oz/10 oz = 30
Answer C, 30 cans
Answer: C
Question: A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.
Options:
A)3hrs 45 min
B)2 hrs
C)4 hrs 15 min
D)5 hrs 30 min
E)2 hrs 20 min
Rationale: 1 hr = 4(1/6)=2/3
==1-1/2=1/2
2/3:1/2::1:X
X=(1/2*1*32)
x=3/4 hrs ==> 3hrs 45 min
ANSWER A
Answer: A
Question: How many words can be formed using the letters of the word “CORPORBTION”?
Options:
A)32441
B)24334
C)23335
D)45566
E)50400
Rationale: In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =	7!	= 2520.
2!
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in	5!	= 20 ways.
3!
Required number of ways = (2520 x 20) = 50400.
E
Answer: E
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $40,000, how much profit did the business make?
Options:
A)$44,000
B)$54,000
C)$64,000
D)$84,000
E)$104,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 40000
P = $64,000
The answer is C.
Answer: C
Question: How many pounds of salt at 50 cents/lb must be mixed with 45 lbs of salt that costs 35 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
Options:
A)20
B)15
C)40
D)50
E)90
Rationale: Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)
Basically, you need to mix 35 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 45 cents/lb (Salt Avg)
weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 45)/(45 - 35) = 1/2
We know that weight of salt 1 is 45 lbs. Weight of salt 2 must be 90 lbs.
Answer (E)
Answer: E
Question: The price of lunch for 15 people was $209.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options:
A) $11.73
B) $12.66
C) $13.80
D) $14.00
E) $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 209 is for 115 then we have to calculate for 100
for 115 209
for 100 x
so by cross multiplication we get 115x=100*209 => x=100*209/110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so
as the question ask the average price person excluding gratuity is 190/15=12.66 so our answer is B)
Answer: B
Question: At a constant Rate of flow, it takes 12 minutes to fill a swimming pool if a large hose is used and 60 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
Options:
A)30
B)10
C)15
D)20
E)25
Rationale: time taken to fill the pool by Large Hose =12 minutes =L or 1/L=1/12 similarly 1/S=1/60
simultaneously it will take 1/L+1/S=1/12+1/60=6/60=10 minutes
Answer : B
Answer: B
Question: The sides of a rectangle are in the ratio 4:3 and its area is 972sq.m find the perimeter of rectangle
Options:
A)120m
B)122m
C)124m
D)126m
E)128m
Rationale: Explanation:
let 4x and 3x be sides of the rectangle
We know that area of rectangle = l×b
4x × 3x = 972
12x2 = 972
X2 = 81
X = 9
Therefore length = 4x = 4×9 = 36m
Breadth = 3x = 3×9 = 27m
Therefore perimeter = 2 (l+b) = 2(36+27) = 126m
Answer: Option D
Answer: D
Question: In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race?
Options:
A)167 sec
B)190 sec
C)390 sec
D)716 sec
E)123 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/25 = 400 sec.
Time taken by A = 400 - 10
= 390 sec.
Answer:C
Answer: C
Question: Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $760; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?
Options:
A) $752
B) $755
C) $765
D) $783
E) $775
Rationale: = (760*6+ 790 *20)/26
= 783
Answer is D.
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Answer: D
Question: An oil cylinder was 3/4th full. When ONE bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
Options:
A)20
B)15
C)40
D)30
E)35
Rationale: (4/5 -3/4) cylinder is filled by 1 bottles
0.8 -0.75 = 0.05 cylinder is filled by 1 bottles
1 cylinder is filled by 1/0.05 = 20 bottles
ANSWER:A
Answer: A
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is :
Options:
A)1520 m2
B)2420 m2
C)2480 m2
D)2520 m2
E)None of these
Rationale: Solution
We have : (l - b) = 23 and 2 (l + b) = 206 or (l + b) = 103.
Solving the two equations, we get, l = 63 and b = 40.
∴ Area = (l × b) = (63 × 40) m2 = 2520 m2. Answer D
Answer: D
Question: In a game of billiards, A can give B 40 points in 120 and he can give C 60 points in 120. How many points can B give C in a game of 200?
Options:
A)55
B)60
C)45
D)50
E)35
Rationale: A scores 120 while B score 80 and C scores 60.
The number of points that C scores when B scores 200 = (200 * 60)/80 = 150.
In a game of 200 points, B gives (200 - 150) = 50 points to C
Answer : D
Answer: D
Question: The area of a square field is 1225 km2. How long will it take for a horse to run around at the speed of 20 km/h ?
Options:
A)7 h
B)10 h
C)8 h
D)6 h
E)None of these
Rationale: Explanation Area of field = 1225 km2. Then, each side of field = √1225=35km Distance covered by the horse = Perimeter of square field = 35× 4 = 140 km ∴ Time taken by horse = distances/peed=140/20=7h Answer A
Answer: A
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9 a.m.
B)10 a.m
C)10.30 a.m.
D)11 a.m.
E)11.30 a.m.
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
= 45x = 135
= x = 3.
So, they meet at 10 a.m.
ANSWER :B
Answer: B
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
Options:
A)87 kmph
B)40 kmph
C)16 kmph
D)15 kmph
E)30 kmph
Rationale: Speed downstream = 60 + 30
= 90 kmph
Speed upstream = 60 - 30
= 30 kmph
Answer:E
Answer: E
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)788
C)266
D)1254
E)1321
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: Find the smallest positive integer n such that tn of the arithmetic sequence 20,19¼ ,18½ ,… is negative
Options:
A)27
B)28
C)29
D)30
E)31
Rationale: Here we have , a= 20 = d = 19 ¼-20=-3/4
We	want	to	find	the	first	positive	integer	n such thattn<0
20+(n-1)(-3/4)<0
n>27.33
hence, 28th term is first negative term
Option B
Answer: B
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with five times the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.80 per glass on the first day, what was the price per glass on the second day?
Options:
A) $015
B) $0.27
C) $0.30
D) $0.40
E) $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.8=6*x --> x=$0.27.
Answer: B.
Answer: B
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability R that 3 of Sam’s 4 funds grew by at least 10% over last year?
Options:
A) 6C3 / 10C4
B) 6C3 * 4C1 / 10C4
C) 6C3 * 4C1 / 10P4
D) 6P3 * 4P1 / 10C4
E) 6P3 * 4P1 / 10P4
Rationale: Look at the answers. B is the only answer choice that uses only combination formulas and takes into account all the factors.
We know this is a combination, not a permutation. This rules out choices C, DE.
A clearly isn't the answer because R=6C3 only accounts for 3 of the funds he chose. 10C4, the denominator, is correct, so the numerator must be wrong.
B it is.
Answer: B
Question: A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly?
Options:
A)55
B)60
C)93
D)82
E)91
Rationale: let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=79 (subtracting twice of incorrect from correct)
3x=279
x=93
ANSWER:C
Answer: C
Question: What is the probability R of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R?
Options:
A)1/13
B)1/20
C)1/26
D)1/50
E)1/100
Rationale: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:
3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26
This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability R of the second letter is 11/11 = 1, > we do not care what's in between.C
Answer: C
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)Rs.370
B)Rs.375
C)Rs.375
D)Rs.350
E)Rs.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
ANSWER:B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?
Options:
A)150 meter
B)200 meter
C)156 meter
D)168 meter
E)154 meter
Rationale: Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 12
= 200 meter
Answer:B
Answer: B