regisss/math_qa huggingface dataset:
Problem: 4 balls of different colors are to be placed in 3 different boxes such that any box contains at least 1 ball . what is the maximum number of different ways in which this can be done ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: since the balls are all of different colors , let ' s permute them and then decide how many balls we put in each box . for example , arrange in a row the balls , then decide : two balls go into the first box , next two in the second box , and the last ball goes to the third box . since in each box there must be at least one ball , we have the possibilities of ( 2 , 2,1 ) , ( 2 , 1,2 ) , ( 1 , 2,2 ) or ( 3 , 1,1 ) , ( 1 , 3,1 ) , ( 1 , 1,3 ) balls in the three boxes . for the 2 , 2,1 type arrangements , we have [ 6 ! / ( 2 ! 2 ! 1 ! ) ] * 3 = 100 possibilities . inside a box , it does n ' t matter the order of the balls . for the 3 , 1,1 type arrangements , we have [ 6 ! / ( 3 ! 1 ! 1 ! ) ] * 3 = 80 possibilities . total of 100 + 80 = 180 possibilities . answer e .
Answer: e
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 6 answer : a"
Answer: a
Problem: find the ones digit of 73 ^ 300
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 330 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer e ."
Answer: e
Problem: find the value of ( 0.75 * 0.75 * 0.75 - 0.001 ) / ( 0.75 * 0.75 - 0.075 + 0.01 )
Options: a ) 0.845 , b ) 0.849 , c ) 0.842 , d ) 0.828 , e ) 0.8419
Rationale: "0.845 answer : a"
Answer: a
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 120 m , b ) 240 m , c ) 300 m , d ) 500 m , e ) 550 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 36 = 15 = > x = 240 m . answer b"
Answer: b
Problem: the length of the bridge , which a train 140 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 255 , b ) 267 , c ) 235 , d ) 277 , e ) 211
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 140 + x ) / 30 = 25 / 2 = > 2 ( 140 + x ) = 750 = > x = 235 m . answer : c"
Answer: c
Problem: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 10 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : d .
Answer: d
Problem: the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 183.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 180 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"
Answer: b
Problem: whats the reminder when 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 is divided by 16
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 454,889 = 65,985 , 241,545 , 898,754 , 582,556 , 898,522 , 450,000 + 4,889 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 16 . 4889 / 16 gives remainder 9 . answer ( e )
Answer: e
Problem: you enter a weight loss challenge game and manage to lose 12 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 10.24 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 12 % ) * ( 100 % + 2 % ) = 0.88 * 1.02 = 10.24 % the weigh in records your weight loss at 10.24 % ! the answer is a"
Answer: a
Problem: if 20 men can build a water fountain 56 metres long in 14 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 21 m , b ) 24 m , c ) 27 m , d ) 29 m , e ) 30 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 14 : 3 : : 56 : x therefore ( 20 x 14 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 280 = 49 hence , the required length is 21 m . answer : a"
Answer: a
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4650 , r will receive
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4650 * ( 6 / 31 ) = 150 * 6 = 900 . answer : option d"
Answer: d
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 8 students is 14 years and that of the other 6 students is 16 years , the age of the 15 th student is
Options: a ) 17 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 8 + 16 * 6 ) ] = 17 years . answer : a"
Answer: a
Problem: if log 2 = 0.3010 and log 3 = 0.4771 then the value of log 4.5 is :
Options: a ) 0.6532 , b ) 0.7727 , c ) 0.3266 , d ) 0.3796 , e ) none of these
Rationale: "log 3 + log 3 = log ( 3 * 3 ) - > log 9 = 0.4771 + 0.4771 = 0.9542 now log 9 - log 2 = log ( 9 / 2 ) = log 4.5 - > log 4.5 = 0.9542 - 0.3010 = 0.6532 answer : a"
Answer: a
Problem: a committee is reviewing a total of 40 x black - and - white films and 10 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 50 / 52 , b ) 55 / 52 , c ) 60 / 52 , d ) 40 / 52 , e ) 30 / 52
Rationale: "say x = y = 10 . in this case we would have : 40 x = 400 black - and - white films ; 10 y = 100 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 100 color films , thus total of 104 films were selected . color films thus compose 100 / 104 = 50 / 52 of the selected films . answer : a"
Answer: a
Problem: a clock shows the time as 10 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 8 hours in between 10 a . m . to 6 p . m . 8 * 5 = 40 minutes . answer : e"
Answer: e
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 23,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 145 % , d ) 150 % , e ) 169 %
Rationale: "the percent increase is ( 23947 - 8902 ) / 8902 = 15045 / 8902 = 1.69 so the approximate answer is e"
Answer: e
Problem: if the cost price of 24 chocolates is equal to the selling price of 16 chocolates , the gain percent is :
Options: a ) 24 % , b ) 8 % , c ) 50 % , d ) 40 % , e ) none of these
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 16 chocolates = rs . 16 ; s . p . of 16 chocolates = rs . 24 . . ' . gain % = 8 * 100 / 16 = 50 % answer : c"
Answer: c
Problem: a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . find out the number of days for which the remaining food will last .
Options: a ) 44 , b ) 42 , c ) 40 , d ) 38 , e ) 36
Rationale: explanation : given that fort had provision of food for 150 men for 45 days hence , after 10 days , the remaining food is sufficient for 150 men for 35 days remaining men after 10 days = 150 - 25 = 125 assume that after 10 days , the remaining food is sufficient for 125 men for x days more men , less days ( indirect proportion ) ( men ) 150 : 125 : : x : 35 ⇒ 150 × 35 = 125 x ⇒ 6 × 35 = 5 x ⇒ x = 6 × 7 = 42 i . e . , the remaining food is sufficient for 125 men for 42 days answer : option b
Answer: b
Problem: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 14 and 15 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 345 , d ) 231 , e ) 121
Rationale: "clearly , the numbers are ( 23 * 14 ) and ( 23 * 15 ) . larger number = ( 23 * 15 ) = 345 . answer : c"
Answer: c
Problem: during a given week a programmer spends 1 / 4 of his time preparing flow chart , 3 / 8 of his time coding and the rest of the time in debugging the programs . if he works 48 hours during the week , how many hours did he spend debugging the program .
Options: a ) 15 hrs , b ) 16 hrs , c ) 18 hrs , d ) 19 hrs , e ) 17 hrs
Rationale: programmer takes 1 / 4 * 48 = 12 hrs a week to make flowchrt same way . . . . . 18 hrs a week for codin . . . so . . . . for debugging = 48 - ( 12 + 18 ) = 18 hrs answer : c
Answer: c
Problem: 1 / 2,16 , 4,15 , 3,56 , _ ?
Options: a ) 28 / 3 , b ) 27 / 3 , c ) 26 / 3 , d ) 25 / 3 , e ) 24 / 3
Rationale: "take alternative no . 1 / 2 , 4,3 16 / 4 = 4 15 / 5 = 3 56 / 6 = 28 / 3 hence ans is 28 / 3 answer : a"
Answer: a
Problem: there is enough provisions for 600 men in an army camp for 25 days . if there were 250 men less , how long will the provision last ?
Options: a ) 10 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 80 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 250 * d 2 d 2 = 600 * 25 / 250 = 60 days . answer : d"
Answer: d
Problem: in what time will a train 200 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 200 / 40 = 5 sec . answer : e"
Answer: e
Problem: in a group of 100 cars , 49 cars do not have air conditioning . if at least 51 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 49 , b ) 47 , c ) 48 , d ) 51 , e ) 53
Rationale: lets assume ac = 51 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 51 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 51 . . we have to assign atleast 2 tocars with ac and racing stripes . hence ac = 51 - 2 = 49 . the answer is a
Answer: a
Problem: at what rate percent on simple interest will rs . 1500 amount to rs . 2000 in 5 years ?
Options: a ) 8.33 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 500 = ( 1500 x 5 xr ) / 100 r = 8.33 % answer : option a"
Answer: a
Problem: last year a certain bond price with a face value of 5000 yielded 10 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 7692 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.08 * 5000 = 0.065 * selling price - - > selling price = 0.1 * 5000 / 0.065 - - > selling price = ~ 7692 answer : a ."
Answer: a
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people c who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , c = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.1 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 11 / 31 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.4 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 22 hours . total hours = 62 . then the fraction would be 22 / 62 = 11 / 31 . therefore answer d ."
Answer: d
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 6 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 6 ( equiped with cable tv ) i . e . 1 / 6 ( 1 / 5 ) = 1 / 30 therefore only video cassette recorder = 1 / 10 - 1 / 30 = 1 / 15 total = 1 / 5 + 1 / 15 + neither cable tv nor videocassette recorders 1 = 4 / 15 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 4 / 15 = 11 / 15 hence b ."
Answer: b
Problem: walking at 3 / 4 of her normal speed , a worker is 8 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 8 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 8 ) t / 4 = 6 t = 24 the answer is b ."
Answer: b
Problem: the total age of a and b is 14 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 14 , b ) 27 , c ) 21 , d ) 18 , e ) 11
Rationale: "( a + b ) - ( b + c ) = 14 a - c = 14 . c is younger than a by 14 years . answer : a"
Answer: a
Problem: in a party every person shakes hands with every other person . if there were a total of 171 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 171 n ( n - 1 ) / 2 = 171 â ˆ ´ n = 19 answer : option e
Answer: e
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 7 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 30 / 7 , b ) 50 / 3 , c ) 70 / 4 , d ) 80 / 5 , e ) 90 / 8
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 3 / 7 = ( r - 10 ) / r 3 r = 7 r - 70 r = 70 / 4 the answer is c ."
Answer: c
Problem: a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is
Options: a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 140 km
Rationale: explanation : let the journey be x km then , 3 x / 5 + 7 x / 20 + 6.5 = x 12 x + 7 x + 130 = 20 x x = 130 km answer : option d
Answer: d
Problem: two trains of length 100 meters and 200 meters are 450 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 450 / 45 = 10 seconds the answer is c ."
Answer: c
Problem: a train travels from new york to chicago , a distance of approximately 540 miles , at an average rate of 60 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 10 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 540 / 60 = 9 hours . therefore , the train depart from new york at 7 : 00 - 9 hours = 10 : 00 in the morning , new york time . answer : e ."
Answer: e
Problem: a train is 360 meter long is running at a speed of 52 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 24.62 seconds , b ) 34.62 seconds , c ) 44.62 seconds , d ) 54.62 seconds , e ) none of these
Rationale: "explanation : speed = 52 km / hr = 52 * ( 5 / 18 ) m / sec = 130 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 130 / 9 = 34.62 seconds answer : b"
Answer: b
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 540 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 269 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 540 y = 2 x + 2 538 = 2 x x = 269 answer : d . 269"
Answer: d
Problem: in what ratio must rice of rs . 16 per kg be mixed with rice of rs . 24 per kg so that cost of mixture is rs . 18 per kg ?
Options: a ) 4 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 4 : 3 , e ) 4 : 5
Rationale: "( 18 - 24 ) / ( 16 - 18 ) = 6 / 2 = 3 : 1 answer : c"
Answer: c
Problem: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) 47 , b ) 45.6 , c ) 44 , d ) 48 , e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 19 * 45 = 1140 average marks of whole class = 1140 / 25 = 45.6 answer : option b"
Answer: b
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 3 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 228 , b ) 350 , c ) 27 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 3 / 100 ) = 15000 - 450 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 450 + 800 = rs . 350 as this is positive , an overall profit of rs . 350 was made . answer : b"
Answer: b
Problem: from a total of 5 boys and 3 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 30 , d ) 120 , e ) 240
Rationale: "answer = c = 30 no of 4 person committees that can be formed = 5 c 2 * 3 c 2 = 30 answer c"
Answer: c
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a woman alone can do it in 6 days and a boy alone in 18 days , how long will a man take to complete the work ?
Options: a ) 5 days , b ) 8 days , c ) 7 days , d ) 9 days , e ) 8 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 wo man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 man alone can finish the work in 9 days . answer : option d"
Answer: d
Problem: a cyclist covers a distance of 750 m in 2 min 30 sec . what is the speed in km / hr of the cyclist ?
Options: a ) 9 km / hr , b ) 7 km / hr , c ) 12 km / hr , d ) 15 km / hr , e ) 18 km / hr
Rationale: "speed = { 750 } m / sec = 5 m / sec = { 5 * 18 } km / hr = 18 km / hr ans : e"
Answer: e
Problem: a train running at the speed of 70 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 227 m , b ) 150 m , c ) 167 m , d ) 175 m , e ) 187 m
Rationale: "speed = 70 * 5 / 18 = 175 / 9 m / sec length of the train = speed * time = 175 / 9 * 9 = 175 m answer : d"
Answer: d
Problem: on my sister ' s birthday , she was 126 cm in height , having grown 5 % since the year before . how tall was she the previous year ?
Options: a ) 124 cm , b ) 120 cm , c ) 116 cm , d ) 112 cm , e ) 110 cm
Rationale: let the previous year ' s height be x . 1.05 x = 126 x = 120 the answer is b .
Answer: b
Problem: what is the probability of drawing a ` ` queen ' ' from a deck of 52 cards ?
Options: a ) 2 / 7 , b ) 1 / 13 , c ) 3 / 5 , d ) 2 / 8 , e ) 1 / 7
Rationale: "explanation : total number of cards , n ( s ) = 52 total number of ` ` queen ' ' cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 answer : b"
Answer: b
Problem: how many multiples of 2 are there between 1 and 58 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "28 multiples of 2 between 1 and 58 exclusive . from 2 * 1 upto 2 * 28 , ( 1,2 , 3,4 , . . . , 28 ) . hence , 28 multiples ! correct option is e"
Answer: e
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 50 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 38500 , e ) $ 48600
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 50 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 50 - - > x = 27 * 50 and 3 x = 3 * ( 27 * 50 ) = 27 * 150 . therefore , the total revenue from ticket sales that day was 27 * 50 * 6 + 27 * 150 * 10 = $ 48,600 . answer : e ."
Answer: e
Problem: sum of 3 numbers 264 , if the first number be twice then second and third number be one third of the first , then the second number is
Options: a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74
Rationale: explanation : let the second number is x , then first is 2 x , and third is 1 / 3 ( 2 x ) = > 2 x + x + 2 x / 3 = 264 < = > 11 x / 3 = 264 = > x = 72 answer : option c
Answer: c
Problem: if n = ( 33 ) ^ 43 + ( 53 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 33 ) ^ 53 is the same as that of 3 ^ 53 and the units digit of ( 53 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 53 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 53 is the same as the units digit of 3 ^ 3 , so 7 ( 53 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 53 + ( 53 ) ^ 33 is 7 + 7 = 4 . answer : c ."
Answer: c
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 200 questions and secures 240 marks , the number of questions he attempts incorrectly , is :
Options: a ) 135 , b ) 200 , c ) 140 , d ) 112 , e ) 48
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 200 â € “ x ) . 4 x â € “ ( 200 â € “ x ) = 240 or 5 x = 440 or x = 88 . number of incorrect answers = 200 - 88 = 112 answer : d"
Answer: d
Problem: a train moves with a speed of 216 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) 60
Rationale: solution speed = 216 kmph = ( 216 x 5 / 18 ) m / sec = 60 m / sec . answer e
Answer: e
Problem: find the least number must be subtracted from 105829 so that remaining no . is divisible by 21 ?
Options: a ) 7 , b ) 10 , c ) 20 , d ) 32 , e ) 35
Rationale: "on dividing 105829 by 21 we get the remainder 10 , so 10 should be subtracted answer is b"
Answer: b
Problem: a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . what will be a ' s share in the total profit of rs . 27000 earned at the end of 2 years from the starting of the business ?
Options: a ) rs . 7500 , b ) rs . 9000 , c ) rs . 9500 , d ) rs . 10,800 , e ) none
Rationale: solution a : b : c = ( 20000 × 24 ) : ( 15000 × 24 ) : ( 20000 × 18 ) = 4 : 3 : 3 a ' s share = rs . ( 27000 × 4 / 10 ) = rs . 10800 . answer d
Answer: d
Problem: the average age of 50 students in a class is 14 years . if the age of teacher is also included , the average becomes 15 years , find the age of the teacher .
Options: a ) 30 , b ) 65 , c ) 60 , d ) 55 , e ) 56
Rationale: "explanation : if teacher ' s age is 14 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 15 . age of teacher = average age of all + total increase in age = 15 + ( 1 x 50 ) = 65 years answer : b"
Answer: b
Problem: the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 60 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 400 , d ) $ 720 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 240 substituting the value of p from the first equation onto the second we get p = 240 . plugging in the value of p in the first equation , we get c = 720 . which leads us to answer choice d"
Answer: d
Problem: twice the larger of two numbers is 3 more than 5 times the smaller , and the sum of 4 times the larger and 3 times the smaller is 71 . what are the numbers ?
Options: a ) 21 , 12 , b ) 9 , 0 , c ) 15 , 6 , d ) 10 , 1 , e ) 14 , 5
Rationale: the larger number : x the smaller number : y twice the larger : 2 x three more than five times the smaller : 5 y + 3 relationship between ( ` ` is ' ' ) : 2 x = 5 y + 3 four times the larger : 4 x three times the smaller : 3 y relationship between ( ` ` sum of ' ' ) : 4 x + 3 y = 71 now i have two equations in two variables : 2 x = 5 y + 3 4 x + 3 y = 71 i will solve , say , the first equation for x : x = ( 5 / 2 ) y + ( 3 / 2 ) then i ' ll plug the right - hand side of this into the second equation in place of the ` ` x ' ' : 4 [ ( 5 / 2 ) y + ( 3 / 2 ) ] + 3 y = 71 10 y + 6 + 3 y = 71 13 y + 6 = 71 13 y = 65 y = 65 / 13 = 5 now that i have the value for y , i can solve for x : x = ( 5 / 2 ) y + ( 3 / 2 ) x = ( 5 / 2 ) ( 5 ) + ( 3 / 2 ) x = ( 25 / 2 ) + ( 3 / 2 ) x = 28 / 2 = 14 answer : e
Answer: e
Problem: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer w that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Problem: 800 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 10 , b ) 8 , c ) 16 , d ) 11 , e ) 15
Rationale: "800 * 20 = 1200 * x x = 16 . answer : c"
Answer: c
Problem: the list price of an article is rs . 70 . a customer pays rs . 59.22 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 6 %
Rationale: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.22 x = 6 %"
Answer: e
Problem: a train crosses a platform of 200 m in 15 sec , same train crosses another platform of length 300 m in 20 sec . then find the length of the train ?
Options: a ) 100 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 152 m
Rationale: "length of the train be ‘ x ’ x + 200 / 15 = x + 300 / 20 4 x + 800 = 3 x + 900 x = 100 m answer : a"
Answer: a
Problem: one man can do a piece of work in 10 days . one boys join him & he complete the work in 6 days . if he gets 50 rs for his work then what will be the share of the boy .
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: 1 day work of man = 1 / 10 , if boy ' s 1 day work = 1 / x , then ( 1 / 10 ) + ( 1 / x ) = 1 / 6 , x = 15 ratio of work of man & boy = 1 / 10 : 1 / 15 = 3 : 2 so out of 50 rs . boy ' s share = 2 * 50 / ( 3 + 2 ) = 20 answer : b
Answer: b
Problem: evaluate : 10111 - 10 * 2 * 5 = ?
Options: a ) 10101 , b ) 10110 , c ) 11100 , d ) 11001 , e ) 11011
Rationale: according to order of operations , 10 ? 2 ? 5 ( division and multiplication ) is done first from left to right 10 / 2 = 5 * 2 = 10 hence 10111 - 10 * 2 * 5 = 10111 - 10 = 10101 correct answer a
Answer: a
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 35 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 35 % 0.4 x + ( m - x ) 0.25 = 0.35 m 0.15 x = 0.10 m x = 0.6666 m x = 66.66 % of m e"
Answer: e
Problem: a rectangular garden is to be twice as long as it is wide . if 150 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 150 so , 2 ( l + b ) = 150 or , l + b = 75 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 80 l = 80 ; b = 40 l + b = 120 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( b )
Answer: b
Problem: a jar of 364 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "364 = 26 * 14 = 28 * 13 there are 26 people in the group today . the answer is d ."
Answer: d
Problem: 80 370 860 ? 2440 3530
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 1550
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : e"
Answer: e
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 15,000 and the marginal cost is $ 200 , and the total cost is $ 25,000 , what is the value of n ?
Options: a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 25,000 = $ 15,000 + n * $ 200 - - > n = 50 . answer : b ."
Answer: b
Problem: peter invested a certain sum of money in a simple interest bond whose value grew to $ 300 at the end of 3 years and to $ 400 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 12 % , b ) 12.5 % , c ) 6.67 % , d ) 6.25 % , e ) 8.33 %
Rationale: "now after a time of 3 years the principal p amounts to $ 300 and after a time of 8 years ( question says after another 5 years so 3 + 5 ) p becomes $ 400 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 300 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 8 r / 100 ) = 400 dividing a 2 by a 1 we get ( 1 + 8 r / 100 ) / ( 1 + 3 r / 100 ) = 4 / 3 after cross multiplication we are left with 12 r = 100 which gives r = 8.33 % answer : e"
Answer: e
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 5 years ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 78 , e ) 2
Rationale: "150 = ( 750 * 5 * r ) / 100 r = 4 % . answer : c"
Answer: c
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 24 kmph ?
Options: a ) 21.21 , b ) 22.26 , c ) 90.9 , d ) 24.86 , e ) 25.25
Rationale: "distance covered in 1 min = ( 24 * 1000 ) / 60 = 400 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 400 / 4.4 = 90.90 answer : c"
Answer: c
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 5000 * 6 * 2 ) / 100 ] - [ ( 5000 * 4 * 2 ) / 100 ] 600 - 400 = 200 gain in 1 year = ( 200 / 2 ) = 100 rs answer : a"
Answer: a
Problem: how many liters of water must be added to 18 liters of milk and water containing 10 % water to make it 70 % water ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "by rule of alligation : 70 % - 10 % = 60 % 100 % - 70 % = 30 % quantity of pure water : quantity of the mixture = 6 : 3 there are 18 liters of mixture , so we need to add 36 liters of pure water . the answer is c ."
Answer: c
Problem: if 1 / 5 th of a number decreased by 5 is 5 , then the number is
Options: a ) 25 , b ) 50 , c ) 60 , d ) 75 , e ) none
Rationale: explanation : let the number be a , then a / 5 − 5 = 5 ⇒ a / 5 = 10 ⇒ a = 50 correct option : b
Answer: b
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 240 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envlpes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 240 envelopes they will take 240 / 60 mins . i . e . , 4 mins . answer : e"
Answer: e
Problem: if ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 , then the difference between the two possible values of x is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: ( x + 3 ) ^ 2 / ( 2 x + 15 ) = 3 ( x + 3 ) ^ 2 = 3 ( 2 x + 15 ) x ^ 2 + 6 x + 9 = 6 x + 45 x ^ 2 - 36 = 0 ( x - 6 ) ( x + 6 ) = 0 x = 6 or x = - 6 the answer is c .
Answer: c
Problem: a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % 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 b ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "yes there is a simple method : consider the following method brand a : 40 % millet and 60 % sunflower brand b : 65 % millet and 35 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 40 % millet , which is 10 % less 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 b i . e . b : ( a + b ) = 2 : 5 = ( 2 / 5 ) * 100 = 40 % here is a pictorial representation : brand a = 40 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 below average , a times - - - - - - - - - - - - - - - - - total below = - 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 b / total = 2 : 5 = 40 % answer : a"
Answer: a
Problem: what is the measure of the angle y made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"
Answer: c
Problem: a placed 3 sheets with two carbons to get two extra copies of the original . then he decided to get more carbon copies and folded the paper in such a way that the upper half of the sheets were on top of the lower half . then he typed . how many carbon copies did he get ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : since the number of carbons is 2 , only two copies can be obtained . answer : b
Answer: b
Problem: the sum of four consecutive even numbers is 84 . what would be the largest number ?
Options: a ) 33 , b ) 88 , c ) 24 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 84 = > x = 11 smallest number is : 2 ( x + 1 ) = 24 . answer : c"
Answer: c
Problem: the average age of applicants for a new job is 30 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 30 - 8 = 22 maximum age = average + 1 standard deviation = 30 + 8 = 38 maximum number of different ages of the applicants = 38 - 22 + 1 = 17 answer c"
Answer: c
Problem: hcf and lcm two numbers are 16 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 176 , e ) 364
Rationale: "16 * 396 = 36 * x x = 176 answer : d"
Answer: d
Problem: a 10000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 60
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 5,000 by that net inflow to get the minutes ) - 60 min . answer e ."
Answer: e
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 3 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 16.25 % , b ) 8.25 % , c ) 4.25 % , d ) 6.25 % , e ) 7.25 %
Rationale: "25 / 4 = 6.25 answer : d"
Answer: d
Problem: in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 60 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 4 / 5 , b ) 5 / 7 , c ) 13 / 15 , d ) 37 / 45 , e ) 79 / 90
Rationale: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.4 * 1200 = 480 the number of males older than 70 years old is 900 - 480 = 420 the number of people who are either male or younger than 70 is 1800 + 420 = 2220 . p ( a person is younger than 70 or male ) = 2220 / 2700 = 37 / 45 the answer is d ."
Answer: d
Problem: . 04 × ? = . 000016 .
Options: a ) 0.0004 , b ) 0.04 , c ) 4 , d ) 0.4 , e ) none of these
Rationale: "solution let . 04 × x = . 000016 . then , x = . 000016 / . 04 = . 0016 / 4 = . 0004 . answer a"
Answer: a
Problem: the cost of 8 dozen pencil and 2 dozen note book is 520 rupee . if cost of 3 pencil and 4 note book is 60 rupee , then sum of the cost of 1 pencil and 1 note book will be ( in rupee )
Options: a ) rs 13.51 , b ) rs 15.51 , c ) rs 16.51 , d ) rs 14.51 , e ) rs 17.51
Rationale: let cost of pencil = rs x cost of notebook = rs y cost of 8 dozen pencils are 96 x cost of 2 dozen pencils are 24 y cost of 3 pencils are 3 x cost of 4 notebooks are 4 y equations are 96 x + 24 y = 520 - - - - - 1 3 x + 4 y = 60 - - - - - 2 multiplying 6 with equation ( 2 ) and then subtracting eqn ( 1 ) - eqn ( 2 ) , we get 96 x + 24 y = 520 18 x + 24 y = 360 after solving the equations , we get x = 2.05 y = 13.46 cost of 1 pencil and 1 notebook is 2.05 + 13.46 = rs 15.51 answer : b
Answer: b
Problem: 8 years ago , p was half of q ' s age . if the ratio of their present ages is 3 : 4 what will be the total of their present ages ?
Options: a ) 33 , b ) 67 , c ) 28 , d ) 31 , e ) 35
Rationale: let present age of p and q be 3 x 3 x and 4 x 4 x respectively . eight years ago , p was half of q ' s age â ‡ ’ ( 3 x â ˆ ’ 8 ) = 1 / 2 ( 4 x â ˆ ’ 8 ) â ‡ ’ 6 x â ˆ ’ 16 = 4 x â ˆ ’ 8 â ‡ ’ 2 x = 8 â ‡ ’ x = 4 total of their present ages = 3 x + 4 x = 7 x = 7 ã — 4 = 28 c
Answer: c
Problem: selling an kite for rs . 30 , a shop keeper gains 15 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 3.5 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 20 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 115 * 30 = rs . 26.08 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.92 / 26.08 * 100 = 3.5 % . answer : a"
Answer: a
Problem: john makes $ 40 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 100 %
Rationale: increase = ( 40 / 40 ) * 100 = ( 1 ) * 100 = 100 % . e
Answer: e
Problem: a part of certain sum of money is invested at 16 % per annum and the rest at 20 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 4 : 1 , e ) 5 : 4
Rationale: "20 : 16 = 5 : 4 answer : e"
Answer: e
Problem: the average of 6 no . ' s is 4.60 . the average of 2 of them is 3.4 , while the average of the other 2 is 3.8 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 6.6 , c ) 3.6 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 4.6 * 6 ) - [ ( 3.4 * 2 ) + ( 3.8 * 2 ) ] = 27.60 - ( 6.8 + 7.6 ) = 27.60 - 14.40 = 13.20 . required average = ( 13.2 / 2 ) = 6.6 . answer : b"
Answer: b
Problem: at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 1.25 to bowl 2 games . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 19 , e ) 21
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 1.25 = 9.84 ( 2 ) = 19.68 < 21 . ~ 19 games answer : d ."
Answer: d
Problem: if the product of the integers from 1 to n is divisible by 378 , what is the least possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "378 = 2 x 3 x 3 x 3 x 7 n must include at least 3 , 2 * 3 , and 3 * 3 . the answer is c ."
Answer: c
Problem: what is the value of ( 3 ) ^ - 4 ?
Options: a ) 1 / 4 , b ) 1 / 81 , c ) 1 / 65 , d ) 1 / 9 , e ) 1 / 3
Rationale: "3 ^ - 4 = 1 / ( 3 ) ^ 4 = 1 / 81 answer : b"
Answer: b
Problem: what least number must be subtracted from 13294 so that the remainder is exactly divisible by 97 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "sol . on dividing 13924 by 97 , we get remainder = 5 . ∴ required number to be subtracted = 5 . answer b"
Answer: b
Problem: the price of an item is discounted 5 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 15 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 76.5 % , e ) 78 %
Rationale: "let initial price be 1000 price in day 1 after 5 % discount = 950 price in day 2 after 10 % discount = 855 price in day 3 after 15 % discount = 726.75 so , price in day 3 as percentage of the sale price on day 1 will be = 726.75 / 950 * 100 = > 76.5 % answer will definitely be ( d )"
Answer: d
Problem: amar takes as much time in running 18 meters as a car takes in covering 12 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 6200 m , b ) 2400 m , c ) 300 m , d ) 4300 m , e ) 1200 m
Rationale: "b 2400 m distance covered by amar = 18 / 1.2 ( 1.6 km ) = 3 / 8 ( 1600 ) = 2400 m answer is b"
Answer: b