regisss/math_qa huggingface dataset:
Problem: how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr ?
Options: a ) 1 1 / 5 min , b ) 4 1 / 5 min , c ) 3 1 / 5 min , d ) 2 1 / 5 min , e ) none of these
Rationale: explanation : we know that , time = distance / speedspeed = 20 km / hr = 20 x 5 / 18 m / sec = 509 m / sectime = ( 400 x 9 / 50 ) = 72 sec = 1 1 / 5 min answer : a
Answer: a
Problem: the ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by 3 chemists is 1 : 4 . the amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 : 25 is
Options: a ) 5 kg , b ) 6.625 kg , c ) 6.25 kg , d ) 6.35 kg , e ) 8.8 kg
Rationale: sodium chloride in 100 kg = 1 / 5 x 100 = 20 kg ammonium in 100 kg = 4 / 5 x 100 = 80 kg now 80 is 25 parts out of ( 25 + 9 ) = 34 parts . hence 9 parts = 9 / 25 x 80 = 28.8 amount to be added = 28.8 - 20 = 8.8 kg answer : e
Answer: e
Problem: a metallic sheet is of rectangular shape with dimensions 20 m x 25 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 2 m , the volume of the box ( in m cube ) is :
Options: a ) 4120 m cube , b ) 4140 m cube , c ) 5140 m cube , d ) 1344 m cube , e ) none of these
Rationale: "explanation : l = ( 20 - 4 ) m = 16 m , [ because 2 + 2 = 4 ] b = ( 25 - 4 ) m = 21 m , h = 2 m . volume of the box = ( 16 x 21 x 4 ) m cube = 1344 m cube . option d"
Answer: d
Problem: the salary of a worker is first increased by 30 % and afterwards reduced by 30 % . what is net change in his salary ?
Options: a ) 3 % decrease , b ) 5 % decrease , c ) 9 % decrease , d ) 4 % decrease , e ) 8 % decrease
Rationale: ( 30 * 30 ) / 100 = 9 % decrease answer : c :
Answer: c
Problem: think of a number , divide it by 6 and add 5 to it . the result is 17 . what is the number thought of ?
Options: a ) 24 , b ) 72 , c ) 297 , d ) 267 , e ) 29
Rationale: "explanation : 17 - 5 = 12 12 x 6 = 72 answer : b"
Answer: b
Problem: x and y are both integers . if x / y = 57.40 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 560 , b ) 616 , c ) 450 , d ) 900 , e ) 1024
Rationale: "remainder = 0.40 - - > 40 / 100 - - > can be written as ( 40 / 4 ) / ( 100 / 4 ) = 10 / 25 so remainders can be 10 , 20 , 30 , 40 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 = 450 answer : c"
Answer: c
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12300 after a year ?
Options: a ) 3630 , b ) 3690 , c ) 2887 , d ) 9977 , e ) 2212
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12300 = 3690 . answer : b"
Answer: b
Problem: $ 406 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 208 , b ) $ 216 , c ) $ 224 , d ) $ 232 , e ) $ 240
Rationale: let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 406 x = 58 4 x = 232 the answer is d .
Answer: d
Problem: what is the dividend . divisor 18 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 130 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 167
Rationale: "d = d * q + r d = 18 * 9 + 5 d = 162 + 5 d = 167 answer e"
Answer: e
Problem: the area of the maximum size of the circle described from the 10 inch square ?
Options: a ) 75.5 sq inch
b ) 76.5 sq inch
c ) 77.5 sq inch
d ) 78.5 sq inch
e ) 79.5 sq inch
Rationale: 10 inch square means sides of sq are 10 inch then circle is within square so diameter would be 10 inch maximum and radius is 5 inch so area of the circle is = pi * r * r = 3.14 * 5 * 5 = 78.5 sq inch answer : d
Answer: d
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 17 th highest price and the 24 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "there were 16 items sold at a higher price than the radio and 23 items sold at a lower price than the radio . including the radio , there were 16 + 23 + 1 = 40 items sold . the answer is c ."
Answer: c
Problem: a 15 lt mixture contains water with 20 % of alcohol . if 5 more lts of water added to the mixture what is the percentage of alcohol ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: initially the mixture contains 20 % of 15 = 15 * ( 20 / 100 ) = 3 lts of alcohol after mixing another 5 lts of water . . . the total liquid is 20 lts . . so alcohol percentage = ( 3 / 20 ) * 100 = 15 % answer : b
Answer: b
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 35 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 4 , b ) 7 , c ) 6 , d ) 8 , e ) 6
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 35 kg joins the group , total weight of boys = 30 x + 35 so 30 x + 35 + 31 ( x + 1 ) = > x = 4 . answer : a"
Answer: a
Problem: by how much does the larger root of the equation 2 c ^ 2 + 5 c = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 c ^ 2 + 5 c = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Problem: in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 3 : 2 , if rs 157300 was their profit , how much amount did b receive .
Options: a ) rs 48000 , b ) rs 47000 , c ) rs 47400 , d ) rs 48400 , e ) none of these
Rationale: "explanation : a : b = 3 : 2 = 6 : 4 = > a : c = 2 : 1 = 6 : 3 = > a : b : c = 6 : 4 : 3 b share = ( 4 / 13 ) * 157300 = 48400 option d"
Answer: d
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 20 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 5 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 20 = 5 / 12 ans c"
Answer: c
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 10 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 260 , b ) $ 360 , c ) $ 160 , d ) $ 460 , e ) $ 560
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 10 a = 10 + b ( 1 ) = = = > c = 30 + 3 b - b = 2 b + 30 = = > 2 b - c = - 30 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 10 = 2.5 b - 10 = = > 2.5 b - c = 10 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 40 b = $ 80 a = $ 90 c = 270 - 80 = $ 190 total amount = 90 + 80 + 190 = $ 360 answer : b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 5 : 3 . if the can is filled with an additional 20 liters of milk , the can would be full and the ratio of milk and water would become 3 : 1 . find the capacity of the can ?
Options: a ) 52 , b ) 56 , c ) 60 , d ) 64 , e ) 68
Rationale: "let c be the capacity of the can . ( 5 / 8 ) * ( c - 20 ) + 20 = ( 3 / 4 ) * c 5 c - 100 + 160 = 6 c c = 60 the answer is c ."
Answer: c
Problem: when the price of a radio was reduced by 20 % , its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 66 % increase , d ) 75 % increase , e ) none of these
Rationale: let the original price be x and sale be of y units . then , the revenue collected initially = x × y now , new price = 0.8 x , new sale = 1.8 y then , new revenue collected = 1.44 xy % increase in revenue = 0.44 xy / xy × 100 = 44 % increase answer a
Answer: a
Problem: two trains of length 100 m and 200 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18 sec , b ) 15 sec , c ) 21 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 200 = 300 m . the time required = d / s = 300 / 20 = 15 sec . answer : b"
Answer: b
Problem: the greatest number that exactly divided 105 , 1001 and 2436 is :
Options: a ) 3 , b ) 7 , c ) 11 , d ) 21 , e ) 24
Rationale: solution h . c . f . of 2436 and 1001 is 7 . also , h . c . f . of 105 and 7 is 7 . ∴ h . c . f . of 105 , 1001 and 2436 is 7 . answer b
Answer: b
Problem: how many integers between 324,700 and 478,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,539
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 478,600 is 478,600 - 324,700 = 153,900 - one number per each hundred gives 153,900 / 100 = 1,539 numbers . answer : e ."
Answer: e
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 37,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 15540
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 37000 × 21 / 50 = 15540 answer is e"
Answer: e
Problem: john would make the 3 - letter codes with 26 alphabets in condition that the middle letter must be vowel and the first letter and the third letter must be different from each other and both are consonant . how many cases of the codes are there ?
Options: a ) 1,980 , b ) 2,020 , c ) 2,100 , d ) 2,200 , e ) 2,500
Rationale: no of vowels : 5 ( a , e , i , o , u ) no of consonants : 21 ( 26 - 5 ) now , the middle letter can be filled up in 5 ways . the first letter can be filled in 21 ways ( as only consonants are allowed ) as one of the consonants is used in the first letter , the third letter can be filled up in 20 ways , so that the letter must be different from each other . so total number of ways = 21 x 5 x 20 = 2100 answer : c
Answer: c
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent . overall he make a . ?
Options: a ) 277 , b ) 209 , c ) 121 , d ) 200 , e ) 128
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . answer : d"
Answer: d
Problem: alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 6000 , his gain percent is ?
Options: a ) 9.1 % , b ) 6.23 % , c ) 7 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 6000 gain = 6000 - 5500 = $ 500 gain % = 500 / 5500 * 100 = 9.1 % answer is a"
Answer: a
Problem: what is the sum of all 3 digit nos formed by { 1 , 3,5 , 7,9 } with nos not repeated
Options: a ) 33300 , b ) 34500 , c ) 38500 , d ) 39800 , e ) 45200
Rationale: "here 3 digit no . can be formed in 5 * 4 * 3 = 60 . thus we hv to find the sum of 60 nos . now 60 / 5 = 12 ; we hv 12 no ' s . starting with 1 , 12 no ' s . with 3,5 , 7,9 . . . . so 12 * 100 * ( 1 + 3 + 5 + 7 + 9 ) + 12 * 10 * ( 1 + 3 + 5 + 7 + 9 ) + 12 * 1 * ( 1 + 3 + 5 + 7 + 9 ) = 30000 + 3000 + 300 = 33300 answer : a"
Answer: a
Problem: a train 180 m long is running with a speed of 55 km / hr . in what time will it pass a man who is running at 7 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5.5 , b ) 10.45 , c ) 7 , d ) 8 , e ) 9.5
Rationale: "speed of train relative to man = 55 + 7 = 62 km / hr . = 62 * 5 / 18 = 155 / 9 m / sec . time taken to pass the men = 180 * 9 / 155 = 10.45 sec . answer : option b"
Answer: b
Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 5 , e ) none of above
Rationale: "explanation : total number of cases = 52 total face cards = 16 [ favourable cases ] so probability = 16 / 52 = 4 / 13 answer : a"
Answer: a
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 13,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4303 , d ) 2343 , e ) 3972
Rationale: let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 13000 . t = 3 years and r = 10 % p . a . c . i . = rs . 13000 x 1 + 10 3 - 1 100 = rs . 13000 x 331 1000 = 4303 . c
Answer: c
Problem: how many times digit 6 is used while writing numbers from 150 to 1000 ?
Options: a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 252 . hence c ."
Answer: c
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 396 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 396 per week 36 x = 396 x = 11 correct option : a"
Answer: a
Problem: 36 men can complete a piece of work in 18 days . in how many days will 54 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 88 , d ) 29 , e ) 12
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 54 : 36 : : 18 : x x = 12 answer : e ) 12 days"
Answer: e
Problem: ramu bought an old car for rs . 34000 . he spent rs . 12000 on repairs and sold it for rs . 65000 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 41 % , e ) 13 %
Rationale: "total cp = rs . 34000 + rs . 12000 = rs . 46000 and sp = rs . 65000 profit ( % ) = ( 65000 - 46000 ) / 46000 * 100 = 41 % answer : d"
Answer: d
Problem: john took a bus from home to market , that travels at 50 kmph . while walking back at 5 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 35 kmph . find the average speed .
Options: a ) 8.5 kmph , b ) 16.0 kmph , c ) 22.5 kmph , d ) 18.6 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 50 , by walking = x / 5 , by cycling = x / 35 hours : . average speed = total distance / total time = 5 x / x / 25 + x / 5 + x / 35 = 5 * 60 / 2.4 + 12 + 1.7 = 18.6 answer : d
Answer: d
Problem: working at a constant rate , p can finish a job in 3 hours . q , also working at a constant rate , can finish the same job in 9 hours . if they work together for 2 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "each hour they complete 1 / 3 + 1 / 9 = 4 / 9 of the job . in 2 hours , they complete 2 ( 4 / 9 ) = 8 / 9 of the job . the time for p to finish is ( 1 / 9 ) / ( 1 / 3 ) = ( 1 / 3 ) hour = 20 minutes the answer is a ."
Answer: a
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 6 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 1 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = - 1 ans : b"
Answer: b
Problem: the average age of a group of persons going for picnic is 16 years . 12 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is
Options: a ) 5 , b ) 10 , c ) 12 , d ) 40 , e ) 50
Rationale: solution let the initial number of persons be x . then 16 x + 12 x 15 = 15.5 ( x + 20 ) = 0.5 x = 6 x = 12 . answer c
Answer: c
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 54 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 54 / 9 = 6 hours , which is 3 hours more than ferry p . the answer is c ."
Answer: c
Problem: the length of a room is 5 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 21375 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 25725
Rationale: "area = 5 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 5 × 4.75 × 900 = 5 × 4275 = rs . 21375 answer is a ."
Answer: a
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 246 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 2535 , b ) rs . 2646 , c ) rs . 2546 , d ) rs . 2656 , e ) rs . 2565
Rationale: "let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 246 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 246 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 2400 . amount = rs . 2646 answer : b"
Answer: b
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1800 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4500
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1800 … ( i ) and 4 x – 2 y = 1800 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1800 - > x = 900 p 1 ’ s income = rs 5 * 900 = rs . 4500 answer : e"
Answer: e
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 24,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 100 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 278 , b ) 366 , c ) 349 , d ) 335 , e ) 295
Rationale: "$ 24500 is a fixed cost each component is $ 104 ( $ 100 to produce , $ 4 to ship ) manufacturer will be producing and selling 100 components so therefore the equation to find price would be 100 * p = 24500 + ( 100 * 100 ) + ( 100 * 4 ) p = ( 24500 + 10000 + 400 ) / 100 p = 349 answer : c"
Answer: c
Problem: a number when divided by 45 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 21
Options: a ) a ) 15 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 45 = 432 = > p = 432 * 45 = 19440 p / 31 = 19440 / 21 = 925 , remainder = 15 answer : option a"
Answer: a
Problem: a 12 by 16 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 5 π , b ) 10 π , c ) 15 π , d ) 20 π , e ) 30 π
Rationale: "the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : d"
Answer: d
Problem: the average temperature for tuesday , wednesday and thursday was 45 ° c . the average temperature for wednesday , thursday and friday was 50 ° c . if the temperature on friday be 53 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 37 ° c , d ) 42 ° c , e ) 38 c
Rationale: "explanation : t + w + t = 45 × 3 = 135 ° c w + t + f = 50 × 3 = 150 ° c also , temperature on friday = 53 ° c temperature on tuesday = 135 + 53 - 150 = 38 ° c answer : option e"
Answer: e
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 2 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 6
Rationale: let ' s say c = 3 , b = 2 , a = 2 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 6 answer e ( hopefully ) ) )
Answer: e
Problem: the sum of three consecutive numbers is 87 . the greatest among these three numbers is :
Options: a ) 22 , b ) 24 , c ) 26 , d ) 30 , e ) 44
Rationale: "sol . let the numbers be x , x + 1 and x + 2 . then , x + ( x + 1 ) + ( x + 2 ) = 87 ⇔ 3 x = 84 ⇔ x = 28 . greatest number = ( x + 2 ) = 30 . answer d"
Answer: d
Problem: in a group of 22 boys , 13 play basketball and 15 play football . 3 of the boys play neither . how many play both ?
Options: a ) 18 , b ) 20 , c ) 21 , d ) 22 , e ) 25
Rationale: 18 boys play something . if b play both , then 13 + 15 - b = 18 answer is a
Answer: a
Problem: a polygon has 44 diagonals , then the number of its sides are
Options: a ) 11
b ) 9
c ) 7
d ) 5
e ) 3
Rationale: let the number of sides be n . the number of diagonals is given by nc 2 - n therefore , nc 2 - n = 44 , n > 0 n ( n - 1 ) / 2 - n = 44 n 2 - 3 n - 88 = 0 n 2 - 11 n + 8 n - 88 = 0 n ( n - 11 ) + 8 ( n - 11 ) = 0 n = - 8 or n = 11 . answer : a
Answer: a
Problem: the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 53 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 106 % of x ) = 102 / 106 = 51 / 53 = 51 : 53 . answer : a"
Answer: a
Problem: two trains of equal length , running with the speeds of 60 and 60 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 1.0 , b ) 8.2 , c ) 7.7 , d ) 2.6 , e ) 8.3
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 60 = 120 * 5 / 18 t = 2500 / 9 * 18 / 600 = 8.3 sec . answer : e"
Answer: e
Problem: in a certain village , 200 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 1 , b ) 20 , c ) 2 , d ) 200 , e ) 2.5
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 200 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 200 * 10 = 2000 ( m * n ) water available is 2000 ( p ) it will last 1 months ( p / m * n ) answer ( a )"
Answer: a
Problem: in a factory , there are 80 % technicians and 20 % non - technicians . if the 80 % of the technicians and 20 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 68 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: "total = 100 t = 80 nt = 20 80 * ( 20 / 100 ) = 24 80 * ( 20 / 100 ) = 24 16 + 16 = 32 = > 100 - 32 = 68 % answer : b"
Answer: b
Problem: what is the units digit of ( 147 ^ 21 ) ^ 48 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 21 has the form 4 n + 1 so the units digit is 7 inside the bracket . the number 48 has the form 4 n , so the units digit is 1 . the answer is a .
Answer: a
Problem: what percentage of numbers from 1 to 70 have 1 or 9 in the unit ' s digit ?
Options: a ) 10 % , b ) 30 % , c ) 20 % , d ) 70 % , e ) 45 %
Rationale: d 20 % clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 70 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 , 61 , 69 . number of such number = 14 required percentage = ( 14 x 100 / 70 ) % = 20 % .
Answer: c
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 19 units ?
Options: a ) 2.8 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 12 units
Rationale: "sides are 8 , 15 and 19 . . . thus it is right angle triangle since 19 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 19 + 15 + 8 / 2 = 21 thus , 60 = 21 * r and hence r = in - radius = 2.8 option a"
Answer: a
Problem: 12 is what % of 80 ?
Options: a ) 6 , b ) 6.67 , c ) 12 , d ) 13 , e ) 15
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x % = 12 therefore , 100 / x = 80 / 12 100 / x = 6.6667 x = 15 e"
Answer: e
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.20 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 612 , e ) $ 2,550
Rationale: total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.20 = $ 612 answer d
Answer: d
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 40 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 297 , e ) 400
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 140 = rs . 400 answer : e"
Answer: e
Problem: find l . c . m of 852 and 1491
Options: a ) 5964 , b ) 5664 , c ) 4964 , d ) 4664 , e ) 5555
Rationale: 852 ) 1491 ( 1 852 639 ) 852 ( 1 639 213 ) 639 ( 3 639 0 h . c . f of 852 and 1491 is 213 : . l . c . m = 852 * 1491 / 213 = 5964 answer is a .
Answer: a
Problem: how many positive integers less than 300 are there such that they are multiples of 17 or multiples of 16 ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "300 / 17 = 17 ( plus remainder ) so there are 17 multiples of 17 300 / 16 = 18 ( plus remainder ) so there are 18 multiples of 16 we need to subtract 1 because 17 * 16 is a multiple of both so it was counted twice . the total is 17 + 18 - 1 = 34 the answer is d ."
Answer: d
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 9 = 5 : 3 . answer b"
Answer: b
Problem: convert 700 miles into meters ?
Options: a ) 784596 , b ) 1126538 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 700 mile = 700 * 1609.34 = 1126538 meters answer is b"
Answer: b
Problem: what is the remainder when 1274 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 0 , b ) 6 , c ) 11 , d ) 9 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 - 2 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 2 ) ( 3 ) ( - 7 ) ( 1 ) = 42 . thus the question becomes : what is the remainder upon division of 42 by 12 ? the answer to this question is 6 . answer : b"
Answer: b
Problem: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 17 inches than that of a rectangular sheet of paper measuring 8.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "area of sheet a = 11 * 17 area of sheet b = 11 * 8.5 difference in area = 11 * 8.5 required % = ( 11 * 8.5 ) * 100 / ( 11 * 8.5 ) % = 100 % answer : c"
Answer: c
Problem: when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e
Answer: e
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 35 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 611 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 35 / 100 = 329 so the cut in amount is 329 the less amount to be spend is 940 - 329 = 611 answer : c"
Answer: c
Problem: a certain article of clothing was discounted during a special sale to 2 / 3 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 22.22 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 2 / 3 * $ 200 = $ 400 / 3 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 400 / 3 - 100 ) / 150 = 1 / 3 = 22.22 % . answer : b ."
Answer: b
Problem: rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 20 were revised only once , 30 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1200 , b ) $ 1500 , c ) $ 1400 , d ) $ 1250 , e ) $ 1350
Rationale: "50 pages typed 1 x 20 pages typed 2 x ( original + one revision ) 30 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 20 ( 10 + 5 ) + 30 ( 10 + 5 + 5 ) = 500 + 300 + 600 = 1400 answer - c"
Answer: c
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 7 more than the average of 10 , 70 , and what number ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 7 = 33 sum of second list = 33 * 3 = 99 therefore the number = 99 - 80 = 19 answer : a"
Answer: a
Problem: there are 2 sections a and b in a class , consisting of 50 and 40 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 58.88 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 40 students = 50 * 50 + 40 * 70 = 2500 + 2800 average weight of the class is = 5300 / 90 = 58.88 kg answer is d"
Answer: d
Problem: dan ' s age after 20 years will be 7 times his age 4 years ago . what is the present age of dan ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let dan ' s present age be x . x + 20 = 7 ( x - 4 ) 6 x = 48 x = 8 the answer is b ."
Answer: b
Problem: a work as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 12 a + b 1 day work = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 a and b can finish the work in 4 days answer is c
Answer: c
Problem: in a group of 6 boys & 4 girls a committee of 4 persons is to be formed . in how many different ways can it be done so that the committee has at least 1 girl ?
Options: a ) 187 , b ) 190 , c ) 192 , d ) 195 , e ) 213
Rationale: the committee of 4 persons is to be so formed that it has at least 1 woman the different ways that we can choose to form such a committee are : ( i ) lw . 3 m in t 6 x 5 x 4 ' x 6 c 3 = 4 x — — 80 3 x 2 x 1 x 6 c 2 = 42 : : x 26 : : = 90 ( ii ) 2 w . 2 m in ° c 2 ( iii ) 3 w . 1 m in 4 c 3 x 6 c 1 = 4 x 6 = 24 ( iv ) 4 w in 6 c 4 = 1 total no . of different ways in which a committee of 4 persons can be formed so that it has at least one woman . = 80 + 90 + 24 + 1 = 195 d
Answer: d
Problem: three circles of radius 3.5 cm are placed in such a way that each circle touches the other two . the area of the portion enclosed by the circles is
Options: a ) 1.967
b ) 1.963
c ) 2.388
d ) 3.388
e ) 2.382
Rationale: explanation : required area = ( area of an equilateral triangle of side 7 cm ) - ( 3 * area of sector with ã = 60 degrees and r = 3.5 cm ) \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 7 \ times 7 ) - ( 3 \ times \ frac { 22 } { 7 } \ times 3.5 \ times 3.5 \ times \ frac { 60 } { 360 } ) } sq cm = \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 49 ) - ( 11 \ times 0.5 \ times 3.5 ) } sq cm = 1.967 sq cm answer : a ) 1.967
Answer: a
Problem: 2 a 33 + b 9 ____ 99 if a and b represent positive single digits in the correctly worked computation above , what is the value of a + 3 b ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: adding the digits in unit ' s place , a + 3 + 9 = 19 ( since a and b are positive single digits ) = > a = 7 now adding the digits in ten ' s place , 2 + 3 + b + 1 = 9 ( 1 has been carried over from nit ' s place addition ) = > b = 3 a + 3 b = 2 + 2 * 3 = 11 answer d
Answer: d
Problem: if ( 5 - x ) / ( 7 + x ) = x , what is the value of x ^ 2 + 8 x - 5 ?
Options: a ) - 4 , b ) - 3 , c ) - 2 , d ) - 1 , e ) 0
Rationale: "( 5 - x ) = x * ( 7 + x ) ( 5 - x ) = 7 x + x ^ 2 0 = x ^ 2 + 8 x - 5 the answer is e ."
Answer: e
Problem: what percent is 300 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 30 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 300 / 1000 ã — 100 = 30000 / 1000 = 30 % answer is c"
Answer: c
Problem: a man two flats for $ 675958 each . on one he gains 11 % while on the other he loses 11 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.21 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 11 / 10 ) ^ 2 = 23 / 19 = 1.21 % answer is a"
Answer: a
Problem: what is the ratio between perimeters of two squares one having 2 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 2 : 1 , e ) 3 : 3
Rationale: "d = 2 d d = d a √ 2 = 2 d a √ 2 = d a = 2 d / √ 2 a = d / √ 2 = > 2 : 1 answer : d"
Answer: d
Problem: richard traveled the entire 60 miles trip . if he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 32 mph , e ) 55 mph
Rationale: average speed = sum of distance / sum of time . if he travelled the first 2 miles at 24 miles / hr , it would take 0.083 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.083 + 1 ) hrs = 55 miles / 1 hr . therefore , the answer is e .
Answer: e
Problem: a man ’ s current age is ( 2 / 5 ) of the age of his father . after 8 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: a 40 let , father ’ s current age is a years . then , man ’ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 8 ] = ( 1 / 2 ) ( a + 8 ) 2 ( 2 a + 40 ) = 5 ( a + 8 ) a = 40
Answer: a
Problem: a feed store sells two varieties of birdseed : brand a , which is 60 % millet and 40 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 55 %
Rationale: yes there is a simple method : consider the following method brand a : 60 % millet and 40 % sunflower brand b : 65 % millet and 35 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 60 % millet , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total above = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 65 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , b times - - - - - - - - - - - - - - - - - total above = + 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : b
Answer: b
Problem: if the cost price of 30 articles is equal to the selling price of 45 articles , what is the % profit or loss made by the merchant ?
Options: a ) 33.33 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 30 articles = 30 * 1 = $ 30 the selling price of 45 articles = cost price of 30 articles = $ 30 . now , we know the selling price of 45 articles . let us find the cost price of 45 articles . cost price of 45 articles = 45 * 1 = $ 45 . therefore , profit made on sale of 45 articles = selling price of 45 articles - cost price of 45 articles = 30 - 45 = - $ 15 . as the profit is in the negative , the merchant has made a loss of $ 15 . therefore , % loss = loss / cp * 100 % loss = - 15 / 45 * 100 = 33.33 % loss . a"
Answer: a
Problem: the average age of 21 students of a class is 21 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 21 th student is
Options: a ) 164 , b ) 152 , c ) 100 , d ) 182 , e ) 195
Rationale: "explanation : age of the 21 th student = [ 21 * 21 - ( 14 * 5 + 16 * 9 ) ] = ( 378 - 214 ) = 164 years . answer : a"
Answer: a
Problem: the length of the bridge , which a train 180 meters long and travelling at 48 km / hr can cross in 70 seconds , is :
Options: a ) 245 , b ) 276 , c ) 987 , d ) 168 , e ) 1981
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 130 + x ) / 30 = 25 / 2 = = > 2 ( 130 + x ) = 750 = = > x = 245 m . answer : a"
Answer: a
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 40 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 10
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 40 + q = > q = 10 answer : e"
Answer: e
Problem: an error 12 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 25.44 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 12 + 12 + ( 12 ã — 12 ) / 100 ) % = 25.44 % answer : d"
Answer: d
Problem: the difference between a number and its two - fifth is 510 . what is 30 % of that number ?
Options: a ) 158 , b ) 200 , c ) 255 , d ) 400 , e ) 280
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 255 . answer : c"
Answer: c
Problem: john and jacob set out together on bicycle traveling at 18 and 15 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 18 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 3
Rationale: "john ' s speed - 18 miles / hr jacob ' s speed - 15 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 18 x 2 / 3 = 12 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 15 x 5 / 3 = 25 miles . now , when john starts riding back , the distance between them is 13 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 18 - 15 = 3 miles / hr . thus , to cover 13 miles at 3 miles / hr , john will take 13 / 3 = 4 1 / 3 hours answer e"
Answer: e
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 56 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 24 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of ( 48 / 112 ) * 56 = 24 cubic inches answer d"
Answer: d
Problem: 800 is increased by 110 % . find the final number .
Options: a ) 1200 , b ) 1210 , c ) 1180 , d ) 1190 , e ) 1680
Rationale: explanation final number = initial number + 110 % ( original number ) = 800 + 110 % ( 800 ) = 800 + 880 = 1680 . answer e
Answer: e
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 40 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 82 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 40 % more than company a ' s assets which is 140 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 70 a + b = 170 kw = 140 kw / ( a + b ) * 100 = 140 / 170 * 100 = 82.35 % or 82 % c"
Answer: c
Problem: if a : b = 2 : 3 , b : c = 4 : 5 and c : d = 5 : 9 then a : d is equal to :
Options: a ) 11 : 17 , b ) 8 : 27 , c ) 5 : 9 , d ) 2 : 9 , e ) none
Rationale: "solution : a / d = ( a / b ) * ( b * c ) * ( c / d ) = ( 2 / 3 ) * ( 4 / 5 ) * ( 5 / 9 ) = ( 2 * 4 * 5 ) / ( 3 * 5 * 9 ) = 8 / 27 . answer : option b"
Answer: b
Problem: if an integer n is to be selected at random from 1 to 105 , inclusive , what is probability n ( n + 1 ) will be divisible by 7 ?
Options: a ) 1 / 7 , b ) 3 / 14 , c ) 1 / 2 , d ) 2 / 7 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 7 , either n or n + 1 has to be a multiple of 7 . thus n must be of the form 7 k or 7 k - 1 . the probability is 2 / 7 . the answer is d ."
Answer: d
Problem: two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) 7 : 5
Rationale: "explanation : let the third number be x . first number ( 120 / 100 ) * x = 6 x / 5 second number ( 150 / 100 ) * x = 3 x / 2 ratio = 6 x / 5 : 3 x / 2 = > 4 : 5 option c"
Answer: c
Problem: the sum of the first 50 positive even integers is 2,000 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 8,050 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2000 sum of 1 st 100 odd numbers = 5050 - 2000 = 3050 so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 5000 + 3050 = 8050 c is the answer ."
Answer: c
Problem: rain is falling at a rate of 3 centimeters per hour all over springfield . somewhere downtown in springfield a group of pigeons is waiting for the rain to stop . if the rain filled a round puddle the with a base area of 350 square centimeters and a depth of 13.5 centimeters , how long did the pigeons wait for the rain to stop ?
Options: a ) 3 hours and 12 minutes .
b ) four hours and 30 minutes
c ) four hours and 45 minutes
d ) five hours and 10 minutes
e ) five hours and 30 minutes
Rationale: the volume of the puddle is irrelevant and only height matters since rain fell all over the city . thus , it takes only . 13.5 / 3 = 4.5 hours of rain to fill the puddle answer is : b , 4 hours and 30 mins
Answer: b
Problem: what is the sum of all possible solutions to | x + 3 | ^ 2 + | x + 3 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: "denote | x + 3 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x + 3 | , so it ' s an absolute value and thus can not be negative . y = | x + 3 | = 4 - - > x = 7 . the sum = 7 . answer : c ."
Answer: c