regisss/math_qa huggingface dataset:
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 20 percent . what percent of the stock ’ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.2 = 108 thus ratio = 108 / 100 = 1.08 ( in % terms = 108 % ) . thus e is the correct answer ."
Answer: e
Problem: a 8 % stock yields 20 % . the market value of the stock is :
Options: a ) rs 48 , b ) rs 45 , c ) rs 40 , d ) rs 50 , e ) rs 55
Rationale: "explanation : for an income of rs . 20 , investment = rs . 100 . for an income of rs 8 , investment = rs . 100 / 20 x 8 = rs 40 market value of rs . 100 stock = rs 40 answer is c"
Answer: c
Problem: the difference between a number and its two fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 50 , c ) 85 , d ) 204 , e ) none
Rationale: "solution let the number be x . then , x - 2 / 5 x = 510 . ‹ = › 3 / 5 x = 510 ‹ = › x = [ 510 x 5 / 3 ] = 850 . therefore 10 % of 850 = 85 . answer c"
Answer: c
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 65 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
Options: a ) 68 % , b ) 70 % , c ) 72 % , d ) 74 % , e ) 77 %
Rationale: "70 % of the class scored 65 % and 30 % of the class scored 95 % . the difference between 65 % and 95 % is 30 % . the average will be 65 % + 0.3 ( 30 % ) = 74 % . the answer is d ."
Answer: d
Problem: the maximum number of student amoung them 1020 pens and 860 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1020 and 860 = 20 . answer a"
Answer: a
Problem: count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5 ?
Options: a ) two , b ) five , c ) six , d ) four , e ) one
Rationale: answer = a ) two numbers between 10 - 99 giving remainder 3 when divided by 9 = 12 , 21 , 30 , 39 , 48 , 57 , 66 , 75 , 84 , 93 the numbers giving remainder 2 when divided by 5 = 12 , 57 = 2
Answer: a
Problem: there were totally 100 men . 80 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 80 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 20 - 25 - 15 - 30 = 100 - 90 = 10 answer : a"
Answer: a
Problem: a boy wanted to calculate his speed on his bike . his starting point was 350 meters from the turning point . he made the round trip 5 times in 30 minutes . what was the boy ' s speed in kilometers per hour ?
Options: a ) 1.75 , b ) 1 , c ) 2.25 , d ) 2.4 , e ) 3.2
Rationale: the distance between the the starting point and the turning point was 350 meters . the boy made the round trip 5 times so that was 10 times he traveled 350 meters . 10 * 350 = 3500 meters or 3.5 km . 30 minutes is half of an hour . divide the 3500 meters in half to put in the right time interval 3500 / 2 = 1750 meters or 1.75 km correct answer is a
Answer: a
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 280 , b ) 370 , c ) 460 , d ) 550 , e ) 640
Rationale: "let x be the minimum number of questionnaires to be mailed . 0.6 x = 222 x = 370 the answer is b ."
Answer: b
Problem: to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . how many parts the company made ?
Options: a ) 675 , b ) 778 , c ) 654 , d ) 412 , e ) 589
Rationale: "let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . correct answer is a ) 675"
Answer: a
Problem: what annual installment will discharge a debt of rs . 1092 due in 3 years at 12 % simple interest ?
Options: a ) 442 , b ) 441 , c ) 440 , d ) 320 , e ) 532
Rationale: "let the installment be rs . x if he keeps the total amount for 3 years , he have to pay the interest of rs . ( 1092 * 12 * 3 ) / 100 . but he paid rs . x after 1 year . so he need not to pay interest for rs . x for remaining 2 years . i . e he need not to pay rs . ( x * 12 * 2 ) / 100 . and he paid another rs . x after 2 years . so he need not to pay interest for for remaining 1 years . i . e . rs . ( x * 12 * 1 ) / 100 . so the total interest he has to pay is rs . ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] . so , the total amount he has to pay is rs . 1092 + rs . ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] . the total amount he paid = 3 x . ( because he paid rs . x for three times ) 1092 + ( ( 1092 * 12 * 3 ) / 100 ) - [ ( ( x * 12 * 2 ) / 100 ) + ( ( x * 12 * 1 ) / 100 ) ] = 3 x by solving , we will get x = 442 . answer : a"
Answer: a
Problem: how many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ninet pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 9 * 10 = 90 hence e .
Answer: e
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 10 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 30 m east
Rationale: "the net distance is 20 + 10 = 30 meters to the east . the answer is e ."
Answer: e
Problem: income and expenditure of a person are in the ratio 3 : 2 . if the income of the person is rs . 21000 , then find his savings ?
Options: a ) 6000 , b ) 7000 , c ) 8000 , d ) 9000 , e ) 10000
Rationale: let the income and the expenditure of the person be rs . 3 x and rs . 2 x respectively . income , 3 x = 21000 = > x = 7000 savings = income - expenditure = 3 x - 2 x = x so , savings = rs . 7000 . answer : b
Answer: b
Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 3 ! = 144 . answer : option a"
Answer: a
Problem: the ratio of the radius of two circles is 4 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 16 : 9 , e ) 1 : 2
Rationale: "r 1 : r 2 = 4 : 3 π r 12 : π r 22 r 12 : r 22 = 16 : 9 answer : d"
Answer: d
Problem: in a function , every person shakes hand with every other person . if there was a total of 28 handshakes in the function , how many persons were present in the function ?
Options: a ) 8 , b ) 7 , c ) 2 , d ) 6 , e ) 5
Rationale: suppose there are nn persons present in a function and every person shakes hand with every other person . then , total number of handshakes = nc 2 = n ( n − 1 ) / 2 n ( n − 1 ) = 28 × 2 n ( n − 1 ) = 56 n = 8 answer a 8
Answer: a
Problem: 3 * 16 + 3 * 17 + 3 * 20 + 11 = ?
Options: a ) 121 , b ) 129 , c ) 138 , d ) 152 , e ) 170
Rationale: "3 * 16 + 3 * 17 + 3 * 20 + 11 = 48 + 51 + 60 + 11 = 170 the answer is e ."
Answer: e
Problem: if x = - 2 and y = - 4 , what is the value of 5 ( x - y ) ^ 2 - xy ?
Options: a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 22
Rationale: "x = - 2 and y = - 4 x - y = - 2 - ( - 4 ) = - 2 + 4 = 2 x * y = - 2 * - 4 = 8 now we apply it in the equation 5 ( x - y ) ^ 2 - xy = 5 ( 2 ) ^ 2 - 8 = = > 5 * 4 - 8 = 20 - 8 = 12 answer : a"
Answer: a
Problem: on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 4 and 6 , what number is halfway between x and y ?
Options: a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5
Rationale: "x = - 2 and y = 1 . the answer is b ."
Answer: b
Problem: a train speeds past a pole in 15 sec and a platform 120 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 120 ) / 25 = x / 15 = > x = 180 m . answer : option e"
Answer: e
Problem: a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 276 , c ) 280 , d ) 310 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 660 x 5 + 240 x 25 ) / 30 ) = 310 answer : option d"
Answer: d
Problem: mr . riddle invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 200000 . in one year , fund x paid 43 % and fund y paid 28 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?
Options: a ) 43 , 870.34 , b ) 56 , 876.45 , c ) 77 , 789.45 , d ) 78 , 450.70 , e ) 87 , 987.34
Rationale: x + y = 200000 0.28 y = 0.43 a + 300 take away decimals first : 28 y + 43 x + 20000 isolate first equation to solve for x ( your goal ) : y = 200000 - y plug in for b : 28 ( 200000 - x ) = 43 x + 30000 5 , 600000 - 28 x = 43 x + 30000 5 , 570000 = 71 x 5 , 570000 / 71 = x 5 , 570000 / 71 = x x = 78 , 450.70 = answer choice d
Answer: d
Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 114 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 438 , b ) 436 , c ) 430 , d ) 442 , e ) 444
Rationale: 312 + 232 - 114 ( since 112 is counted twice ) = 430 c is the answer
Answer: c
Problem: two boats are heading towards each other at constant speeds of 5 miles / hr and 25 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
Options: a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 5
Rationale: "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 25 = 30 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 30 * 1 / 60 = 1 / 2 miles apart . answer : d ."
Answer: d
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ?
Options: a ) 17 , b ) 83 , c ) 12 , d ) 83 , e ) 28
Rationale: "explanation : t = 13 / 45 * 60 = 17 answer : option a"
Answer: a
Problem: a and b together can do a piece of work in 8 days . if a alone can do the same work in 12 days , then b alone can do the same work in ?
Options: a ) 49 , b ) 99 , c ) 24 , d ) 88 , e ) 21
Rationale: b = 1 / 8 – 1 / 2 = 1 / 24 = > 24 days answer : c
Answer: c
Problem: company z has 48 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 48 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e ."
Answer: e
Problem: in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 312.12 $
Rationale: "mini van cost = 65 * 0.6 + 2.05 truck capacity = 65 ( 1 + 120 / 100 ) = 143 lts . cost of truck = 143 + 0.6 + 2.05 total cost = 3 * 41.05 ( car ) + 2 * 87.85 ( truck ) = 298.85 answer : d"
Answer: d
Problem: a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is :
Options: a ) 32 , b ) 24 , c ) 12 , d ) 7 , e ) 45
Rationale: "answer : option b let the ten ' s and unit ' s digit be x and 8 / x respectively . then , ( 10 x + 8 / x ) + 18 = 10 * 8 / x + x 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 so , ten ' s digit = 2 and unit ' s digit = 4 . hence , required number = 24 ."
Answer: b
Problem: by selling 95 pens , a trader gains the cost of 19 pens . find his gain percentage ?
Options: a ) 20 % , b ) 21 % , c ) 22 % , d ) 23 % , e ) 24 %
Rationale: "let the cp of each pen be rs . 1 . cp of 95 pens = rs . 95 profit = cost of 19 pens = rs . 19 profit % = 19 / 95 * 100 = 20 % answer : a"
Answer: a
Problem: there are 193 items that are members of set u . of these items , 41 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 116 , b ) 85 , c ) 94 , d ) 98 , e ) 108
Rationale: "you had the answer almost right . the x = 93 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 93 + set ab = 93 + 23 = 116 a"
Answer: a
Problem: a machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes . if the tank is already half full and both the taps are opened together , then the tank is filled in how many minutes ?
Options: a ) 25 min , b ) 20 min , c ) 10 min , d ) 15 min , e ) 30 min
Rationale: t = 1 / 2 ( 25 * 50 / 50 - 25 ) = 25 minutes tank is filled in 25 minutes answer is a
Answer: a
Problem: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 8 dm by 5 dm . the number of stones required is :
Options: a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1350
Rationale: "area of the hall = 3600 * 1500 area of each stone = ( 80 * 50 ) therefore , number of stones = ( 3600 * 1500 / 80 * 50 ) = 1350 answer : e"
Answer: e
Problem: at company x , senior sales representatives visit the home office once every 16 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: each 48 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c .
Answer: c
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors q ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have q = 2 * 3 * 5 * 7 = 840 thus , answer b ."
Answer: b
Problem: the two lines y = x and x = - 9 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 32.5 , b ) 36.5 , c ) 40.5 , d ) 44.5 , e ) 48.5
Rationale: the point of intersection is ( - 9 , - 9 ) . the triangle has a base of length 9 and a height of 9 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 9 * 9 = 40.5 the answer is c .
Answer: c
Problem: at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 50 ¢ ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 4 oranges . the answer is d ."
Answer: d
Problem: a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 7 , b ) 3 / 11 , c ) 4 / 15 , d ) 5 / 21 , e ) 6 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 5 c 4 * 5 c 2 = 5 * 10 = 50 p ( selling 4 bottles of apple juice ) = 50 / 210 = 5 / 21 the answer is d ."
Answer: d
Problem: a student got 71 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 63 % , b ) 75 % , c ) 77 % , d ) 79 % , e ) 81 %
Rationale: "71 + 81 + x = 3 * 75 x = 73 the answer is a ."
Answer: a
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 9 ) both lie on the line defined by the equation x = ( y / 3 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 3 ) - ( 2 / 5 ) , and so y = 3 x + 6 / 5 . the slope is 3 . ( n + 9 - n ) / ( m + p - m ) = 3 p = 3 the answer is c ."
Answer: c
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 5 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 2 , e ) 1
Rationale: "red : blue = 5 : 5 let red = 5 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 5 x = 5 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 5 x / 3 + 10 x / 3 ) / ( 5 x + 5 x ) = ( 15 x / 30 x ) = 1 / 2 answer : d"
Answer: d
Problem: what is the remainder when 42 * 49 is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 42 * 49 ) / 8 } } = remainder of ( 42 / 8 ) * remainder of ( 49 / 8 ) = 2 * 1 = 2 answer : b"
Answer: b
Problem: 1 + 2 + 3 + . . . + 12 = ?
Options: a ) 76 , b ) 68 , c ) 78 , d ) 66 , e ) 67
Rationale: 1 + 2 + 3 + ⋯ + n = ∑ n = n ( n + 1 ) / 2 1 + 2 + 3 + ⋯ + 12 = n ( n + 1 ) / 2 = ( 12 ( 12 + 1 ) ) / 2 = ( 12 × 13 ) / 2 = 6 × 13 = 78 answer is c
Answer: c
Problem: the largest 4 digit number exactly divisible by 77 is ?
Options: a ) 9935 , b ) 9933 , c ) 9944 , d ) 9954 , e ) 9960
Rationale: "largest 4 - digit number = 9999 77 ) 9999 ( 129 9933 answer : b"
Answer: b
Problem: a room of 6 m 44 cm long and 3 m 00 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 12076 , b ) 12070 , c ) 12077 , d ) 12075 , e ) 12074
Rationale: "explanation : area of the room = 644 * 300 sq cm size of largest square tile = h . c . f of 644 cm and 300 cm = 4 cm area of 1 tile = 4 * 4 sq cm no . of tiles required = ( 644 * 300 ) / ( 4 * 4 ) = 12075 answer : d ) 12075"
Answer: d
Problem: 7 people average age is 30 . youngest person age is 6 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 42 = 161 so average age would be 161 / 7 = 24 answer : b"
Answer: b
Problem: if 4 men can reap 40 acres of land in 15 days , how many acres of land can 16 men reap in 30 days ?
Options: a ) 320 , b ) 240 , c ) 369 , d ) 489 , e ) 125
Rationale: "4 men 40 acres 15 days 16 men ? 30 days 40 * 16 / 4 * 30 / 15 40 * 4 * 2 40 * 8 = 320 answer : a"
Answer: a
Problem: in the excel manufacturing company , 46 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 90 % , b ) 87.5 % , c ) 66.7 % , d ) 50 % , e ) 36 %
Rationale: lets say there are total 100 employees then men = 46 & women = 54 unionized emp = 60 & non unionized emp = 40 men unionized = . 7 * 60 = 42 women unionized = 18 women non - unionized = 54 - 18 = 36 percentage of women non unionized = 36 / 40 * 100 = 90 % the answer is option a
Answer: a
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 4 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 32.5 %
Rationale: "fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 6120 ) * 100 = > 32.5 % hence answer will be ( e )"
Answer: e
Problem: a man was asked to state his age in years . his reply was , ` ` take my age 6 years hence , multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 72 , d ) 26 , e ) 19
Rationale: explanation : let the present age of person be x years . then , 6 ( x + 6 ) - 6 ( x - 6 ) = x < = > ( 6 x + 36 ) - ( 6 x - 36 ) = x < = > x = 72 . . answer : c
Answer: c
Problem: if the average ( arithmetic mean ) of x and y is 40 , and z – x = 60 , what is the average of y and z ?
Options: a ) 20 , b ) 50 , c ) 65 , d ) 70 , e ) 140
Rationale: "x + y / 2 = 40 = > x + y = 80 x = z - 60 . . . sub this value z - 60 + y = 80 = > z + y = 140 = > z + y / 2 = 70 . answer : d"
Answer: d
Problem: find the simple interest on rs . 235 for 3 months at 8 paisa per month ?
Options: a ) s . 57.8 , b ) s . 56.4 , c ) s . 29.3 , d ) s . 33 , e ) s . 74
Rationale: "explanation : i = ( 235 * 3 * 8 ) / 100 = 56.4 answer : option b"
Answer: b
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1800 . the difference between the profit shares of a and c is ?
Options: a ) 720 , b ) 266 , c ) 155 , d ) 600 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1800 = > 5 parts out of 15 parts is rs . 1800 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1800 ) = rs . 720 answer : a"
Answer: a
Problem: the length of a bridge in meters , which a train 120 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 255 , b ) 285 , c ) 315 , d ) 345 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 120 = 375 meters x = 255 meters the answer is a ."
Answer: a
Problem: of 70 players on a football team , 49 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: total = 70 thrower = 49 rest = 70 - 49 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 49 + 14 = 63 so c . 63 is the right answer
Answer: c
Problem: jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be 3 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21
Rationale: method - 1 probability that the number on first die is 3 = 1 / 6 probability that the number on second die is 3 = 1 / 7 probability that both dice result in odd numbers = ( 1 / 6 ) * ( 1 / 7 ) = 1 / 42 answer : option d
Answer: d
Problem: a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "add 44 + 12 = 56 now 56 divided by 12 so we get 8 as reaminder answer : b"
Answer: b
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 16 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4
Rationale: time = 8 / 4 + 8 / 8 = 3 hours the answer is c .
Answer: c
Problem: change the below lagarithm log 255 = 1 / 2 to exponential form
Options: a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 11
Rationale: solution : log 255 = 251 / 2 = 5 answer is a
Answer: a
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle ?
Options: a ) 10 cm , b ) 40 cm , c ) 20 cm , d ) 30 cm , e ) 50 cm
Rationale: "let the breadth of the given rectangle be x then length is 2 x . thus area of the given rect is \ fn _ jvn { \ color { black } 2 x ^ { 2 } } after dec 5 cm from length and inc 5 cm breadth , new lenght becomes 2 x - 5 and breadth is x + 5 . thus new area = ( 2 x - 5 ) ( x + 5 ) = \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 5 x - 25 } since new area is 75 units greater than original area thus \ fn _ jvn { \ color { black } 2 x ^ { 2 } + 75 = 2 x ^ { 2 } + 5 x - 25 } 5 x = 75 + 25 5 x = 100 therefore x = 20 hence length of the rectangle is 40 cm . answer : b"
Answer: b
Problem: by selling 16 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 9 , c ) 12 , d ) 89 , e ) 81
Rationale: "90 % - - - 16 120 % - - - ? 90 / 120 * 16 = 12 answer : c"
Answer: c
Problem: if it takes a machine 2 ⁄ 3 minute to produce one item , how many items will it produce in 1 hours ?
Options: a ) 1 ⁄ 3 , b ) 4 ⁄ 3 , c ) 90 , d ) 120 , e ) 180
Rationale: "1 item takes 2 / 3 min so it takes 60 min to produce x 2 x / 3 = 60 the x = 90 answer : c"
Answer: c
Problem: a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 17 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 65 = 17 x or x = ( 65 – 48 ) = 17 . answer a
Answer: a
Problem: an article is bought for rs . 675 and sold for rs . 1200 , find the gain percent ?
Options: a ) 87 % , b ) 88 % , c ) 78 % , d ) 75 % , e ) 73 %
Rationale: "675 - - - - 525 100 - - - - ? = > = 78 % answer : c"
Answer: c
Problem: the distance between two cities a and b is 1410 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b"
Answer: b
Problem: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4000 . they earned a profit of rs . 4230 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 2000 , b ) 2200 , c ) 2309 , d ) 2350 , e ) 3250
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 4230 = 2350 d"
Answer: d
Problem: a student got twice as many sums wrong as he got right . if he attempted 54 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 54 3 x = 54 x = 18 . answer : c"
Answer: c
Problem: the instructions state that deepthi needs 4 / 17 square yards of one type of material and 3 / 10 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 9 / 30 square yards left that she did not use . what is the total amount of square yards of material deepthi used ?
Options: a ) 1 / 12 , b ) 4 / 17 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: total bought = 4 / 17 + 3 / 10 left part 9 / 30 - - - > 3 / 10 so used part 4 / 17 + 3 / 10 - 3 / 10 = 4 / 17 answer : b
Answer: b
Problem: a certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 9,000 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 108 k x = 9,000 answer : c"
Answer: c
Problem: company p had 15 percent more employees in december than it had in january . if company p had 470 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 408 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 470 j = 470 / 1.15 j = 47,000 / 115 = 408 thus b is the correct answer ."
Answer: b
Problem: a , b and c can do a piece of work in 5 days , 10 days and 15 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 2 8 / 11 , d ) 67 , e ) 9
Rationale: "1 / 5 + 1 / 10 + 1 / 15 = 11 / 30 = > 30 / 11 = > 2 8 / 11 days answer : c"
Answer: c
Problem: two unbiased coins are tossed . find the probability of getting at most one head ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 5 , d ) 2 / 3 , e ) 1 / 4
Rationale: "s = { hh , ht , th , tt } e = event of getting at most one head e = { tt , ht , th } p ( e ) = 3 / 4 answer is b"
Answer: b
Problem: find the annual income derived by investing $ 6800 in 60 % stock at 136 .
Options: a ) 550 , b ) 3000 , c ) 250 , d ) 300 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 60 . by investing $ 6800 , income obtained = $ [ ( 60 / 136 ) * 6800 ] = $ 3000 . answer b ."
Answer: b
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum w of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . w = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616"
Answer: b
Problem: jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 81 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 81 * 3 = 243 jerry wants the average to be = 83 hence total score on 4 tests should be = 83 * 4 = 332 score required on the fourth test = 332 - 243 = 89 option b"
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ?
Options: a ) 34
b ) 59
c ) 68
d ) 88
e ) 92
Rationale: given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 390 breadth = 19.5 feet area to be fenced = 2 b + l = 2 ( 19.5 ) + 20 = 59 feet answer : b
Answer: b
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 2,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 8,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 2000 : 8000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : a"
Answer: a
Problem: what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ?
Options: a ) 2
b ) 3
c ) 5
d ) 7
e ) 11
Rationale: 1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d .
Answer: d
Problem: how many factors of 660 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 15
Rationale: when factorized , 660 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option e )
Answer: e
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 300 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: given that p is smallest integer greater than 300 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 d
Answer: d
Problem: a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . if 60 cubic centimeters of the solution were poured into an empty container , how many grams of sucrose would be in the container ?
Options: a ) 4.00
b ) 6.00
c ) 5.50
d ) 6.50
e ) 6.75
Rationale: we are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of sucrose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of sucrose would be in the container when we have 60 cubic centimeters of solution , we can set up a proportion . we can say : “ 10 grams of sucrose is to 100 cubic centimeters of solution as x grams of sucrose is to 60 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 10 / 100 = x / 60 when we cross multiply we obtain : ( 10 ) ( 60 ) = 100 x 600 = 100 x 6.00 = x there are 6.00 grams of sucrose in the solution in the container . the answer is b .
Answer: b
Problem: a crate measures 6 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 6 for the surface 8 * 12 face . volume = 216 pi answer c"
Answer: c
Problem: a man can row downstream at 20 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 12 , 6 , c ) 16 , 4 , d ) 14 , 4 , e ) none of these
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 4 . answer : option c"
Answer: c
Problem: a and b go around a circular track of length 1200 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 240 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1200 / ( 36 * 5 / 18 ) , 1200 / ( 54 * 5 / 18 ) } = lcm ( 120 , 80 ) = 240 sec . answer : a"
Answer: a
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 24 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 24 ) / 10 = ( 54 - 24 ) / 10 = 3 answer : option e"
Answer: e
Problem: tom read a book containing 560 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 19 , b ) 18 , c ) 9.12 , d ) 20 , e ) none
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 560 ( we want to find the days , sop = 560 / d ) 2 ) ( p + 16 ) ( d - 5 ) = 560 = > pd - 5 p + 16 d - 80 = 560 as the 1 ) stated u can put 1 ) into 2 ) = > 560 - 5 p + 16 d - 80 = 560 = > 16 d - 5 p = 80 put the bold one into it = > 16 d - 5 ( 560 / d ) = 80 the we get the final equation 16 d ^ 2 - 2800 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 175 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 9.12 days ans : c"
Answer: c
Problem: john bought 9.25 m of cloth for $ 407 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 44 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 407 cost per metre = 407 ÷ 9.25 the cost of the cloth per metre = $ 44 answers : d"
Answer: d
Problem: how many pieces can a square pizza be cut into by making 6 linear cuts ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "1 cut makes 2 pieces a second cut can make 4 pieces by cutting through both pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces c"
Answer: c
Problem: on the xy - plane , each point on circle c has coordinates such that x 0 and y 0 . if the center of circle c is the point ( 3 ; 9 ) , what is the maximum possible area of c ?
Options: a ) 6 , b ) 9 , c ) 24 , d ) 32 , e ) 64
Rationale: i think that theintentof this question is that the circle will have no co - ordinates that fit the following 2 forms : ( 0 , y ) or ( x , 0 ) . in real basic terms , this circle will neither touch ( nor cross ) the x - axis nor will it touch ( nor cross ) the y - axis . with a center at ( 3,8 ) , the longest possible radius would almost touch the x - axis , so the radius would be a little less than 3 . if the radius was 3 exactly , then the area would be 9 pi , which is approximately 28.26 since the circle ca n ' t touch the x - axis , the area has to be less than approximately 28.26 as it ' s written , none of the answers is clearly the correct one . c
Answer: c
Problem: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 30 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 48 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 × 0.30 = 12 gallons of grape juice . 40 × 0.70 = 28 gallons of other components . if we add 10 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we will have a total of 50 gallons of the mixture . so 24 / 50 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 24 / 50 = 48 / 100 = 48 % . the correct answer is choice ( c )"
Answer: c
Problem: in a school 10 % of the boys are same in number as 1 / 5 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 2 , d ) 3 : 7 , e ) 2 : 5
Rationale: 10 % of b = 1 / 5 g 10 b / 100 = g / 5 b = g / 2 b / g = 1 / 2 b : g = 1 : 2 answer is c
Answer: c
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ?
Options: a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 40 ) = 180 - - > x = 70 . answer : a ."
Answer: a
Problem: a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ?
Options: a ) 100
b ) 104
c ) 108
d ) 112
e ) none of these
Rationale: one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b
Answer: b
Problem: if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 208 , what is their sum ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 2 and 6 . the answer is a ."
Answer: a
Problem: if s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , how much less is the mean of the numbers in s than the median of the numbers in s ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "mean = ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 median = 4 difference = 4 - 4 = 0 option a"
Answer: a
Problem: 45 x ? = 40 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) 8
Rationale: "answer let 45 x a = ( 40 x 900 ) / 100 ∴ a = ( 40 x 9 ) / 45 = 8 correct option : e"
Answer: e
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 77 , e ) 65
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64900 profit ( % ) = ( 64900 - 55000 ) / 55000 * 100 = 18 % answer : c"
Answer: c
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 8 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 2.6 , b ) 5.6 , c ) 6.3 , d ) 8 , e ) 10
Rationale: let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 8 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2.6 m / s a
Answer: a
Problem: of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 5 / 9 , b ) 8 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 30 given 3 / 5 of the students are females = 18 then males = 2 / 5 = 12 5 / 6 of the females are on honor roll = 15 males on the honor roll = 2 / 3 = 8 ratio of m : f students on honor roll = 8 / 15 b"
Answer: b
Problem: if in a race of 90 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 18 m
Rationale: explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 90 * 5 ) / 25 = 18 m hence , a beats b by 18 m . answer e
Answer: e
Problem: the sum of all two digit numbers divisible by 9 is
Options: a ) 910 , b ) 585 , c ) 785 , d ) 685 , e ) 885
Rationale: required numbers are 18,27 . . . . . 99 this is an a . p . in which a = 18 , d = 9 and l = 99 . let the number of terms in it be n . then t = 99 so a + ( n - 1 ) d = 99 . 18 + ( n - 1 ) * 9 = 99 , 18 + 9 n - 9 = 99 9 + 9 n = 99 9 n = 99 - 9 n = 90 / 9 then n = 10 . required sum = n / 2 ( a + l ) = 10 / 2 ( 18 + 99 ) = 585 answer is b .
Answer: b
Problem: find the least number must be subtracted from 899830 so that remaining no . is divisible by 16 ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 9
Rationale: "on dividing 899830 by 16 we get the remainder 6 , so 6 should be subtracted d"
Answer: d