regisss/math_qa huggingface dataset:
Problem: a cube of side one meter length is cut into small cubes of side 20 cm each . how many such small cubes can be obtained ?
Options: a ) 2878 , b ) 2778 , c ) 1000 , d ) 120 , e ) 125
Rationale: "along one edge , the number of small cubes that can be cut = 100 / 20 = 5 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 5 * 5 * 5 = 125 answer : e"
Answer: e
Problem: the average of 5 consecutive even numbers a , b , c , d and e is 20 . what percent of e is d ?
Options: a ) 90.1 , b ) 91.7 , c ) 97.1 , d ) 101.1 , e ) 107.1
Rationale: explanation : in such a case the middle number ( c ) is the average ∴ c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b
Answer: b
Problem: the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 243 , d ) 992 , e ) 212
Rationale: "2 ( 3 x + x ) = 72 l = 27 b = 9 lb = 27 * 9 = 243 answer : c"
Answer: c
Problem: there are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 19 , b ) 20 , c ) 30 , d ) 32 , e ) 25
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 5 and for second = 4 so total methods = 5 * 4 = 20 answer : b"
Answer: b
Problem: if m is a positive integer and m ^ 2 is divisible by 36 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 12 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? d"
Answer: d
Problem: a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 10 % . their gross income from sales for one month decreases by what percent ?
Options: a ) 1 % , b ) 3 % , c ) 5 % , d ) 7 % , e ) 9 %
Rationale: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.1 x = 0.99 * ( p * x ) , a decrease of 1 % . the answer is a ."
Answer: a
Problem: how many multiples of 2 are less than 2400 , and also multiples of 8 ?
Options: a ) 104 , b ) 208 , c ) 300 , d ) 832 , e ) 833
Rationale: the lcm of 2 and 8 is 8 . divide 2400 / 8 = 300 . xxx . so c is your answer .
Answer: c
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per f glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Problem: in what time will a train 110 m long cross an electric pole , it its speed be 128 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 3.1 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 128 * 5 / 18 = 36 m / sec time taken = 110 / 36 = 3.1 sec . answer : c"
Answer: c
Problem: what is the smallest positive perfect square that is divisible by 9 , 21 , and 49 ?
Options: a ) 225 , b ) 324 , c ) 441 , d ) 529 , e ) 900
Rationale: "the number needs to be divisible by 3 ^ 2 , 3 * 7 , and 7 ^ 2 . the smallest such perfect square is 3 ^ 2 * 7 ^ 2 = 441 the answer is c ."
Answer: c
Problem: two trains 160 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.52 sec , b ) 18.8 sec , c ) 14.52 sec , d ) 10.8 sec , e ) 11.52 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 160 + 160 = 320 m . required time = 320 * 9 / 250 = 288 / 25 = 11.52 sec . answer : e"
Answer: e
Problem: assume all pieces of rope are equal . if 44 pieces of rope measure a feet , how long would b pieces of rope be in inches ?
Options: a ) 44 / ab , b ) 11 / 3 ab , c ) 6 / 11 ab , d ) ab / 44 , e ) 3 ab / 11
Rationale: 44 ropes measure a feet or 12 * a inches 1 rope will measure = 12 * a / 44 = 6 * a / 22 = 3 * a / 11 b piece of rope measure = b * 3 * a / 11 = 3 ab / 11 hence , the answer is e .
Answer: e
Problem: what is the compound interest on rs : 70,000 for 4 months at the rate of 5 % per annum
Options: a ) 1171.98 , b ) 1172.98 , c ) 1173.98 , d ) 1174.98 , e ) 1175.98
Rationale: "it is monthly compound rate = 5 / 12 % per month 70000 * ( 1 + 5 / 1200 ) ^ 4 - 70000 = 1173.98 answer : c"
Answer: c
Problem: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 157.5 sec , d ) 252 sec , e ) none
Rationale: "solution relative speed = ( 48 - 40 ) kmph = 8 kmph = ( 8 x 5 / 18 ) m / sec = ( 40 / 18 ) m / sec time taken = ( 350 x 18 / 40 ) sec = 157.5 sec . answer c"
Answer: c
Problem: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 20 % , b ) 21 % , c ) 21.33 % , d ) 22.109 % , e ) 23 %
Rationale: "lets say the indicated weight is x for $ 10 but the trader actually get 1.1 x for $ 10 now he tells to the customer that its 1.1 ( 1.1 x ) = 1.21 x and charges the price accordingly i . e . 1.21 x * 10 / x = 12.1 so profit % = ( 12.1 - 10 ) / 10 = 0.21 = 21 % answer : b"
Answer: b
Problem: if the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is ?
Options: a ) 26 , b ) 28 , c ) 17 , d ) 12 , e ) 88
Rationale: "2 * 22 / 7 * 14 * x = 2288 = > x = 26 answer : a"
Answer: a
Problem: 18800 / 470 / 20
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "explanation : 18800 / 470 / 20 = ( 18800 / 470 ) / 20 = 40 / 20 = 2 answer : b"
Answer: b
Problem: in the seaside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .
Answer: a
Problem: the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ?
Options: a ) 2379 , b ) 2889 , c ) 5625 , d ) 9000 , e ) 28311
Rationale: let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c
Answer: c
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 38 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 42 km / h . if the distance between city p and city q is 378 km , at what time will the truck and the car meet each other ?
Options: a ) 5 : 30 , b ) 5 : 45 , c ) 6 : 00 , d ) 6 : 15 , e ) 6 : 30
Rationale: "at 2 : 00 pm , the truck and the car are 340 km apart . the truck and the car complete a distance of 80 km each hour . the time it takes to meet is 340 / 80 = 4.25 hours . they will meet at 6 : 15 pm . the answer is d ."
Answer: d
Problem: 0.05 x 0.03 = ?
Options: a ) 0.00015 , b ) 0.015 , c ) 0.0015 , d ) 0.15 , e ) 1.5
Rationale: "5 x 3 = 15 . sum of decimal places = 4 0.05 x 0.03 = 0.0015 answer : option c"
Answer: c
Problem: when 1 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 30 , b ) 81 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 1 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 1 = a / 30 = > a = 30 answer : a"
Answer: a
Problem: in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 5
Rationale: in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f ∩ e } ) + e ] = 15 - 3 ( or ) f + e + ( f ∩ e ) = 12 . . . . . . ( 1 ) also , f + ( f ∩ e ) = 7 ; e + ( f ∩ e ) = 8 . by adding , f + e + 2 ( f ∩ e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f ∩ e ) = 3 . ∴ 3 of them read both french and english . answer : b
Answer: b
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 16 km , c ) 18 km , d ) 29 km , e ) 19 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 14 4 x - 200 = > x = 50 km . answer : a"
Answer: a
Problem: sum of 36 odd numbers is ?
Options: a ) 1294 , b ) 1295 , c ) 1296 , d ) 1297 , e ) 1298
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 36 odd numbers = 36 ^ 2 = 1296 answer : c"
Answer: c
Problem: 15 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 225
Rationale: "though 2 * ( 15 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 14 , so he ' ll play 28 matches . similarly , second guy has to play with the rest of 13 as his 2 games with the first guy are already played . so he plays 26 matches . this continues like this and the total matches are 28 + 26 + 24 . . . + 2 28 + 26 + . . . + 2 = 2 ( 14 + 13 + . . . + 1 ) = 2 ( ( 14 * 15 ) / 2 ) = 14 * 15 = 210 . answer : c"
Answer: c
Problem: the height of the wall is 6 times its width and length of the wall is 8 times its height . if the volume of the wall be 36000 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 48 x 48 x ã — 6 x ã — x = 36000 x = 5 answer : b"
Answer: b
Problem: one - third of 600 is what percent of 120 ?
Options: a ) 313.2 , b ) 30.1 , c ) 12.24 , d ) none of these , e ) 166.6
Rationale: answer let one - third of 600 is n % of 120 . ∵ 600 / 3 = ( n x 120 ) / 100 ∴ n = ( 200 x 100 ) / 120 = 166.6 correct option : e
Answer: e
Problem: how many diagonals does a 58 - sided convex polygon have ?
Options: a ) 870 , b ) 1125 , c ) 1595 , d ) 2560 , e ) 3190
Rationale: "a 58 - sided convex polygon has 58 vertices . if we examine a single vertex , we can see that we can connect it with 55 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be ( 58 ) ( 55 ) = 3190 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3190 by 2 to get 1595 . the answer is c ."
Answer: c
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 545 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 838 , e ) 1,560
Rationale: let weight of side of beef before processing = x ( 65 / 100 ) * x = 545 = > x = ( 545 * 100 ) / 65 = 838 answer d
Answer: d
Problem: miller street begins at baker street and runs directly east for 4.5 kilometers until it ends when it meets turner street . miller street is intersected every 250 meters by a perpendicular street , and each of those streets other than baker street and turner street is given a number beginning at 1 st street ( one block east of baker street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of turner street . what is the highest - numbered street that intersects miller street ?
Options: a ) 15 th , b ) 16 th , c ) 17 th , d ) 18 th , e ) 19 th
Rationale: 4.5 km / 250 m = 18 . however , the street at the 4.5 - km mark is not 18 th street ; it is turner street . therefore , the highest numbered street is 17 th street . the answer is c .
Answer: c
Problem: the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ?
Options: a ) 55522 feet
b ) 45522 feet
c ) 35522 feet
d ) 25522 feet
e ) none
Rationale: solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 × 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a
Answer: a
Problem: in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c
Answer: c
Problem: find the area of a parallelogram with base 26 cm and height 12 cm ?
Options: a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 312
Rationale: "area of a parallelogram = base * height = 26 * 12 = 312 cm 2 answer : e"
Answer: e
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 3 ) = 0 and f ( - 3 ) = 0 , then b + c =
Options: a ) 18 , b ) 15 , c ) - 15 , d ) - 21 , e ) - 9
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 3 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 3 ) = 0 = 9 + 3 b + c - - - taking 9 to the other side - > 3 b + c = - 9 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 6 b = 0 - - - > b = 0 and while substituting b = 0 we get c = - 9 . b + c = - 9 - - - answer e"
Answer: e
Problem: a can do a piece of work in 90 days & y can do it in 80 days . they began working together but a leaves after some days and then b completed the remaining work in 46 days . the number of days after which a left the work was ?
Options: a ) 12 days , b ) 18 days , c ) 16 days , d ) 19 days , e ) 21 days
Rationale: a and b did the work for some days . after that , b completed the remaining work in 46 days . in 46 days , word done by b = 1 80 x 46 = 23 45 remaining work = 1 – 23 / 45 = 17 / 45 remaining work is done by both a and b together = 17 / 45 x 90 x 80 / 90 + 80 = 16 days c
Answer: c
Problem: two numbers are less than a third number by 40 % and 47 % respectively . how much per cent is the second number less than the first ?
Options: a ) 95 % , b ) 88 % , c ) 85 % , d ) 90 % , e ) none of these
Rationale: "here , x = 40 and y = 47 therefore second number = [ [ ( 100 - y ) / ( 100 - x ) ] x 100 ] % of first number = [ [ ( 100 - 47 ) / ( 100 - 40 ) ] x 100 ] % of first number i . e , 88.3 % of the first . answer : b"
Answer: b
Problem: by selling 10 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "75 % - - - 10 125 % - - - ? 75 / 125 * 10 = 6 answer : a"
Answer: a
Problem: 1 / 0.05 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 25 , d ) 20 , e ) none of these
Rationale: "explanation : 1 / 0.05 = ( 1 * 100 ) / 5 = 100 / 5 = 20 option d"
Answer: d
Problem: amit and ananthu can do a work in 15 days and 60 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 38 days , b ) 40 days , c ) 43 days , d ) 45 days , e ) 51 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 60 ananthu can do work in = 4 / 5 * 60 = 48 days so total days = 48 + 3 = 51 days answer : e"
Answer: e
Problem: yesterday it took robert 4 hours to drive from city a to city b . today it took robert 2.5 hours to drive back from city в to city a along the same route . if he had saved 15 minutes in both trips , the speed for the round trip would be 70 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 210 , e ) 300
Rationale: "2 d / 70 = 6 ( because time = 4 + 2.5 - 0.5 hrs ) = > d = 210 answer - d"
Answer: d
Problem: a and b together can do a work in 7 days . if a alone can do it in 56 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 8 , c ) 21 , d ) 20 , e ) 25
Rationale: "b 8 1 / 7 â € “ 1 / 56 = 1 / 8 = > 8"
Answer: b
Problem: shahrukh starts from barabanki to fatehpur , 1 hour after ajay starts . shahrukh meets kajol 1.5 hours after shahrukh starts . if the speed of shahrukh is at least 20 km / h faster than the speed of kajol . what is the minimum speed of shahrukh to overtake ajay , before he meets kajol ?
Options: a ) 32 , b ) 21 , c ) 27 , d ) none of these , e ) 18
Rationale: explanation : let t be the time after kajol starts , when she meets ajay , then \ inline t = \ frac { 300 } { ( x + y ) } this should be less than 2.5 or ( x + y ) > 120 since y = \ inline \ frac { 3 x } { 2 } \ inline \ rightarrow y > 72 this ( y > 72 ) is greater than 67.5 km / h and hence shahrukh will always overtake ajay before he meets kajol . answer : d
Answer: d
Problem: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 180 kilometers ?
Options: a ) 8.5 gallons , b ) 9 gallons , c ) 6.5 gallons , d ) 5.5 gallons , e ) 6 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 180 kilometers ? 180 / 20 = 9 * 1 gallon = 9 gallons correct answer b"
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 98
Rationale: "explanation : we have : l = 20 ft and lb = 680 sq . ft . so , b = 34 ft . length of fencing = ( l + 2 b ) = ( 20 + 68 ) ft = 88 ft . answer : d"
Answer: d
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 9 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 ) 22 , b ) 54 , c ) 88 , d ) 37 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 8 ooov = ( 18000 * 9 ) + 6000 ( v - 9 ) < = > 2000 v = 108000 < = > v = 54 answer : b ) 54"
Answer: b
Problem: find the sum of first 70 odd numbers
Options: a ) 4900 , b ) 4970 , c ) 4990 , d ) 4980 , e ) 4960
Rationale: "explanation : n 2 = 702 = 4900 answer : option a"
Answer: a
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 131.6 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 95 / 100 x = 125 x = 12500 / 95 = $ 131.6 now , s . p . = $ 131.6 , c . p . = $ 100 profit % = 31.6 % . a"
Answer: a
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length q of a cube whose surface area is equal to 6 z ?
Options: a ) q = 16 , b ) q = 8 √ 2 , c ) q = 8 , d ) q = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?
Options: a ) 1500 , b ) 1992 , c ) 9921 , d ) 1000 , e ) 2789
Rationale: "p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d"
Answer: d
Problem: 5 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.1388 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 5 / 36 = . 1388 answer ( b )"
Answer: b
Problem: a room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 144 , c ) 175 , d ) 165 , e ) 130
Rationale: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b"
Answer: b
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?
Options: a ) 35 days , b ) 40 days , c ) 45 days , d ) 50 days , e ) 55 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 300 * d 2 d 2 = 600 * 25 / 300 = 50 days . answer : d"
Answer: d
Problem: two cars start from the opposite places of a main road , 140 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 55 , e ) 21
Rationale: answer : d ) 55 km
Answer: d
Problem: 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = ?
Options: a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5
Rationale: explanation : 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ 1 } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 } ] = 1 ÷ [ 1 + 1 ÷ 2 ] = 1 ÷ [ 1 + ( 1 / 2 ) ] = 1 ÷ 3 / 2 = 1 × 3 / 2 = 1 × 2 / 3 = 2 / 3 answer : option c
Answer: c
Problem: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 15 and 150 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 12 , d ) 4 and 14 , e ) 5 and 14
Rationale: given : 15 < x ( x + 1 ) < 170 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 12 then x ( x + 1 ) = 12 * 13 = 156 > 150 answer : c .
Answer: c
Problem: john had a stock of 1000 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 59.8 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1000 - n = 1000 - 402 = 598 percentage books not sold / total number of books = 598 / 1000 = 59.8 = 59.8 % correct answer a"
Answer: a
Problem: a line that passes through ( – 1 , – 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !"
Answer: d
Problem: p , q and r have $ 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3200 , d ) 2539 , e ) 1930
Rationale: "c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 ."
Answer: c
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes bil can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Problem: of the 3,600 employees of company x , 16 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 57 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %"
Answer: a
Problem: the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) none
Rationale: "solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 ‹ = › 5 x = 1350 . ‹ = › x = 270 . answer d"
Answer: d
Problem: the sum of present age of abe and the age before 7 years is 33 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c"
Answer: c
Problem: if 100 < x < 199 and 9 < y < 100 , then the product xy can not be equal to :
Options: a ) 19,104 , b ) 19,303 , c ) 19 , 956.732 , d ) 19,502 , e ) 19,809
Rationale: "correct answer : ( c ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 9 . the largest value must be less than 199 * 100 . this means that 900 < xy < 19,900 . ( c ) is outside of this range , so it is not a possible product of xy ."
Answer: c
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 9 . what is the value of x ?
Options: a ) 20 , b ) 60 , c ) 100 , d ) 120 , e ) 150
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 9 ( y / 100 ) * x = 9 ( x / 400 ) * x = 9 x ^ 2 = 9 * 400 x = 60 the answer is b ."
Answer: b
Problem: a train running at a speed of 60 kmph crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 120 m , b ) 300 m , c ) 190 m , d ) 150 m , e ) 160 m
Rationale: 60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b
Answer: b
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )"
Answer: a
Problem: the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?
Options: a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these
Rationale: total earning for the week = rs ( 4 × 18 + 4 × 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c
Answer: c
Problem: mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 11 , e ) 10
Rationale: ratio of times taken by mary and rosy = 150 : 100 = 3 : 2 suppose rosy takes x days to do the work . 3 : 2 : : 12 : x = > x = 8 days . hence , rosy takes 8 days to complete the work . answer : b
Answer: b
Problem: the largest 3 digit number exactly divisible by 88 is ?
Options: a ) a ) 9944 , b ) b ) 9954 , c ) c ) 9967 , d ) d ) 9969 , e ) e ) 9970
Rationale: "largest 4 - digit number = 999 88 ) 999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 999 - 55 ) = 9944 . a )"
Answer: a
Problem: points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a
Answer: a
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 174 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 10
Rationale: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 174 - $ 120 = $ 54 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 54 / $ 6 = 9 ans is c"
Answer: c
Problem: the price of rice falls by 25 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 26.67 kg , d ) 30 kg , e ) none
Rationale: solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 25 % of 100 ) = 75 new price of rice = 75 / 20 = rs . 3.75 per kg . rice can bought now at = 100 / 3.75 = 26.67 kg . answer : option c
Answer: c
Problem: in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50000 a year , and engineers make an average of $ 80000 . what is the average salary for managers if the average for all employees is also $ 80000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000
Rationale: for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d .
Answer: d
Problem: john purchased 1370 large bottles at $ 1.99 per bottle and 690 small bottles at $ 1.50 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.83
Rationale: "( 1370 * 1.99 + 690 * 1.50 ) / ( 1370 + 690 ) = ~ 1.83 - option ( e )"
Answer: e
Problem: find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 3 : 5 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 100 = 3 : 5 answer : c"
Answer: c
Problem: 3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?
Options: a ) 120 litres , b ) 57 litres , c ) 60 litres , d ) 50 litres , e ) 100 litres
Rationale: m 1 = 50 litres m 2 = 100 litres m 3 = 150 litres required measurement = h . c . f . of m 1 , m 2 , m 3 = 50 litres answer is d
Answer: d
Problem: 2034 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 2981 , e ) 1984
Rationale: 2034 - 50 = 1984 answer : e
Answer: e
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 8 , d ) 3 / 10 , e ) 1 / 10
Rationale: p ( x is prime ) = 1 / 2 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 2 * 1 / 4 = 1 / 8 the answer is c .
Answer: c
Problem: marty ' s pizza shop guarantees that their pizzas all have at least 75 % of the surface area covered with toppings , with a crust of uniform width surrounding them . if you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust ?
Options: a ) 0.8 inches
b ) 1.1 inches
c ) 1.6 inches
d ) 2.0 inches
e ) 2.5 inches
Rationale: total area = 8 * 8 * pi radius = 64 pi surface = . 75 * 64 * pi = 48 pi radius of surface = 4 sqrt ( 3 ) ~ 6.8 radius width = 8 - 6.8 = 1.2 answer : b
Answer: b
Problem: compute all real solutions to 16 x + 4 x + 1 - 96 = 0
Options: a ) 3 / 2 , b ) 3 / 3 , c ) 2 / 4 , d ) 4 / 4 , e ) 4 / 5
Rationale: if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a
Answer: a
Problem: virginia , adrienne , and dennis have taught history for a combined total of 87 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 38 , d ) 41 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 87 = > 3 d = 87 + 27 = 114 = > d = 38 answer c"
Answer: c
Problem: the edges of a cuboid are 4 cm , 5 cm and 7 cm . find the volume of the cuboid ?
Options: a ) 140 , b ) 278 , c ) 378 , d ) 368 , e ) 367
Rationale: "4 * 5 * 7 = 120 answer : a"
Answer: a
Problem: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?
Options: a ) 567 , b ) 850 , c ) 560 , d ) 923 , e ) 240
Rationale: "in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 20 * 35 i . e . 700 = 1000 / 700 = 1 number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - ( 50 + 28 - 1 ) { using the concept of sets here ) = 923 answer is d"
Answer: d
Problem: the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 6400 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "10000 × 80 / 100 × 80 / 100 = 6400 answer : a"
Answer: a
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 4 , 1 ) , ( 1 , 1 ) , ( 1 , - 3 ) and ( - 4 , - 3 ) ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 30
Rationale: "length of side 1 = 4 + 1 = 5 length of side 2 = 3 + 1 = 4 area of rectangle = 5 * 4 = 20 b is the answer"
Answer: b
Problem: each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?
Options: a ) 65 , b ) 80 , c ) 120 , d ) 180 , e ) 190
Rationale: explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) × ( x + z ) = z . = > ( 25 / 100 ) × x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) × ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 × 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 . answer : b
Answer: b
Problem: the area of a triangle will be when a = 1 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 1 + 4 + 5 ) / 2 = 5 answer : c"
Answer: c
Problem: a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .
Options: a ) 23 , b ) 27 , c ) 32 , d ) 72 , e ) 46
Rationale: let the ten ' s digit be x and unit ' s digit be y . then 10 x + y = 3 ( x + y ) = = > 7 x - 2 y = 0 = = > 7 x - 2 y = 0 - - - - > ( i ) 10 + y + 45 = 10 y + x = = > y - x = 5 = = = > - 2 x + 2 y = 10 - - - - - - ( ii ) by adding ( i ) and ( ii ) we get 5 x = 10 so x = 2 and y = 7 so the required number is 27 . so the correct option is b ) 27 .
Answer: b
Problem: steve traveled the first 2 hours of his journey at 35 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 62 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 35 = 70 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 70 = 310 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 310 / 5 = 62 mph answer : d"
Answer: d
Problem: tom , working alone , can paint a room in 16 hours . peter and john , working independently , can paint the same room in 8 hours and 4 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 2 / 7 , d ) 1 / 7 , e ) 3 / 7
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 16 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 8 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 4 * t part of the job : 1 / 16 * ( t + 4 ) + 1 / 8 * ( t + 2 ) + 1 / 4 * t = 1 - - > multiply by 16 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 16 - - > t = 10 / 7 ; hence peter has done 1 / 8 * ( 10 / 7 + 2 ) = 1 / 8 * 24 / 7 = 3 / 7 answer : e"
Answer: e
Problem: an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x ² / 4 + 100 - 10 x simplifying x ² - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b
Answer: b
Problem: find the distance covered by a man walking for 10 min at a speed of 6 km / hr ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 1.5 km , e ) 4 km
Rationale: "distance = 6 * 10 / 60 = 1 km answer is a"
Answer: a
Problem: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 15 , c ) 25 , d ) 30 , e ) 35
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 15 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 15 x 1 ( a = 1 , b = 5 respectively we have = 5 ) . to ensure , let ' s check ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 15 x 3 = 45 ( a = 4 b = 5 respectively . hey ! that ' s 20 . but we do n ' t have this number in answer choices , move on ) . 15 x 5 = 75 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) 15 x 7 = 105 ( a = 0 , b = 5 . have 0 now . can create a pattern ) imo e ."
Answer: e
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 79 th number in this set ?
Options: a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 629
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 79 th number = 8 * ( 79 - 1 ) + 5 = 629 answer = e"
Answer: e
Problem: the area of a sector of a circle of radius 4 cm formed by an arc of length 4.5 cm is ?
Options: a ) 8.78 , b ) 8.67 , c ) 8.75 , d ) 8.98 , e ) 9
Rationale: "( 4 * 4.5 ) / 2 = 9 answer : e"
Answer: e
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 1 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 1 ) ^ 2 = ( 5 x + 4 ) ^ 2 = 5 y + 16 , for some integer y when we divide this by 5 , the remainder is 1 . the answer is b ."
Answer: b
Problem: when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tom is what percent greater than the quantifying chopped by tommy ? .
Options: a ) 44 % , b ) 100 % , c ) 125 % , d ) 225 % , e ) 400 %
Rationale: "tammy chops 4 lbs in 6 minutes tom chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : c"
Answer: c