regisss/math_qa huggingface dataset:
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 2 is how many times as great as the frequency corresponding to a reading of 8 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 2 to 3 it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 and if richter scale reading goes from 7 to 8 it will be 10 so it will from 2 to 8 i . e 3,4 , 5,6 , 7,8 = 10 * 10 * 10 * 10 * 10 * 10 = 10 ^ 6 answer is e"
Answer: e
Problem: a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 60 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 187 , b ) 279 , c ) 120 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 60 - 40 ) = 2 hours so , the two trains meet at 12 a . m . the two trains meet 2 * 60 = 120 km away from mumbai . answer : c"
Answer: c
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.30 – 6.30 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 0.3
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.30 * = 6 ( the greatest positive even integer less than or equal to 6.30 is 6 ) . hence , 6.30 – 6.30 * = 6.30 - 6 = 0.30 answer : e ."
Answer: e
Problem: the guests at a football banquet consumed a total of 406 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 162 * 2.5 ( max possible amount of food a guest could consume ) = 405 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ."
Answer: d
Problem: in a group of 600 readers who read science fiction or literacy works or both , 200 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 30 , c ) 25 , d ) 100 , e ) 110
Rationale: "consider total number of reader n ( s u l ) = 600 people who read science fiction n ( s ) = 400 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 600 = 400 + 230 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 630 - 600 n ( s â ˆ © l ) = 30 so people read both science fiction and literacy works are 30 answer : b"
Answer: b
Problem: if x : y = 3 : 5 , find the value of ( 2 x + 4 y ) : ( 3 x – y )
Options: a ) 13 : 2 , b ) 11 : 2 , c ) 13 : 3 , d ) 13 : 4 , e ) 13 : 5
Rationale: "explanation : given : x / y = 3 / 5 ( 2 x + 4 y ) / ( 3 x – y ) = ( 2 * 3 + 4 * 5 ) : ( 3 * 3 – 5 ) = 26 : 4 = 13 : 2 answer : a"
Answer: a
Problem: if daily wages of a man is double to that of a woman , how many men should work for 20 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 2 / 40 ã — 30 wages of 1 man for 20 days = 21600 ã — 2 ã — 20 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 2 ã — 20 / 40 ã — 30 ) = 144 / ( 216 ã — 40 / 40 ã — 30 ) = 20 answer : option e"
Answer: e
Problem: persons a and b . person a picks a random no . from 1 to 1000 . then person b picks a random no . from 1 to 1000 . what is the probability of b getting no . greater then what a has picked .
Options: a ) 0.3995 , b ) 0.4995 , c ) 0.5995 , d ) 0.6995 , e ) 0.7995
Rationale: probability of a choosing 1 and b greater = ( 1 / 1000 ) * ( 999 / 1000 ) ; probability of a choosing 2 and b greater = ( 1 / 1000 ) * ( 998 / 1000 ) ; probability of a choosing 3 and b greater = ( 1 / 1000 ) * ( 997 / 1000 ) ; . . . ; probability of a choosing 998 and b greater = ( 1 / 1000 ) * ( 2 / 1000 ) ; probability of a choosing 999 and b greater = ( 1 / 1000 ) * ( 1 / 1000 ) ; total = ( 1 / 1000 ) * ( 1 / 1000 ) * ( 999 + 998 + 997 + . . . + 2 + 1 ) = ( 1 / 1000 ) * ( 1 / 1000 ) * ( 999 * 1000 / 2 ) = 0.4995 answer : b
Answer: b
Problem: cole drove from home to work at an average speed of 50 kmh . he then returned home at an average speed of 110 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66.5 , b ) 70.5 , c ) 72.5 , d ) 75.5 , e ) 82.5
Rationale: "let the distance one way be x time from home to work = x / 50 time from work to home = x / 110 total time = 2 hrs ( x / 50 ) + ( x / 110 ) = 2 solving for x , we get x = 275 / 4 time from home to work in minutes = ( 275 / 4 ) * 60 / 50 = 82.5 minutes ans = e"
Answer: e
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 59 , b ) 65 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 5 x 60 ) = 12 rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 12 x + 20 x + 15 x + 12 x ) = 59 x . for minimum number of pencils x = 1 . the person should have at least 59 pencils . a )"
Answer: a
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many g meters long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Problem: - 88 × 39 + 312 = ?
Options: a ) - 3200 , b ) 3120 , c ) - 3120 , d ) 3200 , e ) 3208
Rationale: - 88 × 39 + 312 = - 88 × ( 40 - 1 ) + 312 = - 88 × 40 + 88 + 312 = - 3520 + 88 + 312 = - 3120 answer is c
Answer: c
Problem: what will be the cost of building a fence around a square plot with area equal to 25 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 1160 , b ) 1251 , c ) 1102 , d ) 1352 , e ) 1450
Rationale: "let the side of the square plot be a ft . a 2 = 25 = > a = 5 length of the fence = perimeter of the plot = 4 a = 20 ft . cost of building the fence = 20 * 58 = rs . 1160 . answer : a"
Answer: a
Problem: a train 280 m long , running with a speed of 63 km / hr will pass a tree in
Options: a ) 15 sec . , b ) 16 sec . , c ) 18 sec . , d ) 20 sec . , e ) none
Rationale: "solution speed = ( 63 x 5 / 18 ) m / sec = 35 / 2 msec time taken = ( 280 x 2 / 35 ) m / sec = 16 sec . answer b"
Answer: b
Problem: a shop owner sells 15 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 100 % , e ) 200 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 15 m cloth ) – ( c . p . of 15 m cloth ) selling price of 5 m cloth = selling price of 15 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 5 m cloth = rs . 500 and s . p . of 5 m cloth = rs . rs . 1500 profit % = 1000 / 500 × 100 = 200 % profit of 200 % was made by the merchant . e"
Answer: e
Problem: if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 7 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 7 . all the answers are positive , so we choose k = 2 . answer = e"
Answer: e
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 348 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 899 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 348 62 % - - - - - - - - ? = > 899 answer : c"
Answer: c
Problem: what is the greatest positive integer t such that 3 ^ t is a factor of 9 ^ 10 ?
Options: a ) 5 , b ) t = 9 , c ) t = 10 , d ) t = 20 , e ) 30
Rationale: "what is the greatest positive integer t such that 3 ^ t is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Problem: in a ratio which is equal to 3 : 4 , if the antecedent is 12 , then the consequent is ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 22 , e ) 25
Rationale: "we have 3 / 4 = 12 / x 3 x = 48 x = 16 consequent = 16 answer is b"
Answer: b
Problem: what is the rate percent when the simple interest on rs . 4000 amount to rs . 640 in 2 years ?
Options: a ) 8.2 % , b ) 8 % , c ) 8.5 % , d ) 9 % , e ) 9.5 %
Rationale: "interest for 1 year = 640 / 2 = 320 interest on rs 4000 p / a = 320 interest rate = 320 / 4000 * 100 = 8 % answer : b"
Answer: b
Problem: if 2 x + y = 7 and x + 2 y = 8 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 5 / 3
Rationale: "we have two equations : 2 x + y = 7 x + 2 y = 8 notice that something nice happens when we add them . we get : 3 x + 3 y = 15 divide both sides by 3 to get : x + y = 5 so , ( x + y ) / 3 = 5 / 3 answer : e"
Answer: e
Problem: farm tax is levied on the 90 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 13.88 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 90 ) = 13.88 % the correct answer is ( d ) ."
Answer: d
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 2711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8500 = 34000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2000 salary of may is rs . 6500 salary of january = rs . 4500 . answer : c"
Answer: c
Problem: don and his wife each receive an 8 percent annual raise . if don receives a raise rs . 800 and his wife receives a raise of rs . 840 , what is the difference between their annual income after their raises ?
Options: a ) 40 , b ) 460 , c ) 500 , d ) 540 , e ) 150
Rationale: don salary 8 % = 800 ; therefore , 100 % = 10000 his wife salary 8 % = 840 ; therefore , 100 % = 10500 after raise 8 % , don salary = 10000 + 800 = 10800 and his wife salary = 10500 + 840 = 11340 difference = 11340 - 10800 = 540 answer : d
Answer: d
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what will be the compound interest on same values
Options: a ) rs . 51.75 , b ) rs 51.50 , c ) rs 51.25 , d ) rs 51 , e ) none of these
Rationale: "explanation : s . i . = p ∗ r ∗ t / 100 p = 50 ∗ 100 / 5 ∗ 2 = 500 amount = 500 ( 1 + 5100 ) 2 500 ( 21 / 20 ∗ 21 / 20 ) = 551.25 c . i . = 551.25 − 500 = 51.25 option c"
Answer: c
Problem: if x + y = 300 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 250 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 300 x - y = 200 2 x = 100 x = 50 y = 250 answer is b"
Answer: b
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 66900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 21.6 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 66900 profit ( % ) = ( 66900 - 55000 ) / 55000 * 100 = 21.6 % answer : d"
Answer: d
Problem: a can do a work in 8 days . b can do the same work in 16 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 days , b ) 16 / 3 days , c ) 3 / 4 days , d ) 9 / 12 days , e ) 5 / 7 days
Rationale: "a rate = 1 / 8 b rate = 1 / 16 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 16 ) = 3 / 16 a & b finish the work in 16 / 3 days correct option is b"
Answer: b
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 6 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 4 / 6 ) = 1 / 2 hours peter worked for 3 / 2 hours so he painted 3 / 2 * 1 / 3 = 1 / 2 of the room . the answer is a ."
Answer: a
Problem: if ( 1 – 1.25 ) n = 5 , then n =
Options: a ) − 20 , b ) − 140 , c ) − 4 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 5 simplify to get : - 0.25 n = 5 rewrite as ( - 1 / 4 ) n = 5 multiply both sides by - 4 to get : n = - 20 answer : a"
Answer: a
Problem: if in a race of 70 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 ) 14 m , d ) 10 m , e ) 15 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 = ( 70 * 5 ) / 25 = 14 m hence , a beats b by 14 m . answer c"
Answer: c
Problem: a certain social security recipient will receive an annual benefit of $ 12000 provided he has annual earnings of $ 9360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360
Rationale: for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d
Answer: d
Problem: a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.2 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 120 km , c ) 100 km , d ) 124 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.2 or , x / 40 + ( 250 - x ) / 60 = 5.2 or , ( 3 x + 500 - 2 x ) / / 120 = 5.2 or 500 + x = 624 x = 124 answer : d"
Answer: d
Problem: jane and ashley take 13 1 / 3 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an 8 day leave from work . this led to jane ' s working for 4 extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 10 days , b ) 15 days , c ) 16 days , d ) 17 days , e ) 20 days
Rationale: let us assume that the work is laying 40 bricks . jane = 3 bricks per day ashley = 1 brick per day together = 4 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 12 remaining bricks = 40 - 20 = 20 so together , they would take 20 / 4 = 5 total no . of days = 8 + 4 + 5 = 17 answer is d
Answer: d
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 82 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 32
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 82 thus m = 656 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 656 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 32 ans : e"
Answer: e
Problem: if the length of the longest chord of a certain circle is 24 , what is the radius of that certain circle ?
Options: a ) 12 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 24 = 2 * 12 so radius of the circle = 12 correct answer - a"
Answer: a
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 4 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5768 , b ) 5760 , c ) 5762 , d ) 5766 , e ) 5712
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 answer : b"
Answer: b
Problem: the class mean score on a test was 60 , and the standard deviation was 10 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 30 , b ) 31 , c ) 45 , d ) 90 , e ) 20
Rationale: 1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 70 to 50 , where 70 is within sd above the mean and 50 within 1 sd below the mean 2 sd = 10 twice = 20 from the the mean , which is 80 to 40 , where 80 is within 2 sd above the mean and 20 is within 2 sd below the mean . answer = e
Answer: e
Problem: if an object travels at eight feet per second , how many feet does it travel in one hour ?
Options: a ) 34880 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 28800
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 28800 answer : e ) 28800"
Answer: e
Problem: the ratio of buses to cars on river road is 1 to 10 . if there are 90 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 50 , b ) 40 , c ) 100 , d ) 30 , e ) 20
Rationale: "b / c = 1 / 10 c - b = 90 . . . . . . . . . > b = c - 90 ( c - 90 ) / c = 1 / 10 testing answers . clearly eliminate abde put c = 100 . . . . . . . . . > ( 100 - 90 ) / 100 = 10 / 100 = 1 / 10 answer : c"
Answer: c
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 57.5 % . what % discount did the merchant offer ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.575 p x = 1.575 / 1.75 = 0.9 which is a discount of 10 % . the answer is a ."
Answer: a
Problem: a certain roller coaster has 5 cars , and a passenger is equally likely to ride in any 1 of the 5 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 5 times , what is the probability that the passenger will ride in each of the 5 cars ?
Options: a ) 0 , b ) 24 / 625 , c ) 2 / 9 , d ) 1 / 3 , e ) 1
Rationale: "if he is to ride 5 times and since he can choose any of the 5 cars each time , total number of ways is = 5 * 5 * 5 * 5 * 5 = 3125 now the number of ways if he is to choose a different car each time is = 5 * 4 * 3 * 2 * 1 = 120 so the probability is = 120 / 3125 = 24 / 625 answer : b"
Answer: b
Problem: jane and ashley take 10 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 10.2 days , b ) 15.2 days , c ) 16.2 days , d ) 18 days , e ) 20 days
Rationale: let us assume that the work is laying 40 bricks . jane = 4 bricks per day ashley = 1 brick per day together = 5 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 16 remaining bricks = 40 - 24 = 16 so together , they would take 16 / 5 = 3.2 total no . of days = 8 + 4 + 3.2 = 15.2 answer is b
Answer: b
Problem: if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance .
Options: a ) 9 km , b ) 2 km , c ) 1 km , d ) 6 km , e ) 7 km
Rationale: "explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer : d"
Answer: d
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 10 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 28 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 10 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 stop . the integers ca n ' t be greater than 3 or we will score above 10 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 the only pair that matches is 3 ^ 2 + 1 ^ 2 = 10 . so 3 ^ 3 + 1 ^ 3 = 28 . answer a . )"
Answer: a
Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 90 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ?
Options: a ) 12 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 40 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.9 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.9 x = 1.1 x the number of students in advanced trigonometry is 0.4 x the percentage in advanced trigonometry is 0.4 x / 2.5 x = 16 % the answer is b ."
Answer: b
Problem: a certain club has 10 members , including jarry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that jarry will be either the member chose to be secretary or the member chose to be treasurer ?
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Rationale: in order to become a secretary the person can not be chosen as a president . this can be done in 9 / 10 ways . then to become a secretary this person ' s probability is 1 / 9 probability to become a secretary = ( 9 / 10 * 1 / 9 ) = 1 / 10 similar concept for treasurer . probability of not president = 9 / 10 , probability of not secretary = 8 / 9 , probability of treasurer 1 / 8 probability to become a treasurer = ( 9 / 10 * 8 / 9 * 1 / 8 ) = 1 / 10 since , the problem is saying jarry secretary or treasurer it is addition : 1 / 10 + 1 / 10 = 1 / 5 = e
Answer: e
Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is not an even ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: total number of cases = 6 * 6 = 36 favourable cases = [ ( 1,3 ) , ( 1,5 ) , ( 1,1 ) , ( 3,1 ) , ( 3,3 ) , ( 3,5 ) , ( 5,1 ) , ( 5,3 ) , ( 5,5 ) ] = 9 so probability = 9 / 36 = 1 / 4 answer is b
Answer: b
Problem: the difference between a number and its two - fifth is 510 . what is 40 % of that number ?
Options: a ) 342 , b ) 340 , c ) 344 , d ) 346 , e ) 348
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 40 % of 850 = 340 . answer : b"
Answer: b
Problem: a and b can do a piece of work in 9 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 11.25 days , b ) 19.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days
Rationale: "c = 1 / 5 – 1 / 9 = 4 / 45 = > 11.25 days answer : a"
Answer: a
Problem: if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 123 , what is the least possible value of n ?
Options: a ) 37 , b ) 123 , c ) 41 , d ) 52 , e ) 87
Rationale: 123 is 3 * 41 , so n needs to be at least 41 , so the answer is c .
Answer: c
Problem: the elevator in an 11 - story office building travels at the rate of one floor per 1 / 4 minute , which allows time for picking up and discharging passengers . at the main floor and at the top floor , the operator stops for 1 minute . how many complete trips will an operator make during a 4 - hour period ?
Options: a ) 88 , b ) 56 , c ) 42 , d ) 34 , e ) 64
Rationale: complete trip = 10 floors up and 10 floors down = 20 floors = 20 * 1 / 4 = 5 minutes plus 2 minutes = 7 minutes . 4 hour = 240 minutes . in 240 minutes operator can make 240 / 7 = 34 trips . answer : d .
Answer: d
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 30 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 4.8 miles , d ) 8 miles , e ) 6.9 miles
Rationale: "answer : e ) 6.9 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 30 / ( 5 + 30 ) = 6.9 m / hr the distance between schoolhome should be half of that . ie . 6.9 miles answer e"
Answer: e
Problem: find the product of the localvalue and absolutevalue of 7 in 20768 ?
Options: a ) 9200 , b ) 1100 , c ) 4900 , d ) 3200 , e ) 1600
Rationale: "local value of 7 = 7 x 100 = 700 place value of 7 = 7 there fore = 7 x 700 = 4900 c"
Answer: c
Problem: a certain no . when divided by 35 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b"
Answer: b
Problem: you have a flashlight that takes 2 working batteries . you have 8 batteries but only 4 of them work . what is the fewest number of pairs you need to test to guarantee you can get the flashlight on ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 4
Rationale: if you break the batteries into 3 groups : two groups of 3 and one group of 2 . by doing this you guarantee that one of the groups has 2 working batteries . both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination . so , 3 + 3 + 1 = 7 tries at most to find two working batteries .
Answer: c
Problem: a certain rectangular window is two times as long as it is wide . if its perimeter is 30 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2 , b ) 11 by 3 , c ) 10.5 by 3.5 , d ) 10 by 5 , e ) 9 by 3
Rationale: "2 x + 2 y = 30 x + y = 15 x + 2 x = 15 3 x = 15 x = 5 answer d"
Answer: d
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ?
Options: a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c"
Answer: c
Problem: in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 16 + 30 = 46 ; next , we find the total # of letters without line : 50 - 46 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 . answer : a"
Answer: a
Problem: evaluate : 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "according to order of operations , inner brackets first where 5 x 3 ã · 3 is first calculated since it has a multiplication and a division . 5 ã — 3 ã · 3 = 15 ã · 3 = 5 hence 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = 13 + sqrt ( - 4 + 5 ) = 13 + sqrt ( 1 ) = 13 + 1 = 14 correct answer c ) 14"
Answer: c
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1125 in 5 years ?
Options: a ) 2 , b ) 10 , c ) 4 , d ) 5 , e ) 6
Rationale: "375 = ( 750 * 5 * r ) / 100 r = 10 % . answer : b"
Answer: b
Problem: if two positive numbers are in the ratio 1 / 6 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 20 %
Rationale: "given ratio = 1 / 6 : 1 / 5 = 5 : 6 let first number be 5 x and the second number be 9 x . the second number is more than first number by 1 x . required percentage = x / 5 x * 100 = 20 % . answer : e"
Answer: e
Problem: given two cylindrical containers - - a and b . cylinder a has a diameter of 12 meters and a height of 10 meters . cylinder b has a radius of 2 meters and a height of 4 meters . if cylinder a is filled to capacity with water , how many cylinder b will be filled to capacity with the content of cylinder a ?
Options: a ) 23
b ) 22
c ) 21
d ) 25
e ) 24
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h cylinder a volume = 1130.97 cylinder b volume = 50.27 therefore the number of cylinders b that can be filled to capacity = 1130.97 / 50.27 = 22.5 answer is b only 22 cylinders b can be filled to capacity .
Answer: b
Problem: a 3 by 4 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 2.5 π , b ) 3 π , c ) 5 π , d ) 4 π , e ) 10 π
Rationale: "if a rectangle is inscribed in a circle , then the diagonal of the rectangle = diameter of the circle . in this case , diagonal = ( 9 + 16 ) ^ ( 1 / 2 ) = 5 hence the radius = 2.5 circumference = 2 π r = 2 π * 2.5 = 5 π correct option : c"
Answer: c
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 6000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,000
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 6000 ) solving for x , we get the shares as 16000 . ans : ( option e )"
Answer: e
Problem: a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 12 % the rate of interest obtained is
Options: a ) 13.09 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 % dividend per share = 60 × 12 × 100 = rs . 7 1 / 5 total dividend = ( 40 × 7 1 / 5 ) ie , he got a dividend of ( 40 × 7 1 / 5 ) for an investment of rs . ( 40 × 55 ) interest obtained = 40 × 7 1 / 5 × 100 / 40 × 55 = 13.09 % answer : option a"
Answer: a
Problem: what is the sum of 60 consecutive integers from - 30 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 29 , c ) - 30 , d ) 30 , e ) 60
Rationale: from - 39 to - 1 - - > 30 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 30 to + 29 sum will be - 30 for total 60 numbers . c is the answer .
Answer: c
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 18 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 5 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: answer : a 18 ° divided by 360 ° equals 0.05 , therefore the sector is equal to 5 % of the total
Answer: a
Problem: what is the remainder when 1201 × 1202 × 1203 × 1204 is divided by 6 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 3 , and 4 . the product is 1 * 2 * 3 * 4 = 24 the remainder when dividing 24 by 6 is 0 . the answer is a ."
Answer: a
Problem: find two numbers whose sum is 26 and whose product is 165 .
Options: a ) 11 and 12 , b ) 11 and 13 , c ) 11 and 15 , d ) 11 and 16 , e ) 11 and 19
Rationale: let the two numbers be a and b and use the sum and product to write two equations with two unknowns a + b = 26 and a b = 165 solve the first equation for b b = 26 - a substitute b in the equation a b = 165 by 26 - a a ( 26 - a ) = 165 write the above equation in standard form - a 2 + 26 a - 165 = 0 solve the above equation for a a = 11 and a = 15 . use b = 26 - a to find b when a = 11 , b = 15 and when a = 15 , b = 11 . the two numbers are 11 and 15 . answer c
Answer: c
Problem: a river 7 m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 54996.5 , b ) 32296.5 , c ) 34996.5 , d ) 34996.5 , e ) 31255.5
Rationale: "rate of water flow - 4 kmph - - 4000 / 60 - - 66.66 m / min depth of river - - 7 m width of river - - 75 m vol of water per min - - 66.66 * 7 * 75 - - - 34996.5 answer c"
Answer: c
Problem: what is the largest 4 digit number exactly divisible by 24 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9984
Rationale: "largest 4 digit number = 9999 9999 ÷ 24 = 416 , remainder = 15 hence largest 4 digit number exactly divisible by 24 = 9999 - 15 = 9984 answer : e"
Answer: e
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 110 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 220
Rationale: "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 110 total = 110 + 110 = 220 answer ( e )"
Answer: e
Problem: if k ^ 3 is divisible by 540 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "540 = 2 ^ 2 * 3 ^ 3 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Problem: the average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person . what could be the weight of the new person ?
Options: a ) 67 kg , b ) 77 kg , c ) 87 kg , d ) 97 kg , e ) none of these
Rationale: "explanation : let the average weight of 8 persons be ‘ x ’ years and the age of the new person be ‘ y ’ years so , ( 8 x – 65 + y ) / 8 = x + 1.5 so , y = 77 kgs 65 + 8 x 1.5 = 77 kgs answer b"
Answer: b
Problem: what is the remainder when ( 71 ) ( 73 ) is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ."
Answer: e
Problem: if the product of 8 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "the product of 8 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 7 correct option : e"
Answer: e
Problem: shopkeeper rise price by 35 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 5.275 % , b ) 4.275 % , c ) 3.275 % , d ) 6.275 % , e ) 7.275 %
Rationale: "let d initial price be 100 35 % rise now price = 135 / 100 * 100 = 135 10 % discount then price = 135 * 90 / 100 = 121.5 15 % discount then price = 121.5 * 85 / 100 = 103.275 so gain = 103.275 - 100 = 3.275 gain % = gain * 100 / cp = = > 3.275 * 100 / 100 = 3.275 % answer : c"
Answer: c
Problem: in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
Rationale: "required ratio = 500 : 500 = 1 : 1 answer a"
Answer: a
Problem: a briefcase has a number - lock system containing a combination of 3 digits ( each digit can be of numbers 0 to 8 ) . if the correct combination is unknown , how much maximum time would be required to open the bag if each “ trial ” of combination takes 3 seconds ?
Options: a ) 36.45 minutes , b ) 36.47 minutes , c ) 36.41 minutes , d ) 36.42 minutes , e ) 36.65 minutes
Rationale: explanation : maximum number of trials required = 9 * 9 * 9 = 729 . since for each combination trial , 3 seconds are required to open the briefcase is given as 3 * 729 = 2187 seconds = 36.45 minutes . answer : a
Answer: a
Problem: a driver just filled the car ' s gas tank with 27 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4
Rationale: let x be the number of liters of ethanol added to the gas tank . 0.05 ( 27 ) + x = 0.1 ( 27 + x ) 0.9 x = 2.7 - 1.35 = 1.35 x = 1.5 liters the answer is b .
Answer: b
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 18 years investment will become $ 8,000 * 2 = $ 16,000 and in another 18 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ."
Answer: c
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 460 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 40 / 23
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 460 km time taken by freddy = 4 hours average speed of freddy = 460 / 4 = 115 km / hour ratio of average speed of eddy to freddy = 200 / 115 = 40 / 23 answer e"
Answer: e
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 42 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24
Rationale: "12 * 42 = 504 504 % 21 = 24 answer : e"
Answer: e
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 7,4 ) , and ( 7,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 4 / 9 , e ) 7 / 10
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 28 . p ( x + y < 4 ) = 8 / 28 = 2 / 7 the answer is c ."
Answer: c
Problem: the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 750 , b ) 650 , c ) 625 , d ) 115 , e ) 400
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 160 ) = rs . 625 . answer : b"
Answer: b
Problem: one - third of 1206 is what percent of 200 ?
Options: a ) 3 , b ) 201 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 200 . ∵ 1206 / 3 = ( n x 200 ) / 100 ∴ n = ( 402 x 100 ) / 200 = 201 correct option : b"
Answer: b
Problem: machine p and machine q are each used to manufacture 660 sprockets . it takes machine p 10 hours longer to produce 660 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 6
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 660 / x = 660 / 1.1 x + 10 1.1 ( 660 ) = 660 + 11 x 11 x = 66 x = 6 the answer is e ."
Answer: e
Problem: a train 280 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 200 m long ?
Options: a ) 32 sec , b ) 42 sec , c ) 45 sec , d ) 18 sec , e ) 49 sec
Rationale: "total length = 280 + 200 = 480 speed = 54 km / h = ( 54 * 5 ) / 18 = 15 / 1 m / s time = ( 480 * 1 ) / 15 = 32 sec . answer : a"
Answer: a
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 10,500 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 3000 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 10500 = > 7 x = 10500 = > x = 1500 total number of motorcycles = 2 x = 2 * 1500 = 3000 answer b"
Answer: b
Problem: what is the sum of the 1 st 6 prime numbers greater than 10 ?
Options: a ) 112 , b ) 111 , c ) 212 , d ) 115 , e ) 113
Rationale: required numbers are = ( 11 + 13 + 17 + 19 + 23 + 29 ) = 112 note : 1 is not a prime number answer a
Answer: a
Problem: $ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95
Rationale: "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c"
Answer: c
Problem: a , b and c can do a piece of work in 9 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ?
Options: a ) 4.12 days , b ) 4.52 days , c ) 3.52 days , d ) 2.52 days , e ) 4.92 days
Rationale: 1 / 9 + 1 / 14 + 1 / 28 = 55 / 252 = > 252 / 55 days = > 4.52 days answer : b
Answer: b
Problem: in a division sum , the divisor is 12 times the quotient and 6 times the remainder . if the remainder is 24 , what is the divident ?
Options: a ) 1738 , b ) 1752 , c ) 1846 , d ) 1648 , e ) none
Rationale: "solution : dividend = [ divisor * quotient ] + remainder - - - - > ( 1 ) . given divisor = 6 * 24 = 144 . 12 * quotient = 144 = > quotient = 144 / 12 = 12 . substitute these values in the ( 1 ) then we get 1752 as dividend . answer b"
Answer: b
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 775 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 775 . as per question we need to take 1 / 4 of 775 to be considered for top 10 movies = 193.75 approximate the value we 194 . imo option b is the correct answer . . ."
Answer: b
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean a . if 68 % of the distribution lies one standard deviation d of the mean , what percent of the distribution is less than a + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ a + d 34 % ________________________________________________ a 34 % ________________________________________________ a - d 16 % since 68 % lies one standard deviation from mean a , = > 50 % of 68 % lies on either side as it is symmetric about a . thus 16 % lie below a - d and 16 % lie above a + d now below a + d = 16 + 34 + 34 = 84 % hence d"
Answer: d