Cheukting/mathqa huggingface dataset:
Question (general): x , a , z , and b are single digit positive integers . x = 1 / 7 a . z = 1 / 7 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 30 , b ) 36 , c ) 42 , d ) 63 , e ) 66
Rationale: "a = 7 x , b = 7 z therefore ( 7 x . 10 + 7 z ) - ( 10 x + z ) = ( 7 - 1 ) ( 10 x + z ) = 6 . ( 10 x + z ) number should be divisible by 6 d"
Answer: d
Question (gain): there are two groups of students in the sixth grade . there are 45 students in group a , and 55 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 40 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?
Options: a ) 23 % , b ) 25 % , c ) 29 % , d ) 31 % , e ) 36 %
Rationale: "number of students in group a = 45 students who forget homework in group a = 20 % of 45 = 9 students number of students in group b = 55 students who forget homework in group b = 40 % of 55 = 22 students total number of students = 45 + 55 = 100 students who forgot homework = 9 + 22 = 31 students percentage of students who forget homework = 31 / 100 * 100 = 31 % answer : d"
Answer: d
Question (general): in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 43 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 8 , d ) 50 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 43 - 25 x 50 = 40 ∴ average for last 5 days = 40 / 5 = 8 c"
Answer: c
Question (geometry): what is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5 v 2 cm ?
Options: a ) 20 v 2
b ) 10
c ) 10 v 2
d ) 20
e ) 25
Rationale: solution : 10 v 2 area of square = 1 / 2 * ( length of diagonal ) 2 area of square 1 = * ( 5 v 2 ) 2 = 25 area of square 2 = 4 * 25 = 100 length of diagonal of square 2 = v 2 * area = v 2 * 100 = v 200 = 10 v 2 cm answer is c
Answer: c
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 12,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 1200 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 12000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1440 - - - - > t = 12000 . d is the correct answer ."
Answer: d
Question (general): if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 73 , what is the value of x ?
Options: a ) 71 , b ) 75 , c ) 85 , d ) 83 , e ) 82
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 73 x = 71 answer : a"
Answer: a
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1904 ?
Options: a ) 1700 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
Rationale: "1904 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1700 . answer : a"
Answer: a
Question (general): the overall age of x and y is 11 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: "a 11 ( x + y ) â € “ ( y + z ) = 11 x â € “ z = 11"
Answer: a
Question (general): the difference between the place value and the face value of 5 in the numeral 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 49995 , e ) none of these
Rationale: "( place value of 5 ) - ( face value of 5 ) = ( 50000 - 5 ) = 49995 answer : option d"
Answer: d
Question (physics): aaron will jog from home at 5 miles per hour and then walk back home by the same route at 10 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 15 , b ) 18 , c ) 10 , d ) 12 , e ) 14
Rationale: "xyt / ( x + y ) x = 5 , y = 10 , t = 3 5 * 10 * 3 / 5 + 10 = 150 / 50 = 10 answer : c"
Answer: c
Question (general): the mean of 50 observations was 36 . it was found later that an observation 47 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.24 , b ) 36.16 , c ) 36.22 , d ) 36.48 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 47 - 23 ) = 1824 . â ˆ ´ correct mean = 1824 / 50 = 36.48 . answer d"
Answer: d
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 324 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 27 m , b ) 24 m , c ) 18 m , d ) 21 m , e ) none of these
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 324 / 3 = 108 sq m l b = 108 i . e . , l * l / 3 = 108 l 2 = 324 = > l = 18 . answer : c"
Answer: c
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 182 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 1000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1300 , e ) s : 1027
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 182 100 % - - - - ? = > rs : 1300 answer : d"
Answer: d
Question (other): the incomes of two persons a and b are in the ratio 3 : 4 . if each saves rs . 100 per month , the ratio of their expenditures is 1 : 4 . find their incomes ?
Options: a ) 112.5 , 158.5 , b ) 180.5 , 150 , c ) 100 , 200 , d ) 112.5 , 150 , e ) 122.5 , 150
Rationale: "the incomes of a and b be 3 p and 4 p . expenditures = income - savings ( 3 p - 100 ) and ( 4 p - 100 ) the ratio of their expenditure = 1 : 4 ( 3 p - 100 ) : ( 4 p - 100 ) = 1 : 4 8 p = 300 = > p = 37.5 their incomes = 112.5 , 150 answer : d"
Answer: d
Question (geometry): a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 10 - sided polygon have ?
Options: a ) 875 , b ) 35 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 10 . plugging it in , we get 35 diagonals ! answer ( b ) ."
Answer: b
Question (general): what is 2 3 / 4 - 1 2 / 5 divided by 2 / 3 - 1 / 3 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 27 / 20 , e ) 51 / 44
Rationale: "2 3 / 4 - 1 2 / 5 = 11 / 4 - 7 / 5 = ( 55 - 28 ) / 20 = 27 / 20 2 / 3 - 1 / 3 = ( 6 - 3 ) / 3 = 3 / 3 = 1 so 27 / 20 / 1 = 27 - 20 answer - d"
Answer: d
Question (physics): a and b start walking towards each other at 5 am at speed of 4 kmph and 8 kmph . they were initially 36 km apart . at what time do they meet ?
Options: a ) 8 am , b ) 6 am , c ) 7 am , d ) 10 am , e ) 8 pm
Rationale: time of meeting = distance / relative speed = 36 / 8 + 4 = 36 / 12 = 3 hrs after 5 am = 8 am answer is a
Answer: a
Question (general): a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 3 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 54 , b ) 58 , c ) 62 , d ) 66 , e ) 70
Rationale: n = 4 k + 1 = 7 j + 3 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 3 . 1 , 5 , 9 , 13 , 17 = 7 ( 2 ) + 3 the next such number is 17 + 4 * 7 = 45 . 17 + 45 = 62 the answer is c .
Answer: c
Question (physics): a train 150 m long running at 72 kmph crosses a platform in 28 sec . what is the length of the platform ?
Options: a ) 410 m , b ) 354 m , c ) 450 m , d ) 350 m , e ) 250 m
Rationale: "a 410 a = ( 72 * 5 / 18 ) * 28 - 150 = 410"
Answer: a
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 367 , c ) 189 , d ) 177 , e ) 191
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 170 x + ( x - 170 ) = 208 2 x = 378 x = 189 runs answer : c"
Answer: c
Question (physics): the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 250 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 1000 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 1000 ) * t = = = > 3 d = ts + 1000 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 1000 t - 2 d = - 2 st + 1000 t 2 d = 2 st - 1000 t d = st - 500 t x 13 : d = s * t st - 500 t = s * t s - 500 = s - 250 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 1000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 1000 2 = 500 d = s * t d = 500 * ( 1 / 2 ) d = 250 answer : a"
Answer: a
Question (gain): in town x , 64 percent of the population are employed , and 35 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 45 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 35 are employed males , hence 29 % are employed females . ( employed females ) / ( total employed people ) = 29 / 64 = 45 % answer : d ."
Answer: d
Question (general): everyone shakes hands with everyone else in a room . total number of handshakes is 91 . number of persons = ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 91 or n ( n - 1 ) = 182 or n = 14 answer is ( a )"
Answer: a
Question (general): 12008 - 50 ÷ 10.00 = ?
Options: a ) 1195 , b ) 120 , c ) 12000 , d ) 12003 , e ) none
Rationale: "answer given expression = 12008 - 50 ÷ 10.00 = 12008 - 5 = 12003 correct option : d"
Answer: d
Question (general): 6 ^ 4 − 4 ^ 4 = ?
Options: a ) 20 , b ) 52 , c ) 104 , d ) 520 , e ) 1040
Rationale: "we can write the above in terms of ( a + b ) ( a - b ) 6 ^ 4 − 4 ^ 4 = ( 6 ^ 2 ) 2 - ( 4 ^ 2 ) 2 = ( 6 ^ 2 − 4 ^ 2 ) * ( 6 ^ 2 + 4 ^ 2 ) = ( 36 − 16 ) * ( 36 + 16 ) = > 20 * 52 = 1040 ans option e ."
Answer: e
Question (general): find the value of ( 950 + 220 / 900 ) × 900
Options: a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450
Rationale: "( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d"
Answer: d
Question (general): __ 2 a x __ b ____ cc in the multiplication problem above , a , b , and c represent distinct digits . if the sum of a and b is equal to 4.6 , what is the value of c ?
Options: a ) 6 , b ) 5.2 , c ) 4 , d ) 3 , e ) 2
Rationale: if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )
Answer: b
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?
Options: a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500
Rationale: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b
Answer: b
Question (general): if ( 4 - x ) / ( 3 + x ) = x , what is the value of x ^ 2 + 4 x - 4 ?
Options: a ) - 4 , b ) - 1 , c ) 0 , d ) 1 , e ) 4
Rationale: "( 4 - x ) = x * ( 3 + x ) ( 4 - x ) = 3 x + x ^ 2 0 = x ^ 2 + 4 x - 4 the answer is c ."
Answer: c
Question (geometry): in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 2 , - 2 ) , ( 2 , 6 ) , ( 14 , 2 ) , ( 14 , - 5 ) ?
Options: a ) 90 , b ) 95 , c ) 104 , d ) 117 , e ) 182
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 8 + 7 ) × 12 = 90 . the answer is a ."
Answer: a
Question (gain): a scuba diver descends at a rate of 40 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3000 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 75 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 3000 / 40 = 75 minutes answer : c"
Answer: c
Question (physics): a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 18 days , how long will a woman take to complete the work ?
Options: a ) 9 days , b ) 21 days , c ) 24 days , d ) 27 days , e ) 28 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the woman alone can finish the work in 9 days . answer : option a"
Answer: a
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 270 pens per minute . at this rate , how many pens could 10 such machines produce in 4 minutes ?
Options: a ) 1500 , b ) 1545.6 , c ) 1640.33 , d ) 1800 , e ) none of these
Rationale: "explanation : let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 | | : : 270 : x time 1 : 4 | = > 6 * 1 * x = 10 * 4 * 270 = > x = ( 10 * 4 * 270 ) / 6 = > x = 1800 answer : d"
Answer: d
Question (physics): a tank with a volume of 45 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 14 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 5184 , b ) 5276 , c ) 5368 , d ) 5460 , e ) 5552
Rationale: "the tank is emptied at this rate : 14 + 6 - 5 = 15 cubic inches / min the tank has a volume of 45 * 12 * 12 * 12 = 77760 cubic inches . the time it takes to empty the tank is 77760 / 15 = 5184 minutes . the answer is a ."
Answer: a
Question (gain): from the sale of sleeping bags , a retailer made a gross profit of 13 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.78 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.13 = selling price - - > cost price * 1.13 = $ 28 - - > cost price = $ 24.78 . answer : c ."
Answer: c
Question (gain): a light has a rating of 86 watts , it is replaced with a new light that has 18 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 95 , c ) 80 , d ) 60 , e ) 101
Rationale: final number = initial number + 18 % ( original number ) = 86 + 18 % ( 86 ) = 86 + 15 = 101 . answer e
Answer: e
Question (physics): a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
Options: a ) 8 / 5 , b ) 8 / 3 , c ) 3 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b
Answer: b
Question (physics): a worker makes a toy in every 1 h . if he works for 100 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) 100
Rationale: "no . of toys = 100 / 1 = 100 answer : e"
Answer: e
Question (gain): there are 3000 students in a school and among them 20 % of them attends chess class . 40 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 240 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "20 % of 3000 gives 600 . so 600 attends chess and 40 % of 600 gives 240 so 240 enrolled for swimming answer : a"
Answer: a
Question (gain): the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 308
Rationale: "p = 280 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 280 * ( 1 + 10 / 100 ) = 280 * ( 11 / 10 ) = 308 answer is e"
Answer: e
Question (general): mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18
Rationale: # of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a
Answer: a
Question (general): a batsman in his 9 th inning makes a score of 75 and their by increasing his average by 7 . what is his average after the 9 th inning ?
Options: a ) 12 , b ) 19 , c ) 26 , d ) 33 , e ) 40
Rationale: 8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b
Answer: b
Question (physics): a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 3.2 km , b ) 3 km , c ) 2.4 km , d ) 3.6 km , e ) none of these
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the requited distance be x km total time taken = 1 hour = > x / 6 + x / 4 = 1 = > 2 x + 3 x = 12 = > 5 x = 12 = > x = 2.4 km . answer : option c"
Answer: c
Question (physics): working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 4 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 8 minutes
Rationale: rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 4 x / 5 x * 10 = 8 min ans : e
Answer: e
Question (general): in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 4 rows in all and a total of 134 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 = 134 4 x - 6 = 134 4 x = 128 x = 32 answer : c"
Answer: c
Question (geometry): if paint costs $ 3.10 per quart , and a quart covers 20 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 16.00 , c ) $ 93.00 , d ) $ 108.00 , e ) $ 196.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c"
Answer: c
Question (general): a man engaged a servant on the condition that he would pay him rs . 1000 and a uniform after one year service . he served only for 9 months and received uniform and rs . 550 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 800 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d"
Answer: d
Question (other): how many distinct prime numbers are factors of 33150 ?
Options: a ) four , b ) five , c ) six , d ) seven , e ) eight
Rationale: start with the prime factorization : 33150 = 50 * 663 = ( 2 * 5 * 5 ) * 3 * 221 = ( 2 ) * ( 3 ) * ( 5 ^ 2 ) * ( 13 ) * ( 17 ) there are five distinct prime factors , { 2 , 3 , 5 , 13 , and 17 } answer : b .
Answer: b
Question (gain): a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.003 % , b ) 0.03 % , c ) 3 % , d ) 2 % , e ) 30 %
Rationale: "in 12 days 12 * 0.06 = 0.72 ounces of water evaporated , which is 0.72 / 24 â ˆ — 100 = 3 of the original amount of water . answer : c ."
Answer: c
Question (general): i chose a number and divide it by 4 . then i subtracted 18 from the result and got 7 . what was the number i chose ?
Options: a ) 600 , b ) 100 , c ) 800 , d ) 900 , e ) none
Rationale: solution : let x be the number i chose , then x / 4 â ˆ ’ 18 = 7 x / 4 = 25 x = 100 answer b
Answer: b