Cheukting/mathqa huggingface dataset:
Question (other): uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 8 : 2 . if 80 % of the toyota bought and 20 % of the honda bought were suv â € ™ s . how many suv â € ™ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 80 and honda 20 , so total number of suv ' s bought for toyota and honda respectively 80 * 80 / 100 = 64 and 20 * 20 / 100 = 4 so total 68 suv ' s were bought out of 100 vehicles bought . . so required % is 68 % answer : c"
Answer: c
Question (general): 10 ^ ( 655 ) ã · 10 ^ ( 650 ) = ?
Options: a ) 100 , b ) 10 , c ) 10000 , d ) 100000 , e ) 1000000
Rationale: "10 ^ ( 655 ) ã · 10 ^ ( 651 ) = 10 ^ ( 655 - 651 ) = 10 ^ 5 = 100000 answer : d"
Answer: d
Question (general): a corporation that had $ 115.19 billion in profits for the year paid out $ 250.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.22 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 250.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 250.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2.2 / 1000 ) * 100 = 0.22 % so answer is ( e )"
Answer: e
Question (gain): a reduction of 10 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 1.1 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.9
Rationale: "100 * ( 10 / 100 ) = 10 - - - 10 ? - - - 1 = > rs . 1 100 - - - 90 ? - - - 1 = > rs . 1.1 answer : a"
Answer: a
Question (general): the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 62 = 930 so , the score of the person who left is 70 ( 1000 - 930 ) answer will be ( e )"
Answer: e
Question (other): the triplicate ratio of 2 : 3 is ?
Options: a ) 1 : 64 , b ) 1 : 62 , c ) 1 : 34 , d ) 8 : 27 , e ) 5 : 64
Rationale: 2 ^ 3 : 3 ^ 3 = 8 : 27 answer : d
Answer: d
Question (physics): if 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 15 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: we can try the logic of time and work , our work is to kill the deers so 15 ( lions ) * 15 ( min ) / 15 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 15 answer : b
Answer: b
Question (general): what is the least number that should be added to 1076 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( 1076 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e .
Answer: e
Question (general): the sum of two numbers is 40 and their product is 375 . what will be the sum of their reciprocals ?
Options: a ) 1 / 40 , b ) 8 / 75 , c ) 75 / 4 , d ) 75 / 8 , e ) 75 / 6
Rationale: ( 1 / a ) + ( 1 / b ) = ( a + b ) / ab = 40 / 375 = 8 / 75 answer : b
Answer: b
Question (probability): in a throw of a coin find the probability of getting a tail ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Rationale: "s = { h , t } e = { t } p ( e ) = 1 / 2 answer is a"
Answer: a
Question (physics): on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 3 of the total distance and again after she traveled 1 ⁄ 2 of the distance remaining between her first stop and her destination . she then drove the remaining 100 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 550
Rationale: "let d = total distance traci traveled 1 / 3 = d / 3 i . e . remaining distance = 2 d / 3 she traveled 1 / 2 th of 2 d / 3 = d / 3 thus : d = ( d / 3 ) + ( d / 3 ) + 100 d = 300 answer : b"
Answer: b
Question (physics): pavan travelled for 15 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan .
Options: a ) 408 km , b ) 409 km , c ) 410 km , d ) 412 km , e ) 419 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 15 = > x / 60 + x / 50 = 15 = > ( 5 x + 6 x ) / 300 = 15 = > x = 409 km answer : b
Answer: b
Question (general): how many quarters are equal to 5 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 20 , e ) 7
Rationale: "5 * 4 = 20 quarters answer : d"
Answer: d
Question (general): when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 204.06 , what is value of j ?
Options: a ) 100 , b ) 500 , c ) 600 , d ) 800 , e ) 200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.06 here 204 is the quotient . given that remainder = 12 so , 204.06 = 204 + 12 / j so , j = 200 answer : e"
Answer: e
Question (general): if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.25 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.50 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.25 ) = $ 3.5 ( as the charge is 0.25 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 3.5 = 4.5 answer is d ."
Answer: d
Question (general): during a particular baseball game , the probability of a team ' s pitcher throwing a strike on each throw is 2 / 5 . what is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50 % .
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a ∩ b ) = p ( a ) p ( b ) the probability that the pitcher throws a strike at least once in 2 guesses is 1 - ( 3 / 5 ) ^ 2 = 1 - 9 / 25 = 16 / 25 > 50 % . answer : b
Answer: b
Question (general): y = x ^ 2 + bx + 64 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 65 , b ) - 64 , c ) - 32 , d ) 32 , e ) 64
Rationale: "as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form ofax ^ 2 + bx + c = 0 , the product of the roots = c / a = 64 / 1 = 256 and the sum of the roots = - b / a = - b 64 can be expressed as product of two numbers in the following ways : 1 * 64 2 * 32 4 * 16 the sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64 = 65 . the least value possible for b is therefore - 65 . b"
Answer: b
Question (gain): a merchant marks his goods up by 20 % and then offers a discount of 5 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 6 % , c ) 21 % , d ) 14 % , e ) 17 %
Rationale: "let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 5 % on 120 . profit = 114 - 100 14 % answer d"
Answer: d
Question (gain): a fruit seller sells mangoes at the rate of rs . 16 per kg and thereby loses 12 % . at what price per kg , he should have sold them to make a profit of 20 % ?
Options: a ) rs . 21.81 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 88 : 16 = 120 : x x = ( 16 ã — 120 / 88 ) = rs . 21.81 hence , s . p per kg = rs . 21.81 answer a"
Answer: a
Question (general): a batsman scored 120 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 , b ) 58.33 % , c ) 600 / 11 , d ) 55 , e ) 35
Rationale: "explanation : number of runs made by running , = > 120 − ( 5 × 4 + 5 × 6 ) . = > 120 − ( 50 ) . = > 70 . hence , the required percentage is : - = > 70 / 120 * 100 = > 58.33 % answer : b"
Answer: b
Question (other): right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 30 years . what is molly ' s age right now ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "now , sandy is 30 - 6 = 24 molly ' s age is ( 3 / 4 ) * 24 = 18 the answer is d ."
Answer: d
Question (physics): a goods train runs at a speed of 72 kmph and crosses a 290 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 290 + x / t 72 * 5 / 18 = 290 + x / 26 x = 230 answer : a"
Answer: a
Question (gain): two years ago , ram put $ 1000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1000 ?
Options: a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
Rationale: investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %
Answer: e
Question (general): in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many r eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000
Rationale: "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there r = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ."
Answer: c
Question (gain): an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 200 - a ) = 30 - - > a = 50 . answer : e ."
Answer: e
Question (gain): what quantity of water should taken out to concentrate 24 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 24 ( 60 - 40 ) / 60 = 8 liters answer is d"
Answer: d
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then 2 xy / 3 = ?
Options: a ) 1 , b ) 2 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 * 1 ) / 3 = 6 / 3 = 2 b"
Answer: b
Question (other): in a colony of 50 residents , the ratio of the number of men and women is 3 : 2 . among the women , the ratio of the educated to the uneducated is 1 : 3 . if the ratio of the number of education to uneducated persons is 4 : 6 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 5 , e ) 5 : 7
Rationale: "number of men in the colony = 3 / 5 ( 50 ) = 30 number of women in the colony = 2 / 5 ( 50 ) = 20 number of educated women in the colony = 1 / 4 ( 20 ) = 5 number of uneducated women in the colony = 3 / 4 ( 20 ) = 15 number of educated persons in the colony = 4 / 10 ( 50 ) = 20 as 5 females are educated , remaining 15 educated persons must be men . number of uneducated men in the colony = 30 - 15 = 15 number of educated men and uneducated men are in the ratio 15 : 15 = > 1 : 1 answer : a"
Answer: a
Question (gain): a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 135 ( multiplying factor is 9 : ( 135 / 15 ) ) then typical dosage would be 2 * 9 = 18 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 18 ) * 100 = 11.11 % c is the answer ."
Answer: c
Question (physics): a train running at the speed of 72 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 160 meter , d ) 135 meter , e ) none of these
Rationale: "explanation : speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time = 20 * 8 = 160 meter option c"
Answer: c
Question (general): 1,000 ^ 2 + 1,001 ^ 2 =
Options: a ) 6 , 030,053 , b ) 6 , 002,001 , c ) 6 , 030,055 , d ) 6 , 030,056 , e ) 6 , 030,057
Rationale: "interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 total - > * 1 answer b ."
Answer: b
Question (general): a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container ?
Options: a ) 26.34 litres , b ) 27.36 litres , c ) 28 litres , d ) 29.16 litres , e ) 30 litres
Rationale: "amount of milk left after 3 operations = [ 40 ( 1 - 4 / 40 ) ^ 3 ] litres = 40 x 9 / 10 x 9 / 10 x 9 / 10 = 29.16 litres answer : d"
Answer: d
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 3000 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 6000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 3000 = > x = 3000 . b ' s share = rs . 2 x = 2 * 3000 = rs . 6000 . answer : c"
Answer: c
Question (gain): last year a certain bond price with a face value of 5000 yielded 5 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 3846 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.05 * 5000 = 0.065 * selling price - - > selling price = 0.05 * 5000 / 0.065 - - > selling price = ~ 3,846 answer : b ."
Answer: b
Question (probability): in how many ways can 5 people be arranged in a circle ?
Options: a ) 2 ! , b ) 5 ! , c ) 4 ! , d ) 3 ! , e ) 6 !
Rationale: "( 5 − 1 ) ! = 4 ! = 24 ways ans - c"
Answer: c
Question (general): if 3 a – 2 b – 2 c = 30 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c"
Answer: c
Question (gain): a man can row his boat with the stream at 8 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 8 us = 4 s = ? s = ( 8 - 4 ) / 2 = 2 kmph answer : b"
Answer: b
Question (general): in a class of 30 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48.5 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 26 * 45 = 1455 average marks of whole class = 1455 / 30 = 48.5 answer : option d"
Answer: d
Question (general): a , b and c have rs . 350 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 200 , b ) b ) 190 , c ) c ) 180 , d ) d ) 170 , e ) e ) 160
Rationale: "a + b + c = 350 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 350 - - - - - - - - - - - - - - - - c = 200 answer : a"
Answer: a
Question (general): what is the decimal equivalent of ( 1 / 6 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.278 , e ) 0.5
Rationale: "( 1 / 6 ) ² = ( 1 / 6 ) ( 1 / 6 ) = 1 / 36 approach # 1 : use long division to divide 36 into 1 to get 1 / 36 = 0.0278 d"
Answer: d
Question (general): there are 32 balls which are red , blue or green . if 15 balls are green and the sum of red balls and green balls is less than 23 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "r + g + b = 32 g = 15 r + g < 23 = > r + 15 < 23 = > r < 8 = > at most 7 red balls answer : d"
Answer: d
Question (physics): the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in metres ) is :
Options: a ) 400 , b ) 525 , c ) 750 , d ) 850 , e ) none
Rationale: "sol . speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x metres . then , 2 x / 60 = 25 ⇔ x = 25 * 60 / 2 = 750 answer c"
Answer: c
Question (general): of 30 applicants for a job , 11 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 8 , d ) 7 , e ) 5
Rationale: "c . 8 30 - 3 = 27 27 - 11 - 18 = - 8 then 8 are in the intersection between 4 years experience and degree . answer c"
Answer: c
Question (general): what is the sum of all remainders obtained when the first 200 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 401 . answer : b ."
Answer: b
Question (general): linda spent 2 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 700 , e ) $ 800
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 2 / 4 = 1 / 2 on a tv but the tv cost her $ 300 . so 1 / 2 of her savings is $ 300 . so her original savings are 2 times $ 300 = $ 600 correct answer c"
Answer: c
Question (physics): what is the speed of the stream if a canoe rows upstream at 3 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 4.5 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 3 ) kmph = 4.5 kmph . answer e"
Answer: e
Question (other): the ratio of the number of females to males at a party was 1 : 2 but when 3 females and 3 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 3 ) = 2 x - 3 x = 6 there were 3 x = 18 people at the party originally . the answer is c ."
Answer: c
Question (gain): one fourth of one third of two fifth of a number is 30 . what will be 40 % of that number
Options: a ) a ) 360 , b ) b ) 150 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 30 then x = 30 * 30 = 900 40 % of 900 = 360 answer : option a"
Answer: a
Question (gain): 5 percent of 255 =
Options: a ) 5 , b ) 12.5 , c ) 14.5 , d ) 12.75 , e ) 25
Rationale: 255 / 100 = 2.55 1 % = 2.55 5 % = 2.55 * 5 = 12.75 answer : d
Answer: d
Question (physics): a certain number of men can do a work in 20 days . if there were 4 men less it could be finished in 5 days more . how many men are there ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: the original number of men = 4 ( 20 + 5 ) / 5 = 20 men answer is b
Answer: b
Question (physics): a train running at the speed of 36 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 299 meter , c ) 666 meter , d ) 90 meter , e ) 144 meter
Rationale: "speed = 36 * ( 5 / 18 ) m / sec = 10 m / sec length of train ( distance ) = speed * time ( 10 ) * 9 = 90 meter answer : d"
Answer: d
Question (general): if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 11 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 11 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 11 is 3 . answer : d ."
Answer: d
Question (general): point ( m , n ) is on the circle represented by m ^ 2 + n ^ 2 = 10 , and m , n are integers . how many such points are possible ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: m ^ 2 + n ^ 2 = 10 and m , n are integers means that 10 is the sum of two perfect squares . 10 is the sum of only one pair of perfect squares 1 and 9 . so , there can be 8 such points , 4 in each quadrant : ( 1 , 3 ) ; ( 1 , - 3 ) ; ( - 1 , 3 ) ; ( - 1 , - 3 ) ; ( 3 , 1 ) ; ( 3 , - 1 ) ; ( - 3 , 1 ) ; ( - 3 , - 1 ) . answer : e .
Answer: e