divelab/Sys2Bench huggingface dataset:
Question: The length of the bridge, which a train 110 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)265
B)288
C)245
D)776
E)232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (110 + X)/30 = 25/2 ==> 2(110 + X) = 750 ==> X
= 265 m.
Answer:A
Answer: A
Question: A bag contains 8 red, 6 blue and 4 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/13
B)2/23
C)5/26
D)7/30
E)3/23
Rationale: P(Both are red),
=8C216C2=8C216C2
=28/120=7/30
D
Answer: D
Question: A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds.The speed of the second train is
Options:
A)60 kmph
B)66 kmph
C)72 kmph
D)99 kmph
E)89 kmph
Rationale: Given that two trains are of same length i.e..150 mtrs
first train passes the km stone in 15 seconds. here we have time and distance so speed=150/15=10 m/s
we need to find out the second train speed.
suppose the speed of the 2nd train is x m/s
Relative speed of two trains is (10+x)
==> (150+150)/(10+x)=8
==> (300)/(10+x)=8
==> 300=80+8x
==> 300-80=8x
==> 220=8x
:- x=55/2 m/s
convert m/s into km/ph
(55/2)*(18/5)=99kmph
ANSWER:D
Answer: D
Question: A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)120
B)160
C)200
D)240
E)300
Rationale: The number of ways to select two men and three women = 4C2 * 6C3 = 6 * 20 = 120
The answer is A.
Answer: A
Question: The sides of a cube are in the ratio of 1:2 the ratio of their volumes is ?
Options:
A)1:2
B)1:4
C)1:8
D)2:1
E)2:4
Rationale: 1:8Answer : C
Answer: C
Question: A alone can do a work in 12 days. A and B together finished work and got rs.54 and rs.18 respectively. In how many days was the work finished?
Options:
A)12
B)14
C)9
D)10
E)8
Rationale: A does the work in 12 days
and A and B together finished work and got rs.54 and rs.18 respectively
so B will do work in 12*3 = 36 days (because he got 1/3 money relative to other)
so one day work = 1/12 + 1/36 = 4/36 = 1/9
so total days required = 9
ANSWER:C
Answer: C
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
Options:
A)14
B)45
C)54
D)65
E)41
Rationale: Just check the answers and reverse the numbers until you get 27.
41 - 14 = 27
Answer E
Answer: E
Question: A batsman scored 130 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45(4/11) %
B)45 %
C)53(11/13) %
D)44(5/11) %
E)None of these
Rationale: Explanation :
Total runs scored = 130
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 130 - 60 = 70
Required % = (70/130) × 100 = 700/13 = 53(11/13)%
Answer : Option C
Answer: C
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 4:3. The sum of numbers is:
Options:
A)28
B)30
C)40
D)50
E)60
Rationale: Let the numbers be 4x and 3x.
Then, their L.C.M = 12x. So, 12x = 48 or x = 4.
The numbers are 16 and 12.
Hence, required sum = (16 + 12) = 28.
ANSWER:A
Answer: A
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Options:
A)150
B)190
C)100
D)240
E)280
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon.
Answer: D
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 8 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
Options:
A)61
B)62
C)65
D)63
E)64
Rationale: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-8) = 594000
(568/x + 1)(x-8) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 8 = 63 bikes this month
Answer (D)
Answer: D
Question: Convert the following unit:
2.5 hectares in ares
Options:
A)200 ares.
B)210 ares.
C)220 ares.
D)250 ares.
E)240 ares.
Rationale: 2.5 hectares in ares
1 hectare = 100 ares
Therefore, 2.5 hectares = 2.5 × 100 ares
= 250 ares.
ANSWER : OPTION D
Answer: D
Question: A teacher will pick a group of 4 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible four-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa?
Options:
A)1/7
B)3/14
C)1/4
D)1/21
E)3/7
Rationale: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 4 out of 9 = 9C4 = 9! / (5! * 4!) = 126
Favorable Outcomes= Total No. of ways of Picking Group of 4 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining one out of remaining 6 as J, B and L must be there is group) = 6C1 = 6
Hence,Probability=6/126=1/21
Answer: Option D
Answer: D
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.7
C)62.9
D)62.1
E)62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: A
Question: Which of the following must be an integer if the integer x is divisible by both 15 and 21?
Options:
A)x/252
B)x/189
C)x/126
D)x/105
E)x/81
Rationale: the integer has to be multiple of LCM of 15 and 21, which is 105..
so x/105 will be an integer
ans D
Answer: D
Question: If you cut a 20ft piece of wood into two pieces making one piece 6ft longer than the other. What size is the smaller piece?
Options:
A)4ft
B)7ft
C)8ft
D)10ft
E)12ft
Rationale: Total length is 20ft, one piece is 6ft longer (x+6), leaving the other piece to figure out (x).
(x)+ (x+4)=20
x+x+6-6=20-6
2x=14
2x/2=14/2
x=7
The piece is B) 7ft.
Answer: B
Question: If 2a = 3b and ab ≠0, what is the ratio of a/3 to b/2?
Options:
A)27/8
B)8/27
C)1
D)9/4
E)81/64
Rationale: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 2a = 3b
Here's one pair: a =3 and b =2
What is the ratio of a/3 to b/3?
In other words, what is the value of (a/3)/(b/2)?
Plug in values to get: (a/3)/(b/2) = (3/3)/(2/2)
= 1/1
= 1
C
Answer: C
Question: If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?
Options:
A)2:1
B)2:7
C)2:2
D)2:6
E)2:3
Rationale: Let 1 man's 1 day work = x and 1 boy's 1 day work = y.
Then, 12x + 16y = 1/5 and 13x + 24y = 1/4
Solving these two equations, we get:
x = 1/100 and y = 1/200
Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer:A
Answer: A
Question: The mean of (54,821)^2 and (54,823)^2 =
Options:
A)(54,821)^2
B)(54,821.5)^2
C)(54,820.5)^2
D)(54,821)^2 + 1
E)(54,822)^2 + 1
Rationale: 54821^2 = (54822-1)^2 = 54822^2 + 1^2 - 2*54822*1
54823^2 = (54822+1)^2 = 54822^2 +1^2 + 2*54821*1
Taking the average of above 2 , we get (54822)^2 +1
hence the answer is E
Answer: E
Question: What number should replace the question mark?
105, 87, 70, 52, 35,?
Options:
A)49
B)37
C)70
D)17
E)83
Rationale: D
17
The sequence progresses -18, -17, -18, -17.
Answer: D
Question: A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ?
Options:
A)650 meter
B)555 meter
C)500 meter
D)458 meter
E)None of these
Rationale: Explanation:
Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
=>800+x=65/3∗60
=>800+x=20∗65=1300
=>x=1300−800=500
So the length of the tunnel is 500 meters.
Option C
Answer: C
Question: What is the unit’s digit of 7^6
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 7^6=9
Answer E
Answer: E
Question: In how many different ways can 3 identical green boots and 3 identical red boots be distributed among 6 people such that each person receives a pair of boots?
Options:
A)7209
B)4059659
C)2169
D)20
E)7291
Rationale: How to solve:
1st Person: 6 has options
2nd Person: 5 has options…
Therefore, for all people: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the reds are identical, we divide by 3! Since the greens are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: D)
Answer: D
Question: How long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length?
Options:
A)18.6 sec
B)14.9 sec
C)12.4 sec
D)16.8 sec
E)11.8 sec
Rationale: A
18.6 sec
D = 110 + 200 = 310 m
S = 60 * 5/18 = 50/3
T = 310 * 3/50 = 18.6 sec
Answer is A
Answer: A
Question: 8 is 6% of a, and 6 is 8% of b. c equals b/a. What is the value of c?
Options:
A)3/8
B)8/15
C)9/16
D)12/25
E)16/27
Rationale: 6a/100 = 8
a = 400/3
8b/100 = 6
b = 75
c = b/a = 75*3/ 400 = 9/16
The answer is C.
Answer: C
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 6 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
Options:
A)d = p/1.06 - 0.18
B)d= (p-0.18)/1.06
C)d = (p-0.06)/1.18
D)d = p-0.24
E)d = p/1.24
Rationale: Let dealers price (d) be 1. so adding 6% to dealers price is d+ 6% of d. i.e. 1 + 6% of 1 which is1 + 0.06. then add 0.18 to the value.
Now 1.06 + 0.18. this is now 1.24. you have the gasoline stations price (p) as 1.24 dollars.
Now sub 1.24 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : B
Answer: B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)42 6/8%
B)42 8/7%
C)72 6/7%
D)42 6/7%
E)42 6/1%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: D
Question: If the product of the integers from 1 to n is divisible by 1029, what is the least possible value of n?
Options:
A)7
B)14
C)21
D)28
E)35
Rationale: 1029 = 7 x 7 x 7 x 3
N must include at least 7, 2*7, and 3*7.
The answer is C.
Answer: C
Question: If b, x, y, and z are positive integers and (x)×(y)×(z)=b^2, which of the following could be the values of x, y, and z?
Options:
A)3, 16, 25
B)9, 25, 24
C)2, 81, 32
D)2, 9, 16
E)8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*81*32 = 2*9*9*8*4 = 9*9*8*8
ans C
Answer: C
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 9 maps and 6 books for a total of $20.00, and on Tuesday the store sold 9 maps and 8 books for a total of $30.00. At this store, how much less does a map sell for than a book?
Options:
A) $0.25
B) $0.50
C) $0.75
D) $3.9
E) $l.25
Rationale: 9x+6y=20
9x+8y=30
subtracting 1 from 2
-2y=-10
y=5
therefore
x=1.1
difference in price =3.9
D
Answer: D
Question: The compound interest on Rs.2,000 at 10% per annum for 3 years payable half yearly is
Options:
A)Rs.600
B)Rs.630
C)Rs.660
D)Rs.680
E)Rs.690
Rationale: amt=2000(1+r/2/100)^2n formulae as it is half yearlly
amt=2000(1+1/20)^4
amt=2680.19
ci= 2680.19-2000 = 680.00
ANSWER:D
Answer: D
Question: A boat can move upstream at 35 kmph and downstream at 65 kmph, then the speed of the current is?
Options:
A)15
B)8
C)9
D)12
E)10
Rationale: US = 35
DS = 65
M = (65- 35)/2
= 15
Answer:A
Answer: A
Question: Find the missing number in the given sequence : 1,4,7,?,13,16,?
Options:
A)10 & 19
B)8 & 17
C)9 & 18
D)11 & 20
E)12 & 21
Rationale: 1+3=4
4+3=7
7+3=10
10+3=13
13+3=16
16+3=19
ANSWER:A
Answer: A
Question: In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 4 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
Options:
A)3
B)6
C)8
D)9
E)12
Rationale: the choices give away the answer..
36 machines take 4 hours to fill 4 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*12/4 = 6
Ans B
Answer: B
Question: N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N?
Options:
A)1 1/2
B)1 1/3
C)5/3
D)3/2
E)2/3
Rationale: "N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer B
Answer: B
Question: A cylinder of height h is 8/9 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
Options:
A)25%
B)50%
C)68%
D)80%
E)100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 8/9
New cylinder 3/5
So 3/5/8/9 = 3/5 * 9/8 = 12/15 = 4/5 = 0.680 or 68%.
Answer C
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)10 m
B)16 m
C)245 m
D)19 m
E)27 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
Answer: C
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
Options:
A)33 1/3%
B)51 23/27%
C)50%
D)62 1/2%
E)75%
Rationale: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27%
Answer B
Answer: B
Question: 15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
Options:
A)14
B)18
C)24
D)28
E)None of these
Rationale: Binders Books Days
15 1400 21
x 1600 20
x/15 = (1600/1400) * (21/20) => x = 18
ANSWER:B
Answer: B
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 54. What is the difference between the two digits of the number?
Options:
A)4
B)6
C)3
D)Cannot be determined
E)None of these
Rationale: Let the two-digit no. be l0x + y.
Then, (10x + y) â€“ (10y + x) = 36
or, 9(x â€“ y) = 54
or, x â€“ y = 6
Answer B
Answer: B
Question: On dividing number by 357, we get 39 as remainder. On dividing the same number by 17, what will be the remainder?
Options:
A)0
B)3
C)5
D)11
E)13
Rationale: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x2 = (5k + 3)2 = (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
ANSWER:C
Answer: C
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)24
B)73
C)26
D)82
E)72
Rationale: Explanation:
Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
Answer: A
Answer: A
Question: A box contains 4 red chips and 3 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
Options:
A)1/2
B)12/21
C)7/12
D)2/3
E)7/10
Rationale: Total selection ways: 7C2=7!/3!4!=21
Selecting one blue chip out of two: 3C1=3!/2!1!=3
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (3C1*4C1)/7C2=(3*4)/21=12/21=B
Answer: B
Question: 894.7 – 573.07 – 95.007 = ?
Options:
A)226.623
B)224.777
C)233.523
D)414.637
E)None of these
Rationale: Solution
Given expression = 894.7 - (573.07 + 95.007) = 894.7 - 668.077 = 226.623. Answer A
Answer: A
Question: A train when moves at an average speed of 60 kmph, reaches its destination on time. When its average speed becomes 45 kmph, then it reaches its destination 30 minutes late. Find the length of journey.
Options:
A)70 km
B)76 km
C)85 km
D)90 km
E)None of these
Rationale: Explanation :
Solution: Difference between timings = 30 min. = 30/60 hr = 1/2 hr.
Let the length of the journey be x km.
Then, x/45 - x/60 = 1/2
=> 4x -3x = 180/2
=> x = 90 km.
Answer : D
Answer: D
Question: A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.40, find the sum of money?
Options:
A)782
B)276
C)727
D)205
E)628
Rationale: A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer:D
Answer: D
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)8 sec
B)7 sec
C)2 sec
D)6 sec
E)9 sec
Rationale: T = 60/36 * 18/5
= 6 sec
Answer:D
Answer: D
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Options:
A)Rs.2166.67
B)Rs.2224
C)Rs.2270.72
D)Rs.2145
E)Rs.2165
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: A
Question: The roots of the equation axpower2 + bx + c =0 will be reciprocal if:
Options:
A)a=b
B)a-bc
C)c=a
D)c=b
E)c=ab
Rationale: based on the problem 1/k will be the other root of the given equation. root equation = c/a. k*1/k=c/a. c/a= 1 or a = c[multiplying on both sides].
the roots of the equation axsquared + bc + c= 0 will be reciprocal if a= c. correct answer: (C)
Answer: C
Question: a plane travelled k miles in 1st 96 miles of flight time.if it completed remaining 300 miles of the trip in 1 minute what is its average speed in miles/hr for entire trip ?
Options:
A)396/60+k
B)376/60+k
C)386/60+k
D)366/60+k
E)356/60+k
Rationale: k=96+300
tot distance= 396 miles
tot time= 1min + k
avg speed= 396/60+k
ANSWER:A
Answer: A
Question: How many keystrokes are needed to type numbers from 1 to 500?
Options:
A)1750
B)1000
C)1500
D)1529
E)1392
Rationale: Explanatory Answer
While typing numbers from 1 to 500, there are 9 single digit numbers: from 1 to 9.
Each of these numbers requires one keystroke.
That is 9 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 401 three-digit numbers: from 100 to 500.
Each of these numbers requires 3 keystrokes.
Therefore, 1203 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 9 + 180 + 1203 = 1392 keystrokes.
Choice E is the correct answer.
Answer: E
Question: An archer is shooting arrows from various distances. She shoots at a target from 60 yards, 70 yards, and 80 yards. The probability that she hits within the bullseye from 60 yards is 2/3, the probability that she hits within the bullseye from 70 yards is 3/5, and the probability that she hits within the bullseye from 80 yards is 1/2. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
A)19/20
B)29/30
C)49/50
D)9/10
E)14/15
Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 60 yards)*(prob that she misses from 70 yards)*(prob that she misses from 80 yards)
Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5; Prob that she misses from 80 yards = 1 - 1/2 = 1/2
Thus the probability that she misses all shots = (1/3)*(2/5)*(1/2) = 2/30 = 1/15
Thus the probability that she makes at least one shot = 1 - (1/15) = 14/15
E
Answer: E
Question: In a function they are distributing noble prize. In how many ways can 2 prizes be distributed among 5 boys when a boy gets any no. of prizes?
Options:
A)25
B)30
C)64
D)70
E)80
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the two prizes can be given in 5 ways, i.e. (5 x 5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways
Answer: A
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)20 kmph
B)13 kmph
C)65 kmph
D)55 kmph
E)14 kmph
Rationale: Speed of the boat in still water
= (40+80)/2
= 60 kmph. Speed of the stream
= (80-40)/2
= 20 kmph.
Answer: A
Answer: A
Question: There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?
Options:
A)108
B)112
C)126
D)140
E)None of these
Rationale: Explanation :
Initially, let's remove the 4 stopping stations
Then we are left with 8 non-stopping stations (=12-4) as shown below
(non-stopping stations are marked as 1,2 ... 8)
Now there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations
such that no two stopping stations are consecutive
This can be done in 9C4 ways
Hence, required number of ways = 9C4
=((9)(8)(7)(6)/(4)(3)(2)(1))=126
Answer C
Answer: C
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 6 * 9 =?
Options:
A)65
B)59
C)72
D)80
E)77
Rationale: (9 * 6) + 5 = 59
B
Answer: B
Question: Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with 2 their digits may shift ,but no new digit will include or no digit will disappear. Example: 12 is not such a number. Because if you multiply 2 with 12, it will become 24. And 24 includes a new digit 4 ,and fails to obtain the previous digit 1. Can you find one of them?
Options:
A)138687
B)142587
C)144487
D)142667
E)142577
Rationale: B
142587
142587*2=285174
These type of numbers are called cyclic numbers where a number multiplied by any digit the result will contain all the digit in the original number and no other digit.
cyclic numbers are generated by full reptend prime 7,17,19,23 etc.
where 1/7=0.142857……
1/17=0.058823529411764
Answer: B
Question: Find the lowest common multiple of 25, 35 and 50.
Options:
A)350
B)420
C)510
D)320
E)280
Rationale: LCM=2*5*5*7=350.
Answer is A
Answer: A