Cheukting/mathqa huggingface dataset:
Question (general): if n is an integer from 1 to 96 ( inclusive ) , what is the probability for n * ( n + 1 ) * ( n + 2 ) being divisible by 8 ?
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 72.5 % , e ) 75 %
Rationale: ( a ) 25 % , to be divisible by 8 the number needs to have 3 2 s in it . only a multiple of 4 can provide that . number of numbers divisible by 4 = 96 / 4 = 24 . so p ( 8 ) = 24 / 96 = 25 % .
Answer: a
Question (gain): by selling an article for $ 90 , a person gains $ 15 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 90 gain = $ 15 c . p . = 90 - 15 = 75 gain % = 15 / 75 * 100 = 20 % answer is d"
Answer: d
Question (other): on multiplying a number b by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number b is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Question (general): if a computer program generates 3 - digit odd numbers using the numbers 9 , 7 , 0 , 8 , and 1 , and the digits can be repeated , what is the probability that the number formed from the program is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: a
Answer: a
Question (gain): how many pounds of salt at 70 cents / lb must be mixed with 45 lbs of salt that costs 40 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 5 , b ) 9 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 40 cents / lb ( salt 1 ) with 70 cents / lb ( salt 2 ) to get a mixture costing 45 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 70 - 45 ) / ( 45 - 40 ) = 5 / 1 we know that weight of salt 1 is 45 lbs . weight of salt 2 must be 9 lbs . answer ( b )"
Answer: b
Question (physics): the length of a side of a hexagon is 5 inches . what is the perimeter ?
Options: a ) 116 , b ) 25 , c ) 30 , d ) 24 , e ) 15
Rationale: "hexagon . it means 6 equal sides . p = 5 + 5 + 5 + 5 + 5 + 5 = 10 + 10 + 10 = 30 inches answer c"
Answer: c
Question (gain): one fourth of a solution that was 12 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 28 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.12 + 25 * x = 100 * 0.16 - - > x = 0.28 . answer : a .
Answer: a
Question (general): a house wife saved $ 4 in buying an item on sale . if she spent $ 28 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 13 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 28 + 4 = $ 32 saving = 4 / 32 * 100 = 13 % approximately answer is b"
Answer: b
Question (physics): a can do a work in 3 days . b can do the same work in 6 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 200,400
Rationale: "ratio of their works a : b = 3 : 6 ratio of their wages a : b = 1 : 2 a ' s share = ( 1 / 5 ) 1000 = 200 b ' s share = ( 2 / 5 ) 1000 = 400 correct option is e"
Answer: e
Question (physics): two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9 pm and 10 pm . the first person to come waits for some time and leaves . if the other one does not turn up by that time . if deepak comes first , he waits for 45 minutes and if rajeev comes first , he waits for 15 minutes . what is the probability of meeting between deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random ?
Options: a ) 3 / 4 , b ) 11 / 16 , c ) 7 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: deepak : 45 / 60 = 3 / 4 rajeev : 15 / 60 = 1 / 4 as these are independent events total probability = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 answer : d
Answer: d
Question (general): claire has a total of 90 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 66 , d ) 57 , e ) 60
Rationale: g + h = 90 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 90 - h or 3 ( 90 - h ) + 4 h = 300 h = 300 - 270 = 30 then g = 96 - 30 = 66 c
Answer: c
Question (general): what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 444 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 4 . final answer : c"
Answer: c
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 30 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: explanation : let the cp of the article = rs . 100 . then labeled price = rs . 130 . sp = rs . 130 - 10 % of 130 = rs . 130 - 13 = rs . 117 . gain = rs . 117 – rs . 100 = rs . 17 therefore , gain / profit percent = 17 % . answer : option c
Answer: c
Question (general): what is the area inscribed by the lines y = 10 , x = 1 , y = 3 x + 1 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 3 , d ) d ) 6 , e ) e ) 12
Rationale: "first , let ' s graph the lines y = 10 and x = 1 at this point , we need to find the points where the line y = 3 x + 1 intersects the other two lines . for the vertical line , we know that x = 1 , so we ' ll plug x = 1 into the equation y = 3 x + 1 to get y = 3 ( 1 ) + 1 = 4 perfect , when x = 1 , y = 5 , so one point of intersection is ( 1,4 ) for the horizontal line , we know that y = 10 , so we ' ll plug y = 10 into the equation y = 3 x + 1 to get 10 = 3 x + 1 . solve to get : x = 3 so , when y = 10 , x = 3 , so one point of intersection is ( 3,10 ) now add these points to our graph and sketch the line y = 3 x + 1 at this point , we can see that we have the following triangle . the base has length 2 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 6 ) = 6 answer : d"
Answer: d
Question (gain): what is rate of interest if principal . amount be 400 , simple interest 100 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 100 = 800 r / 100 r = 100 / 8 = 12.5 % answer b"
Answer: b
Question (general): harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 4 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 4 x = 10 x august tips as a fraction of total tips = 4 x / 10 x = 2 / 5 . so b"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 7 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 7 ) m = 140 m answer : option c"
Answer: c
Question (geometry): the ratio of the volumes of two cubes is 6859 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 1 : 21 , b ) 12 : 7 , c ) 1 : 15 , d ) 21 : 17 , e ) 13 : 13
Rationale: "ratio of the sides = ³ √ 6859 : ³ √ 1331 = 19 : 11 ratio of surface areas = 192 : 112 = 12 : 7 answer : b"
Answer: b
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 14 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 400 , b ) 410 , c ) 460 , d ) 420 , e ) 430
Rationale: "( 3500 * 4 * 3 ) / 100 = > 420 answer : d"
Answer: d
Question (physics): a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 6 days . b can do the work alone in ?
Options: a ) 19 , b ) 36 , c ) 11 , d ) 19 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 6 6 / x = 1 / 6 = > x = 36 so , b takes 18 hours to finish the work . answer : b"
Answer: b
Question (physics): a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 350 - meter long platform ?
Options: a ) 43 , b ) 45 , c ) 47 , d ) 49 , e ) 51
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 350 ) / 10 = 49 seconds the answer is d ."
Answer: d
Question (gain): mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 110 mangoes .
Options: a ) 367 , b ) 380 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 110 mangoes = 110 * 3.33 = 367 . answer a"
Answer: a
Question (general): there are two numbers . if 20 % of the first number is added to the second number , then the second number increases to its 5 - fourth . what is the ratio of the first number to the second number ?
Options: a ) 2 : 9 , b ) 3 : 8 , c ) 8 : 5 , d ) 5 : 4 , e ) 7 : 3
Rationale: let the two numbers be x and y . ( 2 / 10 ) * x + y = ( 5 / 4 ) * y ( 2 / 10 ) * x = ( 1 / 4 ) * y x / y = 10 / 8 = 5 / 4 the answer is d .
Answer: d
Question (physics): a train is 560 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 56 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 560 + 140 = 700 meter time = distance / speed = 700 * ( 2 / 25 ) = 56 seconds answer : a"
Answer: a
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 88 , d ) 160 , e ) 12
Rationale: "given that the area of the square = 1600 sq . units = > side of square = √ 1600 = 40 units the radius of the circle = side of the square = 40 units length of the rectangle = 2 / 5 * 40 = 16 units given that breadth = 10 units area of the rectangle = lb = 16 * 10 = 160 sq . units answer : d"
Answer: d
Question (general): the average age of 28 students in a group is 11 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 29 × 12 – 28 × 11 ) years = 40 years . answer c"
Answer: c
Question (gain): a man can row his boat with the stream at 10 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 2 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 4 kmph
Rationale: "ds = 10 us = 6 s = ? s = ( 10 - 6 ) / 2 = 2 kmph answer : a"
Answer: a
Question (general): if the product of 12 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 11
Rationale: "the product of 12 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 11 correct option : e"
Answer: e
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Question (physics): the distance from steve ' s house to work is 28 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 28 km = > speed = 14 kmph c"
Answer: c
Question (general): 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 (general): there are 20 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 ) 190 , d ) 60 , e ) 90
Rationale: "20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct"
Answer: c
Question (physics): the sum of four consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296
b ) 252
c ) 344
d ) 388
e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Question (physics): p is 40 % more efficient than q . p can complete a work in 24 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 14 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 24 let work done by q in 1 day = q q × ( 140 / 100 ) = 1 / 24 q = 100 / ( 24 × 140 ) = 10 / ( 24 × 14 ) the work done by p and q in 1 day = 1 / 24 + 10 / ( 24 × 14 ) = 24 / ( 24 × 14 ) = 1 / 14 p and q together can do the work in 14 days . the answer is d ."
Answer: d
Question (general): if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is :
Options: a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 46 km
Rationale: "let the actual distance travelled be x km . then , x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Question (general): ( 422 + 404 ) 2 − ( 4 × 422 × 404 ) = ?
Options: a ) none of these , b ) 342 , c ) 324 , d ) 312 , e ) can not be determined
Rationale: "explanation : given equation is in the form ( a + b ) 2 − 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 − 4 ab = ( a − b ) 2 = ( 422 − 404 ) 2 = 182 = 324 , answer : option c"
Answer: c
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 98 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 112
Rationale: "explanation : a / 98 = 8 * 8 = > a = 8 * 8 * 98 x * 2 x = 8 * 8 * 98 x = 56 = > 2 x = 112 answer : option e"
Answer: e
Question (general): there are 50 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 ) 1000 , b ) 3000 , c ) 1225 , d ) 6000 , e ) 9000
Rationale: "50 players are there . two players play one game with one another . so 50 c 2 = 50 * 49 / 2 = 1225 so option c is correct"
Answer: c
Question (gain): 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 1 / 4 % , then the amount invested at 11 % was ?
Options: a ) 12500 , b ) 37500 , c ) 29977 , d ) 26777 , e ) 19871
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 * 37 / 4 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 37000 / 4 = 925000 x = 87500 sum invested at 9 % = rs . 87500 sum invested at 11 % = rs . ( 100000 - 87500 ) = rs . 12500 . answer : a"
Answer: a
Question (physics): a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed y of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = y ans = c"
Answer: c
Question (physics): a and b can do a piece of work in 10 days , b and c in 5 days , c and a in 15 days . how long will c take to do it ?
Options: a ) 77 days , b ) 55 days , c ) 12 days , d ) 33 days , e ) 11 days
Rationale: 2 c = 1 / 5 + 1 / 15 – 1 / 10 = 1 / 6 c = 1 / 12 = > 12 days answer : c
Answer: c
Question (general): when 1 / 10 percent of 1,000 is subtracted from 1 / 10 of 1,000 , the difference is
Options: a ) 10 , b ) 100 , c ) 999 , d ) 99 , e ) 9
Rationale: "( 1 / 10 ) * 1000 - ( 1 / 10 ) % * 1000 = 100 - ( 1 / 1000 ) * 1000 = 100 - 1 = 99 the answer is d ."
Answer: d
Question (geometry): a rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 14 cms
b ) 21 cms
c ) 42 cms
d ) none of these
e ) 56 cms
Rationale: explanation : 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 21 cm . answer : b
Answer: b
Question (general): if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number e of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see e = 5 or 1 will give you same equation . . ans d"
Answer: d
Question (physics): convert 1.3 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.3 hectares in ares 1 hectare = 100 ares therefore , 1.3 hectares = 1.3 × 100 ares = 130 ares . answer - a"
Answer: a
Question (gain): on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 40 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 16.7 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 40 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 2 y / 5 . it means 3 y / 5 received the ticket . hence , 3 y / 5 = x / 10 or y / x = 1 / 6 or y / x * 100 = 1 / 6 * 100 = 16.7 % c"
Answer: c
Question (gain): there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 54 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 33 , e ) 22.75
Rationale: 60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 54 / 100 = 50.40 so x = 33.33 answer : d
Answer: d