Cheukting/mathqa huggingface dataset:
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 450 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 678 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is b : 678 solution : total number of students studying both are 450 + 226 - 134 = 542 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 542 , so 100 % is approx . 678 ."
Answer: b
Question (geometry): the volume of the sphere q is ( 37 / 64 ) % less than the volume of sphere p and the volume of sphere r is ( 19 / 27 ) % less than that of sphere q . by what is the surface area of sphere r less than the surface area of sphere p ?
Options: a ) 77.77 %
b ) 75 %
c ) 67.5 %
d ) 87.5 %
e ) none of these
Rationale: explanation : let the volume of sphere p be 64 parts . therefore volume of sphere q = > 64 − ( 37 / 64 ) % of 64 . = > 64 − 37 = 27 parts . the volume of r is : - = > 27 − ( 19 / 27 ) × 27 . = > 27 − 19 = 8 parts . volume ratio : = > p : q : r = 64 : 27 : 8 . radius ratio : = > p : q : r = 4 : 3 : 2 . the surface area will be 16 : 9 : 5 . surface area of r is less than the surface area of sphere p . = > 16 k − 4 k = 12 k . now , = > ( 12 k / 16 k ) × 100 . = > 75 % . hence , the surface area of sphere r is less than the surface area of sphere p by 75 % . answer : b
Answer: b
Question (physics): what is the radius of a circle that has a circumference of 3.14 meters ?
Options: a ) 2.5
b ) 2
c ) 1.5
d ) 1
e ) 0.5
Rationale: circumference of a circle = 2 π r . given , circumference = 3.14 meters . therefore , 2 π r = circumference of a circle or , 2 π r = 3.14 . or , 2 ? 3.14 r = 3.14 , [ putting the value of pi ( π ) = 3.14 ] . or , 6.28 r = 3.14 . or , r = 3.14 / 6.28 . or , r = 0.5 . answer : 0.5 meter . correct answer e
Answer: e
Question (general): the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 8 , b ) 15 , c ) 14 , d ) 12 , e ) 10
Rationale: since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let the ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 * 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer a
Answer: a
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first ratio = 3 / 20 = 15 % second ratio = ( 3 + 12 ) / ( 9 + 108 ) = 15 / 117 = 12,8 % decrease = 2,2 % 2,2 % / 15 % = 15 % approximately . answer : b"
Answer: b
Question (general): the difference of two numbers is 11 and one fifth of their sum is 9 . the numbers are :
Options: a ) 31 , 20 , b ) 30 , 19 , c ) 29 , 18 , d ) 28 , 17 , e ) none
Rationale: "x − y = 11 , x + y = 5 × 9 x − y = 11 , x + y = 45 , y = 17 , x = 28 answer : d"
Answer: d
Question (gain): an internet recently hired 8 new network , in addvertisement 20 network already employed . all new network cam from university a . in addition 75 % of computer addvertisement came from same university a . what fraction of original 20 network addvertisement came from same univerity a ? pls help to solve
Options: a ) 13 / 20 , b ) 15 / 20 , c ) 14 / 20 , d ) 12 / 20 , e ) 11 / 20
Rationale: new networks = 8 already employed networks = 20 total networks = 28 computer advt . from uni . a = 28 * ( 75 / 100 ) = 21 out 28 networks 21 came from uni . a among these 21 we know 8 are newly hired so 21 - 8 = 13 networks among previously employed networks came from uni . a answer is : 13 / 20 answer : a
Answer: a
Question (general): dividing by 3 ⁄ 9 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 5 / 2 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 9 * 5 / 6 = x * 9 / 3 * 5 / 6 = x * 5 / 2 d"
Answer: d
Question (physics): if it takes a machine 1 ⁄ 3 minute to produce one item , how many items will it produce in 2 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 80 , d ) 120 , e ) 360
Rationale: "1 item takes 1 / 3 min so it takes 120 min to produce x x / 3 = 120 the x = 360 answer : e"
Answer: e
Question (general): a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many s apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons s = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Question (gain): a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 7700 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 7700 x ( 2 / 11 ) ) = rs . 1400 . answer is c"
Answer: c
Question (general): if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 5 ] ] ?
Options: a ) 39 , b ) 9 , c ) 15 , d ) 19 , e ) 25
Rationale: "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 5 ] ] = 5 ^ 2 + 2 * 5 + 4 = 39 . option a"
Answer: a
Question (general): sobha ' s father was 38 years of age when she was born while her mother was 36 years old when her brother 4 years younger to her was born . what is the difference between the ages of her parents ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 2
Rationale: age of sobha ' s father when sobha was born = 38 age of sobha ' s mother when sobha was born = 36 − 4 = 32 required difference of age = 38 − 32 = 6 answer is b .
Answer: b
Question (physics): a train travels from albany to syracuse , a distance of 100 miles , at the average rate of 50 miles per hour . the train then travels back to albany from syracuse . the total travelling time of the train is 5 hours and 24 minutes . what was the average rate of speed of the train on the return trip to albany ?
Options: a ) 31.25 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "50 * t = 100 therefore t = 100 / 50 = 2 on return speed * ( 5.4 - 2 ) = 100 therefore t = 100 / 3.2 = 31.25 a"
Answer: a
Question (general): if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 74 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 74 a = 28 the answer is c ."
Answer: c
Question (other): the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 2 : 3 , b ) 2 : 5 , c ) 3 : 7 , d ) 4 : 9 , e ) 5 : 6
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 7 , thus the smaller number must have a ratio of 3 . the ratio of the smaller number to the larger number is 3 : 7 . the answer is c ."
Answer: c
Question (gain): find number which is 60 % less than 120 .
Options: a ) 18 , b ) 22 , c ) 28 , d ) 48 , e ) 98
Rationale: "explanation : 60 % less is 40 % of the given number therefore , 40 % of 120 is 48 . answer : d"
Answer: d
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 182 votes . find the total number of valid votes ?
Options: a ) 455 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 182 = > 4 x / 10 = 182 = > 4 x = 1820 = > x = 455 . answer : a"
Answer: a
Question (general): find the number which is nearest to 457 and is exactly divisible by 11 .
Options: a ) 450 , b ) 451 , c ) 460 , d ) 462 , e ) none
Rationale: "solution on dividing 457 by 11 , remainder is 6 . required number is either 451 or 462 nearest to 456 is = 462 . answer d"
Answer: d
Question (general): what is the remainder when 1201 × 1202 × 1205 × 1210 is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 5 , and 4 . the product is 1 * 2 * 5 * 4 = 40 the remainder when dividing 40 by 6 is 4 . the answer is d ."
Answer: d
Question (gain): a cycle is bought for rs . 450 and sold for rs . 520 , find the gain percent ?
Options: a ) 18 , b ) 14 , c ) 20 , d ) 15 , e ) 15.55
Rationale: "450 - - - - 70 100 - - - - ? = > 15.55 % answer : e"
Answer: e
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration r of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration r would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Question (general): 12.1212 + 17.0005 - 9.1103 = ?
Options: a ) 20.0015 , b ) 20.0105 , c ) 20.0115 , d ) 20.0114 , e ) none
Rationale: solution given expression = ( 12.1212 + 17.0005 ) - 9.1103 = ( 29.1217 - 9.1103 ) = 20.0114 . answer d
Answer: d
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 104 . what was the number he chose ?
Options: a ) 123 , b ) 121 , c ) 277 , d ) 267 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 104 2 â ‹ … x â ˆ ’ 138 = 104 x = 121 answer : b"
Answer: b
Question (geometry): one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 18 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 18 cm 2 more than the first area . therefore a 1 + 18 = a 2 x ( x − 3 ) + 18 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 18 = x 2 + x − 2 x − 2 2 x = 20 x = 10 . so , the sides of the rectangle are 10 cm and ( 10 − 3 ) = 7 cm long . so answer is c ."
Answer: c
Question (general): john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 75 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 25 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 75 = 25 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 25 / 100 ) * 100 = ( 0.25 ) * 100 = 25 % . d"
Answer: d
Question (gain): an investment compounds annually at an interest rate of 30 % what is the smallest investment period by which time the investment will more than double in value ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "1 year : 100 / 3 = 33.33 approx $ 34 : total : 134 2 nd year : 134 / 3 = 45 : total : 134 + 45 = 179 3 rd year : 179 / 3 = 60 : total : 179 + 60 = 239 > 2 ( 100 ) ; 3 years ; answer : a"
Answer: a
Question (general): what is the remainder when ( 55 ) ( 57 ) is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: ( 55 ) ( 57 ) = ( 56 - 1 ) ( 56 + 1 ) = 56 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e .
Answer: e
Question (general): in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.25 as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 2050 , e ) 2060
Rationale: in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 2060 : ri = 120 , ro = 150 thus ans : e
Answer: e
Question (general): a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord q , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . q = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d
Answer: d
Question (physics): a person crosses a 300 m long street in 4 minutes . what is his speed in km per hour ?
Options: a ) 1.6 , b ) 4.5 , c ) 8.2 , d ) 6.5 , e ) 2.9
Rationale: "distance = 300 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 300 / 240 = 1.25 m / s = 1.25 ã — 18 / 5 km / hr = 4.5 km / hr answer : b"
Answer: b
Question (general): jerry and michelle play a card game . in the beginning of the game they have an equal number of cards . each player , at her turn , gives the other a third of her cards . michelle plays first , giving jerry a third of her cards . jerry plays next , and michelle follows . then the game ends . jerry ended up with 28 more cards than michelle . how many cards did each player have originally ?
Options: a ) 51 , b ) 52 , c ) 53 , d ) 54 , e ) 56
Rationale: "gamemichelle jerry initially 54 54 assume after game 1 36 72 after game 2 60 48 after game 3 40 68 now merry has 28 cards more than michelle . this option gives us exactly what number of cards they had initially . so the answer is d"
Answer: d
Question (gain): if albert ’ s monthly earnings rise by 26 % , he would earn $ 693 . if , instead , his earnings rise by only 20 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 660 , d ) 690 , e ) 693
Rationale: = 693 / 1.26 ∗ 1.2 = 660 = 660 answer is c
Answer: c
Question (gain): what is the normal price of an article sold at $ 36 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 45 , b ) $ 48 , c ) $ 50 , d ) $ 54 , e ) $ 56
Rationale: "0.8 * 0.9 * cost price = $ 36 cost price = $ 50 the answer is c ."
Answer: c
Question (general): if | x + 3 | = 5 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 12 , c ) - 8 , d ) - 6 , e ) 12
Rationale: "there will be two cases x + 3 = 5 or x + 3 = - 5 = > x = 2 or x = - 8 sum of both the values will be - 8 + 2 = - 6 answer : d"
Answer: d
Question (general): in a group of cows and hens , the number of legs are 14 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 14 2 x = 14 x = 7 . answer : c"
Answer: c
Question (gain): a and b invests rs . 3000 and rs . 6000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 3 : 8 , c ) 3 : 1 , d ) 9 : 9 , e ) 3 : 4
Rationale: "( 3 * 6 + 6 * 6 ) : ( 6 * 12 ) 18 : 24 = > 3 : 4 . answer : e"
Answer: e
Question (gain): albert buys 4 horses and 9 cows for rs . 13,400 . if he sells the horses at 10 % profit and the cows at 20 % profit , then he earns a total profit of rs . 1880 . the cost of a horse is ?
Options: a ) 1299 , b ) 2788 , c ) 2000 , d ) 2981 , e ) 2881
Rationale: explanation : let c . p . of each horse be rs . x and c . p . of each cow be rs . y . then , 4 x + 9 y = 13400 - - ( i ) and , 10 % of 4 x + 20 % of 9 y = 1880 2 / 5 x + 9 / 5 y = 1880 = > 2 x + 9 y = 9400 - - ( ii ) solving ( i ) and ( ii ) , we get : x = 2000 and y = 600 . cost price of each horse = rs . 2000 . answer : c
Answer: c
Question (general): when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 76.4 , what is the value of y ?
Options: a ) 20 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 76.4 - - > x = 76 y + 0.4 y ( so q above equals to 76 ) ; 0.4 y = 8 - - > y = 20 . answer : a ."
Answer: a
Question (general): a family pays $ 850 per year for an insurance plan that pays 80 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,250 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 850 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 850 + 200 = 1050 $ total amount paid by insurance plan for first 1000 $ = 850 $ total amount paid by family will equal amount paid by plan when medical expense = 1250 $ ( since insurance plan will pay 100 % of amount that exceeds 1050 $ ) answer b"
Answer: b
Question (general): in a group of 120 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 60 / 120 , b ) 15 / 120 , c ) 30 / 120 , d ) 80 / 120 , e ) 40 / 120
Rationale: "number of people whose age is less than 20 is given by 120 - 90 = 30 probability p that a person selected at random from the group is less than 20 is gieven by 30 / 120 = 0.25 correct answer c"
Answer: c
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 81 %
Rationale: "original price = 100 day 1 discount = 10 % , price = 100 - 10 = 90 day 2 discount = 10 % , price = 90 - 9 = 81 day 3 discount = 10 % , price = 81 - 8.1 = 72.9 which is 72.9 / 90 * 100 of the sale price on day 1 = ~ 81 % answer e"
Answer: e
Question (general): given that 268 x 74 = 19432 , find the value of 2.68 x . 74 .
Options: a ) 1.9432 , b ) 1.0025 , c ) 1.5693 , d ) 1.0266 , e ) none
Rationale: "solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9432 answer a"
Answer: a
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 22 percent alcohol by volume ?
Options: a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: "22 % is 12 % - points higher than 10 % but 8 % - points lower than 30 % . thus there should be 2 parts of solution x for 3 parts of solution y . we should add 450 ml of solution y . the answer is d ."
Answer: d
Question (geometry): find the area of circle whose radius is 7 m ?
Options: a ) 121 sq m
b ) 184 sq m
c ) 174 sq m
d ) 124 sq m
e ) 154 sq m
Rationale: the area of circle = pie * r ^ 2 = 22 / 7 * 7 * 7 = 154 sq m answer : e
Answer: e
Question (physics): walking at 5 / 6 of its usual speed , a train is 10 minutes too late . find its usual time to cover the journey .
Options: a ) 50 min , b ) 20 min , c ) 1 hour , d ) 30 min , e ) 45 min
Rationale: "new speed = 5 / 6 of the usual speed new time taken = 6 / 5 of the usual time taken so , ( 6 / 5 of the usual time ) - ( usual time ) = 10 min 1 / 5 of the usual time = 10 min usual time = 10 * 5 = 50 min correct option is a"
Answer: a
Question (geometry): in the rectangle below , the line mn cuts the rectangle into two regions . find x the length of segment nb so that the area of the quadrilateral mnbc is 40 % of the total area of the rectangle .
Options: a ) 1 meter , b ) 2 meter , c ) 3 meter , d ) 4 meter , e ) 5 meter
Rationale: solution we first note that mc = 20 - 5 = 15 the quadrilateral mnbc is a trapezoid and its area a is given by a = ( 1 / 2 ) × 10 × ( x + mc ) = 5 ( x + 15 ) 40 % of the area of the rectangle is equal to 40 % × ( 20 × 10 ) = ( 40 / 100 ) × 200 = 80 since the area of mnbc is equal to 40 % the area of the rectangle , we can write 5 ( x + 15 ) = 80 5 x + 75 = 80 5 x = 5 x = 1 meter answer is a
Answer: a
Question (physics): two trains of equal lengths take 15 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 15 = 8 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 8 + 6 = 14 m / sec . required time = ( 120 + 120 ) / 14 = 17 sec . answer : c"
Answer: c
Question (general): 3,7 , 12,18 , 25,33 , . . . . . . . . . . . . . . 7 th terms
Options: a ) 43 , b ) 42 , c ) 63 , d ) 65 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 answer : b"
Answer: b
Question (geometry): the floor of a rectangular room is 20 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 144 m 2 , b ) 120 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 24 ã — 16 = 384 m 2 area of the inner rectangle = 20 ã — 12 = 240 m 2 required area = ( 304 â € “ 180 ) = 144 m 2 answer a"
Answer: a
Question (general): the average weight of a class is x pounds . when a new student weighing 90 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 99
Rationale: when the student weighs 90 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 90 = 20 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 20 / 5 = 4 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 90 = 6 ( x - 1 ) - - > x = 96 pounds . answer : e .
Answer: e