Cheukting/mathqa huggingface dataset:
Question (general): a person has 12004 coins of silver . how much would he need to add so that he can distribute equally among his 7 children in whole numbers ?
Options: a ) 1 coin , b ) 2 coins , c ) 3 coins , d ) 4 coins , e ) coins
Rationale: he would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins . so the correct answer is a
Answer: a
Question (physics): a cistern 7 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55.5 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 7 x 1.25 ) + 7 x 4 ] m 2 = 55.5 m 2 . answer : option d"
Answer: d
Question (general): a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 162 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 570 , e ) 457
Rationale: "10 * 162 = 1620 3 * 100 + 5 * 150 = 1050 1620 – 1050 = 570 answer : d"
Answer: d
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 12 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 16 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 12 days whole work will be done by a in 12 * 4 / 3 = 16 days answer is d"
Answer: d
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 20 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 466.7 , d ) 297 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 120 = rs . 466.7 answer : c"
Answer: c
Question (other): the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 4 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 1 x and 4 x . then , their l . c . m = 4 x . so , 4 x = 48 or x = 12 . the numbers are 12 and 48 . hence , required sum = ( 12 + 48 ) = 60 . answer : e"
Answer: e
Question (gain): the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is
Options: a ) 6.06 % , b ) 6.07 % , c ) 6.08 % , d ) 6.09 % , e ) none
Rationale: "solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x ( 1 + 3 / 100 ) 2 ] = rs . 106.09 % . effective rate = ( 106.09 - 100 ) % = rs . 6.09 % . answer d"
Answer: d
Question (gain): on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 1,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 2.5 , b ) $ 15 , c ) $ 50 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 1,000 ( 1.05 ) ^ 2 = 1,000 ( 1.1025 ) = 1102.5 thus , tim earned 105 dollars , while lana earned 102.5 dollars the difference is $ 2.5 and the answer is a ."
Answer: a
Question (general): two trains of equal are running on parallel lines in the same direction at 49 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 , b ) 88 , c ) 65 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 49 - 36 = 13 km / hr . = 13 * 5 / 18 = 65 / 18 m / sec . 2 x / 36 = 65 / 18 = > x = 65 . answer : c"
Answer: c
Question (general): evaluate : 1222343 - 12 * 3 * 2 = ?
Options: a ) 122336 , b ) 145456 , c ) 122347 , d ) 126666 , e ) 383838
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1222343 - 12 * 3 * 2 = 122343 - 8 = 122336 correct answer a"
Answer: a
Question (other): the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 60 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 60 / ( 60 + x ) = 4 / 5 x = 15 the answer is b ."
Answer: b
Question (gain): a candidate got 33 % of the votes polled and he lost to his rival by 833 votes . how many votes were cast ?
Options: a ) 2250 , b ) 2450 , c ) 2650 , d ) 2850 , e ) 3050
Rationale: "let x be the total number of votes . 0.33 x + 833 = 0.67 x 0.34 x = 833 x = 833 / 0.34 = 2450 the answer is b ."
Answer: b
Question (geometry): calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 18 % and its breadth is decreased by 16 % ?
Options: a ) 5.88 % decrease , b ) 0.88 % decrease , c ) 0.88 % increase , d ) 1.88 % decrease , e ) 2.88 % decrease
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 18 % = 118 b decrease by 16 % = 84 118 * 84 = 9912 0.88 % decrease answer : b"
Answer: b
Question (physics): a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 6 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 6 / 4 = 1 hrs 30 min answer : d"
Answer: d
Question (physics): jane makes toy bears . when she works with an assistant , she makes 71 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 90 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 68.4 bears per 36 hours a week or 1.9 bears / hr ( [ 40 bears * 1.71 ] / [ 40 hrs * . 90 ] ) . [ ( 1.9 - 1 ) / 1 ] * 100 % = 90 % answer : c"
Answer: c
Question (geometry): 34 . the side surface of a cylinder can is rolled with a rectangular plate . if the height of a cylinder tank is 8 feet and the perimeter of the circular base is 6 feet , what is the diagonal of the rectangular plate ?
Options: a ) 10
b ) 12
c ) 8
d ) 14
e ) 9
Rationale: think of a can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 10 . ( correct answer : a )
Answer: a
Question (physics): a train 120 meters long completely crosses a 480 meters long bridge in 55 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 545 , c ) 39 , d ) 40 , e ) 09
Rationale: s = ( 120 + 480 ) / 45 = 600 / 55 * 18 / 5 = 39 answer : c
Answer: c
Question (physics): the length of the bridge , which a train 170 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 205 , b ) 210 , c ) 215 , d ) 250 , e ) 260
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 170 + x ) / 30 = 25 / 2 = > 2 ( 170 + x ) = 750 = > x = 205 m . answer : option a"
Answer: a
Question (general): employees of a certain company are each to receive a unique 6 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , and 5 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 72 , e ) 80
Rationale: "there are 4 ! ways to make codes starting with 12 . there are 4 ! ways to make codes starting with 24 . the number of codes is 2 * 4 ! = 48 . the answer is a ."
Answer: a
Question (geometry): the diagonals of a rhombus are 22 cm and 30 cm . find its area ?
Options: a ) 358 , b ) 329 , c ) 350 , d ) 330 , e ) 317
Rationale: "1 / 2 * 22 * 30 = 330 answer : d"
Answer: d
Question (general): in an examination , a pupil ’ s average marks were 63 per paper . if he had obtained 20 more marks for his geography paper and 2 more marks for his history paper , his average per paper would have been 65 . how many papers were there in the examination ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: solution let the number pf papers be x . then , 63 x + 20 + 2 = 65 x 65 x - 63 x = 22 2 x = 22 x = 11 . answer d
Answer: d
Question (gain): if 15 % of 40 is greater than 25 % of a number by 2 , then find the number is ?
Options: a ) 20 , b ) 15 , c ) 16 , d ) 25 , e ) 30
Rationale: "15 / 100 * 40 - 25 / 100 * x = 2 or x / 4 = 4 so x = 16 answer c"
Answer: c
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 144 in 4 years ?
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 4.5 % , e ) 1 %
Rationale: "144 = ( 800 * 4 * r ) / 100 r = 4.5 % answer : d"
Answer: d
Question (general): if p / q = 2 / 7 , then 2 p + q = ?
Options: a ) 11 , b ) 14 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 2 , q = 7 then 2 * 2 + 7 = 11 so 2 p + q = 11 . answer : a"
Answer: a
Question (gain): martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.60 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.6 0.4 x = 1.6 = > x = 4 discounted tickets = 10 - x = 6 ans : d"
Answer: d
Question (general): the sum of the non - prime numbers between 50 and 60 , non - inclusive , is
Options: a ) 263 , b ) 293 , c ) 323 , d ) 353 , e ) 383
Rationale: sum of consecutive integers from 51 to 59 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 51 + 59 ) / 2 * 9 = 55 * 9 = 495 sum of non - prime numbers b / w 50 and 60 , non inclusive = = = > 495 - 112 ( i . e . , 53 + 59 , being the prime # s in the range ) = 383 answer : e
Answer: e
Question (geometry): frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 500 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 70 , d ) 180 , e ) 240
Rationale: "area = length x breadth 500 = 40 x breadth so , breadth = 15 units fencing required is - breadth + breadth + length 15 + 15 + 40 = > 70 feet answer must be ( c ) 70"
Answer: c
Question (general): the class mean score on a test was 80 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 30 , b ) 31 , c ) 50 , d ) 90 , e ) 89
Rationale: "1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 95 to 65 , where 95 is within sd above the mean and 65 within 1 sd below the mean 2 sd = 15 twice = 30 from the the mean , which is 95 to 50 , where 90 is within 2 sd above the mean and 50 is within 2 sd below the mean . answer = c"
Answer: c
Question (general): there are 3 red chips and 3 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 200
Rationale: "using anagram method : @nl 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ b _ b _ b so . . 6 ! / number of repeated letters ( 3 ! ) ( 3 ! ) = 20 ans : e"
Answer: e
Question (general): the average age of applicants for a new job is 32 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 77 , c ) 7 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 32 - 8 = 24 maximum age = average + 1 standard deviation = 32 + 8 = 40 maximum number of different ages of the applicants = 30 - 24 + 1 = 7 answer c"
Answer: c
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is :
Options: a ) 36 , b ) 77 , c ) 88 , d ) 55 , e ) 221
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Question (physics): in a kilometer race , a beats b by 48 meters or 6 seconds . what time does a take to complete the race ?
Options: a ) 22 , b ) 119 , c ) 110 , d ) 109 , e ) 12
Rationale: "time taken by b run 1000 meters = ( 1000 * 6 ) / 48 = 125 sec . time taken by a = 125 - 6 = 119 sec . answer : b"
Answer: b
Question (gain): a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 200 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 10000 , d ) 20027 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 200 = > x = 10000 answer : c"
Answer: c
Question (general): the average weight of 10 person ' s increases by 5 kg when a new person comes in place of one of them weighing 60 kg . what is the weight of the new person ?
Options: a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 110 , e ) 89.5
Rationale: "total increase in weight = 10 × 5 = 50 if x is the weight of the new person , total increase in weight = x − 60 = > 50 = x - 60 = > x = 50 + 60 = 110 answer : d"
Answer: d
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 22 seconds , b ) 65 seconds , c ) 78 seconds , d ) 12 seconds , e ) 21 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 60 / 5 = 12 seconds . answer : d"
Answer: d
Question (other): solution a is 10 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 3 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 10 ) = 3 / 4 so the volume of the two solutions will be equal . answer has to be 3 : 4 . c"
Answer: c
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 12 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 67.5 , c ) 62.7 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 88 / 100 ) = 59.375 mp = 67.5 answer : b"
Answer: b
Question (general): if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 6 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 , d ) 4 / 5 , e ) 4 / 7
Rationale: p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 6 / 15 ) / ( 2 / 15 ) = 3 . c
Answer: c
Question (general): if x + y = 9 and x – y = 3 , then x ^ 2 - y ^ 2 =
Options: a ) - 4 , b ) 4 , c ) 10 , d ) 27 , e ) 40
Rationale: the fastest approach has already been shown . here ' s one more option . given : x + y = 9 x – y = 3 add the two equations to get : 2 x = 12 , which means x = 6 if x = 6 , we can plug that value into either equation , to conclude that y = 3 if x = 6 and y = 3 , then x ² - y ² = 6 ² - 3 ² = 27 answer : d
Answer: d
Question (other): in a primary school , the ratio of the number of girls to boys is 5 : 8 . if there are 160 girls , the total number of students in the college is :
Options: a ) 100 , b ) 250 , c ) 260 , d ) 300 , e ) 350
Rationale: let the number of girls and boys be 5 x and 8 x . total number of students = 13 x = 13 x 32 = 416 . answer : d
Answer: d
Question (general): a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 35 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 525 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 35 customers equally . so , total number of pastry must be a multiple of 35 only option a satisfies the condition , and hence is the answer"
Answer: a
Question (general): ( 74 + 75 + 76 + 77 + . . . . . + 149 + 150 ) = ?
Options: a ) 8624 , b ) 8634 , c ) 8654 , d ) 8644 , e ) 8677
Rationale: "explanation : sum of first n natural numbers = ( 1 + 2 + 3 + . . . . . + n ) = n ( n + 1 ) / 2 ( 74 + 75 + 76 + . . . . . + 150 ) = ( 1 + 2 + . . . . + 73 + 74 + 75 + . . . . . + 150 ) - ( 1 + 2 + . . . . + 73 ) = ( 1 / 2 x 150 x 151 ) - ( 1 / 2 x 73 x 74 ) = 11325 - 2701 = 8624 answer : option a"
Answer: a
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 17 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 75.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 27 % , thus he must pay slightly more than $ 73 . only answer choice e fits . answer : e"
Answer: e
Question (physics): a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 2870 , e ) 4320
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3 = 4320 . answer : e"
Answer: e
Question (gain): a feed store sells two varieties of birdseed : brand a , which is 65 % millet and 35 % sunflower , and brand b , which is 40 % millet and 60 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "yes there is a simple method : consider the following method brand a : 65 % millet and 35 % sunflower brand b : 40 % millet and 60 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 a - - - - - - - - - - - - - - - i similarly , brand b has 40 % millet , which is 10 % less than the weighted average of mix = - 0.10 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.15 a = 0.10 b therefore a / b = 0.10 / 0.15 = 2 / 3 a : b : ( a + b ) = 2 : 3 : ( 3 + 2 ) = 2 : 3 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 2 : 5 = ( 2 / 5 ) * 100 = 40 % here is a pictorial representation : brand a = 65 % - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.15 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 40 % - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.10 b since the amount below the average has to equal the average above the average ; therefore , 0.15 a = 0.10 b a / b = 2 / 3 a : b : total = 2 : 3 : 5 therefore a / total = 2 : 5 = 40 %"
Answer: a
Question (other): of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 16 boys and 44 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 16 boys . so 16 - 6 - 6 = 4 boys must be neither happy nor sad . answer ( b )
Answer: b
Question (physics): pipe p can drain the liquid from a tank in 1 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 3 / 23 , c ) 3 / 8 , d ) 17 / 29 , e ) 3 / 4
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 1 / 4 ) rq ] = 4 also , rp = rr / ( 2 / 3 ) = > 4 = rr / ( 2 / 3 ) = > rr = 8 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 + 8 / 3 = 23 / 3 = 1 / ( 3 / 23 ) thus running simultaneously , pipe q will drain 3 / 23 of the liquid . thus answer = b ."
Answer: b
Question (general): a box contains 10 apples , 9 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "when you choose ( and then eat ) the first apple , the probability of that apple being red is 9 / 10 . so if we do the activity 1 times , the probability of it being red is 9 / 10 . for 2 times , it is ( 9 / 10 ) * ( 8 / 9 ) for 3 times , it is ( 9 / 10 ) * ( 8 / 9 ) * ( 7 / 8 ) you can notice that the numerator of the first term cancels with the denominator of the second . so we can see that the probability becomes 0.5 when the last term is 5 / 6 & it becomes less than 0.5 when the last term is 4 / 5 . 9 accounts for n = 1 , so 4 will account for n = 6 , answer . d"
Answer: d