Cheukting/mathqa huggingface dataset:
Question (physics): nicky and cristina are running a 400 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 40 , b ) 25 , c ) 35 , d ) 30 , e ) 50
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . d"
Answer: d
Question (general): a mixture of 70 liters of wine and water contains 10 % water . how much water must be added to make water 12 ½ % of the total mixture ?
Options: a ) 12 liters , b ) 10 liters , c ) 4 liters , d ) 2 liters , e ) 3 liters
Rationale: "70 * ( 10 / 100 ) = 7 wine water 87 1 / 2 % 12 1 / 2 % 87 1 / 2 % - - - - - - - 63 12 1 / 2 % - - - - - - - ? = > 9 - 7 = 2 answer : d"
Answer: d
Question (physics): danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 35 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 17.5 minutes . , b ) 35 minutes . , c ) 52.5 minutes . , d ) 70 minutes . , e ) 105 minutes .
Rationale: "danny ' s time is 35 minutes . the time to reach halfway is 17.5 minutes . steve ' s time is 70 minutes . the time to reach halfway is 35 minutes . the time difference is 35 - 17.5 = 17.5 minutes the answer is a ."
Answer: a
Question (general): a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 28 % .
Rationale: "20 % of 2 litres = 0.4 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.8 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 28 % answer : e"
Answer: e
Question (physics): in a kilometer race , a beats b by 60 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 199 sec , b ) 156.7 sec , c ) 726 sec , d ) 127 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 60 = 166.7 sec . time taken by a = 166.7 - 10 = 156.7 sec . answer : b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 120 metres ?
Options: a ) 18 , b ) 24 , c ) 17 , d ) 12 , e ) 13
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 120 m = 120 / 5 = 24 seconds . answer : b"
Answer: b
Question (geometry): the perimeter of one face of a cube is 24 cm . its volume will be :
Options: a ) 216 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 24 / 4 = 6 cm volume = a * a * a = 6 * 6 * 6 = 216 cm cube option a"
Answer: a
Question (physics): when a train moves at an average speed of 100 kmph it reaches its destination on time . when its average speed becomes 80 kmph , then it reaches its destination 20 minutes late . find the length of journey rounded to two decimal places .
Options: a ) 99.33 km , b ) 133.33 km , c ) 125.33 km , d ) 156.66 km , e ) none
Rationale: sol . difference between timings = 20 min = 1 / 3 hr . let the length of journey be x km . then , x / 80 - x / 100 = 1 / 3 â ‡ ” 5 x - 4 x = 133.33 â ‡ ” x = 133.33 km . answer b
Answer: b
Question (physics): a certain bacteria colony doubles in size every day for 20 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 19
Rationale: "simultaneous grow = same amount of time in 20 days we should expect to have p ( 2 ) ^ 20 so if we have two things doing the job of getting us there then ; 2 ^ x + 2 ^ x = 20 2 ( 2 ) ^ x = 2 2 ^ ( x + 1 ) = 2 ^ 20 x + 1 = 20 x = 19 ; answer : e"
Answer: e
Question (gain): julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 6 yearned with the compound interest is the percent yearned on percent . so , $ 6 is yearned on $ 60 , which means that the interest = 10 % . this on the other hand means that half of the savings = 60 * 10 = $ 600 . twice of that = $ 1,200 . answer : d ."
Answer: d
Question (general): find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1234 , b ) 1540 , c ) 1650 , d ) 1632 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (general): joan and karl each bought a sofa and the sum of their purchases was $ 600 . if twice of what joan paid was $ 90 more than what karl paid , what did joan pay for her sofa ?
Options: a ) $ 190 , b ) $ 210 , c ) $ 230 , d ) $ 250 , e ) $ 270
Rationale: j + k = 600 so k = 600 - j 2 j = k + 90 2 j = ( 600 - j ) + 90 3 j = 690 j = 230 the answer is c .
Answer: c
Question (probability): a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 36 , b ) 40 , c ) 45 , d ) 51 , e ) 56
Rationale: "the total number of ways to choose 5 managers is 8 c 5 = 56 we need to subtract the number of groups which include the two managers , which is 6 c 3 = 20 . 56 - 20 = 36 the answer is a ."
Answer: a
Question (gain): a reduction of 18 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 1080 , what is the reduced price for kg ?
Options: a ) 72.15 , b ) 27.24 , c ) 24.25 , d ) 28.46 , e ) 20.9
Rationale: "1080 * ( 18 / 100 ) = 194 - - - - 8 ? - - - - 1 = > rs . 24.25 answer : c"
Answer: c
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 38 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 152 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 38 = > 4 / x = 1 / 38 x = 38 ∗ 4 = 152 mins option d"
Answer: d
Question (general): a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 6 ) = 4 x . the fraction of sensors which have been upgraded is x / ( x + 4 x ) = x / 5 x = 1 / 5 the answer is b ."
Answer: b
Question (physics): a copy machine , working at a constant rate , makes 30 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 4,500 , d ) 2,550 , e ) 324,000
Rationale: "together the two machines make 30 + 55 = 85 copies per minute . so , in half an hour they will make 85 * 30 = 2,550 copies . answer : d ."
Answer: d
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 5 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 5 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ."
Answer: b
Question (general): the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 450 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 495 , e ) 510
Rationale: let no . of non - officers be x 15 * 450 + x * 110 = ( x + 15 ) 120 x = 495 d
Answer: d
Question (general): there are 15 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 105 , d ) 60 , e ) 90
Rationale: 15 players are there . two players play one game with one another . so 15 c 2 = 15 x 14 / 2 = 105 so option c is correct
Answer: c
Question (general): two heavily loaded sixteen - wheeler transport trucks are 855 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 135 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 855 - 90 = 765 k ratio of speeds 9 : 8 - > 765 / 17 = 45 truck a = 90 + 45 * 9 = 495 truck b = 45 * 8 = 360 delta = 135 km answer c"
Answer: c
Question (general): 5357 x 51 = ?
Options: a ) 273232 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273207
Rationale: "5357 x 51 = 5357 x ( 50 + 1 ) = 5357 x 50 + 5357 x 1 = 267850 + 5357 = 273207 e )"
Answer: e
Question (general): a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 300 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 750 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 300 = 750 answer : b"
Answer: b
Question (general): a student is ranked 16 th from right and 6 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 16 , from left 6 total = 16 + 6 - 1 = 21 answer : d"
Answer: d
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum w of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : w = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Question (general): if a number x is 10 % less than another number y and y is 10 % more than 125 , then x is equal to
Options: a ) 143 , b ) 150 , c ) 123.75 , d ) 140.55 , e ) none
Rationale: solution y = 125 + 10 % of 125 = 125 + 12.50 = 137.50 . x = 137.50 - 10 % of 137.50 = 137.50 - 13.75 = 123.75 . answer c
Answer: c
Question (general): 575.104 x 15.98 ã · 9.001 + 21.25 = ?
Options: a ) 983.578 , b ) 1043.65 , c ) 1033.65 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 575.104 x 15.98 ã · 9.001 + 21.25 â ‰ ˆ ( 575.104 x 16 / 9 ) + 21.25 â ‰ ˆ 1022.40 + 21.25 â ‰ ˆ 1043.65 answer : option b"
Answer: b
Question (physics): if a car had traveled 30 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 90 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 45 kmh , c ) 60 kmh , d ) 75 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 90 / x - 90 / ( x + 30 ) = 1 / 2 substitute the value of x from the options . - - > x = 60 - - > 90 / 60 - 90 / 90 = 3 / 2 - 1 = 1 / 2 answer : c"
Answer: c
Question (geometry): the length and width of a rectangle are integer values . what is the area of the smallest such rectangle that can be inscribed in a circle whose radius is also an integer
Options: a ) 12
b ) 45
c ) 36
d ) 48
e ) 60
Rationale: if we consider all pythagorean triplets with integral values , we have the following results : - ( 3 , 4,5 ) , ( 6 , 8,10 ) . . . . . . . . the diameter of the circle is 5 in the 1 st case and 10 in the 2 nd . but the question says that radius of the circle is also an integer hence the 1 st triplet will be ruled out . we are left with the 2 nd triplet where radius of the circle = 5 , hence the sides of the rectangle are 6 and 8 making the area = 45 . b
Answer: b
Question (gain): if the selling price of 8 articles is same as the cost price of 12 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 50 % gain , d ) 50 % loss , e ) 60 % loss
Rationale: "explanation : let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 12 articles = rs . 12 / - now , c . p of 8 articles = rs . 8 / - , s . p of 8 articles = rs 12 / - gain = rs ( 12 - 10 ) = rs 4 / - . gain % = ( 4 / 8 * 100 ) % = 50 % gain answer : option c"
Answer: c
Question (other): janet invited her boy and girl friends to her party at the ratio of 3 : 7 . if 30 % of the boys and 70 % of the girls will be coming for the party from texas , how many janet invited friends will be coming from texas .
Options: a ) 62 % , b ) 52 % , c ) 57 % , d ) 56 % , e ) 58 %
Rationale: let total no of janet invited friends be 100 , boys 30 and girls 70 , so total number of janet ' s invited guests coming from texas for both boys and girls respectively 30 * 30 / 100 = 9 and 70 * 70 / 100 = 49 so total 58 of janet ' s invited guest out of the 100 invited guests will be coming from texas . . so required % is 58 % answer : e
Answer: e
Question (physics): david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 13,500 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 6500 , b ) 3500 , c ) 2500 , d ) 4500 , e ) 2000
Rationale: "let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 13,500 thus we have 500 ( x ^ 3 ) = 13,500 = 27 thus x = 3 therefore population at 3 pm = 500 ( 9 ) = 4,500 answer : d"
Answer: d
Question (physics): a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 3 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 3 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 . b ' s 1 hour ' s work = ( 7 / 12 - 1 / 3 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"
Answer: e
Question (general): 2 , 5 , 10 , 17 , . .
Options: a ) 5 , b ) 8 , c ) 26 , d ) 7 , e ) 12
Rationale: "explanation : numbers are ( 1 * 1 ) + 1 = 2 ( 2 * 2 ) + 1 = 5 ( 3 * 3 ) + 1 = 10 ( 4 * 4 ) + 1 = 17 ( 5 * 5 ) + 1 = 26 answer : c"
Answer: c
Question (general): cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent of the original cost ?
Options: a ) 200 , b ) 600 , c ) 800 , d ) 1600 , e ) 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Question (general): 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 17 , 28 and 35 , 45 what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) a 17 , b ) b ) 28 , c ) c ) 35 , d ) d ) 45 , e ) e ) 80
Rationale: it is finding the minimum range between all their scores , if all test taker scores are between 0 and maximum range we will have : a - 0 and 17 b - 0 and 28 c - 0 and 35 d - 0 and 45 therefore the minimum range is 45 , it cant be any lower however you play with the numbers . d
Answer: d
Question (general): a sum of money is distributed among a , b , c , d in the proportion of 5 : 3 : 2 : 3 . if a gets $ 1000 more than b , what is the c ' s share ?
Options: a ) $ 2000 , b ) $ 5000 , c ) $ 8000 , d ) $ 1500 , e ) $ 1000
Rationale: "let the shares of a , b , c , d are 5 x , 3 x , 2 x , 3 x 5 x - 3 x = 1000 x = 500 c ' s share = 2 x = $ 1000 answer is e"
Answer: e
Question (physics): a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is :
Options: a ) 22 , b ) 50 , c ) 99 , d ) 35 , e ) 12
Rationale: speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : d
Answer: d
Question (gain): two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 32 km apart ?
Options: a ) 18 , b ) 16 , c ) 19 , d ) 15 , e ) 34
Rationale: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 32 km time = distance / speed = 32 / 2 = 16 hr answer : b"
Answer: b
Question (physics): two thirds of the roads from a to b are at least 5 miles long , and 1 / 2 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ?
Options: a ) 5 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12
Rationale: "so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 2 = 5 / 6 . answer : a ."
Answer: a
Question (general): the difference between a number and its two - fifth is 510 . what is 15 % of that number ?
Options: a ) 152.01 , b ) 85 , c ) 76 , d ) 168.2 , e ) 127.5
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 15 % of 850 = 127.5 . answer : e"
Answer: e
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 42 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 18000 x 7 ) + 6000 ( x - 7 ) x = 42 answer c"
Answer: c
Question (general): a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is ?
Options: a ) 23 , b ) 87 , c ) 84 , d ) 26 , e ) 19
Rationale: given total sum = rs . 427 and given that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . = > 3 a = 4 b = 7 c but given = > a + b + c = 427 now express a and b in terms of c i . e = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c
Answer: c
Question (general): if x and t are integers and 2 x – t = 11 , then 4 x + t can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - t = 11 . . . . t = 2 x - 11 4 x + t = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Question (physics): excluding stoppages , the speed of a bus is 40 kmph and including stoppages , it is 30 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 12 min , c ) 18 min , d ) 15 min , e ) 20 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 40 x 60 ) min = 15 min answer : d"
Answer: d
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 54 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 15 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: answer : a 54 ° divided by 360 ° equals 0.15 , therefore the sector is equal to 15 % of the total
Answer: a
Question (physics): nicky and cristina are running a 100 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 25 , e ) 60
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . a"
Answer: a