regisss/math_qa huggingface dataset:
Problem: the price of 2 sarees and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) 2500 , b ) 2700 , c ) 2200 , d ) 2900 , e ) 2400
Rationale: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . answer is e .
Answer: e
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number y of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible y : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.80 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 98.73 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 102.07 , e ) $ 105.3
Rationale: there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.73 or 2 ) 25 + 25 + 25 = $ 96.75 a
Answer: a
Problem: in the manufacture of a certain product , 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.2 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 5 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 5 / 100 ) * 100 % = ( 20 / 10000 ) * 100 % = ( 20 / 100 ) % = . 2 % answer b"
Answer: b
Problem: a student appeared in the mock cat . the test paper contained 3 sections namely qa , di and va . the percentage marks in all va was equal to the average of percentage marks in all the 3 sections . coincidentally , if we reverse the digit of the percentage marks of qa we get the percentage marks of di . the percentage marks in va scored by student could be :
Options: a ) 81 , b ) 48 , c ) 66 , d ) 69 , e ) none of these
Rationale: solution : let the percentage marks in qa = ( 10 a + b ) % let the percentage marks in di = ( 10 b + a ) % let the percentage marks in va = x % . now , according to the question , we have , [ ( 10 a + b ) + x + ( 10 b + a ) ] / 3 = x → 11 a + 11 b + x = 3 x . or , x = 11 ( a + b ) / 2 . clearly , we can see that the percentage of the va section will be a multiple of 11 . so , required answer will be 66 . answer : option c
Answer: c
Problem: a cube of side 5 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 10781 , b ) 1276 , c ) 1000 , d ) 8000 , e ) 5000
Rationale: "along one edge , the number of small cubes that can be cut = 500 / 25 = 20 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : d"
Answer: d
Problem: two trains of equal are running on parallel lines in the same direction at 45 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 45 , b ) 88 , c ) 66 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 45 - 36 = 9 km / hr . = 9 * 5 / 18 = 5 / 2 m / sec . 2 x / 36 = 5 / 2 = > x = 45 . answer : a"
Answer: a
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 6 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 5 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 6 + 1 ) / ( 6 - 1 ) = 7 / 5 answer : d"
Answer: d
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 2 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 120 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.02 ) m 3 = 0.12 m 3 . mass of man = volume of water displaced × density of water = ( 0.12 × 1000 ) kg = 120 kg . answer d"
Answer: d
Problem: the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250 . the sum of the numbers is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 5
Rationale: "let the numbers be 3 x , 4 x , 5 x then , 9 x ^ 2 + 16 x ^ 2 + 25 x ^ 2 = 1250 50 x ^ 2 = 1250 x ^ 2 = 25 x = 5 answer is e"
Answer: e
Problem: in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 kg ?
Options: a ) 7 : 3 , b ) 3 : 7 , c ) 4 : 6 , d ) 5 : 7 , e ) 8 : 9
Rationale: "required rate = 3.50 : 1.50 = 7 : 3 . answer a"
Answer: a
Problem: if the personal income tax rate is lowered from 46 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36000 ?
Options: a ) $ 3500 , b ) $ 5040 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 46 - 32 ) % of 36000 = 5040 . answer : b"
Answer: b
Problem: how many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 10 , c ) 11 , d ) 12 , e ) 15
Rationale: the question basically asks how many positive odd integers less than 100 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 , 85,95 = 10 ans b
Answer: b
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 625 meters in length ?
Options: a ) 62 , b ) 72 , c ) 55 , d ) 82 , e ) 52.7
Rationale: "explanation : t = ( 625 + 165 ) / 54 * 18 / 5 t = 52.7 answer : option e"
Answer: e
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 4 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 3 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 2 - 1 / 4 = ( 2 - 1 ) / 4 = 1 / 4 so 17 / 12 / 1 / 4 = 17 / 12 * 4 = 17 / 3 answer - d"
Answer: d
Problem: the length of a rectangle is one fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 784 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 5 units ?
Options: a ) 35 sq . units
b ) 45 sq . units
c ) 55 sq . units
d ) 50 sq . units
e ) 40 sq . units
Rationale: given that the area of the square = 784 sq . units = > side of square = â ˆ š 784 = 28 units the radius of the circle = side of the square = 28 units length of the rectangle = 1 / 4 * 28 = 7 units given that breadth = 5 units area of the rectangle = lb = 7 * 5 = 35 sq . units answer : a
Answer: a
Problem: 33 1 / 3 % of 36 ?
Options: a ) 16 , b ) 21 , c ) 18 , d ) 12 number , e ) 18
Rationale: explanation : 33 1 / 3 % = 1 / 3 1 / 3 * 36 = 12 answer : option d
Answer: d
Problem: an engine moves at the speed of 30 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 18 kmph . what will be the speed of train when 16 coaches are attached .
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 16 swr root = 4 decrease = 4 * 4 = 16 new speed = 30 - 16 = 14 a"
Answer: a
Problem: if 20 typists can type 50 letters in 30 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 400 , b ) 500 , c ) 350 , d ) 250 , e ) 200
Rationale: "no . of letters typing by 20 typists in 30 minutes = 50 no . of letters typing by 20 typists in 60 minutes = 50 * 2 = 100 no . of letters typing by 40 typists in 60 minutes = 100 / 10 * 40 = 400 answer : a"
Answer: a
Problem: a man whose speed is 3 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 7 , b ) 4 , c ) 3 , d ) 9 , e ) 3.6
Rationale: "m = 3 s = 1.5 ds = 4.5 us = 3 as = ( 2 * 4.5 * 3 ) / 7.5 = 3.6 answer : e"
Answer: e
Problem: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 10.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 4.30
Rationale: "manager wages per hour = $ 10.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 10.50 ) = = > $ 5.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 5.25 = ( 20 * ( $ 5.25 ) ) / 100 - - > ( $ 95 ) / 100 - - > $ 0.95 therefore , chef wages per hour = $ 5.25 + $ 0.95 = = > $ 6.20 difference of wages between manager and chef = $ 10.50 - $ 6.20 = = > $ 4.30 answer : e"
Answer: e
Problem: if the height of a cone is increased by 140 % then its volume is increased by ?
Options: a ) 100
b ) 140
c ) 998
d ) 729
e ) 2879
Rationale: 140 % answer : b
Answer: b
Problem: 1345 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 1295 , e ) none of these
Rationale: "1345 - 50 = 1295 answer : d"
Answer: d
Problem: the guests at a football banquet consumed a total of 325 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 162 * 2 ( max possible amount of food a guest could consume ) = 324 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ."
Answer: d
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 24 / r years . if pat ' s parents invested $ 6,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 30000
Rationale: "since investment doubles in 24 / r years , then for r = 8 it ' ll double in 24 / 8 = ~ 3 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 6 = $ 30,000 . answer : e ."
Answer: e
Problem: how many 3 - digit numbers abc , in which a , b , and c are each digits , satisfy the equation 2 b = a + c ?
Options: a ) 33 , b ) 36 , c ) 41 , d ) 45 , e ) 50
Rationale: possible solutions are diff of 0 - - 111222 , . . . . . . . . , 999 = 9 diff of 1 - - 123 , 234 , . . . . . , 789 = 7 x 2 = 14 diff of 2 - - 135 , 246 . . . . . . . 579 = 5 x 2 = 10 diff of 3 - - 147 , 258369 = 3 x 2 = 6 diff of 4 - - 159 = 1 x 2 = 2 last 210 , 420 , 630840 = 4 so total is 9 + 14 + 10 + 6 + 2 + 4 = 45 . answer : d
Answer: d
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 2 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 180 , b ) 45 , c ) 60 , d ) 90 , e ) 135
Rationale: we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 2 / 3 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 3 / 2 ) = 60 total sedimentary rocks = 2 * total igneous rocks = 2 * 60 = 120 total number of rocks = 60 + 120 = 180 answer ( a )
Answer: a
Problem: 3 sets of 40 , 50 and 60 students appeared for an examination and the pass percentage was 100 , 90 and 80 respectively . the pass percentage of the whole set is
Options: a ) 88.33 , b ) 84.33 , c ) 88.66 , d ) 84.66 , e ) none of these
Rationale: total passed student = 40 + 45 + 48 = 133 133 is 88.66 % of 150 answer : c
Answer: c
Problem: a bag of potatoes weighs 60 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 11 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 66 ÷ 6 = 11 . answer : b"
Answer: b
Problem: ake can dig a well in 16 days . paul can dig the same well in 24 days . jake , paul and hari together dig the well in 8 days . hari alone can dig the well in
Options: a ) 48 , b ) 39 , c ) 37 , d ) 27 , e ) 29
Rationale: simple one . let the total work to be done is 48 meters . now jake can dig 3 mts , paul can dig 2 mts a day . now all of them combined dug in 8 days so per day they dug 48 / 8 = 6 mts . so of these 8 mts , hari capacity is 1 mt . so he takes 48 / 1 = 48 days to complete the digging job . answer : a
Answer: a
Problem: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 3 : 1 , e ) none
Rationale: "sol . let man ’ s rate upstream be x kmph . then , his rate downstream = 2 x kmph . ∴ ( speed in still water ) : ( speed of stream ) = [ 2 x + x / 2 ] : [ 2 x - x / 2 ] 3 x / 2 : x / 2 = 3 : 1 . answer d"
Answer: d
Problem: a can complete the job in 6 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 9 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 9
Answer: a
Problem: list r contains 5 numbers that have an average value of 60 . if the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number , what is the smallest possible value in the list ?
Options: a ) 25 , b ) 28 , c ) 31 , d ) 34 , e ) 37
Rationale: the middle number is 60 . let the smallest number be x . then the largest number is 2 x + 20 . to make x as small as possible , let ' s make the remaining numbers as large as possible . so the second largest = the largest = 2 x + 20 . the second smallest should be equal to the median . the numbers are x , 60 , 60 , 2 x + 20 , 2 x + 20 . x + 60 + 60 + 2 x + 20 + 2 x + 20 = 5 * 60 = 300 5 x = 140 x = 28 the answer is b .
Answer: b
Problem: evaluate : 98612 / 22 * 11 * 70 = ?
Options: a ) 700.4 , b ) 704.4 , c ) 740.4 , d ) 744.4 , e ) 700.0
Rationale: "according to order of operations , 22 ? 11 ? 70 ( division and multiplication ) is done first from left to right 22 / 11 = 2 * 70 = 140 hence 98612 / 24 * 11 * 70 = 98612 / 140 = 704.4 correct answer b"
Answer: b
Problem: if a - b = 6 and a 2 + b 2 = 50 , find the value of ab .
Options: a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 50 - 36 = 14 ab = 7 . answer : a"
Answer: a
Problem: in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards m will he need to gain this sunday if he wants to keep his season average above 100 yards ?
Options: a ) 101 , b ) 116 , c ) m = 130 , d ) m = 131 , e ) m = 141
Rationale: sorry the answer m = 141 is d .
Answer: d
Problem: the price of 3 pants and 6 t - shirts is rs . 750 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 150 , b ) 250 , c ) 400 , d ) 450 , e ) 550
Rationale: "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 750 . . . . ( i ) and x + 12 y = 750 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 250 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 750 ( - ) x + 2 y = 250 - - - - - - - - - - - - - - - - 10 y = 500 - - - - - - - - - - - - - - - - y = 50 cost of 8 t - shirts = 8 * 50 = 400 answer : c"
Answer: c
Problem: a certain debt will be paid in 65 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 455 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 65 payment per installment for the first 20 installments = 410 payment per installment for the remaining 45 installments = 410 + 65 = 475 average = ( 20 * 410 + 45 * 475 ) / 65 = 455 answer b"
Answer: b
Problem: in 7 given numbers , the average of first 4 numbers is 4 and that of last 4 numbers is also 4 . if the average of these 7 numbers is 3 , the fourth number is ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 11 , e ) 12
Rationale: let 7 numbers are a , b , c , d , e , f , g . given avg of first 4 nums are 4 . . . i . e ( a + b + c + d ) / 4 = 4 a + b + c + d = 16 given avg of last 4 nums are also 4 . . i . e . ( d + e + f + g ) / 4 = 4 d + e + f + g = 16 e + f + g = 16 - d given avg of 7 nums are 3 . . . . i . e ( a + b + c + d + e + f + g ) / 7 = 3 a + b + c + d + e + f + g = 21 16 + 16 - d = 21 d = 32 - 21 d = 11 answer : d
Answer: d
Problem: in a certain parking lot , 4 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 4 % * x = 20 % * y y / x = 1 / 5 = 20 % the answer is a ."
Answer: a
Problem: at the beginning of a year , the owner of a jewel shop raised the price of all the jewels in his shop by x % and lowered them by x % . the price of one jewel after this up and down cycle reduced by rs . 100 . the owner carried out the same procedure after a month . after this second up - down cycle , the price of that jewel was rs . 2304 . find the original price of that jewel ( in rs . )
Options: a ) 2500 , b ) 550 , c ) 2600 , d ) 2650 , e ) none of these
Rationale: solution : let the original price = y , after first change , it becomes , y * ( 1 + ( x / 100 ) ) after second change , it becomes y * ( 1 + ( x / 100 ) ) ( 1 - ( x / 100 ) ) = y ( 1 - ( x / 100 ) ^ 2 ) thus , x 2 * y = 106 - - - - - - - ( 1 ) x 2 = 106 / y now , y ( 1 - ( 106 / 10000 y ) ) 2 = 2304 ( similar to above ) y ( 1 - 100 / y ) 2 = 2304 y = 2500 . answer : option a
Answer: a
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "since the problem does n ' t depend on the number of birds in reserve you can suppose that there are 100 birds . from them 100 * 0.3 = 30 are hawks . so , there are 70 non - hawks . there are 0.4 * 70 = 28 paddyfield - warblers . therefore , there are 0.25 * 28 = 7 kingfishers . the total number of birds in the nature reserve that are not hawks , paddyfield - warblers , or kingfishers is 100 - 30 - 28 - 7 = 35 . the answer is b"
Answer: b
Problem: a bag contains 6 black and 4 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 4 ) = 10 . number of white balls = 4 . p ( drawing a white ball ) = 4 / 10 = 2 / 5 . option b ."
Answer: b
Problem: alfred buys an old scooter for $ 4700 and spends $ 600 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 9.43 % , e ) 10 %
Rationale: c . p . = 4700 + 600 = $ 5300 s . p . = $ 5800 gain = 5800 - 5300 = $ 500 gain % = 500 / 5300 * 100 = 9.43 % answer is d
Answer: d
Problem: ( 4300531 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764913 , d ) 1675123 , e ) none of them
Rationale: "let 4300531 - x = 2535618 then x = 4300531 - 2535618 = 1764913 answer is c"
Answer: c
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long answer : d"
Answer: d
Problem: the sum of two numbers is 66 . how much should be added to the sum for it to be exactly divisible by 9 leaving 0 as the reminder ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1
Rationale: the sum is 66 . adding 6 to 66 = 66 + 6 = 72 . 72 is exactly divisible by 9 leaving 0 as the reminder = 8 . so the answer is a = 6
Answer: a
Problem: what is next no . 11 23 47 83 131 191 263 347 443 551 ? ? ?
Options: a ) 171 , b ) 181 , c ) 191 , d ) 201 , e ) 671
Rationale: 11 + 12 * 1 = 23 23 + 12 * 2 = 47 47 + 12 * 3 = 83 83 + 12 * 4 = 131 131 + 12 * 5 = 191 191 + 12 * 6 = 263 263 + 12 * 7 = 347 347 + 12 * 8 = 443 443 + 12 * 9 = 551 551 + 12 * 10 = 671 answer : e
Answer: e
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 31.5 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 31.5 kg zinc , mixture , melted = [ 20 / 9 x 31.5 ] kg = 70 kg . answer d"
Answer: d
Problem: a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 16 , b ) 14 , c ) 15 , d ) 18 , e ) 20
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years = > ( x + 20 ) + 2 = 2 ( x + 2 ) = > x + 22 = 2 x + 4 so , x = 18 . answer : d"
Answer: d
Problem: a person buys an article at rs . 400 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 600 , b ) 277 , c ) 560 , d ) 261 , e ) 281
Rationale: "cost price = rs . 400 profit = 40 % of 400 = rs . 160 selling price = cost price + profit = 400 + 160 = 560 answer : c"
Answer: c
Problem: an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq m ?
Options: a ) rs . 3642.40 , b ) rs . 3868.80 , c ) rs . 4216.20 , d ) rs . 4082.40 , e ) none of these
Rationale: "length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 * 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer : d"
Answer: d
Problem: jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jill and sandy will make a basket but jack will miss ?
Options: a ) 3 / 168 , b ) 5 / 168 , c ) 7 / 168 , d ) 5 / 336 , e ) 7 / 336
Rationale: the probability that jill and sandy will make a basket but jack will miss is 5 / 6 * 1 / 7 * 1 / 8 = 5 / 336 . the answer is d .
Answer: d
Problem: a man sitting in a train which is travelling at 100 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 12 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 100 ) kmph = 12 kmph . answer c"
Answer: c
Problem: a 11 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 137.50 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 11 , investment = rs . ( 100 / 8 x 11 ) = rs . 137.50 ∴ market value of rs . 100 stock = rs . 137.50 answer b"
Answer: b
Problem: the ratio of the present age of viju to that of aju is 7 : 2 . 4 years from now , the ratio of the ages of viju to aju will be 5 : 2 . what was viju age 5 years ago ? ( rbi assistant 2015 )
Options: a ) 24 , b ) 18 , c ) 12 , d ) 16 , e ) 13
Rationale: let the present age of viju be 7 x years and that of aju be 2 x years . then , 4 years from now 7 x + 4 / 2 x + 4 = 5 / 2 or 4 x = 12 or x = 3 viju present age = 7 * 3 = 21 years viju age 5 years ago = 21 - 5 = 16 years answer : d
Answer: d
Problem: yesterday it took robert 3 hours to drive from city a to city b . today it took robert 2.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 80 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 180 , c ) 150 , d ) 240 , e ) 300
Rationale: "2 d / 80 = 4.5 ( because time = 3 + 2.5 - 1 hrs ) = > d = 180 answer - b"
Answer: b
Problem: if abc = ab ^ 3 = 180 where a , b and c are positive integers , what is the value of ` c ’ ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: abc = a ( b ^ 3 ) = 180 on solving abc = a ( b ^ 3 ) we get c = b ^ 2 and for a ( b ^ 3 ) = 180 , there is only one possibility a = 180 and b = 1 so c = 1 ^ 2 = 1 answer : b
Answer: b
Problem: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 95 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 20 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 95 % water and 5 % of non - water , so now 1 pound of non - water composes 5 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.05 = 20 pounds . answer : b ."
Answer: b
Problem: a customer went to a shop and paid a total of $ 40 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?
Options: a ) $ 19.54 , b ) $ 2076 , c ) $ 21.36 , d ) $ 22.72 , e ) $ 23.58
Rationale: "the total cost was $ 40 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 40 - $ 16 - $ 1.28 = $ 22.72 the answer is d ."
Answer: d
Problem: what is the sum of all remainders obtained when the first 100 natural numbers are divided by 8 ?
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
Problem: the average of first 12 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 13 , e ) 17
Rationale: "sum of 12 even numbers = 12 * 13 = 156 average = 156 / 12 = 13 answer : d"
Answer: d
Problem: if all 6 are replaced by 9 , the algebric sum of all numbers from 1 to 100 ( both inclusive ) varies by ,
Options: a ) 980 , b ) 330 , c ) 660 , d ) 990 , e ) 300
Rationale: 6 , 16,26 , 36,46 , 56,76 , 86,96 replace by 9 then 3 * 9 = 27 60,61 , 62,63 , 64,65 , 66,67 , 68,69 then increase by 30 i . e , 30 * 10 = 300 + 3 99 - 66 = 33 - 30 it will be 330 answer : b
Answer: b
Problem: how many seconds will a 1000 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 300 , c ) 500 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 1000 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 1000 + x = ( 65 / 3 ) * 60 1000 + x = 20 * 65 = 1300 x = 1300 - 1000 = 300 meters answer : b"
Answer: b
Problem: if n = 2.0563 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0037 , e ) 0.0153
Rationale: "n * = 2.06 n * - n = 2.06 - 2.0563 0.0037 answer : d"
Answer: d
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number h of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible h : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Problem: a family pays $ 700 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,100 , b ) $ 1,300 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 700 + $ 300 = $ 1000 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 700 . the insurance will pay another $ 300 when the medical expenses are $ 1300 . the answer is b ."
Answer: b
Problem: a batsman in his 12 th innings makes a score of 60 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 38 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 60 ∴ x = 38 answer a"
Answer: a
Problem: john can complete a given task in 18 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 6 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 11 , b ) 34 / 5 , c ) 44 / 5 , d ) 54 / 5 , e ) 12
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 6 * ( 1 / 18 ) = 1 / 3 of the work . so 2 / 3 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 18 + 1 / 12 = 5 / 36 time taken to complete 2 / 3 of the work = ( 2 / 3 ) / ( 5 / 36 ) = 24 / 5 days . so total number of days taken to complete the work = 24 / 5 + 6 = 54 / 5 days . d"
Answer: d
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 7 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 328 , e ) 330
Rationale: "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 7 = 28 minutes . total time = 300 + 28 = 328 minutes . answer : d ."
Answer: d
Problem: by selling an article for $ 225 a person gains $ 75 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 225 gain = $ 75 c . p . = 225 - 75 = 150 gain % = 75 / 150 * 100 = 50 % answer is c"
Answer: c
Problem: a mixture of 150 liters of wine and water contains 15 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 17
Rationale: "number of liters of water in 150 liters of the mixture = 15 % of 150 = 15 / 100 * 150 = 22.5 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 22.5 + p ) and total volume of mixture is ( 150 + p ) . ( 22.5 + p ) = 25 / 100 * ( 150 + p ) 90 + 4 p = 150 + p p = 20 liters . answer : c"
Answer: c
Problem: it is only in the second option we find the sentence a in continuation with the opening sentence d . sentence a alone explains , why the fear has such enormous effect on the human beings .
Options: a ) 28 , b ) 99 , c ) 728 , d ) 27 , e ) 271
Rationale: answer : b
Answer: b
Problem: on a sum of money , the simple interest for 2 years is rs . 327 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 7.95 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 327 = 13 ( r ã — si ) / ( 2 ã — 100 ) = 13 ( r ã — 327 ) / ( 2 ã — 100 ) = 13 r = 7.95 % answer : option c"
Answer: c
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 120 years . can you tell me my age in years ?
Options: a ) 65 , b ) 72 , c ) 44 , d ) 73 , e ) 89
Rationale: "b i am 72 years old . let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 120 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows . m / 12 + 365 m / ( 52 x 12 ) + m = 120 or 52 m + 365 m + 624 m = 624 x 120 or m = 624 x 120 / 1041 = 72 . so , i am 72 years old ."
Answer: b
Problem: the simple form of the ratio 4 / 3 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 2 / 5 = 20 : 6 = 10 : 3 answer : b"
Answer: b
Problem: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 6 : 5 : 4 , respectively , by weight . if 60 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 4 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 4 x we are given that 60 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 6 x + 5 x + 4 x = 60 15 x = 60 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 4 ) ( 4 ) = 16 pounds of apples = ( 6 ) ( 4 ) = 24 thus we know that there are 24 - 16 = 8 more pounds of apples than grapes . answer is c ."
Answer: c
Problem: the ratio between speed of the two trains is 7 : 8 . if the 2 nd train runs 400 km in 4 hrs , what is the speed of the 1 st train ?
Options: a ) 87.9 , b ) 87.5 , c ) 87.7 , d ) 87.6 , e ) 43.3
Rationale: answer : b explanation : speed of 2 nd train = 400 / 4 = 100 kmph since the ratios are in 7 : 8 speed of first train = 7 / 8 × 100 = 87.5 kmph answer : b
Answer: b
Problem: the circulation for magazine p in 1961 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1962 - 1970 . what is the ratio of the circulation in 1961 to the total circulation during 1961 - 1970 for magazine p ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1 / 7
Rationale: "there are 9 years from 1962 - 1970 , inclusive . let ' s say the average circulation every year between 1962 - 1970 inclusive is x . so the total circulation is 9 x from 1962 - 1970 , inclusive . in 1961 , the circulation is 4 x . so total circulation for 1961 - 1970 is 4 x + 9 x = 13 x . ratio of circulation in 1961 to total circulation during 1961 - 1970 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : a"
Answer: a
Problem: in how many years rs 100 will produce the same interest at 5 % as rs . 200 produce in 2 years at 10 %
Options: a ) 8 , b ) 10 , c ) 9 , d ) 12 , e ) 11
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 200 , time 2 years and rate 10 % , it will be rs . 40 then we can get the time as time = ( 100 * 40 ) / ( 100 * 5 ) = 8 option a"
Answer: a
Problem: the profit obtained by selling an article for rs . 54 is the same as the loss obtained by selling it for rs . 40 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 47
Rationale: "s . p 1 - c . p = c . p – s . p 2 54 - c . p = c . p - 40 2 c . p = 54 + 40 ; c . p = 94 / 2 = 47 answer : e"
Answer: e
Problem: mary , peter , and lucy were picking chestnuts . mary picked twice as much chestnuts than peter . lucy picked 2 kg more than peter . together the 3 of them picked 26 kg of chestnuts . how many kilograms did mary pick ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 52 , e ) 37
Rationale: let x be the amount peter picked . then mary and lucy picked 2 x and x + 2 x , respectively . so x + 2 x + x + 2 = 26 4 x = 24 x = 6 so 2 x = 2 * 6 = 12 correct answer is a ) 12
Answer: a
Problem: a train traveling at 72 kmph crosses a platform in 35 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 340 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 35 = 700 m . so , length of platform = 700 - 360 = 340 m imo , answer a"
Answer: a
Problem: how many integers between 1 and 10 ^ 16 are such that the sum of their digits is 2 ?
Options: a ) 106 , b ) 116 , c ) 126 , d ) 136 , e ) 146
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 15 and there are 16 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 15 thus , the total number of integers is 1 + 2 + . . . + 15 + 16 = 16 * 17 / 2 = 136 the answer is d ."
Answer: d
Problem: a train of 30 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3.3 , c ) 4 , d ) 9 , e ) 2
Rationale: "d = 30 * 60 + 1500 = 3300 m t = 3300 / 60 * 18 / 5 = 198 sec = 3.3 mins answer : b"
Answer: b
Problem: in the manufacture of a certain product , 8 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.2 % , b ) 0.4 % , c ) 0.8 % , d ) 1.2 % , e ) 2.0 %
Rationale: "0.08 * 0.05 = 0.004 = 0.4 % the answer is b ."
Answer: b
Problem: a number when divided by 779 gives a remainder 47 . by dividing the same number by 19 , what would be the remainder ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "number = ( 779 x a ) + 47 , where ` ` a ' ' is the quotient = ( 19 x 41 x a ) + ( 19 x 2 ) + 9 = 19 x ( 41 a + 2 ) + 9 = 19 x ( new quotient ) + 9 \ inline \ fn _ jvn \ therefore required remainder = 9 answer : a"
Answer: a
Problem: a and b start a business , with a investing the total capital of rs . 10000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1000 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 59000 , b ) b ) 37000 , c ) c ) 48000 , d ) d ) 59000 , e ) e ) 67000
Rationale: "interest received by a from b = 10 % of half of rs . 10000 = 10 % * 5000 = 500 . amount received by a per annum for being a working partner = 1000 * 12 = rs . 12000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 500 + 12000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 500 + 12000 + p ) = 2 ( p ) p = 12500 total profit = 2 p + 12000 = 2 * 12500 + 12000 = 37000 answer : b"
Answer: b
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 15 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 10 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 15 = 85 km / hr time taken = 100 / 85 = 1 hr 10 min answer is b"
Answer: b
Problem: if z is a multiple of 8778 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the sum of the digits is 8 + 7 + 7 + 8 = 30 . thus 3 is a factor of 8778 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a ."
Answer: a
Problem: what is the least number of squares tiles required to pave the floor of a room 4 m 5 cm long and 2 m 25 cm broad ?
Options: a ) 14 , b ) 20 , c ) 40 , d ) 44 , e ) 45
Rationale: "length of largest tile = h . c . f . of 405 cm and 225 cm = 45 cm . area of each tile = ( 45 x 45 ) cm 2 . required number of tiles = 405 x 225 / ( 45 ^ 2 ) = 45 . answer : e"
Answer: e
Problem: $ 4,000 is deposited in a savings account that pays 8 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 4326.40 , b ) $ 4116.20 , c ) $ 4256.21 , d ) $ 4316.54 , e ) $ 4312.45
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 8 / 2 = 4 % now , ca = 4000 ( 1 + 4 / 100 ) ^ 2 = $ 4326.40 hence answer is a"
Answer: a
Problem: the cost price of 30 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the cost price = y the cost price of 30 articles = 30 y the selling price of x articles = 1.20 y * x 1.20 y * x = 30 y x = 30 / 1.2 = 25 the answer is d ."
Answer: d
Problem: if 32.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 550 , d ) 594 , e ) 880
Rationale: "students enrolled in biology are 32.5 % and therefore not enrolled are 67.5 % . so of 880 is 880 * . 675 = 594 answer is d 594"
Answer: d
Problem: a train which has 430 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 43 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 430 / ( ( 45 - 9 ) ( 5 / 18 ) = 430 / 36 * ( 5 / 18 ) = 430 / 10 = 43 sec answer : b"
Answer: b
Problem: a sum fetched a total simple interest of $ 4151.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8928
Rationale: "e 8928 principal = $ 100 x 4151.25 / 9 x 5 = $ 415125 / 45 = $ 8928 ."
Answer: e
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 6 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "total time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 6 = 8 gallons - - - > 2 / 8 = 25 % of the fuel used . c is the correct answer ."
Answer: c
Problem: a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?
Options: a ) 6.5 , b ) 7.5 , c ) 8.5 , d ) 9.5 , e ) 10.5
Rationale: let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 34 t 8 t = 210 - 150 t = 7.5 the answer is b .
Answer: b
Problem: what will be the compound interest on a sum of rs . 29,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 11123.77 , b ) s . 11742.91 , c ) s . 11123.20 , d ) s . 10123.28 , e ) s . 10123.21
Rationale: "amount = [ 29000 * ( 1 + 12 / 100 ) 3 ] = 29000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 40742.91 c . i . = ( 40742.91 - 29000 ) = rs . 11742.91 answer : b"
Answer: b
Problem: if jack walked 6 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.8 , c ) 6 , d ) 6.25 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 6 miles speed per hour = distance / time = 6 / ( 5 / 4 ) = 4.8 miles per hour answer b"
Answer: b
Problem: in a group of cows and hens , the number of legs are 8 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 4
Rationale: let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 8 2 x = 8 x = 4 . answer : e
Answer: e
Problem: the number of positive integer solutions for the equation x + y + z + t = 30 is
Options: a ) 3854 , b ) 3654 , c ) 3764 , d ) 3960 , e ) 4964
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 30 - 1 c 4 - 1 = 29 c 3 = 3654 answer : b"
Answer: b
Problem: reeya obtained 55 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 73 , d ) 85 , e ) 90
Rationale: "explanation : ( 55 + 67 + 76 + 82 + 85 / 5 ) = 73 option c"
Answer: c