divelab/Sys2Bench huggingface dataset:
Question: A beekeeper has 100,000 bees living in five beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
Options:
A)2381
B)24000
C)34000
D)26000
E)37000
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+4*(0.8)*x = 100,000 => 4.2x = 100,000 => x = 2381.
A is the answer.
Answer: A
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 410 m long?
Options:
A)33 Seconds
B)22 Seconds
C)41 Seconds
D)24 Seconds
E)29 Seconds
Rationale: Distance travelled = 140 + 410m = 550m
Speed = 60 * 5/8 = 50/3m
Time = 550 * 3/50 = 33 Seconds
ANSWER A
Answer: A
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $460. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $560. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
Options:
A)12
B)14
C)16
D)15
E)18
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 460 ... eq1
8x +32y = 560....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 920
8x = 560.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 560... then we get 32y = 480 then y = 15
Differenece between X and Y is 5
Answer : D
Answer: D
Question: If x/y=4 and y is not '0' what % of x is 2x-y
Options:
A)100%
B)125%
C)175%
D)185%
E)195%
Rationale: x/y=4
or,x=4y....(1)
"what % of x is 2x-y" means
what % of (4y)x is (2*4y-y)2x-y.
or,(7y/4y)*100=175%
ANSWER:C
Answer: C
Question: It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
Options:
A)8:28 am
B)8:35 am
C)8:42 am
D)8:49 am
E)8:56 am
Rationale: Since Megan will run s miles after s × 7 minutes and Mike will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 7 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 7 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 7 and 8 is 56, so in the context of the question, this would be 56 minutes. Therefore, the first time they will finish running a mile at the same time is 8:00 + 56 minutes, or 8:56 a.m. The answer is (E).
Answer: E
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)12
B)15
C)16
D)13
E)18
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: A batsman hits a score of 78 runs in the 16th inning and thus increases his average by 4. Find his average after 16th inning.
Options:
A)13
B)18
C)27
D)39
E)40
Rationale: Explanation :
Let the average after 16th inning = x.
Average after 15th inning =(x-4).
=> 15(x-4)+78 = 16x
=> x = 18.
Answer : B
Answer: B
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)29
B)68
C)92
D)23
E)23
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: B
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 8% p.a for 2 years. Find his gain in the transaction per year.
Options:
A)167.5
B)150
C)200
D)112.5
E)212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 8% p.a for 2 years
Simple interest that he gets = PRT/100=5000×8×2/100=800
His overall gain in 2 years = Rs.800 - Rs.400 = Rs.400
His overall gain in 1 year = 400/2 = Rs.200
Answer : Option C
Answer: C
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units D digit of (a+2)^2?
Options:
A)1
B)3
C)5
D)6
E)C. 14
Rationale: I also got A. By punching in numers:
D...7^2=...9
...8^2=...4
...9^2=...1.A
Answer: A
Question: The H.C.F. of two numbers is 28 and the other two factors of their L.C.M. are 12 and 15. The larger of the two numbers is
Options:
A)420
B)430
C)312
D)322
E)None
Rationale: Solution
Clearly, the numbers are (28 x 12) and (28 x 15).
Larger number = (28 x 15)	= 420.
Answer A
Answer: A
Question: If n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=6, is n divisible by 48? No. So, n is not always divisible by 48.
A
Answer: A
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold a bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2a
II. y > a
III. y > 3
Options:
A)I only
B)II only
C)I and II
D)II and III
E)I, II, and III
Rationale: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(a-12) where x is the total number of bikes sold (when a>12).
A = cycles sold last week
AS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2AS
lets test all statements with A=0;
AS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with A=1;
AS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with A=6;
AS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Answer: D
Question: Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)3!
B)8!
C)11!
D)12!
E)14!
Rationale: Ans.(A)
Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways
Answer: A
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 2 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)15
B)30
C)45
D)60
E)90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 2.
So, x = 32.5 ounces.
Water = (60 / 65) * (65/2) = = 30 ounces.
Ans B
Answer: B
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
Options:
A)150,222
B)150,209
C)150,200
D)150,202
E)150,201
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer: C
Answer: C
Question: In a card game, a combination of three aces beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
Options:
A)1/5000
B)1/5520
C)1/5525
D)1/5545
E)1/5600
Rationale: he best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 aces in it.
Probability of first card to be ace = 4/52
Probability of Second card to be ace = 3/51
Probability of third card to be ace = 2/50
Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525
C
Answer: C
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 50 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)46 2/3%
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
50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3%
Answer B
Answer: B
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish?
Options:
A)7: 00 p.m.
B)8: 00 p.m.
C)6: 00 a.m.
D)8: 00 a.m.
E)10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 1 PM, we get 7 AM as the answer.
Option A
Answer: A
Question: Ram's salary is 25% more than Raja's. How much percent is Raja's salary less than Ram's?
Options:
A)10%
B)15%
C)20%
D)25%
E)50%
Rationale: Raja's salary less than Ram's by 25/(100+25) * 100% = 20%
Answer is C
Answer: C
Question: A box contains 7 pairs of shoes (14 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
Options:
A)1/190
B)1/20
C)1/19
D)1/13
E)1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 14, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/13(as after taking one at random there are 13 shoes left and only one is the pair of the first one)=1/13
Answer: D.
Answer: D
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a two. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
Options:
A)11/16
B)15/32
C)14/36
D)23/48
E)17/56
Rationale: The answer is D
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 2 =1/6
Probability picking a spades card =1/4
so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.7 sec
C)3.5 sec
D)2.9 sec
E)9.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Answer: A
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 100
Total = 100 + 100 = 200
Answer (D)
Answer: D
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
Options:
A)18
B)99
C)77
D)55
E)44
Rationale: Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Answer: A
Answer: A
Question: If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in only median being modified not the mean.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
Options:
A)1) A and B
B)2) A and E
C)3) A,C,E
D)4) None of them
E)5) All of them
Rationale: There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where median will change and mean will not change.
Answer: D
Answer: D
Question: A tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)56 hours
B)28 hours
C)55 hours
D)66 hours
E)47 hours
Rationale: 1/A + 1/B + 1/C = 1/16 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/16
=> (1 + 2 + 4)/2B = 1/16
=> 2B/7 = 16
=> B = 56 hours.
Answer: A
Answer: A
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
Options:
A)21
B)24
C)27
D)36
E)42
Rationale: Let the numbers be 3x, 3x + 3, 3x + 6
Then, 3x + 3x + 3 + 3x + 6 = 72 ===> 9x = 63 ==> x = 7.
so the largest number is 3x + 6 = 27.
hence the correct answer is option C) 27.
Answer: C
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is more than 17?
Options:
A)1/5
B)1/10
C)2/15
D)1/45
E)2/45
Rationale: The number of ways to choose two cards is 10C2=45.
There are 2 ways, {9,10} and {8,10}, to get a sum more than 17.
P(sum more than 17)=2/45
The answer is E.
Answer: E
Question: Sum of 36 odd numbers is?
Options:
A)1294
B)1295
C)1296
D)1297
E)1298
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 36 odd numbers = 36^2 = 1296
ANSWER:C
Answer: C
Question: Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
Options:
A)3.2 hr
B)3.4 hr
C)3.6 hr
D)3.8 hr
E)4.2 hr
Rationale: let see d/t =v then x/20 + (400-x)/70 =8
x= 64 kmh
t = 64/20 = 3.2 hr
ANSWER:A
Answer: A
Question: A train passes a station platform in 31 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)228
B)240
C)165
D)166
E)1811
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/31 = 15 => x = 165 m.
Answer: C
Answer: C
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)7 cm
B)6 cm
C)4 cm
D)3 cm
E)9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer: E
Answer: E
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Options:
A)7/15
B)14/31
C)3/7
D)17/35
E)1/2
Rationale: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.5 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 30 hours.
Total hours = 70.
Then the fraction would be 30/70 = 3/7 Therefore answer
C.
Answer: C
Question: In a six-sided polygon WQRSTV ∠W measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠W equal to, in degrees?
Options:
A) 72
B) 80
C) 88
D) 96
E) 104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + W = 720, we know ∠W=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠W= 128-48 = 80
Ans B.
Answer: B
Question: Calculate the value of r: 6r^2-17r+6 = 254
Options:
A)8
B)10
C)5
D)9
E)3
Rationale: Using the elimination method substitute options for x and find the correct option.
Answer: A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)2888
B)288
C)178
D)150
E)2821
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Answer: D
Question: A person crosses a 600600 metre long street in 55 minutes. What is his speed in km per hour?
Options:
A)8.2
B)4.2
C)6.1
D)7.2
E)9.1
Rationale: Explanation:
Solution 1Distance =600=600 metre =0.6=0.6 km
Time =5=5 minutes =112=112 hour
Speed=distancetime=0.6(112)Speed=distancetime=0.6(112) =7.2 km/hr
Answer is D
Answer: D
Question: If M/N = 6/5,then 3M+2N = ?
If p/q = 5/4 , then 2p+q= ?
If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
Options:
A)18/5
B)28/5
C)27/5
D)26/5
E)38/5
Rationale: 3M+2N (divide by N)
3M/N+2
3*(6/5)+2
28/5 ANSWER:B
Answer: B
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 2). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
Options:
A)$0.50
B)$1.00
C)$1.25
D)$1.50
E)$1.75
Rationale: OA is definitely wrong. The answer should be E.
Answer: E
Question: If a and b are positive integers and (3^a)^b = 3^3, what is the value of 3^a*3^b?
Options:
A)3
B)9
C)81
D)27
E)243
Rationale: 3^ab =3^3 therefore ab=3 either a=1or3 or b=3 or 1
therefore 3^a* 3^b = 3^(a+b)= 3^4 =81
C
Answer: C
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
Options:
A)1/9
B)1/7
C)1/2
D)1/1
E)1/5
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability
= 1/7
Answer:B
Answer: B
Question: A man can row upstream at 55 kmph and downstream at 65 kmph, and then find the speed of the man in still water?
Options:
A)27
B)70
C)60
D)80
E)24
Rationale: US = 55
DS = 65
M = (55 + 65)/2
= 60
Answer:C
Answer: C
Question: In a room with 10 people, 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
Options:
A)5/21
B)3/7
C)4/5
D)5/7
E)16/21
Rationale: (6/10)(7/9) + (5/10)(6/9) if you choose one of the 6 with one other friend, then you have a 7/9 chance of not picking their friend 2nd. If you choose one of the 5 with 2 friends, you have a 6/9 chance of not picking one of their friends second. Add them up.
42/90 + 30/90
72/90 = 4/5
C. 4/5
Answer: C
Question: If an integer x is to be selected at random from 1 to 100, inclusive, what is probability x(x+1) will be divisible by 2?
Options:
A)3
B)1
C)2
D)4
E)5
Rationale: because x(x+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
1*1=1
Answer : B
Answer: B
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)77.14 cm
B)25.14 cm
C)84.92 cm
D)94.94 cm
E)23.57 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 14) = 64 cm Parameter of the square = 64 cm
i.e. 4a = 64
A = 16
Diameter of the semicircle = 16 cm
Circimference of the semicircle
= 1/2(∏)(16)
= 1/2(22/7)(16) = 352/14 = 25.14 cm to two decimal places
ANSWER:B
Answer: B
Question: A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream?
Options:
A)6 hr
B)2 hr
C)4 hr
D)1 hr
E)None of these
Rationale: Explanation :
Speed downstream = 96⁄8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12-4 = 8 kmph
Speed upstream = 8-4 = 4 kmph
Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B
Answer: B
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 75 marks in that test. Find the pass mark in the first test?
Options:
A)768
B)243
C)246
D)288
E)224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 75 marks in the second test.
pass mark in the second test = 249 + 75 = 324
45/100 M = 324
Pass mark in the first test = 40/100 M = 40/45 * 324 = 288.
Answer:D
Answer: D