divelab/Sys2Bench huggingface dataset:
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.12.60 less, he would have gained 30%. Find the cost of the article.
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 12.60 when C.P=(100*12.60)/21=60
ANSWER:D
Answer: D
Question: A snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 300 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
Options:
A)190
B)180
C)150
D)200
E)300
Rationale: let no of sits in vip enclosure is x then x*40 +15( 300-x) =7500 or 25x = 7500 -4500 , x = 3000/25 =120
vip =120 general 200
D
Answer: D
Question: In a sports club with 28 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(19-x)+x+2=28
38-2x+x=28
38-x=28
x=10
So 8 members play both badminton and tennis.
D
Answer: D
Question: Look at this series: 15, 15, ?, 27, 39, 39, ... What number should fill the blank?
Options:
A)51
B)39
C)27
D)15
E)None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option C
Answer: C
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Options:
A)27%
B)28%
C)20%
D)16%
E)25%
Rationale: Rs.1440 - 1200
= Rs.240 is the interest on Rs.1200 for one year.
Rate of interest
= (100 * 240) / (100 * 1)
= 20% p.a
Answer: C
Answer: C
Question: A trader sells 20 meters of cloth for Rs. 4500 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)Rs. 380
B)Rs. 215
C)Rs. 190
D)Rs. 395
E)None of these
Rationale: SP of 1m of cloth = 4500/20= Rs. 225
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 225 - Rs. 10 = Rs. 215.
ANSWER:C
Answer: C
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options:
A)59000
B)92828
C)59282
D)22888
E)12991
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% of Rs. 25000 = Rs.2500.
Amount received by A per annum for being a working partner = 1500 x 12 = Rs.18000
Let 'P' be the part of the remaining profit that A receives as his share.
So,total income of A = (Rs.2500 + Rs.18000 + Rs. P )
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
We know that income of A = Twice the income of B
So, (2500 + 18000 + P ) = 2(P)
P = 20500
Thus, the total profit = 2P + Rs.18000
= 2(20500) + 18000 = Rs.59000.
Answer: E
Answer: E
Question: A train with 1200m crosses a tree in 120sec, how much time will I take to pass a platform 700m long?
Options:
A)150sec
B)130sec
C)190sec
D)200sec
E)100sec
Rationale: s=1200/120
s-10m/sec
total length = 1900m
t=d/s
t=1900/10
t=190sec
ANSWER C
Answer: C
Question: When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Asha=25 Nisha =n Usha =3n
Asha=2a Nisha =a Usha =34
The difference of all ages must be same
25-2a=n-a=3n-34
We will get two equation
2n+a=34
n+a=25
From the equation we will get n=9 and a=16
The ages are Asha=2a=32 Nisha =16 and Usha =34
Sum of the ages =100
(32+x)+(16+x)+(34+x)=100
82+3x=100
3x=18
x=6
Age of Usha =34+6=40
ANSWER:D
Answer: D
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 3/7th share. How much money is contributed by B?
Options:
A)A)Rs.12829
B)B)Rs.12800
C)C)Rs.24000
D)D)Rs.12804
E)E)Rs.12830
Rationale: 16*8: x*4 = 4:3
x = 24 =>
Rs.2400
Answer: C
Answer: C
Question: A shipment of 240 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Options:
A)1/250
B)9/74
C)1/11
D)1/9
E)1/3
Rationale: Probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = (84/240)
Probability of chosing one defective phone from a lot of 239(we already picked one) which ontains 83(we already picked one) defective phones is = (83/239)
Combined probability of series of events = product of the probabilities = (84/240)*(83/239)
84/240 is close to (7/20) and (83/239)= (25/72)
so answer is (7/20)*(25/72) (9/74)
So, answer will be B
Answer: B
Question: A circular ground whose radius is 15 metres, has a 1.2 metre-broad garden around it. What is the area of the garden in square metres?
Options:
A)118.67
B)116.67
C)117.67
D)120.56
E)120.57
Rationale: Req. area = Ï€[(16.2)2 â€“ (15)2]
= 22â„7 Ã— (31.2 Ã— 1.2)[since a2 - b2 = (a + b)(a - b)]
= (22 Ã— 31.2 Ã— 1.2)/7 = 117.67sq m
Answer C
Answer: C
Question: A 230 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)230m
B)240m
C)250m
D)260m
E)270m
Rationale: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 230 + x
therefore, D= speed*time
thus 230 + x = 500/9 * 9
x= 500-230=270 m
ANSWER:E
Answer: E
Question: In how many ways can the letters A, M, A, Z, O, N be arranged so that the two A's are not next to each other?
Options:
A)36
B)48
C)72
D)96
E)240
Rationale: 2 A
1 M
1 Z
1 O
1 N
Number of ways these letters can be arranged = 6!/2! (2! to account 2 same As) = 360
Consider 2 As as 1 entity and thus the number of arrangements for (AA)MZON = 5! = 120
Total allowed cases = 360-120 =240
E is the correct answer.
Answer: E
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
Options:
A)37507
B)37500
C)83887
D)29978
E)29912
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)
(9x + 1100000 - 11x)/100 = 39000/4 = 9750
x = 62500
Sum invested at 9% = Rs. 62500
Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.
Answer:B
Answer: B
Question: A fair red coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
Options:
A)A)37/256
B)B)56/256
C)C)65/256
D)D)70/256
E)E)81/256
Rationale: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?
Options:
A)5/5
B)5/9
C)5/1
D)5/7
E)5/2
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: B
Question: A box contains six bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
Options:
A)21/81
B)16/81
C)65/81
D)2/3
E)1/2
Rationale: Required probability
= 1 - 16/81
= 65/81
Answer: C
Answer: C
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
Options:
A)194 seconds
B)195 seconds
C)196 seconds
D)197 seconds
E)None of these
Rationale: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128:1::25:x=>x=25∗1 /0.128
=>x=195.31
So time will be approx 195 seconds
Option B
Answer: B
Question: A train 150 m long can cross an electric pole in 3 sec and then find the speed of the train?
Options:
A)180
B)120
C)72
D)27
E)28
Rationale: Length = Speed * time
Speed = L/T
S = 150/3
S = 50 M/Sec
Speed= 50*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 180 Kmph
Answer:A
Answer: A
Question: A certain deck of cards contains 2 white cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both be not white?
Options:
A)15/28
B)1/4
C)9/16
D)1/32
E)1/16
Rationale: The question asks they will both be not white. Considering that these are draws without replacement there are following possibilities :
draw 1, draw 2
===== =====
1) Not white, white;
2) white, Not white;
3) white, white;
4) Not white, not white;
The answer has to be either P(4) OR all exclusion of the 3 previous conditions i.e. 1- [P(1) + P(2) + P(3)] => neither of the draws are white
P(4) = 6/8*5/7=15/28
1- [P(1) + P(2) + P(3)] = 1 - [ (6/8 * 2/7) + (2/8*6/7) + (2/8*1/7)] = 1 - [26/8*7] = 1 - [13/28] = 15/28
A
Answer: A
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)1 kmph
B)6 kmph
C)5 kmph
D)8 kmph
E)7 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: D
Question: A box contains 3red, 5yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
Options:
A)2/7
B)3/11
C)1/4
D)3/7
E)2/9
Rationale: Total number of balls = 3+5+4 = 12
n(S) = 12C3 = 12*11*10/3*2 = 220 n(E) = 3C1*5C1*4C1 = 3*5*4 = 60 P(E) = 60/220 = 3/11 Answer is B
Answer: B
Question: If you roll a fair-sided die twice, what is the probability of getting a double (5,5)?
Options:
A)1/24
B)1/36
C)1/12
D)1/18
E)1/3!
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(5,5) = 6
Probability= 6/6*6= 1/6=1/3!
E
Answer: E
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
A)46
B)28
C)25
D)22
E)29
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780
=46.
Answer: A
Answer: A
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%?
Options:
A)299
B)466
C)578
D)600
E)677
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84
5x/100 + 90 – 6x/100 = 84
x/100 = 6
=> x = 600
Answer:D
Answer: D
Question: A sum of money deposited at C.I. amounts to Rs.3000 in 3 years and to Rs.3600 in 4 years. Find the rate percent?
Options:
A)25%
B)5%
C)10%
D)15%
E)20%
Rationale: 3000 --- 600
100 --- ? => 20%
Answer: E
Answer: E
Question: Tough and Tricky questions: Probability.
Medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?
Options:
A)16/81
B)37/64
C)2/3
D)19/27
E)65/81
Rationale: At the end of each day we will have 3/4 alive. So after 3 days we will have (3/4)^3 people alive. Therefore, fraction of dead people will be 1-(3/4)^3=37/64.
The correct answer is B.
Answer: B
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value Q?
Options:
A)2r
B)2s
C)r +s
D)2r-s
E)2s-r
Rationale: The simplest way to do this is to assume values.
We are told that r and s are positive integers Q.
Also, r-s = 6 => r = 6+s
Hence r is 6 more than s.
Let s be 10. Hence r = 16.
Option A: 2r = 2*16 = 32
Option B: 2s = 2 * 10 = 20
Option C: r + s = 16 + 10 = 26
Option D: 2r - s = 2(16) - 10 = 32 - 10 = 22
Option E: 2s - r = 2(10) - 16 = 20 - 16 = 4
Hence option A is the greatest.
Answer: A
Question: How many pieces of 75 cm can be cut from a rope 54 meters long?
Options:
A)30
B)40
C)60
D)72
E)Cannot be determined
Rationale: Explanation :
Total pieces of 75 cm that can be cut from a rope of 54 meters long is
= (54 meters)/(75 cm)
= (54 meters)/(0.75 meters)
= 72
Answer : D
Answer: D
Question: If in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it, then what will be the maximum number of the small boxes that can be kept in it?
Options:
A)2288
B)1000
C)2877
D)2667
E)1311
Rationale: 6 * 5 * 4 = 60/100 * 50/100 * 40/100 * x
1 = 1/10 * 1/10 * 1/10 * x => x = 1000
Answer: B
Answer: B
Question: Ravi jogs 7 km at a speed of 5 kmph. at what speed would she need to jog during the next 2.5 hour to have an average of 7 km per hr at the entire jogging session?
Options:
A)17.8 kmph
B)8.9kmph
C)5.8kmph
D)5.8kmph
E)4.9kmph
Rationale: let speed of the jogging be xkmph
total time taken=(7/5+2.5)=3.9hrs
total distance covered=(7+2.5x)
7+2.5x/3.9=9
x=17.8kmph
Answer(A)
Answer: A
Question: An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 3 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
Options:
A)9:10
B)19:20
C)29:30
D)39:40
E)49:50
Rationale: Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be 4y and 3y.
2(3x + 2x) = 2(4y + 3y)
5x = 7y
(5/7) * x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : 4y * 3y
= 6x^2 : 12y^2
= x^2 : 2y^2
= x^2 : 2*(25/49) * x^2
= 49 : 50
The answer is E.
Answer: E
Question: 8^100 is divisible by 17. Find the remainder?
Options:
A)10
B)12
C)16
D)18
E)20
Rationale: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C
Answer: C
Question: If a survey shows that 26 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
Options:
A) 56%
B) 64%
C) 72%
D) 87%
E) 86%
Rationale: 26 out of 200 supports the bill and we are asked to find the percent who the does not support the bill.
26 out of 200 supports the bill = 13 out of 100 supports the bill ( taking in % terms )
14 out of 100 supports the bill = 87 (100-13) doesn't support the bill
So, answer is (D) 87%
Answer: D
Question: There are 16 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)267
C)261
D)211
E)306
Rationale: The total number of stations = 18
From 18stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 18P₂ ways.
18P₂ = 18* 17= 306.
Answer: E
Answer: E
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)45 m
B)60 m
C)50 m
D)67 m
E)78 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: The rhombus (AFCE) is inscribed in rectangle (ABCD). The length of BF = DE.
If the rectangle has a width of 20 yards and a length of 25 yards, what would be the total length (the perimeter) of a fence along the sides defined by AFCE?
Options:
A)80 yards
B)82 yards
C)84 yards
D)85 yards
E)90 yards
Rationale: The definition of a rhombus states that every side is of equal length. This definition is the key to solving this question.
1) We state that the hypotenuse of either side triangle is x. For this solution, I will be working with the left triangle.
2) We state that the bottom and top sides of the rhombus are also x, due to the definition of a rhombus.
3) We will define the bottom of the left triangle as y. That is, for the rectangle bottom itself, we can define it as 25 = y + x, where x is a side for the rhombus and y is the bottom part of the left triangle.
4) From (1), we know that x = 202+y2−−−−−−−√202+y2.
5) From (3), we know x = 25 - y.
6) From (4) and (5), we have the equation 202+y2−−−−−−−√=25−y202+y2=25−y
7) Solving for y, we get 4.5.
8) 25 - 4.5 = 20.5 = x
9) Since all sides of the rhombus are the same, 20.5 * 4 = 41 * 2 = 82.
The answer is B, 82
Answer: B
Question: There are 5 boxes in a cargo. The weight of the 1st box is 200 KG, the weight of the 2nd box is 20% higher than the third box, whose weight is 25% higher than the 1st box weight. The 4th box which weighs 350 KG is 30% lighter than the 5th box. Find the difference in average weight of the 4 heaviest boxes and the four lightest boxes.
Options:
A)22
B)75
C)25
D)70
E)11
Rationale: weight of 1st box=200
weight of 3rd box=(125/100)*200=250
weight of 2nd box=(120/100)*250=300
weight of 4th box =350
weight of 5th box=(10/7)*350=500
average of 4 highest weighted boxes=(500+350+300+250)/4=350
average of 4 lightest boxes=(350+300+250+200)/4=275
therefore difference=350-275=75
Answer:B
Answer: B
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)290 sec
B)190 sec
C)199 sec
D)192 sec
E)193 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Answer: B
Answer: B
Question: A wooden cube whose edge length is 7 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
Options:
A)59.8%
B)63.6%
C)67.2%
D)70.5%
E)73.6%
Rationale: There are a total of 7*7*7 = 343 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 5*5*5 = 125 cubes.
The number of cubes with at least one side painted red is 343 - 125 = 218 cubes
The probability that a cube has at least one side painted red is 218/343 which is about 63.6%
The answer is B.
Answer: B
Question: A school has received 80% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Options:
A)$200
B)100
C)$105
D)$250
E)$300
Rationale: Let us suppose there are 100 people. 40% of them donated $ 24000 ( 600 * 40 )
$24000 is 80% of total amount.
So total amount = 24000 * 100/80
Remaining amount is 20% of total amount.
20% of total amount = 24000 * (100/80) * (20/100) =6000
This amount has to be divided by 60 ( remaining people are 60 )
So per head amount is 6000/ 60 = $100
ANSWER:B
Answer: B
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 6 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Options:
A)15 litres
B)10 litres
C)30 litres
D)12 litres
E)8 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+6)=4/5
20x=4(3x+6)
8x=24
x=3
Quantity of alcohol = (4 x 3) litres = 12 litres.
Answer is D
Answer: D
Question: In what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way?
Options:
A)3
B)5.4
C)4.3
D)6.5
E)7
Rationale: T = 75/50 * 18/5 = 5.4 sec
Answer:B
Answer: B
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
Options:
A)32
B)36
C)33
D)37
E)None of them
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Answer is B.
Answer: B
Question: Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 8 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
Options:
A)80
B)90
C)30
D)72
E)60
Rationale: D
72
Sum = (n x n) + n
Hence, 8 x 8 = 64 + 8 = 72
Answer: D
Question: A basketball coach is choosing her starting lineup from a team of 11 girls. 7 of the girls are post players and 4 are guards. If she chooses 3 post players and 2 guards, how many different lineups can be made?
Options:
A)210
B)220
C)240
D)260
E)270
Rationale: (7c3)*(4c2)
[7!/(3!*4!)]*[4!/(2!*2!)]
35*6
210
A
Answer: A
Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)87 Kmph
B)97 Kmph
C)72 Kmph
D)90 Kmph
E)19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 500/20
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer: D
Answer: D
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.12 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1440
B)1200
C)2832
D)1299
E)1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 12 = 1440
Answer: Option A
Answer: A
Question: Bill has d animals, 28 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
Options:
A)6
B)12
C)18
D)24
E)42
Rationale: Total d animals, suppose each has price of x - total price = dx
now 28 were sold at profit of 10%, making equation - - 28*1.1x
now d-28 were sold at loss of 20%, making eqn --- (d-28)*0.8x
Now he made no profit or loss so,
dx = 28*1.1x + (d-28)*0.8x
solving for d, we get d=42
Ans E
Answer: E
Question: A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 303 test scores with a standard deviation less than d?
Options:
A) 75 and 80
B) 75 and 75
C) 70 and 75
D) 75 and 70
E) 70 and 80
Rationale: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.
B
Answer: B