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Question: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5830 , what is the length of the plot in metres ?
A.333.
B.200.
C.288.
D.276.
e ) 220E.
"let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5830 [ 4 l - 40 ] = 5830 / 26.50 = 220 4 l = 260 l = 260 / 4 = 65 meters . answer : e" | null |
Question: there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 hours . the speed of the bus is 3 / 4 th of the speed of the train . how much distance will the car cover in 5 hours ?
A.300 km.
B.325 km.
C.375 km.
D.425 km.
e ) 450 kmC.
"the speed of the bus is 480 / 8 = 60 km / hr the speed of the train is ( 60 * 4 ) / 3 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 5 hours is 75 Γ 5 = 375 km the answer is c ." | null |
Question: if a town of 65,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
A.a . 66000.
B.b . 67000.
C.c . 68000.
D.d . 69000.
e ) e . 70000A.
1 % is quite small and hence the answer is a ) | null |
Question: two trains , a and b , started simultaneously from opposite ends of a 75 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 75 - mile trip in 3 hours ; train b , traveling at a constant rate , completed the 75 - mile trip in 2 hours . how many miles had train a traveled when it met train b ?
A.20.
B.22.5.
C.30.
D.37.5.
e ) 45C.
"as the ratio of the rates of a and b is 2 to 3 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 2 / ( 2 + 3 ) = 2 / 5 of 75 miles : 75 * 2 / 5 = 30 miles . answer : c ." | null |
Question: in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
A.9.4 %.
B.9.33 %.
C.9.6 %.
D.9.8 %.
e ) 10 %B.
"the amount of chromium in the new 15 + 30 = 45 kg alloy is 0.12 * 15 + 0.08 * 30 = 4.2 kg , so the percentage is 4.2 / 45 * 100 = 9.33 % . answer : b ." | null |
Question: what is the remainder when 135 ^ 77 is divided by 7 ?
A.0.
B.1.
C.2.
D.3.
e ) 4E.
"( 15 ^ 77 * 9 ^ 77 ) / 7 ; ( 15 ^ 77 ) / 7 * ( 9 ^ 77 ) / 7 ; 1 * 2 ^ 77 / 7 ; ( ( 2 ^ 3 ) ^ 25 * 2 ^ 2 ) / 7 ; 1 * 4 = 4 answer : e" | null |
Question: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 45 . what is the difference between the two digits of that number ?
A.4.
B.5.
C.6.
D.8.
e ) 9B.
"sol . let the ten β s digit be x and unit β s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 45 β 9 ( x - y ) = 45 β x - y = 5 answer b" | null |
Question: if 42.30 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
A.6.
B.7.
C.8.
D.9.
e ) 10C.
"42.30 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.30 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.30 = km / 50 . . . . . . 40 / 100 = 3 m / 50 . . . . . . m = 5 k + m = 3 + 5 = 8 answer : c" | null |
Question: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many j cubes are painted on only 2 faces ?
A.12.
B.8.
C.6.
D.10.
e ) 16A.
"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . j = 4 + 4 + 4 = 12 . answer a" | null |
Question: at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun ' s age will be 36 years . what is the age of deepak at present ?
A.35 years.
B.25 years.
C.42 years.
D.39 years.
e ) 40 yearsC.
"let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak ' s age = 7 x = 42 years answer is c" | null |
Question: the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 10 students is 16 years . tee age of the 15 th student is ?
A.18 years.
B.16 years.
C.14 years.
D.12 years.
e ) 10 yearsE.
"age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 10 ) ] = ( 240 - 230 ) = 10 years . answer : e" | null |
Question: excluding stoppages , the speed of a bus is 75 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
A.15.
B.24.
C.17.
D.19.
e ) none of theseB.
"due to stoppages , it covers 30 km less . time taken to cover 30 km = ( ( 30 / 75 ) Γ£ β 60 ) = 24 min . option ( b ) is correct" | null |
Question: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 130 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
A.90.
B.120.
C.160.
D.360.
e ) 520E.
if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 130 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 130 n = 520 answer = ( e ) | null |
Question: when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ?
['A.1296', 'B.1369', 'C.1681', 'D.1764', 'e ) 2500']A.
let β s call the two perfect squares x ^ 2 and y ^ 2 , respectively . then the given information translates as x ^ 2 + 148 = y ^ 2 . subtracting x ^ 2 gives 148 = y ^ 2 β x ^ 2 , a difference of squares . this , in turn , factors as ( y + x ) ( y β x ) = 148 . the next step is tricky . it begins with factoring 148 , which breaks down as 2 β 2 β 37 . since we β re dealing with perfect squares , x and y are positive integers , and ( y + x ) and ( y β x ) must be paired integer factors of 148 . the options are 148 β 1,74 β 2 , and 37 β 4 . but our number properties establish that ( y + x ) and ( y β x ) must be either both odd or both even , so only 74 β 2 is an actual possibility . and because for any positive integers ( y + x ) > ( y β x ) , we can conclude that y + x = 74 and y β x = 2 . solving by elimination , 2 y = 76 , y = 38 , and x = 36 . finally , we just need to square 36 . but rather than multiplying it out , note that 36 ^ 2 ends in 6 β as does only one answer , choice a . this answer must be the one we want . | null |
Question: train a is 13 miles ahead of train b , which is traveling the same direction along the same route as train a . if train a is traveling at an average speed of 37 miles per hour and train b is traveling at an average speed of 43 miles per hour , how long will it take train b to overtake and drive 17 miles ahead of train a ?
A.4 hours.
B.2 hours.
C.2 hours 30 minutes.
D.5 hours.
e ) 3 hours 20 minutesD.
relative speed = 43 - 37 = 6 miles per hour dist required = 13 + 17 = 30 miles time taken to overtake = 30 / 6 = 5 hours . d is the answer . | null |
Question: x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
A.1 / 20.
B.1 / 12.
C.2 / 15.
D.3 / 10.
e ) 1 / 7B.
"p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is b ." | null |
Question: on increasing the price of t . v . sets by 30 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
A.4.
B.5.
C.56.
D.2.
e ) 7A.
"explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 Γ 100 ) = rs . 10000 new sale value = rs . ( 130 Γ 80 ) = rs . 10400 increase % = 4001000040010000 Γ 100 = 4 % answer : a" | null |
Question: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
A.$ 374.
B.$ 330.
C.$ 385.
D.$ 392.
e ) $ 399B.
"( 348 / 116 ) 110 = 330 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 110 = 330 ( 300 + 30 ) answer b" | null |
Question: if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
A.$ 160.
B.$ 350.
C.$ 282.
D.$ 274.
e ) $ 286B.
"total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 14 = 16 * 14 = 224 $ total charge = 126 + 224 = 350 $ answer b" | null |
Question: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 125 mangoes .
A.360.
B.380.
C.400.
D.416.
e ) 412D.
"mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 125 mangoes = 125 * 3.33 = 416 . answer d" | null |
Question: calculate the time it will take for a full tank of water to become completely empty due to a leak given that the tank could be filled in 10 hours , but due to the leak in its bottom it takes 11 hours to be filled ?
A.90 hours.
B.80 hours.
C.50 hours.
D.120 hours.
e ) 110 hoursE.
part filled without leak in 1 hour = 1 / 10 part filled with leak in 1 hour = 1 / 11 work done by leak in 1 hour = 1 / 10 Γ’ Λ β 1 / 11 = 110 hours answer : e | null |
Question: in the first 25 overs of a cricket game , the run rate was only 5.4 . what should be the run rate in the remaining 25 overs to reach the target of 400 runs ?
A.16.5.
B.13.2.
C.10.6.
D.11.2.
e ) 7.25C.
required run rate = 400 - ( 5.4 x 25 ) / 25 = 265 / 25 = 10.6 option c | null |
Question: if one positive integer is greater than another positive integer by 3 , and the difference of their cubes is 279 , what is their sum ?
A.5.
B.7.
C.9.
D.11.
e ) 13D.
"1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 7 ^ 3 = 343 the two numbers are 4 and 7 . the answer is d ." | null |
Question: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12100 after a year ?
A.3630.
B.3877.
C.2667.
D.2977.
e ) 2378A.
"explanation : 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3630 answer : a" | null |
Question: what is the unit digit in 4 ^ 100 ?
A.0.
B.1.
C.6.
D.3.
e ) 5C.
unit digit in 4 ^ 100 = unit digit in [ ( 4 ^ 4 ) ^ 25 ] but unit digit in 4 ^ 4 = 6 unit digit 4 ^ 100 = 6 answer is c | null |
Question: the average age of 37 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
A.35 years.
B.45 years.
C.51 years.
D.52 years.
e ) none of theseD.
"explanation : age of the teacher = ( 38 * 15 - 37 * 14 ) years = 52 years . answer : d" | null |
Question: pipe a can fill a tank in 12 hours . due to a leak at the bottom , it takes 18 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
A.36.
B.87.
C.40.
D.37.
e ) 86A.
"let the leak can empty the full tank in x hours 1 / 12 - 1 / x = 1 / 18 = > 1 / x = 1 / 12 - 1 / 18 = ( 3 - 2 ) / 36 = 1 / 36 = > x = 36 . answer : a" | null |
Question: if one and a half women , drink one and a half tea in one and a half minutes . how many tea can 9 women drink in 3 minutes ?
A.11.
B.8.
C.37.
D.15.
e ) 18E.
e 18 explanation : more minutes implies more tea . more women implies more tea . the time become twice ( 3 minutes / 1.5 minutes ) . women become six times ( 9 / 1.5 ) . number of tea = 2 * 6 * original ( 1.5 ) | null |
Question: a can run 2 km distance in 2 min 20 seconds , while b can run this distance in 3 min 5 sec . . by how much distance can a beat b ?
A.900 m.
B.500 m.
C.120 m.
D.180 m.
e ) 190 mB.
a takes time 2.20 minutes = 140 sec b takes time 3 minutes = 185 sec difference = 185 - 140 = 45 sec now we are to find distance covered in 40 sec by b 180 sec = 2000 m 1 sec = 100 / 9 m 45 sec = 45 x 100 / 9 = 500 m answer : b | null |
Question: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is :
A.rs . 3900.
B.rs . 3990.
C.rs . 4000.
D.rs . 4100.
e ) rs . 4200A.
"let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a" | null |
Question: if the remainder is 15 when the integer n is divided by 28 , what is the remainder when 2 n is divided by 14 ?
A.0.
B.1.
C.2.
D.3.
e ) 4C.
"n = 28 k + 15 2 n = 2 ( 28 k + 15 ) = 4 k * 14 + 30 = 4 k * 14 + 2 * 14 + 2 = 14 j + 2 the answer is c ." | null |
Question: rice weighing 25 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
A.40.
B.50.
C.60.
D.70.
e ) 80B.
"25 / 2 Γ· 4 = 25 / 8 pounds in each container 25 / 8 pounds * 16 ounces / pound = 50 ounces in each container the answer is b ." | null |
Question: a man sold 18 toys for rs . 21000 , gaining thereby the cost price of 3 toy find the cost price of a toy
A.s . 600.
B.s . 800.
C.s . 500.
D.s . 900.
e ) s . 1000E.
"let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 21000 . gain = sp Γ’ β¬ β cp 3 x = 21000 Γ’ β¬ β 18 x 21 x = 21000 x = rs . 1000 . answer : option e" | null |
Question: in a school of 700 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
A.109.
B.119.
C.129.
D.139.
e ) 149B.
45 + 23 + 15 = 83 % 100 β 83 = 17 % 700 * 17 / 100 = 119 the answer is b . | null |
Question: two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 9 . find the probability that both of them are selected .
A.2 / 69.
B.2 / 60.
C.2 / 63.
D.2 / 29.
e ) 2 / 10C.
"explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 9 . let c be the event that both are selected . p ( c ) = p ( a ) Γ p ( b ) as a and b are independent events : = ( 1 / 7 ) Γ ( 2 / 9 ) = 2 / 63 answer : c ) 2 / 63" | null |
Question: 150 metres long yard , 11 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
A.10.
B.15.
C.14.
D.16.
e ) 17B.
"11 trees have 10 gaps between them , required distance ( 150 / 10 ) = 15 b" | null |
Question: a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 231 for it , the cost price of the cricket bat for a is :
A.150.
B.120.
C.154.
D.160.
e ) 210C.
125 % of 120 % of a = 231 125 / 100 * 120 / 100 * a = 231 a = 231 * 2 / 3 = 154 . answer c | null |
Question: the length of the bridge , which a train 150 m long and traveling at 45 km / hr can cross in 30 sec is ?
A.377.
B.225.
C.237.
D.245.
e ) 267B.
"speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 x = 225 m . answer : b" | null |
Question: a boat running up stram takes 4 hours to cover a certain distance , while it takes 8 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
A.2 : 3.
B.5 : 6.
C.4 : 5.
D.3 : 1.
e ) 8 : 1D.
"explanation : let speed of boat is x km / h and speed stream is y km / hr 4 ( x + y ) = 8 ( x - y ) 4 x + 4 y = 8 x - 8 y 12 y = 4 x 3 y = x x / y = 3 / 1 3 : 1 answer : option d" | null |
Question: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many w acres were used for corn ?
A.188.
B.258.
C.376.
D.470.
e ) 517C.
"consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn w = 4 * 94 = 376 correct option - c" | null |
Question: find the l . c . m of 22 , 25 , 44 and 20 .
A.1240.
B.1600.
C.1320.
D.1150.
e ) 1100E.
"explanation : 2 x 2 x 11 x 5 x 5 = 1100 answer : option e" | null |
Question: 3 models ( f , g , and h ) of cars are distributed among 3 showrooms . the number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom . there are 19 cars of model f , 17 cars of model g , and 15 cars of model h . what is the maximum number of cars of model f in any showroom ?
A.17.
B.16.
C.15.
D.14.
e ) 13C.
the total number of cars is 51 . so each showroom has 17 cars ( since the number of cars in each showrooms should be equal 51 / 3 = 17 ) . moreover that the number of model f is maximum means that the numbers of model g and h should be minimum . since each model must be represented by at least one car in every showroom that minimum number should be 1 . so maximum number of model f is 17 - 2 = 15 . the answer is ( c ) | null |
Question: the timing of a college is from 12 p . m to 5.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
A.56 minutes.
B.45 minutes.
C.30 minutes.
D.48 minutes.
e ) 44 minutesA.
"explanation : total time a student spends in college = 5 hours 00 minutes = 300 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 300 Γ’ β¬ β 20 ) / 5 = 56 minutes answer a" | null |
Question: if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
A.0 and 3.
B.3 and 6.
C.6 and 9.
D.9 and 12.
e ) 12 and 15B.
my attempt : if q = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 . | null |
Question: what is the units digit of 29 ! + 50 ! + 3 ! + 3 ! ?
A.0.
B.2.
C.4.
D.6.
e ) 8B.
"for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 6 = 12 the units digit is 2 . the answer is b ." | null |
Question: a train 285 m long , running with a speed of 54 km / hr will pass a tree in
A.19 sec.
B.15 sec.
C.16 sec.
D.20 sec.
e ) noneA.
"sol . speed = ( 54 x 5 / 18 ) m / sec . = 15 m / sec . time taken = ( 285 x 1 / 15 ) sec = 19 sec answer a" | null |
Question: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 7 adults have their meal , find the total number of children that can be catered with the remaining food .
A.33.
B.54.
C.81.
D.17.
e ) 01C.
"explanation : as there is meal for 70 adults and 7 have their meal , the meal left can be catered to 63 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 63 adults = 81 children hence , the meal can be catered to 81 children . answer : c" | null |
Question: if 42 / 330 = 0.1272 , what is the 32 nd digit to the right of the decimal point of the fraction ?
A.1.
B.4.
C.5.
D.7.
e ) 2E.
"we are not concerned what 42 / 330 means . . we have to look at the decimal . . 0 . . 1272 means 0.1272727 . . . so leaving first digit to the right of decimal , all odd numbered are 7 and all even numbered are 2 . here 32 is even , so ans is 2 answer is e" | null |
Question: a began business with rs . 36000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
A.1.
B.6.
C.7.
D.8.
e ) 2D.
"36 * 12 : 54 * x = 2 : 1 x = 4 12 - 4 = 8 answer : d" | null |
Question: find the value of β ( 25 / 16 ) .
A.5 / 2.
B.3 / 4.
C.2 / 3.
D.1 / 3.
e ) 5 / 4E.
"β ( 25 / 16 ) = β 25 / β 16 = 5 / 4 answer is e ." | null |
Question: how many of the positive factors of 24 are not factors of 25
A.2.
B.3.
C.4.
D.1.
e ) 5D.
"factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 25 - 1,5 , 25 comparing both , we have 1 factor of 24 which are not factors of 25 - 1 answer : d" | null |
Question: a man can do a piece of work in 4 days , but with the help of his daughter , he can do it in 3 days . in what time can his daughter do it alone ?
A.12.
B.28.
C.26.
D.19.
e ) 112A.
explanation : daughter β s 1 day β s work = ( 1 / 3 β 1 / 4 ) = 1 / 12 daughter alone can do the work in 12 / 1 = 12 days answer : a | null |
Question: john had a stock of 900 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
A.50.4 %.
B.23.8 %.
C.66.5 %.
D.34.9 %.
e ) 55.3 %E.
"let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 900 - n = 900 - 402 = 498 percentage books not sold / total number of books = 498 / 900 = 0.553 = 55.3 % correct answer e" | null |
Question: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is :
A.647.
B.738.
C.654.
D.847.
e ) 976B.
"s . i . for 1 year = rs . ( 854 - 825 ) = rs . 29 . s . i . for 3 years = rs . ( 29 x 3 ) = rs . 87 . principal = rs . ( 825 - 87 ) = rs . 738 answer : b" | null |
Question: the age of father 7 years ago was 5 times the age of his son . 5 years hence , father ' s age will be thrice that of his son . the ratio of their present ages is :
A.67 : 19.
B.65 : 17.
C.61 : 19.
D.63 : 15.
e ) 67 : 17A.
let the ages of father and son 7 years ago be 5 x and x years respectively . then , ( 5 x + 7 ) + 5 = 3 [ ( x + 7 ) + 5 ] 5 x + 12 = 3 x + 36 x = 12 . required ratio = ( 5 x + 7 ) : ( x + 7 ) = 67 : 19 . answer : option a | null |
Question: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 14 inches on a side and costs $ 10 , and a large pizza that measures 21 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
A.5 square inches.
B.10 square inches.
C.49 square inches.
D.25 square inches.
e ) 350 square inchesC.
"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 14 * 14 = 196 ) for the small pizza and ( 21 * 21 = 441 ) for the large pizza . in total sq inches that would be ( 196 + 441 ) * 2 = 1274 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 441 = 1323 sq inches . hence , the difference is 49 square inches more ( 1323 - 1274 ) . the correct answer is c" | null |
Question: if the lcm of a and b is 72 and their hcf is 6 , what is the product of a & b ?
A.432.
B.433.
C.434.
D.435.
e ) 436A.
the most important property of lcm ( the least common multiple ) and gcd ( the greatest common divisors ) is : for any positive integers x and y , x β y = gcd ( x , y ) β lcm ( x , y ) so ab = 72 * 6 = 432 . answer : a | null |
Question: in a 120 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
A.22 seconds.
B.12 seconds.
C.10 seconds.
D.8 seconds.
e ) 28 secondsD.
"b runs 56 m in 7 sec . = > b runs 120 m in 7 / 56 * 120 = 15 seconds since a beats b by 7 seconds , a runs 120 m in ( 15 - 7 ) = 8 seconds hence , a ' s time over the course = 8 seconds answer : d" | null |
Question: if x is a randomly chosen integer between 1 and 20 , inclusive , and y is a randomly chosen integer between 21 and 40 , inclusive , what is the probability that xy is a multiple of 4 ?
A.1 / 4.
B.1 / 3.
C.3 / 8.
D.7 / 16.
e ) Β½E.
there are two ways that i see of getting a multiple of 4 1 ) x and / or y is a multiple of 4 2 ) x is a multiple of 2 and y is a multiple of 2 for 1 we have p ( option 1 ) = ( 5 / 20 ) ( 20 / 20 ) + ( 5 / 20 ) ( 20 / 20 ) - ( 5 / 20 ) ( 5 / 20 ) = 1 / 2 - 1 / 16 since 5 of the numbers in each range are divisible by 4 , and if either x or y is selected to be divisible by 4 the selection of the other variable does not matter . notice the last subtraction term which corrects the fact that we have counted the possibility of both being divisible by 4 twice ( e . g . p ( a union b ) = p ( a ) + p ( b ) - p ( a and b ) ) . notice at this point that the probability of option one is already 7 / 16 , the second largest available option . if we can come up with any other possibilities for getting xy divisble by 4 we must go with option e . of course this is the case because if we select a multiple of 2 that is not a multiple of 4 from both ranges of numbers , the product is divisible by 4 . we can formally compute this as : p ( option 2 ) = ( 5 / 20 ) * ( 5 / 20 ) = 1 / 16 since we do not wish to double count possibilities that fall into category 1 , we only count the probability of selecting even numbers from each set that are not divisible by 4 ( e . g . the other 5 even integers in each set ) . total probability is then p ( option 1 ) + p ( option 2 ) = 1 / 2 | null |
Question: the average of 20 number is zero of them at the most , how many may be greater than zero ?
A.0.
B.1.
C.10.
D.19.
e ) 20D.
solution average of 20 numbers = 0 . β΄ sum of 20 numbers = ( 0 Γ 20 ) = 0 . it is quite possible that 19 of these number may be positive and if their sum is a , then 20 th number is ( - a ) . answer d | null |
Question: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1792 ?
A.1600.
B.2777.
C.2889.
D.27670.
e ) 2771A.
"1792 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1600 . answer : a" | null |
Question: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,800 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
A.38,000.
B.40,000.
C.42,500.
D.45,800.
e ) 48,500D.
"median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.8 so , answer is d ." | null |
Question: there are 200 female managers in a certain company . find the total number r of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
A.r = 300.
B.r = 400.
C.r = 500.
D.600.
e ) none of theseC.
"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ." | null |
Question: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 49 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
A.70.
B.245.
C.150.
D.35.
e ) 350E.
"since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 49 , so 0.14 * { total } = 49 - - > { total } = 350 . answer : e ." | null |
Question: how many litres of pure acid are there in 8 litres of a 20 % solution ?
A.2 litres.
B.1.4 litres.
C.1 litres.
D.1.6 litres.
e ) none of theseD.
"explanation : quantity of pure acid = 8 Γ ( 20 / 100 ) = 1.6 answer : option d" | null |
Question: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 500 m long ?
A.266 sec.
B.170 sec.
C.776 sec.
D.166 sec.
e ) 997 secB.
"l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1700 m t = d / s t = 1700 / 10 t = 170 sec answer : b" | null |
Question: what is the least number which when divided by 6 , 7 , 9 and 18 leaves remainder 4 in each care ?
A.130.
B.140.
C.136.
D.156.
e ) 166A.
"explanation : lcm of 6 , 7 , 9 and 18 is 126 required number = 126 + 4 = 130 answer : option a" | null |
Question: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 50 % profit ?
A.277.
B.960.
C.277.
D.266.
e ) 121B.
"let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 150 % of rs . 640 = 150 / 100 * 640 = rs . 960 . answer : b" | null |
Question: a room 14 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
A.22636.
B.22640.
C.22647.
D.22533.
e ) 22675D.
"explanation : area of the room = ( 1421 x 777 ) cm 2 . size of largest square tile = h . c . f . of 1421 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 1147 Γ 777 ) / ( 7 Γ 7 ) = 22533 answer : option d" | null |
Question: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 5 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
A.32 km.
B.20 km.
C.65 km.
D.18 km.
e ) 16 kmA.
"distance = relative speed * time = ( 5 + 3 ) * 4 = 32 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : a" | null |
Question: the number which exceeds 16 % of it by 105 is :
A.125.
B.52.
C.58.
D.60.
e ) 62A.
solution solution let the number be x . x - 16 % of x = 105 x - 16 / 100 x = 105 x - 4 / 25 x = 105 21 / 25 x = 105 x = ( 105 x 25 / 21 ) = 125 answer a | null |
Question: sachin is younger than rahul by 7 years . if the ratio of their ages is 6 : 9 , find the age of sachin
A.24.5.
B.14.
C.24.21.
D.27.
e ) 25B.
"explanation : if rahul age is x , then sachin age is x - 7 , so , 9 x - 63 = 6 x 3 x = 63 x = 21 so sachin age is 21 - 7 = 14 answer : b ) 14" | null |
Question: a man has some hens and cows . if the number of heads be 44 and the number of feet equals 140 , then the number of hens will be :
A.22.
B.23.
C.18.
D.26.
e ) 28C.
"let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 44 implies , 2 x + 4 y = 140 and x + y = 44 solving these two equations , we get x = 18 and y = 26 therefore , hens are 26 . answer : c" | null |
Question: in the x - y plane , there are 4 points ( 00 ) , ( 04 ) , ( 54 ) , and ( 50 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
A.2 / 3.
B.2 / 5.
C.3 / 4.
D.3 / 7.
e ) 5 / 8B.
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 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b . | null |
Question: the probability of two events a and b are 0.25 and 0.35 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
A.0.55.
B.0.4.
C.0.5.
D.0.05.
e ) 0.6A.
"we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 35 - . 15 = . 45 but the probability of neither a nor b = 1 - . 45 = 0.55 answer : a" | null |
Question: in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 8 nches . find the % correction made by the candidate from his stated height to his actual height ?
A.10.
B.20.
C.30.
D.17.
e ) 50D.
"his height was = 5 feet 8 inch = 8 + 60 = 68 inch . required % correction = 68 * ( 1.25 - 1 ) = 17 d" | null |
Question: the tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10 . then the first number is
A.67.
B.73.
C.53.
D.82.
e ) 89D.
let the number be 10 x + y according to the question x = 4 y x + y = 10 4 y + y = 10 or y = 2 and x = 8 so required number is = 10 * 8 + 2 = 82 answer : d | null |
Question: a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
A.100 m.
B.120 m.
C.130 m.
D.150 m.
e ) none of theseC.
explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c | null |
Question: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 40 liters and they are all empty , how much money total will it cost to fuel all cars ?
A.333 $.
B.380 $.
C.420 $.
D.450 $.
e ) 480 $A.
"total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 40 ) = 21 + 312 = > 333 hence answer will be ( a ) 333" | null |
Question: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is
A.50 liters.
B.55 liters.
C.60 liters.
D.70 liters.
e ) 75 litersC.
"quantity of milk = 60 x 2 litres = 40 litres . 3 quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = 40 . 20 + x now , 40 = 1 20 + x 2 20 + x = 80 x = 60 . quantity of water to be added = 60 liters . c" | null |
Question: a 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
A.210 m.
B.220 m.
C.230 m.
D.240 m.
e ) 250 mB.
"relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 280 / 9 = 500 / 9 x = 220 ans is 220 m answer : b" | null |
Question: find the average of all the numbers between 11 and 34 which are divisible by 5 ?
A.10.
B.20.
C.22.
D.30.
e ) 15C.
"average = ( 15 + 20 + 25 + 30 ) 4 = 90 / 4 = 22 answer is c" | null |
Question: x and y can do a piece of work in 20 days and 12 days respectively . x started the work alone and then after 4 days y joined him till the completion of work . how long did the work last ?
A.8 days.
B.10 days.
C.12 days.
D.13 days.
e ) 14 daysB.
"let the total units of work to be completed be 60 . units of work completed by x in a single day = 60 / 20 = 3 units . units of work completed by y in a single day = 60 / 12 = 5 units . thus , 8 units of work can be done by them in a single day working together . x works for 4 days alone = 12 units of work . remaining work = ( 60 - 12 ) = 48 units . now , x and y works together to complete the remaining work = 48 / 8 = 6 days hence , total days taken to complete the work = ( 6 + 4 ) = 10 days . answer : b" | null |
Question: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 8 ?
A.1 / 4.
B.1 / 3.
C.1 / 2.
D.2 / 3.
e ) 3 / 4A.
"because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 1 * 1 / 4 = 1 / 4 answer : a" | null |
Question: find the curved surface area , if the radius of a cone is 7 m and slant height is 14 m ?
A.308.
B.369.
C.434.
D.476.
e ) 513A.
"cone curved surface area = Γ― β¬ rl 22 / 7 Γ£ β 7 Γ£ β 14 = 22 Γ£ β 14 = 308 m ( power 2 ) answer is a ." | null |
Question: if | x | = 9 x - 16 , then x = ?
A.1.
B.1 / 2.
C.2.
D.4.
e ) - 1 / 2C.
substituted option c i . e x = 2 . inequality satisfied . this eliminates all options except answer is c | null |
Question: sonika deposited rs . 8000 which amounted to rs . 10200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
A.9680.
B.10680.
C.2999.
D.2774.
e ) 1212B.
"( 8000 * 3 * 2 ) / 100 = 480 10200 - - - - - - - - 10680 answer : b" | null |
Question: the average monthly salary of 24 employees in an organisation is rs . 2400 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
A.rs . 3601.
B.rs . 3618.
C.rs . 4900.
D.rs . 3619.
e ) rs . 3610C.
"manager ' s monthly salary = rs . ( 2500 * 25 - 2400 * 24 ) = rs . 4900 answer : c" | null |
Question: the s . i . on a certain sum of money for 6 years at 16 % per annum is half the c . i . on rs . 8000 for 2 years at 20 % per annum . the sum placed on s . i . is ?
A.3000.33.
B.2802.33.
C.1833.33.
D.2990.33.
e ) 2982.33C.
c . i . = [ 8000 * ( 1 + 20 / 100 ) 2 - 8000 ] = ( 8000 * 6 / 5 * 6 / 5 - 8000 ) = rs . 3520 . sum = ( 3520 * 100 ) / ( 6 * 16 ) = rs . 1833.33 answer : c | null |
Question: a farmer wishes to start a 100 square metres rectangular vegetable garden . since he has only 30 m barbed wire , he fences three sides of the garden letting his house compound wall act as the fourth side fencing . the dimension of the garden is :
['A.15 m Γ 6.67 m', 'B.20 m Γ 5 m', 'C.30 m Γ 3.33 m', 'D.40 m Γ 2.5 m', 'e ) none of these']B.
we have : 2 b + l = 30 β l = 30 β 2 b . area = 100 m 2 β l Γ b = 100 β b ( 30 β 2 b ) = 100 β b 2 β 15 b + 50 = 0 β ( b β 10 ) ( b β 5 ) = 0 β b = 10 or b = 5 . when b = 10 , l = 10 and when b = 5 , l = 20 . since the garden is rectangular , so its dimension is 20 m Γ 5 m . answer b | null |
Question: if z is a multiple of 9402 , what is the remainder when z ^ 2 is divided by 9 ?
A.0.
B.2.
C.4.
D.6.
e ) 8A.
"the sum of the digits is 9 + 4 + 2 = 15 . thus 3 is a factor of 9402 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a ." | null |
Question: a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be :
A.12 %.
B.12.5 %.
C.13.5 %.
D.13 %.
e ) 14 %B.
explanation : the original profit is : - = > 70000 β 42000 β 12000 = 16000 . if 7.14 % of 14 i . e . one of the machines closed throughout the year , then the change in profit will be : - = > ( 13 / 14 ) Γ [ 70000 β 42000 ] . = > 14000 . thus , decrease in the profit % is : - = > ( 2000 / 16000 ) Γ 100 . = > 12.5 % . answer : b | null |
Question: p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
A.35 days.
B.10 days.
C.14 days.
D.22 days.
e ) 26 daysA.
"explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 8 days = 8 Γ£ β ( 1 / 80 ) = 1 / 10 remaining work = 1 Γ’ β¬ β 1 / 10 = 9 / 10 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 9 / 10 ) / ( 1 / 30 ) = 27 total days = 8 + 27 = 35 answer : option a" | null |
Question: a and b together can complete work in 6 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
A.3.
B.8.
C.5.
D.6.
e ) 7A.
explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 3 days so a can complete the whole work in 6 days a β s one day work = 1 / 6 b β s one day work = 1 / 6 - 1 / 6 = 1 / 6 b alone can complete the work in 6 days so half of the work in 3 days answer : option a | null |
Question: let f ( x ) = x ^ 2 + bx + c . if f ( 4 ) = 0 and f ( - 3 ) = 0 , then b + c =
A.18.
B.15.
C.- 13.
D.- 21.
e ) - 24C.
"f ( x ) = x ^ 2 + bx + c . if f ( 4 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 4 ) = 0 = 16 + 4 b + c - - - taking 16 to the other side - > 4 b + c = - 16 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 7 b = - 7 - - - > b = - 1 and while substituting b = - 1 we get c = - 12 . b + c = - 13 - - - answer c" | null |
Question: how many even number in the range between 25 to 100 inclusive are not divisible by 3
A.27.
B.30.
C.31.
D.33.
e ) 46A.
"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 26 , 28,30 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 38 . for 6 , 36 , 42 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 11 . hence , only divisible by 2 but not 3 = 38 - 11 = 27 . hence , answer a" | null |
Question: sum of two numbers is 30 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
A.A.5.
B.B.9.
C.C.11.
D.D.13.
e ) e ) 15C.
"explanation : x + y = 30 2 x β 3 y = 5 x = 19 y = 11 c )" | null |
Question: the sum of three consecutive multiples of 3 is 72 . what is the larget number ?
A.26.
B.27.
C.46.
D.57.
e ) noneB.
"sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 β 9 x = 63 β x = 7 . β΄ largest number = 3 x + 6 = 27 . answer b" | null |
Question: 9 log 9 ( 6 ) = ?
A.1.
B.6.
C.3.
D.4.
e ) 5B.
"exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 6 ) = 6 correct answer b" | null |
Question: two mixtures of a and b have a and b in the ratio 3 : 2 and 3 : 4 . in what proportion should these two mixtures be mixed to get a new mixture in which the ration of a to b is 5 : 4 ?
A.6 : 1.
B.5 : 4.
C.20 : 7.
D.10 : 9.
e ) 14 : 11C.
i got c but with a different , yet slightly longer approach , which i constantly use for proportion problems such as this one . usually , this approach is very efficient when used with slightly difficult questions , but this problem is quite hard so i had to slightly tweak it . i will show you how i usually use the approach and later show you how to use it with this specific problem . example . 1 liter of solution a contains 45 % alcohol , while 1 liter of solution b contains 20 % alcohol . in what ratio must the two solutions be used to get a solution with 30 % alcohol solution : 1 . 45 / 100 * [ a / ( a + b ) ] + 20 / 100 * [ b / ( a + b ) ] = 30 / 100 2 . multiply 100 to both sides to arrive at 45 a / ( a + b ) + 20 b / ( a + b ) = 30 3 . multiply ( a + b ) to both sides to arrive at 45 a + 20 b = 30 a + 30 b 4 . distribute to arrive at 15 a = 10 b 5 . thus the ratio is a / b = 10 / 15 = 2 / 3 now using this same approach , we tackle gopu 106 β s question . it is important to first think of x in the mixture as the alcohol in the problem above ; hence , a mixture of x and y in the ratio of 3 : 2 translates to x is 3 / 5 of the solution . applying this concept to all three equations , we write : 1 . 3 / 5 * [ a / ( a + b ) ] + 3 / 7 * [ b / ( a + b ) ] = 5 / 9 2 . now here is the tweak that must be made to continue with this approach . you must find the common denominator for all three numbers and organize the fractions accordingly . by finding the common denominator of 5 , 79 ( or 315 ) we re - write the equations as follows 3 . 189 / 315 * [ a / ( a + b ) ] + 135 / 315 * [ b / ( a + b ) ] = 175 / 315 4 . multiply 315 to both sides to arrive at 189 a / ( a + b ) + 135 b / ( a + b ) = 175 5 . multiply ( a + b ) to both sides to arrive at 189 a + 135 b = 175 a + 175 b 6 . distribute to arrive at 14 a = 40 b 7 . thus the ratio is a / b = 40 / 14 = 20 / 7 or answer c | null |
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