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Question: a school has 9 english 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
A.7.
B.8.
C.9.
D.10.
e ) 11E.
total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e | null |
Question: if in a certain code ` ` range ' ' is coded as 12345 and ` ` random ' ' is coded as 123678 . then the code for the word ` ` rand ' ' would be
A.1236.
B.1365.
C.1200.
D.1526.
e ) 1325A.
r - 1 a - 2 n - 3 d - 6 so for mango the code is 1236 answer : a | null |
Question: a goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds . what is the length of the goods train ?
A.230 m.
B.270 m.
C.643 m.
D.832 m.
e ) 290 mE.
"speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 230 / 26 = 20 x + 230 = 520 x = 290 . answer : e" | null |
Question: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
A.9.
B.12.
C.13.
D.14.
e ) 15A.
"let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 3 + x = 6 4 x = 6 x + 18 = > 2 x = 18 x = 9 a" | null |
Question: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 9 ) , how many units is p from the y - axis ?
A.18.
B.12.
C.9.
D.4.5.
e ) 3A.
"the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a ." | null |
Question: if a ' s height is 45 % less than that of b , how much percent b ' s height is more than that of a ?
A.66.66 %.
B.81.81 %.
C.66.766 %.
D.86.66 %.
e ) 66.65 %B.
"excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )" | null |
Question: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 4 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
A.50.
B.90.
C.100.
D.105.
e ) 140B.
"rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 4 of all one - bedroom : 1 / 4 * { all one bedroom } = 40 - - > { all one - bedroom } = 160 { all two - bedroom } = 490 - 160 = 330 two - bedroom not rented = 330 - 240 = 90 b" | null |
Question: in how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate ?
A.1063800.
B.1083600.
C.1036800.
D.1053800.
e ) 1073600C.
"number of ways = 2 * 6 ! * 6 ! = 1036800 answer is c" | null |
Question: the cost price of 12 articles is equal to the selling price of 10 articles . what is the profit percent ?
A.10 %.
B.20 %.
C.30 %.
D.40 %.
e ) 50 %B.
"10 * sp = 12 * cp sp = 1.2 * cp the profit percent is 20 % . the answer is b ." | null |
Question: a man rows his boat 65 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
A.5 kmph.
B.4 kmph.
C.9 kmph.
D.8 kmph.
e ) 1 kmphB.
"speed downstream = d / t = 65 / ( 2 1 / 2 ) = 26 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 26 - 18 ) / 2 = 4 kmph answer : b" | null |
Question: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 9 from the product of their ages a year from today . what is their age today ?
A.2 ..
B.4 ..
C.5 ..
D.7.
e ) 9 .B.
"ad = ( a + 1 ) ( d + 1 ) - 9 0 = a + d - 8 a + d = 8 a = d ( as they are twin brothers ) a = d = 4 b is the answer" | null |
Question: 27 * 27 * 27 * 27 = 3 ^ ?
A.7.
B.12.
C.5.
D.6.
e ) 8B.
"3 ^ 3 * 3 ^ 3 * 3 ^ 3 * 3 ^ 3 = 3 ^ ( 3 + 3 + 3 + 3 ) = 3 ^ 12 answer : 12 option : b" | null |
Question: there were two candidates in an election . winner candidate received 60 % of votes and won the election by 240 votes . find the number of votes casted to the winning candidate ?
A.228.
B.720.
C.255.
D.199.
e ) 231B.
"w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 240 60 % - - - - - - - - ? = > 720 answer : b" | null |
Question: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 153 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
A.2.
B.1.
C.3.
D.5.
e ) 4C.
"we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 152 / 25 = 6 . . . . so the max is 6 152 / 20 = 7 . . . so the max is 7 153 - 150 = 3 ( 6 big box ) answer : c" | null |
Question: what least number should be subtracted from 997 so that the remainder when divided by 5 , 9 , and 11 will leave in each case the same remainder 3 ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
the lcm of 5,9 and 11 is 495 . the next multiple is 2 * 495 = 990 . 990 + { remainder } = 990 + 3 = 993 , which is 4 less than 997 . answer : d . | null |
Question: a garden center sells a certain grass seed in 5 - pound bags at $ 13.82 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
A.$ 94.03.
B.$ 96.75.
C.$ 98.75.
D.$ 102.07.
e ) $ 105.3C.
"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c" | null |
Question: in a group of cows and chickens , the number of legs was 14 more than twice the number of heads . the number of cows was :
A.3.
B.5.
C.9.
D.7.
e ) 8D.
d 7 let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 14 more than twice the number of heads . therefore , 2 Γ ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 14 = 4 x + 2 y . or , 2 x + 14 = 4 x [ subtracting 2 y from both sides ] . or , 14 = 4 x β 2 x [ subtracting 2 x from both sides ] . or , 14 = 2 x . or , x = 7 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 . | null |
Question: what least number should be subtracted from 13604 such that the remainder is divisible by 87 ?
A.32.
B.29.
C.28.
D.30.
e ) 31A.
"13604 Γ· 87 = 156 , remainder = 32 hence 32 is the least number which can be subtracted from 13604 such that the remainder is divisible by 87 answer is a" | null |
Question: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 153 grams of water ?
A.16.
B.72.
C.112.
D.136.
e ) 142D.
"since the ratio , by mass , of hydrogen to oxygen is 2 : 16 , then oxygen is 16 / ( 2 + 16 ) = 8 / 9 of mass of water . therefore there are 153 * 8 / 9 = 136 grams of oxygen in 153 grams of water . answer : d ." | null |
Question: how many zeros does 135 ^ 19 x 42 ^ 17 end with ?
A.0.
B.2.
C.5.
D.13.
e ) 17E.
"to know the zeros we need to know how many 10 ' s are there for this need to find number of 2 s and 5 s ( 2 * 5 = 10 ) 135 = ( 5 x 3 ^ 3 ) ^ 19 so number of 5 s are = 19 42 = ( 2 x 7 x 3 ) ^ 17 so number of 2 s = 17 so tot number of 10 s in this number is ( 17 - > 2 s x 17 - > 5 s ) so answer is 17 answer : e" | null |
Question: due to construction , the speed limit along an 5 - mile section of highway is reduced from 40 miles per hour to 22 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A.A.3.12.
B.B.8.
C.C.10.
D.D.15.
e ) e ) 6.13E.
"old time in minutes to cross 5 miles stretch = 5 * 60 / 40 = 5 * 3 / 2 = 7.5 new time in minutes to cross 5 miles stretch = 5 * 60 / 22 = 5 * 30 / 11 = 13.63 time difference = 6.13 ans : e" | null |
Question: 2 : 5 = 4 / 3 : x . the value of x is ?
A.10 / 3.
B.2.
C.3.
D.4.
e ) 5A.
x * 2 = 5 * 4 / 3 x * 2 = 20 / 3 x = 10 / 3 answer : a | null |
Question: how many even integers n , such that 20 < = n < = 200 are of the form 3 k + 4 , where k is any natural number ?
A.26.
B.30.
C.34.
D.38.
e ) 42B.
"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 196 = 16 + 6 ( 30 ) there are 30 numbers in the list . the answer is b ." | null |
Question: find a sum for 1 st 4 prime number ' s ?
A.25.
B.17.
C.30.
D.34.
e ) 36B.
"required sum = ( 2 + 3 + 5 + 7 ) = 17 note : 1 is not a prime number option b" | null |
Question: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 5 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
A.12 : 5.
B.11 : 5.
C.13 : 5.
D.14 : 5.
e ) 9 : 5B.
"vessel a = 300 gallons - - > milk = 250 , water = 50 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 550 , water 250 the ratio = 550 / 250 - - > 11 : 5 answer : b" | null |
Question: how many seconds will a 750 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
A.48.
B.36.
C.26.
D.11.
e ) 45E.
"explanation : here distance d = 750 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 45 sec . answer : e" | null |
Question: a certain country had a total annual expenditure of $ 7.2 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
A.$ 500.
B.$ 1,000.
C.$ 2,000.
D.$ 3,000.
e ) $ 5,000D.
"total expenditure / population = per capita expenditure hence , ( 7,2 x 10 ^ 11 ) / 240 000 000 = ( 7,2 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 3 x 10 ^ ( 11 - 8 ) = 3 x 10 ^ 3 = 3000 . answer is d ." | null |
Question: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 5 per item . if the manufacturer β s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150,000 ?
A.2,858.
B.18,667.
C.28,000.
D.35,000.
e ) 40,000C.
"let the items manufactured or sold bex 130000 + 5 x = 15 x - 150000 10 x = 280000 x = 28000 ans : c" | null |
Question: what should be added to 4529 so that it may become a perfect square ?
A.94.
B.95.
C.96.
D.97.
e ) 98B.
"68 x 68 = 4624 4624 - 4529 = 95 if added to 95 get perfect square answer = b" | null |
Question: barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 8 % of her entire investment ?
A.1200.
B.3000.
C.1000.
D.3600.
e ) 2400D.
"let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.08 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.08 * 2400 0.02 x = 2400 ( 0.08 - 0.05 ) x = 2400 * 0.03 / 0.02 = 3600 ans : d" | null |
Question: if x : y = 3 : 4 , find ( 4 x + 5 y ) : ( 5 x - 2 y ) .
A.32 / 7.
B.13 / 7.
C.2 / 7.
D.32 / 17.
e ) 2 / 17A.
". x / y = 3 / 4 ο³ ( 4 x + 5 y ) / ( 5 x + 2 y ) = ( 4 ( x / y ) + 5 ) / ( 5 ( x / y ) - 2 ) = ( 4 ( 3 / 4 ) + 5 ) / ( 5 ( 3 / 4 ) - 2 ) = ( 3 + 5 ) / ( 7 / 4 ) = 32 / 7 answer a 32 / 7" | null |
Question: find two integers , neither of which ends in a zero , and whose product is exactly 1 , 000,000
A.64 and 15,625.
B.60 and 15,625.
C.64 and 15,620.
D.64 and 15,635.
e ) 64 and 16,625A.
"1 , 000,000 = 10 ^ 6 = 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 6 ) x ( 5 ^ 6 ) = 64 x 15625 so the numbers are 64 and 15,625 answer : a" | null |
Question: the average of 17 numbers is 59 . average of the first 9 of them is 56 and that of the last 9 is 63 . find the 9 th number ?
A.64.
B.68.
C.65.
D.66.
e ) 67B.
sum of all the 17 numbers = 17 * 59 = 1,003 sum of the first 9 of them = 9 * 56 = 504 sum of the last 9 of them = 9 * 63 = 567 so , the 8 th number = 504 + 567 - 1,003 = 68 . answer : b | null |
Question: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 56 km downstream
A.2 hours.
B.4 hours.
C.5 hours.
D.6 hours.
e ) 7 hoursA.
"explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 56 km time taken = distance / speed = 56 / 28 = 2 hours answer : option a" | 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 7 % . what is the approximate interest he pays annually ?
A.1000.
B.1500.
C.3000.
D.2500.
e ) 2400C.
"an easy way too attempt this is by approximation : for the first quarter , he pays 7 % of 10,000 which is $ 700 . so for the four quarters in the year , he will approximately play 700 * 4 = 2800 over the entire year . because of compound interest it will be more than 2800 . approx . option c is correct . answer : c" | null |
Question: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
A.rs . 450.
B.rs . 600.
C.rs . 800.
D.rs . 375.
e ) rs . 400E.
"c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 24 . a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . c ' s share ( for 3 days ) = rs . ( 3 x 1 / 24 x 3200 ) = rs . 400 . correct option ` ` e ' ' ." | null |
Question: 1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 =
A.29 / 16.
B.19 / 16.
C.15 / 16.
D.9 / 13.
e ) 0E.
"1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 = 1 / 2 - [ ( 1 / 16 ) + 1 ] + 9 / 16 = 1 / 2 - [ 17 / 16 ] + 9 / 16 = 8 / 16 - 17 / 16 + 9 / 16 = 0 the answer is e ." | null |
Question: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 20 candidates . she plans to have one working interview with 3 of the 20 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
A.520.
B.120.
C.300.
D.30.
e ) 333A.
520 . answer a | null |
Question: the area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm . what is the perimeter of the square ?
A.802.
B.800.
C.829.
D.389.
e ) 245B.
"area of the square = s * s = 5 ( 125 * 64 ) = > s = 25 * 8 = 200 cm perimeter of the square = 4 * 200 = 800 cm . answer : b" | null |
Question: when positive integer x is divided by 10 , the quotient is y and the remainder is 3 . when 2 x is divided by 7 , the quotient is 3 y and the remainder is 1 . what is the value of 11 y β x ?
A.2.
B.- 2.
C.3.
D.- 3.
e ) 4A.
"( 1 ) x = 10 y + 3 ( 2 ) 2 x = 21 y + 1 ( 2 ) - ( 1 ) : x = 11 y - 2 11 y - x = 2 the answer is a ." | null |
Question: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 160.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
A.$ 21.
B.$ 27.
C.$ 31.
D.$ 39.
e ) it can not be determinedD.
"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 39 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d" | null |
Question: if 300 ! / 10 ^ n is an integer , what is the largest possible value of n ?
A.75.
B.74.
C.79.
D.77.
e ) 72D.
"the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 300 factorial will have 74 as - 300 / 5 = 60 60 / 5 = 12 12 / 5 = 2 so answer will be ( d ) 74" | null |
Question: 15.06 * 0.0001 = ?
A.15060000.
B.0.001506.
C.0.01506.
D.0.1506.
e ) none of theseB.
"explanation : clearly after decimal 6 digits should be there . option b" | null |
Question: addison high school β s senior class has 200 boys and 160 girls . if 60 % of the boys and 75 % of the girls attended college , what percentage of the total class that did not attend college ?
A.33.33.
B.60.
C.80.
D.66.67.
e ) 64D.
"number of boys attending the college : 0.60 * 200 = 120 number of girls attending the college : 0.75 * 160 = 120 total attending = 120 + 120 = 240 total people = 200 + 160 = 360 % of people attending = 240 / 360 = 66.67 % . d is the correct answer" | null |
Question: find the fraction which has the same ratio to 1 / 13 that 5 / 34 has to 7 / 48 .
A.110 / 1547.
B.120 / 1547.
C.140 / 1547.
D.160 / 1547.
e ) 220 / 1547B.
p : 1 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 1 / 13 * 5 / 34 p * 7 / 48 = 5 / 442 p = 240 / 3094 = > p = 120 / 1547 answer : b | null |
Question: two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are
A.6.
8.
B.9.
12.
C.12.
16.
D.16.
20.
e ) noneA.
solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 βΉ = βΊ 16 x 2 = 72 x 2 - 224 βΉ = βΊ 56 x 2 = 224 . βΉ = βΊ x 2 = 4 . βΉ = βΊ x = 2 . so , the numbers are 6 and 8 . answer a | null |
Question: a and b invests rs . 3500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
A.21 : 5.
B.21 : 16.
C.21 : 2.
D.9 : 9.
e ) 21 : 11B.
"( 3.5 * 6 + 7 * 6 ) : ( 4 * 12 ) 63 : 48 = > 21 : 16 answer : b" | null |
Question: a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
A.5 / 6.
B.3 / 4.
C.2 / 3.
D.1 / 2.
e ) 3 / 5C.
"the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 10 / 30 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is c ." | null |
Question: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 4 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 ?
A.7 / 15.
B.9 / 20.
C.11 / 25.
D.13 / 27.
e ) 15 / 31D.
"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 ) / ( 3 / 4 ) = 4 / 9 hours peter worked for 13 / 9 hours so he painted 13 / 9 * 1 / 3 = 13 / 27 of the room . the answer is d ." | null |
Question: the distance from city a to city b is 30 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
A.45.
B.88.
C.120.
D.152.
e ) 154C.
"the time it takes bob to drive to city b is 30 / 40 = 0.75 hours . alice needs to take less than 0.25 hours for the trip . alice needs to exceed a constant speed of 30 / 0.25 = 120 miles per hour . the answer is c ." | null |
Question: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 83 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
A.$ 550.
B.$ 650.
C.$ 750.
D.$ 850.
e ) $ 950B.
"0.1 x = 0.08 ( 2000 - x ) + 83 0.18 x = 243 x = 1350 then the amount invested at 8 % is $ 2000 - $ 1350 = $ 650 the answer is b ." | null |
Question: line q has the equation 5 y β 3 x = 90 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s β s exist ? ( note : intersections on one of the axes do not count . )
A.58.
B.61.
C.64.
D.67.
e ) 70D.
5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d . | null |
Question: the ratio of expenditure and savings is 3 : 2 . if the income increases by 15 % and the savings increases by 6 % , then by how much percent should his expenditure increases ?
A.22.
B.21.
C.88.
D.76.
e ) 29B.
answer : b ) 21 | null |
Question: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote β s majority . what is the total number of votes polled ?
A.750.
B.400.
C.800.
D.850.
e ) none of theseB.
"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b" | null |
Question: the sum of three consecutive even numbers is 48 . find the middle number of the three ?
A.14.
B.16.
C.18.
D.24.
e ) 64E.
"three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 48 6 p = 48 = > p = 8 . the middle number is : 8 p = 64 . answer : e" | null |
Question: there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
A.2.
B.3.
C.4.
D.5.
e ) 6C.
"9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let ' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ." | null |
Question: if a train , travelling at a speed of 80 kmph , crosses a pole in 5 sec , then the length of train is ?
A.110.111 m.
B.121.111 m.
C.111.11 m.
D.141.111 m.
e ) 181.111 mC.
"d = 80 * 5 / 18 * 5 = 111.11 m answer : c" | null |
Question: in how many ways can the integer 120 be expressed as a product of two different positive integers ?
A.10.
B.8.
C.5.
D.4.
e ) 2C.
"120 = ( 2 ^ 3 ) * 3 * 5 since 120 is not a perfect square , no of ways = 5 answer c" | null |
Question: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 4 : 5 : 2 , respectively , by weight . if 44 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
A.15.
B.12.
C.8.
D.6.
e ) 4C.
"we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 4 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 4 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 4 x + 5 x + 2 x = 44 11 x = 44 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 2 ) ( 4 ) = 8 pounds of apples = ( 4 ) ( 4 ) = 16 thus we know that there are 16 β 8 = 8 more pounds of apples than grapes . answer is c ." | null |
Question: if an integer n is to be selected at random from 1 to 99 , inclusive , what is probability n ( n + 1 ) will be divisible by 3 ?
A.1 / 4.
B.1 / 3.
C.1 / 2.
D.2 / 3.
e ) 3 / 4D.
"for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ." | null |
Question: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3267 in 3 years . find the rate percent ?
A.11.
B.10.
C.28.
D.24.
e ) 35E.
"explanation : 2420 - - - 847 100 - - - ? = > 35 % answer : option e" | null |
Question: workers in a factory store products inside two different sized boxes . the bigger of the boxes can store 50 products while the smaller box can store 40 products . if a fresh batch of products numbering 212 in total were to be stored , what is the least number of products that will not be boxed ?
A.23.
B.11.
C.2.
D.10.
e ) 12E.
total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e | null |
Question: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes william can make using this recipe ?
A.5.
B.6.
C.7.
D.8.
e ) 9A.
"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a" | null |
Question: in a hostel , the number of students decreased by 5 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
A.19 %.
B.12.3 %.
C.25 %.
D.40 %.
e ) 9.4 %B.
cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb ) | null |
Question: at 15 : 00 there were 21 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
A.7.
B.14.
C.25.
D.27.
e ) 30D.
initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d | null |
Question: a boy wants to make cuboids of dimension 5 m , 6 m and 7 m from small cubes of . 03 m 3 . later he realized he can make same cuboids by making it hollow . then it takes some cubes less . what is the number of the cubes to be removed ?
['A.1000', 'B.2000', 'C.3000', 'D.4000', 'e ) 5000']E.
volume of the small cube = 0.03 m ^ 3 so side of this cube = cubic root of 0.03 m ^ 3 = . 312 m so after removing the outermost layer the dimensions for the inner cuboid will be ( 5 - 2 * 0.312 ) , ( 6 - 2 * 0.312 ) , ( 7 - 2 * 0.312 ) so total volume will be ( 4.376 ) * ( 5.376 ) * ( 6.376 ) = 150 m ^ 3 so no of cubes will be 150 / 0.03 = 5000 so we can remove 5000 inner cubes answer : e | null |
Question: if a speaks the truth 70 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
A.0.49.
B.0.48.
C.0.41.
D.0.42.
e ) 0.411D.
"explanation : probability that a speaks truth is 70 / 100 = 0.7 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) Γ p ( b ) = 0.7 Γ 0.6 = 0.42 answer : d" | null |
Question: find the curved surface area , if the radius of a cone is 21 m and slant height is 15 m ?
['A.660', 'B.770', 'C.880', 'D.900', 'e ) 990']E.
cone curved surface area = Γ― β¬ rl 22 / 7 Γ£ β 21 Γ£ β 15 = 66 Γ£ β 15 = 990 m ( power 2 ) answer is e . | null |
Question: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 130 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
A.280.
B.400.
C.540.
D.650.
e ) 840D.
"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d ." | null |
Question: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 22 sec . what is the length of the goods train ?
A.299.
B.190.
C.276.
D.270.
e ) 281B.
"speed = 72 * 5 / 18 = 20 m / sec . time = 22 sec . let the length of the train be x meters . then , ( x + 250 ) / 22 = 20 x = 190 m . answer : b" | null |
Question: john was thrice as old as tom 6 years ago . john will be 9 / 7 times as old as tom in 6 years . how old is tom today ?
A.6.
B.8.
C.10.
D.12.
e ) 14B.
"j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 9 / 7 * ( t + 6 ) 7 j + 42 = 9 t + 54 7 ( 3 t - 12 ) + 42 = 9 t + 54 12 t = 96 t = 8 the answer is b ." | null |
Question: how many integers from 0 to 48 , inclusive , have a remainder of 1 when divided by 3 ?
A.15.
B.16.
C.17.
D.18.
e ) 19B.
"my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 46 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 46 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 45 or , n - 1 = 15 or , n = 16 b" | null |
Question: what is the prime factors β number of 36 ?
A.2.
B.3.
C.4.
D.5.
e ) 6C.
"prime factors β number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 2 prime factors β number will be 2 + 2 = 4 . hence , answer is c ." | null |
Question: how much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
A.55.
B.99.
C.88.
D.76.
e ) 12A.
"the distance to be covered = sum of their lengths = 250 + 300 = 550 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 550 / 10 = 55 sec . answer : a" | null |
Question: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v =
A.36.
B.39.
C.42.
D.45.
e ) 48D.
"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d ." | null |
Question: ( 4300231 ) - ? = 2535618
A.1865113.
B.1775123.
C.1764613.
D.1675123.
e ) none of themC.
"let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c" | null |
Question: the difference of 2 digit no . & the no . obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?
A.6.
B.8.
C.10.
D.12.
e ) 13B.
let the number be xy . given xy β yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten β s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) β ( 10 y + x ) = 36 = > x β y = 4 = > 2 y β y = 4 . hence , ( x + y ) β ( x β y ) = 3 y β y = 2 y = 8 b | null |
Question: the average of 5 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
A.12.5.
B.26.2.
C.6.5.
D.7.5.
e ) 12D.
"5 * 15 + 36 β 26 = 75 / 10 = 7.5 answer : d" | null |
Question: the length of a rectangle is reduced by 10 % . by what % would the width have to be increased to maintain the original area ?
A.10 %.
B.11.1 %.
C.25 %.
D.30 %.
e ) 35 %B.
"sol . required change = ( 10 * 100 ) / ( 100 - 10 ) = 11.1 % b" | null |
Question: rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
A.s 4000.
B.s 2800.
C.s 1800.
D.s 1500.
e ) s 1550E.
"explanation : average rate = ( 144 / 3500 ) * 100 = 4.11 ratio = 8.85 : 11.14 so , first part = ( 8.85 / 20 ) * 3500 = rs 1550 . answer : e" | null |
Question: a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
A.7 sec.
B.6 sec.
C.4 sec.
D.2 sec.
e ) 9 secB.
"speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b" | null |
Question: what is the sum of all 4 digit integers formed using the digits 2 , 3 , 4 and 5 ( repetition is allowed )
A.444440.
B.610000.
C.666640.
D.995456.
e ) 880000D.
n = 4 * 4 * 4 * 4 = 256 < x > = ( 5555 + 2222 ) / 2 = 3888.5 sum = number of integers x average value n * < x > = 256 * 3888.5 = 711040 answer = d | null |
Question: length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
A.55 m.
B.60 m.
C.80 m.
D.82 m.
e ) 84 mA.
"let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m a" | null |
Question: what is the diagonal of a square field whose perimeter is 24 m ?
['A.8 m', 'B.2 m', 'C.7 m', 'D.10 m', 'e ) 6 β 2 m']E.
sol : let the side of the square be x meters . therefore , 4 x = 24 x = 6 diagonal of the square is = β 2 * ( 6 ) ^ 2 = 6 β 2 answer : e | null |
Question: due to construction , the speed limit along an 5 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A.3.12.
B.8.
C.10.
D.15.
e ) 24A.
"old time in minutes to cross 5 miles stretch = 5 * 60 / 55 = 5 * 12 / 11 = 5.45 new time in minutes to cross 5 miles stretch = 5 * 60 / 35 = 5 * 12 / 7 = 8.57 time difference = 3.12 ans : a" | null |
Question: the average age of an adult class is 40 years . 2 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was the original strength of class ?
A.10.
B.12.
C.16.
D.2.
e ) 22D.
"let original strength = y then , 40 y + 2 x 32 = ( y + 2 ) x 36 Γ’ β‘ β 40 y + 64 = 36 y + 72 Γ’ β‘ β 4 y = 8 Γ’ Λ Β΄ y = 2 d" | null |
Question: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 9 hours respectively . the ratio of their speeds is ?
A.4 : 5.
B.4 : 3.
C.4 : 4.
D.4 : 9.
e ) 3 : 4E.
"let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = β b : β a = β 9 : β 16 = 3 : 4 answer : e" | null |
Question: a person travels equal distances with speeds of 3 km / hr , 4 km / hr , 5 km / hr . and takes a total time of 47 minutes . find the total distance ?
A.3.
B.2.
C.5.
D.4.
e ) 6A.
"let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 4 ) + ( x / 5 ) = 47 / 60 x = 1 total distance = 3 * 1 = 3 km correct option is a" | null |
Question: the product of a and b is equal to 11 more than twice the sum of a and b . if b = 5 , what is the value of b - a ?
A.- 2.
B.5.
C.7.
D.24.
e ) 35A.
"ab = 11 + 2 ( a + b ) 5 a = 11 + 2 a + 10 3 a = 21 a = 7 b - a = 5 - 7 = - 2 a is the answer" | null |
Question: in town x , 64 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
A.16 %.
B.25 %.
C.32 %.
D.40 %.
e ) 52 %B.
"let population be 100 total employed people = 64 % of the population = 64 employed males = 48 % of the population = 48 employed females = 16 % of the population = 16 employed females % in terms of employed people = ( 16 / 64 ) * 100 = 25 % answer is b ." | null |
Question: if s is a positive integer , and if the units ' digit of s ^ 2 is 4 and the units ' digit of ( s + 1 ) ^ 2 is 1 , what is the units ' digit of ( s + 2 ) ^ 2 ?
A.0.
B.2.
C.4.
D.6.
e ) 8A.
a for me . _ 1 Β² = _ 1 _ 2 Β² = _ 4 _ 3 Β² = _ 9 _ 4 Β² = _ 6 _ 5 Β² = _ 5 _ 6 Β² = _ 6 _ 7 Β² = _ 9 _ 8 Β² = _ 4 _ 9 Β² = _ 1 _ 0 Β² = _ 0 on the list , the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _ 8 . so , s = _ 8 , that has square 4 . the next square is 1 andnext nextsquare is 0 . | null |
Question: in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?
A.30.
B.35.
C.40.
D.45.
e ) 50B.
"make a venn diagram , and enter your data . let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10 + 25 = 35 answer b" | null |
Question: the arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
A.10.5.
B.11.
C.11.5.
D.12.
e ) 12.5B.
"the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.0 - 2 * 1.5 = 11 . answer : b ." | null |
Question: if a * b denotes the greatest common divisor of a and b , then ( ( 16 * 20 ) * ( 18 * 24 ) ) = ?
A.24.
B.12.
C.6.
D.4.
e ) 2E.
the greatest common divisor of 16 and 20 is 4 . hence 16 * 20 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 16 * 20 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e . | null |
Question: the average weight of a group of boys is 30 kg . after a boy of weight 39 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
A.A.4.
B.B.8.
C.C.6.
D.D.2.
e ) e ) 1B.
"let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 39 kg joins the group , total weight of boys = 30 x + 39 so 30 x + 39 = 31 ( x + 1 ) = > x = 8 . answer : b" | null |
Question: by selling a book for 260 , 20 % profit was earned . what is the cost price of the book ?
A.A.215.
B.B.216.
C.C.230.
D.D.235.
e ) e ) 240B.
"sp = 120 % of cp ; : . cp = 260 Γ 100 / 120 = 216 option ' b '" | null |
Question: a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 12 seconds to pass him . if the goods train is 300 m long , find its speed
A.52 kmph.
B.56 kmph.
C.58 kmph.
D.30 kmph.
e ) 34 kmphD.
"explanation : relative speed = 300 / 12 m / sec = ( ( 300 / 12 ) Γ ( 18 / 5 ) ) kmph = 90 kmph . speed of goods train = ( 90 - 60 ) kmph = 30 kmph answer : option d" | null |
Question: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 65 percent carbonated water , what percent of the volume of the mixture is p ?
A.20 %.
B.40 %.
C.50 %.
D.60 %.
e ) 80 %B.
"65 % is 15 % - points below 80 % and 10 % - points above 55 % . so the ratio of solution p to solution q is 2 : 3 . mixture p is 2 / 5 = 40 % of the volume of mixture pq . the answer is b ." | null |
Question: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 12 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
A.3.
B.4.
C.5.
D.6.
e ) 7C.
"the class borrowed a total of 40 * 2 = 80 books . the 26 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 12 * 2 = 36 . to maximize the number of books borrowed by 1 student , let ' s assume that 13 students borrowed 3 books and 1 student borrowed the rest . 80 - 36 - 3 * 13 = 5 the maximum number of books borrowed by any student is 5 . the answer is c ." | null |
Question: shop offered 40 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
A.500.
B.550.
C.600.
D.933.
e ) 750D.
"sp * ( 60 / 100 ) = 560 sp = 9.33 * 100 = > cp = 933 answer : d" | null |
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