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Question: evaluate combination 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) !
A.1617.
B.4753.
C.1417.
D.4353.
e ) none of theseB.
explanation : ncr = n ! / ( r ) ! ( n β r ) ! 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) ! = 98 β 97 * 96 ! / ( 96 ) ! ( 2 ) ! = 98 * 97 / 2 β 1 = 4753 option b | null |
Question: a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
A.116.
B.132.
C.148.
D.164.
e ) 180D.
3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 4 = 84 . the minimum number of horses and ponies is 164 . the answer is d . | null |
Question: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 8 other amateurs , what is the total number of chess games possible to be played in the tournament ?
A.10.
B.20.
C.40.
D.60.
e ) 120B.
"method 2 : each person is one participant of 4 games . so there are in all 8 * 5 = 40 instances of one participant games . but each game has 2 participants so total number of games = 40 / 2 = 20 b" | null |
Question: the speed of a train is 90 kmph . what is the distance covered by it in 12 minutes ?
A.15.
B.18.
C.77.
D.52.
e ) 42B.
90 * 12 / 60 = 18 kmph answer : b | null |
Question: in a chess competition involving some men and women , every player needs to play exactly one game with every other player . it was found that in 45 games , both the players were women and in 190 games , both players were men . what is the number of games in which one person was a man and other person was a woman ?
A.40.
B.120.
C.180.
D.200.
e ) 220D.
this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n β ( n β 1 ) / 2 no . of women be xx and given x β ( x β 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y β ( y β 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d | null |
Question: 11 is subtracted from 40 % of a number and results is 23 . what is the number ?
A.160.
B.92.
C.88.
D.85.
e ) 34D.
"( 40 / 100 ) * x Γ’ β¬ β 11 = 23 4 x = 340 x = 85 answer : d" | null |
Question: 0.1 + 0.1 ^ 2 + 0.1 ^ 3 =
A.0.1.
B.0.111.
C.0.1221.
D.0.2341.
e ) 0.3B.
"you have a mistake in your question . choice b should be ( . 111 ) and not ( . 11 ) . the equation in the solution can be simplified to ( . 1 + . 01 + . 001 ) . adding those together you get : . 100 . 010 . 001 - - - - - - . 111 - which is answer choice ( b )" | null |
Question: an article is bought for rs . 675 and sold for rs . 900 , find the gain percent ?
A.33 1 / 8 %.
B.33 9 / 3 %.
C.33 1 / 3 %.
D.93 1 / 3 %.
e ) 33 2 / 3 %C.
"675 - - - - 225 100 - - - - ? = > 33 1 / 3 % answer : c" | null |
Question: in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required is :
A.4.
B.5.
C.6.
D.8.
e ) 9D.
"explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 8 : : 12 : x = > 8 x 15 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 15 ) = > x = 8 answer : d" | null |
Question: what is the maximum number of pieces of birthday cake of size 4 β by 4 β that can be cut from a cake 20 β by 20 β ?
A.5.
B.10.
C.16.
D.20.
e ) 25E.
"each length = 20 ' ' each piece = 4 ' ' cake could be divided to maximum of 25 pieces answer : e" | null |
Question: the present worth of rs . 845 due in 2 years at 4 % per annum compound interest is
A.rs . 150.50.
B.rs . 154.75.
C.rs . 781.25.
D.rs . 158.
e ) noneC.
"solution present worth = rs . [ 845 / ( 1 + 4 / 100 ) Β² ] = rs . ( 845 x 25 / 26 x 25 / 26 ) = rs . 781.25 answer c" | null |
Question: on the first of the year , james invested x dollars at proudstar bank in an account that yields 4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
A.22.04 %.
B.26.12 %.
C.28 %.
D.16.25 %.
e ) 30 %D.
per quarter , interest = 4 % so for a year , interest = 16 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 16.25 % answer = 16.25 % = answer : d | null |
Question: if a store owner increases a product β s price by 20 percent and then increases this price by another 15 percent , what percent of the original price is the total price increase ?
A.20 %.
B.35 %.
C.38 %.
D.65 %.
e ) 135 %C.
let the initial price be 100 1 st increase = 20 % the price now is 120 2 nd increase of 15 % on 120 = 18 final price = 138 , total increase = 38 % answer : c | null |
Question: if 5 students are made to sit in a row , then 6 do n ' t have seats . if 12 students are made to sit in a row , then 3 rows are empty . how many students have to sit a row such that each row has equal number of students and all students are seated ?
A.0.
B.1.
C.4.
D.5.
e ) 6E.
let there be a rows . then 5 a + 6 = 12 ( a - 3 ) [ equating the number of students ] = > a = 6 and total number of students = 36 therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated . option ( e ) | null |
Question: a pupil ' s marks were wrongly entered as 85 instead of 33 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
A.30.
B.104.
C.20.
D.25.
e ) 26B.
"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 33 ) = > x / 2 = 52 = > x = 104 . answer : b" | null |
Question: if the ratio of two number is 6 : 7 and lcm of the number is 450 then what is the number .
A.11.
B.20.
C.25.
D.30.
e ) 35A.
"product of two no = lcm * hcf 6 x * 7 x = 450 * x x = 11 answer : a" | null |
Question: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 54 minutes . the total distance is ?
A.1 km.
B.2 km.
C.3 km.
D.3.4 km.
e ) 5 kmD.
"d 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 54 / 60 47 x / 60 = 54 / 60 = > x = 1.14 total distance = 3 * 1.14 = 3.4 km ." | null |
Question: jim is able to sell a hand - carved statue for $ 620 which was a 25 % profit over his cost . how much did the statue originally cost him ?
A.$ 496.00.
B.$ 512.40.
C.$ 555.40.
D.$ 574.90.
e ) $ 588.20A.
"620 = 1.25 * x x = 620 / 1.25 = 496.00 which rounds to $ 496.00 , which is ( a ) ." | null |
Question: praveen starts business with rs . 3780 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari β s contribution in the capital ?
A.s . 7500.
B.s . 8000.
C.s . 8500.
D.s . 9720.
e ) s . 6000D.
"let hari β s capital be rs . x . then , 3780 * 12 / 7 x = 2 / 3 = > 14 x = 136080 = > x = 9720 . answer : d" | null |
Question: find the greatest number that will divide 48 , 210 and 136 leaving 4 , 12 and 4 as remainders respectively
A.19.
B.17.
C.13.
D.22.
e ) 21D.
"explanation : answer will be hcf of ( 48 - 4 , 210 - 12 , 136 - 4 ) hcf of ( 44 , 198 , 132 ) = 22 option d" | null |
Question: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are ?
A.450.
B.300.
C.500.
D.610.
e ) 175C.
"let the maximum marks be x then , 33 % of x = 125 + 40 33 x / 100 = 165 x = 500 answer is c" | null |
Question: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 524 different signs . if the company used 522 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 524 signs ?
A.46.
B.248.
C.2092.
D.15,128.
e ) 30,256C.
# of 2 - letter codes possible from 524 different signs = 524 * 524 . # of 2 - letter codes possible from 522 different signs = 522 * 522 . the difference = 524 ^ 2 - 522 ^ 2 = ( 524 - 522 ) ( 524 + 522 ) = 2092 . answer : c . | null |
Question: a case contains c cartons . each carton contains b boxes , and each box contains 200 paper clips . how many paper clips are contained in 2 cases ?
A.200 bc.
B.200 b / c.
C.400 bc.
D.400 b / c.
e ) 400 / bcC.
"2 cases * c cartons / case * b boxes / carton * 200 clips / box = 400 bc paper clips the answer is c ." | null |
Question: what is the value of x ^ 2 yz β xyz ^ 2 , if x = β 2 , y = 1 , and z = 1 ?
A.6.
B.24.
C.30.
D.32.
e ) 48A.
4 * 1 * 1 - ( - 2 * 1 * 1 ) = 4 + 2 = 6 ans : a | null |
Question: 2.205 divided by 0.3 gives
A.7.35.
B.6.25.
C.8.15.
D.6.95.
e ) none of theseA.
"explanation : 2.205 / 0.3 = 22.05 / 3 = 7.35 . answer : option a" | null |
Question: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.88 at the candy store . what is john β s weekly allowance ?
A.$ 2.70.
B.$ 3.00.
C.$ 3.30.
D.$ 3.60.
e ) $ 3.90C.
"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 88 4 x / 15 = 88 x = 330 = $ 3.30 the answer is c ." | null |
Question: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 4 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage lesser than the typical dosage ?
A.8 %.
B.9 %.
C.11 %.
D.12.5 %.
e ) - 87.5 %E.
"typical dosage per 15 pound of the body weight = 4 c . c typical dosage per 120 pound of the body weight = 4 * ( 120 / 15 ) = 4 * 8 = 32 c . c dosage prescribed by doctor for 120 pound patient = 18 c . c % prescribed dosage greater than the typical dosage = ( 18 - 32 / 16 ) * 100 % = ( - 14 / 16 ) * 100 % = - 87 . . 5 % answer e" | null |
Question: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 2 / 3 of its own speed and got to its destination in 20 hours ?
A.5.67 hrs.
B.9.67 hrs.
C.8.95 hrs.
D.8.67 hrs.
e ) 6.67 hrsD.
"new speed = 2 / 3 of usual speed new time = 2 / 3 of usual time 2 / 3 of usual time = 20 hrs usual time = 20 * 2 / 3 = 13.33 hrs time saved = 22 - 13.33 = 8.67 hrs answer is d" | null |
Question: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 10 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
A.21.
B.35.
C.39.
D.30.
e ) 65D.
"the total number of the people in the room must be a multiple of both 7 and 10 ( in order 3 / 7 and 5 / 10 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 10 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 7 * 70 = 30 people in the room under the age of 21 . answer : d ." | null |
Question: a 5 - digit number is formed by the digits 2 , 45 , 68 ( each digit used exactly once ) . what is the probability that the number formed is divisible by 4 ?
A.2 / 5.
B.3 / 5.
C.4 / 5.
D.6 / 5.
e ) 7 / 5A.
a no . is divisible by 4 if last two digit is divisible by 4 so numbers ending with 2428 , 4852 , 5664 , 6884 are divisible by 4 last two places are fixed by 2428 , 4852 , 5664 , 6884 so remaining 3 places can be filled in 3 ! ways for each total = 8 * 3 ! = 48 = n ( e ) n ( s ) = 5 c 4 = 120 p = 48 / 120 = 2 / 5 answer : a | null |
Question: if x is 20 percent more than y and y is 60 percent less than z , then x is what percent of z ?
A.500 %.
B.48 %.
C.500 / 3 %.
D.125 %.
e ) 60 %B.
"z = 100 ; y = 40 so x = 48 x as % of z = 48 / 100 * 100 = > 48 % answer will be ( b )" | null |
Question: the area of one square is x ^ 2 + 4 x + 4 and the area of another square is 4 x ^ 2 β 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
A.0.
B.2.
C.2.5.
D.4.67.
e ) 3E.
"spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 2 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 2 l 2 = 2 x - 3 p 1 = 4 ( x + 2 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 2 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 3 answer : e" | null |
Question: from mumbai railway station , two trains a and b start simultaneously from stations 400 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 40 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
A.112.
B.133.
C.150.
D.167.
e ) 180E.
since we know the distance ( 400 ) and the combined rate ( 80 ) , we plug it into the formula : distance = rate * time 400 = 80 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 400 / 80 from dividing 80 on both sides to isolate time in the equation above . time will be 20 hours so now you can plug that in for train a β s distance . distance = rate * time distance = 40 * 20 distance = 180 according to answer choice e . | null |
Question: a batsman scored 80 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets ?
A.45 %.
B.500 / 11.
C.75 %.
D.55 %.
e ) 35 %C.
"explanation : number of runs made by running , = > 80 β ( 2 Γ 4 + 2 Γ 6 ) . = > 80 β 20 = > 60 hence , the required percentage is : - = > 60 / 80 * 100 = > 75 % answer : c" | null |
Question: a certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
A.16.67 %.
B.20 %.
C.25 %.
D.30 %.
e ) 40 %A.
"let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 60 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 20 mins ( @ 60 miles / hr ) = ( 60 / 60 ) * 20 = 20 miles fuel used to travel 80 miles = ( 80 / 20 ) = 4 gallon i . e . used fuel = ( t - 8 ) = 4 gallon i . e . t = 12 gallons i . e . used fuel = ( 2 / 12 ) * 100 = 16,67 % a" | null |
Question: there is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall . there is one each bird sitting on top of both the towers . they fly at a constant speed and time to reach a grain in b / w the towers at the same time . at what distance from the church is the grain ?
A.170 meters.
B.160 meters.
C.150 meters.
D.140 meters.
e ) 130 metersC.
if x ft is the distance of grain from 200 ft tall tower , then 150 ^ 2 + ( 350 - x ) ^ 2 = 200 ^ 2 + x ^ 2 then x = 150 meters answer : c | null |
Question: for 1 rs 4 p interest wat will be for 5000 rs ?
A.350 rs.
B.450 rs.
C.200 rs.
D.30 rs.
e ) 448 rsC.
for 1 rs , 4 p interest for 5000 rs , x x = 5000 / 1 * 4 p = = > 20000 paise to express in rs , 20000 / 100 = 200 rs answer : c | null |
Question: a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train .
A.150 m.
B.145 m.
C.240 m.
D.135 m.
e ) 250 mE.
"speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : e" | null |
Question: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 600 more . what was the sum ?
A.rs . 1200.
B.rs . 1300.
C.rs . 1400.
D.rs . 1500.
e ) none of theseA.
"explanation : at 5 % more rate , the increase in s . i for 10 years = rs . 600 ( given ) so , at 5 % more rate , the increase in si for 1 year = 600 / 10 = rs . 60 / - i . e . rs . 60 is 5 % of the invested sum so , 1 % of the invested sum = 60 / 5 therefore , the invested sum = 60 Γ 100 / 5 = rs . 1200 answer : a" | null |
Question: a shop owner sells 60 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
A.20 %.
B.40 %.
C.50 %.
D.60 %.
e ) 70 %A.
"here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 60 m cloth ) β ( c . p . of 60 m cloth ) selling price of 50 m cloth = selling price of 60 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 50 m cloth = rs . 5000 and s . p . of 50 m cloth = rs . rs . 6000 profit % = 10 / 50 Γ 100 = 20 % 20 profit of 20 % was made by the merchant . a" | null |
Question: a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
A.3.
B.6.
C.9.
D.10.
e ) 12C.
"221 + 43 = 264 / 17 = 9 ( remainder ) c" | null |
Question: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?
A.42.
B.66.
C.98.
D.112.
e ) 154D.
"let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )" | null |
Question: albert invested rs . 6500 in a scheme for 2 years at compound interest rate 6.5 % p . a . how much amount will albert get on maturity of the fixed deposit ?
A.s . 8829.
B.s . 7200.
C.s . 7200.5.
D.s . 4000.
e ) s . 7372.46E.
amount = [ 6500 * ( 1 + 6.5 / 100 ) 2 ] = 6500 * 106.5 / 100 * 106.5 / 100 = rs . 7372.46 answer : e | null |
Question: keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
A.47 %.
B.59 %.
C.71 %.
D.83 %.
e ) 95 %C.
"let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c ." | null |
Question: if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =
A.19.
B.20.
C.21.
D.27.
e ) 29D.
3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d | null |
Question: the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?
A.165.
B.185.
C.190.
D.198.
e ) 194E.
194 answer is e | null |
Question: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
A.$ 1600.
B.$ 6000.
C.$ 6050.
D.$ 7050.
e ) $ 8000E.
"let t be the tier price , p be total price = 14000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1440 - - - - > t = 8000 . e is the correct answer ." | null |
Question: a sum fetched a total simple interest of rs . 144 at the rate of 15 p . c . p . a . in 1 year 6 months . what is the sum ?
A.490.
B.850.
C.580.
D.640.
e ) 760D.
"sol . principal = rs . [ 100 * 144 / 15 * ( 18 / 12 ) ] = rs . [ 14400 / 22.5 ] = rs . 640 . answer d" | null |
Question: the ` ` racing magic ' ' takes 120 seconds to circle the racing track once . the ` ` charging bull ' ' makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
A.3.
B.6.
C.9.
D.12.
e ) 15D.
time taken by racing magic to make one circle = 120 seconds = 2 mins time taken by ` ` charging bull ' ' to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 120 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d | null |
Question: find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )
A.11.
B.12.
C.16.
D.14.
e ) 15C.
"- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c" | null |
Question: 102 Γ£ β 102 + 98 Γ£ β 98 = ?
A.20018.
B.20028.
C.20108.
D.10008.
e ) 20008E.
"explanation : ( a + b ) 2 + ( a Γ’ Λ β b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 Γ’ Λ β 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e" | null |
Question: two trains 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
A.11.88 sec.
B.13.8 sec.
C.53.8 sec.
D.10.8 sec.
e ) 10.4 secA.
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 190 = 330 m . required time = 330 * 9 / 250 = 11.88 sec . answer : a :" | null |
Question: mary works in a restaurant a maximum of 70 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
A.600.
B.620.
C.660.
D.320.
e ) 400C.
"mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 50 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 50 ( 20 ) = $ 500 . the total amount is $ 160 + $ 500 = $ 660 answer c 660 ." | null |
Question: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately
A.4457.
B.4567.
C.5943.
D.4547.
e ) 4675C.
"explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . Ο r 2 = 175600 β ( r ) 2 = ( 175600 x ( 7 / 22 ) ) β r = 236.37 m . circumference = 2 Ο r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c" | null |
Question: 49 Γ 49 Γ 49 Γ 49 = 7 ?
A.4.
B.7.
C.8.
D.16.
e ) none of theseC.
"49 Γ 49 Γ 49 Γ 49 = 7 ? or , 7 ( 2 ) Γ 7 ( 2 ) Γ 7 ( 2 ) Γ 7 ( 2 ) = 7 ? or 7 ( 8 ) = 7 ? or , ? = 8 answer c" | null |
Question: 30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .
A.20.
B.11.
C.12.
D.13.
e ) 14A.
"since average price of a pencil = 2 β΄ price of 75 pencils = 150 β΄ price of 30 pens = ( 750 β 150 ) = 600 β΄ average price of a pen = 600 β 60 = 20 answer a" | null |
Question: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :
A.338.
B.278.
C.322.
D.231.
e ) 391E.
"clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e" | null |
Question: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two - fifth of its present ?
A.52.5.
B.62.5.
C.72.5.
D.82.5.
e ) 81.5B.
explanation : let the capacity of 1 bucket = x . then , capacity of tank = 25 x . new capacity of bucket = 2 / 5 x . required no of buckets = 25 x / ( 2 x / 5 ) = 62.5 answer is b | 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 110 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 ) 440E.
"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 ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )" | null |
Question: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area r covered by the two roads ?
A.400.
B.1550.
C.1575.
D.1600.
e ) 1625C.
"area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads r = 1000 + 600 - 25 = 1575 answer : option c" | null |
Question: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 21 days , a finished the remaining work . in how many days a alone can finish the job ?
A.10.
B.25.
C.60.
D.30.
e ) 28E.
"a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 21 days whole work will be done by a in 21 * 4 / 3 = 28 days answer is e" | null |
Question: how many integers are between 6 and 74 / 5 , inclusive ?
A.4.
B.5.
C.6.
D.7.
e ) 9E.
"74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . since the values are small , we can write down the integers . the different integers between 6 and 74 / 5 would be 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 9 option e" | null |
Question: what is the smallest positive integer x such that 180 - x is the cube of a positive integer
A.50.
B.52.
C.60.
D.55.
e ) 12D.
"given 180 - x is a perfect cube so we will take 125 = 5 * 5 * 5 180 - x = 125 x = 180 - 125 = 55 correct option is d" | null |
Question: what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?
['A.120', 'B.240', 'C.360', 'D.380', 'e ) 840']E.
let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e | null |
Question: in the youth summer village there are 175 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
A.70.
B.75.
C.85.
D.80.
e ) 100B.
"total = 175 not working = 100 having family = 75 like to sing in shower = 125 working = 175 - 100 = 75 not having family = 175 - 75 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 b" | null |
Question: if it takes a tub 3 minutes to drain 6 / 7 of its content , how much more time will it take for the tub to be empty ?
A.30 seconds.
B.1 minute.
12 seconds.
C.1 minute.
50 seconds.
D.2 minutes.
14 seconds.
e ) 4 minutes.
12 secondsA.
"if 6 / 7 of tub ' s content is drained 1 / 7 th of tub still needs to be drained . if it takes 3 minutes to drain 6 / 7 th of tub it takes 3 * ( 7 / 6 ) minutes to drain the entire tub and 3 * ( 7 / 6 ) * ( 1 / 7 ) min to drain 1 / 7 th of the tub which is 6 / 5 minutes or 0.5 minutes or 30 seconds so answer is a" | null |
Question: exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?
A.0.184.
B.0.16.
C.0.18.
D.0.147.
e ) 0.148D.
total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d | null |
Question: the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?
A.31355.
B.38.44.
C.29.55.
D.97.66.
e ) 45.66B.
total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b | null |
Question: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 4 % . what is the approximate interest he pays annually ?
A.$ 1750.
B.$ 2000.
C.$ 2150.
D.$ 2500.
e ) $ 12000A.
"an easy way too attempt this is by approximation : for the first quarter , he pays 4 % of 10,000 which is $ 400 . so for the four quarters in the year , he will approximately play 400 * 4 = 1600 over the entire year . because of compound interest it will be more than 1600 . approx . option a is correct . answer : a" | null |
Question: jack and jill work at a hospital with 7 other workers . for an internal review , 2 of the 9 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
A.1 / 3.
B.1 / 4.
C.1 / 15.
D.3 / 8.
e ) 1 / 36E.
"1 / 9 c 2 = 1 / 36 . answer : e ." | null |
Question: a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?
A.510.
B.520.
C.530.
D.540.
e ) 440E.
"let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e" | null |
Question: the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
A.rs . 200.
B.rs . 250.
C.rs . 300.
D.rs . 450.
e ) none of theseD.
"explanation : let the cost of one pen is β 5 x β and pencil is β x β 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d" | null |
Question: car dealership x , the total profit from sales increased by 8 percent over the previous years , while the number of cars sold decreased by 8 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
A.17.39 %.
B.20 %.
C.22 %.
D.23 %.
e ) 25 %A.
"let profit be x and cars sold be y originally profit / car = x / y now it is 1.08 x / 0.92 y = 108 / 92 ( x / y ) increase in profit per car = ( ( 16 / 92 ) ( x / y ) ) / ( x / y ) * 100 = 17.39 % answer = a" | null |
Question: the product z of two prime numbers is between 16 and 40 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 12 but less than 30 then what is z ?
A.21.
B.22.
C.28.
D.35.
e ) 39E.
"the smallest possible product is 39 which is 3 * 13 . all other products are too big . the answer is e ." | null |
Question: if 4 people are selected from a group of 8 married couples , what is the probability that none of them would be married to each other ?
A.1 / 33.
B.2 / 33.
C.8 / 13.
D.16 / 33.
e ) 11 / 12C.
"if we are to select 4 people from 8 couples without any restriction , how many ways can we make the selection ? 16 ! / 4 ! 12 ! = 1820 if we are to select 4 people from 8 couples with restriction that no married couple can both make it to the group , only a representative ? 8 ! / 4 ! 4 ! = 70 but we know that to select a person from each couple , take 2 possibilities 70 * 2 * 2 * 2 * 2 = 1120 probability = desired / all possibilities = 1120 / 1820 = 8 / 13 answer : c" | null |
Question: the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?
A.20 %.
B.19 %.
C.15 %.
D.12 %.
e ) 24 %D.
"answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %" | null |
Question: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 72 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
A.55.
B.84.
C.63.
D.75.
e ) 70C.
"let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 72 or 1 / 7 t + 1 t = 60 therefore t = 72 * 7 / 8 = 63 c" | null |
Question: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?
A.1875.
B.1250.
C.1300.
D.1600.
e ) 1625A.
"300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer" | null |
Question: at 3 : 40 , the hour hand and the minute hand of a clock form an angle of
A.160 Β°.
B.180 Β°.
C.130 Β°.
D.110 Β°.
e ) 150 Β°C.
"angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h β m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 β h ) β m / 2 degree here h = 3 , m = 40 and minute hand is ahead of the hour hand . hence the angle = 30 ( m / 5 β h ) β m / 2 = 30 ( 40 / 5 β 3 ) β 40 / 2 = 30 ( 8 β 3 ) β 20 = 30 Γ 5 β 20 = 130 Β° answer is c ." | null |
Question: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 20 litres of tomato juice ?
A.2.8 liters ..
B.2.5 liters ..
C.8.5 liters ..
D.2.6 liters ..
e ) 2.1 liters .B.
"answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . β β 10 % ( 20 ) = 80 % ( x ) β β x = 2.5 liters . answer : b" | null |
Question: if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
A.26.
B.39.
C.42.
D.65.
e ) 168E.
here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e | null |
Question: a and b can finish a work in 10 days while b and c can do it in 18 days . a started the work , worked for 5 days , then b worked for 10 days and the remaining work was finished by c in 15 days . in how many days could c alone have finished the whole work ?
A.30 days.
B.15 days.
C.45 days.
D.24 days.
e ) none of theseC.
let c completes the work in x days . work done by ( a + b ) in 1 day = 1 β 10 work done by ( b + c ) in 1 day = 1 β 18 a β s 5 days β work + b β s 10 days β work + c β s 15 days β work = 1 or ( a + b ) β s 5 days β work + ( b + c ) β s 5 days β work + c β s 10 days β work = 1 or 5 β 10 + 5 β 18 + 10 β x = 1 or x = 45 days answer c | null |
Question: a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it take 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
A.1 : 3.
B.3 : 8.
C.6 : 3.
D.8 : 3.
e ) noneD.
"sol . let the man rate upstream be x kmph and that downstream be y kmph . then , distance coverd upstream in 8 hrs 48 min . = distance coverd downstream in 4 hrs . β [ x 8 4 / 5 ] = ( y * 4 ) β 44 / 5 x = 4 y β y = 11 / 5 x . β΄ required ratio = [ y + x / 2 ] : [ 6 x / 5 * 1 / 2 ] : [ 6 x / 5 * 1 / 2 ] = 8 / 5 : 3 / 5 = 8 : 3 . answer d" | null |
Question: if 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 , where x and y are non negative integers , what is the greatest possible value of | x Γ’ β¬ β y | ?
A.0.
B.1.
C.2.
D.3.
e ) 4A.
| x Γ’ β¬ β y | for x and y 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 a . x = y x = y = 0 1 + 1 = 1 + 1 right b . 1 x = 2 , y = 1 4 + 2 = 1 + 1 wrong c . 2 x = 3 , y = 1 8 + 2 = 1 + 1 wrong d . 3 x = 4 , y = 1 16 + 2 = 1 + 1 wrong e . 4 x = 5 , y = 1 32 + 2 = 1 + 1 wrong my answer is a . | null |
Question: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?
A.36.
B.40.
C.44.
D.48.
e ) 54E.
for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52 | null |
Question: find the length of the wire required to go 15 times round a square field containing 69696 m 2 ?
A.15840.
B.19879.
C.27997.
D.15842.
e ) 15823A.
"a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a" | null |
Question: p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
A.rs . 3000.
B.rs . 3600.
C.rs . 2400.
D.rs . 2800.
e ) none of theseD.
"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d" | null |
Question: rahul put his timepiece on the table in such a way that at 6 p . m . hour hand points to north . in which direction the minute hand will point at 9.15 p . m . ?
A.233.
B.37.
C.27.
D.west.
e ) 271D.
explanation : at 9.15 p . m . , the minute hand will point towards west . answer : d ) west | null |
Question: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach a target of 282 runs ?
A.6.25.
B.6.5.
C.6.75.
D.7.0.
e ) none of the aboveA.
"total runs in the first 10 overs = 10 Γ 3.2 = 32 run rate required in the remaining 40 overs = 282 β 32 / 40 = 250 / 40 = 6.25 runs per over . answer a" | null |
Question: a and b together can complete a piece of work in 10 days . if a alone can complete the same work in 15 days , in how many days , in how many days can b alone complete that work ?
A.10.
B.30.
C.25.
D.15.
e ) 45B.
( a + b ) ' s 1 day ' s work = 1 / 10 a ' s 1 day ' s work = 1 / 15 b ' s 1 days ' s work = ( 1 / 10 ) - ( 1 / 15 ) = 1 / 30 hence , b alone can complete the work in 30 days . answer is b | null |
Question: the triplicate ratio of 2 : 4 is ?
A.1 : 64.
B.1 : 8.
C.1 : 34.
D.3 : 64.
e ) 5 : 64B.
"2 ^ 3 : 4 ^ 3 = 8 : 64 = 1 : 8 answer : b" | null |
Question: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 32 % iodine solution ?
A.35.
B.49.
C.100.
D.102.
e ) 140D.
"solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 32 / 100 40 x + 700 = 32 x + 1120 8 x = 820 x = 102 lts correct option : d" | null |
Question: a garrison of 2000 men has provisions for 54 days . at the end of 18 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
A.1977.
B.1600.
C.1979.
D.1900.
e ) 1278B.
"2000 - - - - 54 2000 - - - - 36 x - - - - - 20 x * 20 = 2000 * 36 x = 3600 2000 - - - - - - - 1600 answer : b" | null |
Question: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
A.95 kg.
B.90 kg.
C.85 kg.
D.data inadequate.
e ) none of theseA.
"a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg ." | null |
Question: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?
A.$ 1,600.
B.$ 1,850.
C.$ 2,250.
D.$ 2,440.
e ) $ 2,560E.
"let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e ." | null |
Question: the β length of integer x β refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 Γ 2 Γ 3 Γ 5 . ) what is the greatest possible length of integer z if z < 1,080 ?
A.13.
B.10.
C.9.
D.7.
e ) 6B.
to maximize the length of z we should minimize its prime base . the smallest prime is 2 and since 2 ^ 10 = 1,024 < 1,080 then the greatest possible length of integer z is 10 . answer : b . | null |
Question: how many multiples of 3 are less than 6500 , and also multiples of 7 ?
A.104.
B.208.
C.310.
D.340.
e ) 454C.
"lcm of 3 & 7 = 21 tried dividing 6500 by 21 got quotient 309.5 ' so c is answer" | null |
Question: a can finish a piece of work in 4 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?
A.3.
B.5.
C.6.
D.7.
e ) 8A.
2 / 4 + ( 2 + x ) / 10 = 1 = > x = 3 days answer : a | null |
Question: if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?
A.120.
B.772.
C.180.
D.266.
e ) 2848C.
"the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c" | null |
Question: two trains , a and b , started simultaneously from opposite ends of a 125 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 125 - mile trip in 12 hours ; train b , traveling at a constant rate , completed the 125 - mile trip in 8 hours . how many miles had train a traveled when it met train b ?
A.25.
B.37.5.
C.40.
D.45.5.
e ) 50E.
as the ratio of the rates of a and b is 8 to 12 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 a would cover 8 / ( 8 + 12 ) = 8 / 20 of 125 miles : 125 * 8 / 20 = 50 miles . answer : e . | null |
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