Cheukting/mathqa huggingface dataset:
Question (probability): there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %
Rationale: "there is a 5 % chance that tigers will not win at all during the whole season we can infer that there is 95 % chance tigers will win . similarly there is a 5 % chance that federer will not play at all in the whole season we can also infer that there is 95 % chance that federer will play . answer e"
Answer: e
Question (gain): at a florist shop on a certain day , all corsages sold for either $ 25 or $ 40 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 40 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 300
Rationale: "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 25 = x , no . of corsages @ $ 40 = y and revenue = r so , 25 x + 40 y = r . . . . . . . . . ( 1 ) now , given the situation , 25 ( x + 8 ) + 40 ( y - 8 ) = r - . 4 r = > 25 x + 200 + 40 y - 320 = . 6 r = > 25 x + 40 y = . 8 r + 120 . . . . . . . . . . . . ( 2 ) so , r = . 6 r + 120 = > r = 300 the answer is e ."
Answer: e
Question (gain): in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
Options: a ) 900 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2100
Rationale: "let v be the total number of votes . 0.4 v = 480 v = 1200 the answer is b ."
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 38 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c"
Answer: c
Question (physics): pipe a that can fill a tank in an hour and pipe b that can fill the tank in 15 are opened simultaneously when the tank is empty . pipe b is shut 15 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 40 mins , b ) 35 mins , c ) 30 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 15 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 4 = 5 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 5 = 3 / 20 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : c
Answer: c
Question (general): john has exactly 31 pens , and each pen is either bule , black , or red . if he has 5 more black pens than red pens , and twice as many blue pens as black pens , how many blue pens does john has ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 22 , e ) 17
Rationale: x = the number of blue pens y = the number of black pens z = the number of red pens from the first sentence we have equation # 1 : x + y + z = 31 . . . he has 5 more black pens than red pens . . . equation # 2 : y = 5 + z . . . twice as many blue pens as black pens . . . equation # 3 : x = 2 y solve equation # 1 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 5 ) = 31 4 y - 5 = 31 4 y = 36 y = 9 there are 9 black pens . this is 5 more than the number of red pens , so z = 4 . hence the answer is . x = 18 , and just for check 18 + 9 + 4 = 31 . answer = 18 , ( b )
Answer: b
Question (general): what is the average ( arithmetic mean ) of the numbers 5 , 6 , 7 , 7 , 8 , and 9 ?
Options: a ) 4.2 , b ) 6.5 , c ) 6 , d ) 7 , e ) 8
Rationale: "{ 5 , 6 , 7 , 7 , 8 , 9 } = { 7 - 2,7 - 1 , 7 , 7,7 + 1,7 + 2 } - - > the average = 7 . answer : d ."
Answer: d
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 500 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 1288 , d ) rs . 16108 , e ) rs . 12000
Rationale: "explanation : manager ' s monthly salary rs . ( 2000 * 21 - 1500 * 20 ) = rs . 12000 . answer : e"
Answer: e
Question (geometry): a rectangular tiled patio is composed of 50 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 50 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "r * c = 50 and ( 6 + 4 ) ( 7 - 2 ) = 50 - - > r = 6 and c = 7 . answer : b ."
Answer: b
Question (general): the tax on a commodity is diminished by 20 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 8 %
Rationale: "explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )"
Answer: e
Question (other): the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 15 of her stamps , the ration of the number of kaye had to the number of alberto had was 4 : 3 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 70 , d ) 60 , e ) 90
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 15 a 2 = 3 x + 15 k 2 / a 2 = 7 / 5 ( 5 x - 15 ) / ( 3 x + 15 ) = 4 / 3 3 * ( 5 x - 15 ) = 4 * ( 3 x + 15 ) 15 x - 45 = 12 x + 60 3 x = 105 x = 35 k 2 = 5 * 35 - 15 = 160 a 2 = 3 * 35 + 15 = 90 k 2 - a 2 = 70 answer : c"
Answer: c
Question (geometry): find the area of a parallelogram with base 24 cm and height 10 cm ?
Options: a ) 240 cm 2 , b ) 384 cm 2 , c ) 279 cm 2 , d ) 200 cm 2 , e ) 297 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 10 = 240 cm 2 answer : a"
Answer: a
Question (general): what is the unit digit in 7 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "unit digit in 7 ^ 100 = unit digit in [ ( 7 ^ 4 ) ^ 25 ] but unit digit in 7 ^ 4 = 1 unit digit 7 ^ 100 = 1 answer is b"
Answer: b
Question (physics): beginning in town a , biker bob rides his bike 8 miles west , 5 miles north , 4 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 25 miles , b ) 20.4 miles , c ) 30 miles , d ) 32 miles , e ) 33 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 8 - 4 = 4 m now this third side or the distance between town a and town b = 20 ^ 2 + 4 ^ 2 = sq root 416 = 20.4 miles answer : b"
Answer: b
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
Options: a ) 44 ft , b ) 88 ft , c ) 74 ft , d ) 11 ft , e ) 66 ft
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft"
Answer: c
Question (general): in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 140 ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 140 5 x - 20 = 140 5 x = 160 x = 32 the answer is e ."
Answer: e
Question (gain): a chemical supply company has 60 liters of a 45 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 6 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "60 liters of a 45 % hno 3 solution means hno 3 = 27 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 27 + x = 50 % of ( 60 + x ) or x = 6 . hence , a"
Answer: a
Question (general): a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.20 % c is the answer"
Answer: c
Question (gain): company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 8.00 each , what was company c ’ s gross profit ?
Options: a ) $ 2,250 , b ) $ 2,500 , c ) $ 2,100 , d ) $ 2,150 , e ) $ 2,700
Rationale: cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 8 = $ 4000 profit : 4000 - 1900 = $ 2100 option c is correct
Answer: c
Question (gain): rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 50000 + y so y = 20000 then x = 50000 - 20000 = 30000 first part = 30000 answer : a"
Answer: a
Question (general): excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 20 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 77 , d ) 40 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d"
Answer: d
Question (general): find the remainder when 2 ^ 31 is divided by 5 .
Options: a ) 3 , b ) 7 , c ) 1 , d ) 9 , e ) none of them
Rationale: 2 ^ 10 = 1024 . unit digit of 2 ^ 10 x 2 ^ 10 x 2 ^ 10 is 4 [ as 4 x 4 x 4 gives unit digit 4 ] . unit digit of 231 is 8 . now , 8 when divided by 5 , gives 3 as remainder . hence , 231 when divided by 5 , gives 3 as remainder . answer is a .
Answer: a
Question (physics): laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 25 kmph and prasanna moves southward at a speed of 35 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 60 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 25 kmph x 1 hr = 25 km total southward prasanna ' s distance = 35 kmph x 1 hr = 35 km total distance between prasanna and laxmi is = 25 + 35 = 60 km . answer : c"
Answer: c
Question (general): john was thrice as old as tom 6 years ago . john will be 15 / 13 times as old as tom in 6 years . how old is tom today ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 15 / 13 * ( t + 6 ) 13 j + 78 = 15 t + 90 13 ( 3 t - 12 ) + 78 = 15 t + 90 24 t = 168 t = 7 the answer is b .
Answer: b
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 50 % profit on the first article and 50 % loss on second article . find the net profit or loss percent ?
Options: a ) 500 , b ) 768 , c ) 276 , d ) 280 , e ) 279
Rationale: "profit on first article = 50 % of 1000 = 500 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : a"
Answer: a
Question (physics): a can complete a project in 10 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 15 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 10 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 10 ) + ( x / 30 ) - 1 ) = 1 4 x / 30 = 2 x = 15 therefore , the answer is b : 15 ."
Answer: b
Question (general): a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 8 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 8 / 8 * c : ( b + c ) / 2 = ( 8 / 8 ) * c b = ( 1 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 * c ) / 2 = ( 1 / 2 ) * c median = ( a + c ) / 2 = ( 1 / 2 * c + c ) / 2 = ( 3 / 2 ) * c / 2 = ( 3 / 4 ) * c ( answer e )"
Answer: e
Question (physics): a car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 65 , e ) 78
Rationale: time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 10 = 55 seconds = 55 / 3,600 hours = 1 / 65 hours ; so , we get that to cover 1 kilometer 1 / 65 hours is needed - - > regular speed 65 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : d
Answer: d
Question (physics): a bus trip of 210 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "the time is the distance / speed . the time difference is 1 hour . 210 / v - 210 / ( v + 5 ) = 1 210 ( v + 5 ) - 210 v = ( v ) ( v + 5 ) 1050 = ( v ) ( v + 5 ) 30 * 35 = ( v ) ( v + 5 ) v = 30 mph the answer is b ."
Answer: b
Question (physics): if the 5 th date of a month is tuesday , what date will be 3 days after the 3 rd friday in the month ?
Options: a ) 17 , b ) 18 , c ) 20 , d ) 22 , e ) 33
Rationale: b 18 5 th date of a month is tuesday friday will be on = 5 + 3 = 8 th of a month 1 st friday is on 1 st of a month 2 nd friday is on 8 th of a month 3 rd friday will be on 15 th of a month 3 days after 15 th = 15 + 3 = 18
Answer: b
Question (general): what is the dividend . divisor 19 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 176 , e ) e ) 160
Rationale: "d = d * q + r d = 19 * 9 + 5 d = 171 + 5 d = 176 answer d"
Answer: d
Question (gain): 30 % of a number is more than 60 % of 150 by 120 . find the number ?
Options: a ) 770 , b ) 712 , c ) 720 , d ) 740 , e ) 700
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 650 = 190 2 / 7 x = 210 x = 700 answer : e"
Answer: e
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = c = 6 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 5 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 5 = 3 ( 3 x - 6 ) - 5 6 x - 5 = 9 x - 23 x = 6"
Answer: c
Question (general): one day a car rental agency rented 3 / 4 of its cars , including 2 / 3 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "the cars with cd players which were not rented is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 5 ) / ( 1 / 4 ) = 4 / 5 the answer is d ."
Answer: d
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 178 , e ) 150
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : e"
Answer: e
Question (gain): an investor deposited $ 5,000 to open a new savings account that earned 12 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 5300.50 , b ) $ 5304.50 , c ) $ 5405.50 , d ) $ 5604.50 , e ) $ 5805.50
Rationale: "the amount in the account after 6 months is 1.03 * 1.03 ( $ 5,000 ) = $ 5304.50 . the answer is b ."
Answer: b
Question (physics): a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in ?
Options: a ) 8 , b ) 4 , c ) 6 , d ) 12 , e ) 10
Rationale: ( a + b + c ) ' s 1 day work = 1 / 6 ; ( a + b ) ' s 1 day work = 1 / 8 ( b + c ) ' s 1 day work = 1 / 12 ( a + c ) ' s 1 day work = ( 2 * 1 / 6 ) - ( 1 / 8 + 1 / 12 ) = ( 1 / 3 - 5 / 24 ) = 1 / 8 so , a and c together will do the work in 8 days . answer a
Answer: a
Question (geometry): oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?
Options: a ) 64
b ) 4
c ) 16
d ) 9
e ) 5
Rationale: explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b
Answer: b
Question (general): how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ?
Options: a ) 2128 , b ) 3458 , c ) 4207 , d ) 5184 , e ) 8104
Rationale: all three digits are different and first digit is not zero . so first digit can be filled in 8 ways . and , second digit can be filled in 9 ways . and , third digit can be filled in 9 ways . and , fourth digit can be filled in 8 ways . total ways = 8 * 9 * 9 * 8 = 5184 hence option ( d ) .
Answer: d
Question (general): the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 80 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 9 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 9 ways . . b"
Answer: b
Question (general): 32 = a + 2 b | a | > 2 if ‘ a ’ and ‘ b ’ are both integers , then what is the smallest possible values of ‘ a ’ that can be used to solve the above equation .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: let us understand the meaning of | a | > 2 mod is very easy concept if you solve mod question by considering as a distance . when a mod is written as | x - ( a ) | = b , this means the distance from point ' a ' ( both side left and right of ' a ' on number line ) is b . | x - ( a ) | < b means the distance is between the two extreme distance ( left and right side of ' a ' on number line , considering the max distance is ' b ' from ' a ' - as per this scenario . . . . . hence the value of ' a ' must be between these two extremes . | x - ( a ) | > b means the distance is greater than the distance of ' b ' . . i . e the value of a could be anywhere more than ' b ' ( i . e . current case ) . now come to the question . first its given | a | > 2 = = > a > 2 i . e . a can have any value bigger than 2 ( i . e . 3 , 4 , 5 … ) . now , lets move to equation a + 2 b = 32 = = > b = ( 32 – a ) / 2 = = > b = 16 – ( a / 2 ) . according to question , b is an integer , hence to make ‘ b ’ integer a must be divisible by 2 . minimum possible value of ‘ a ’ that is divisible by 2 is 4 ( a is greater than 2 so the next number that is divisible by 2 is 4 ) . so the answer is c ( value 4 ) .
Answer: c
Question (general): a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 495 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 315 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 495 = $ 2170 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2170 = $ 1330 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1330 - $ 700 = $ 730 for 2 weeks avg weekly commission = $ 315 answer a
Answer: a
Question (general): at company x , senior sales representatives visit the home office once every 15 days , and junior sales representatives visit the home office once every 10 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 30 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Question (other): two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 99 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 7 total : 19 + 32 - 7 = 44 hence , widgets not inspected : 99 - 44 = 55 option e"
Answer: e
Question (general): the guests at a football banquet consumed a total of 411 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 165 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 164 * 2.5 ( max possible amount of food a guest could consume ) = 410 pounds , so there must be more than 164 guests , next integer is 165 . answer : a ."
Answer: a