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Al_Challenge

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14,882
general
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 $ 0.92 at the candy store . what is john ’ s weekly allowance ?
"x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d ."
a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75
d
14,883
physics
two goods trains each 750 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
"relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : option a"
a ) 72 , b ) 45 , c ) 48 , d ) 51 , e ) 44
a
14,884
gain
a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 4400 . what is the share of b ?
let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 4400 x ( 2 / 11 ) ) = rs . 800 . answer is b
a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
b
14,885
general
if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ?
"the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 12 is 6 . hence 18 * 12 = 6 . hence ( ( 12 * 16 ) * ( 18 * 12 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
e
14,886
physics
a group of men decided to do a work in 50 days , but 10 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
"original number of men = 10 * 60 / ( 60 - 50 ) = 60 answer is a"
a ) 60 , b ) 50 , c ) 40 , d ) 100 , e ) 25
a
14,887
physics
a train 200 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
"answer : c . speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 200 m at 50 / 3 m / sec = 200 * 3 / 50 sec = 12 sec"
a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
c
14,888
general
if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9000 ?
"required difference = [ 3 Β½ % of rs . 9000 ] – [ 3 1 / 3 % of rs . 9000 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9000 = 1 / 6 % of rs . 9000 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9000 ] = rs . 15 . answer is c ."
a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 10
c
14,889
physics
working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
"assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 15 x + y = 30 so xy = 150 the answer choices are : 26 days 15 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 15 days for jose and 10 days for jane . answer : b"
a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days
b
14,890
other
at an international conference , β€œ red ” world countries and β€œ blue ” world countries are the only participants . the ratio of β€œ red ” world participants to β€œ blue ” world participants is 2 : 1 . if one - third of β€œ red ” world participants are left - handed and two - thirds of β€œ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
"red : blue = 2 : 1 let red = 2 x and blue = 1 x 1 / 3 of red are left handed = > 1 / 3 * 2 x = 2 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 1 x = 2 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 2 x / 3 + 2 x / 3 ) / ( 2 x + 1 x ) = 4 / 9 answer : e"
a ) 2 / 3 , b ) 4 / 5 , c ) 6 / 2 , d ) 5 / 2 , e ) 4 / 9
e
14,891
general
in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 3 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
"number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 3 = ~ 4.14 passengers using logan airport = 4.14 / 4 = ~ 1.01 so e"
a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.01
e
14,892
general
every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 4 / 5 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
"let total number of juniors = j total number of seniors = s ( 4 / 5 ) j = ( 1 / 2 ) s = > s = 8 / 5 j total number of students = j + s = ( 13 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 13 / 5 ) j ] = 5 / 13 answer c"
a ) 13 / 20 , b ) 11 / 3 , c ) 5 / 13 , d ) 12 / 17 , e ) 17 / 20
c
14,893
gain
350 is increased by 50 % . find the final number .
explanation final number = initial number + 50 % ( original number ) = 350 + 50 % ( 350 ) = 350 + 175 = 525 . answer d
a ) 725 , b ) 625 , c ) 225 , d ) 525 , e ) 425
d
14,894
geometry
a certain cube floating in a bucket of water has between 75 and 85 percent of its volume below the surface of the water . if between 9 and 16 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
if sides are 7 , vol = 7 ^ 3 = 343 75 % = 257.25 , 85 % = 291.55 so vol above water , between 85.75 and 51.45 - - > too big if side are 4 , vol = 64 75 % = 48 , 85 % = 54.4 vol above water between 16 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 75 % = 93.75 , . 85 % = 106.25 vol above water between 18.75 - 31.25 ( sides are 4 cubic centimeters ) a
['a ) 4', 'b ) 5', 'c ) 7', 'd ) 8', 'e ) 9']
a
14,895
general
a primitive village follows a strange custom . they have babies only to have a boy . whenever a boy is born in a family , they stop having babies and whenever a girl is born , they have a baby again and again till a boy is born . the probability of having a boy is same as the probability of having a girl . what will be the proportion of boys to girls in the village after some time ?
e 1 : 1 ( approx ) explanation : we know that the probability of having a boy or having a girl is same and thus , half of the couples will stop after having a boy child . half of the others will have a girl and will have a baby again . out of those half of the couples , half will have a boy and will stop and half will have a girl again . this will keep on going like this . now , if there are x number of couples , there will be x boys . 1 / 2 have a boy and stop : 0 girls 1 / 4 have a girl , then a boy : x / 4 girls 1 / 8 have 2 girls , then a boy : 2 * x / 8 girls 1 / 16 have 3 girls , then a boy : 3 * x / 16 girls 1 / 32 have 4 girls , then a boy : 4 * x / 32 girls … total : x boys and 1 x 2 x 3 x 4 x – + – + – + β€” + … = ~ x therefore , the proportion of boys to girls will be extremely close to 1 : 1
a ) 2.1 , b ) 1.3 , c ) 5.1 , d ) 2.3 , e ) 1.1
e
14,896
general
in a simultaneous throw of a pair of dice , find the probability of getting a total more than 9
"total number of cases = 8 * 8 = 64 favourable cases = [ ( 2,8 ) , ( 3,6 ) , ( 3,7 ) , ( 4,6 ) , ( 4,7 ) , ( 4,8 ) , ( 5,5 ) , ( 5,6 ) , ( 5,7 ) , ( 5,8 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) , ( 6,7 ) , ( 6,8 ) , ( 7,3 ) , ( 7,4 ) , ( 7,5 ) , ( 7,6 ) , ( 7,7 ) , ( 7,8 ) , ( 8,2 ) , ( 8,3 ) , ( 8,4 ) , ( 8,5 ) , ( 8,6 ) , ( 8,7 ) , ( 8,8 ) ] = 28 so probability = 28 / 64 = 7 / 18 answer is b"
a ) 1 / 2 , b ) 7 / 18 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17
b
14,897
physics
a 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
"speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 36 = 50 / 3 3 x + 900 = 1800 = > x = 300 m . answer : b"
a ) 288 , b ) 300 , c ) 889 , d ) 276 , e ) 234
b
14,898
general
if x ^ 2 + y ^ 2 = 13 and xy = 3 , then ( x βˆ’ y ) ^ 2 =
"but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 13 - 2 * 3 = 7 . . answer a"
a ) 7 , b ) 11 , c ) 14 , d ) 17 , e ) 20
a
14,899
gain
an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
"in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ."
a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
e
14,900
general
what is the sum of all the even numbers between 31 and 99 , inclusive ?
"to figure this problem out , you just have to add all the even numbers , starting with 32 . 32 + 34 + 36 + 38 and so on , all the way up to 98 . you ' ll get 2,180 , so final answer : d"
a ) 3,000 , b ) 2,562 , c ) 2,500 , d ) 2,180 , e ) 2,766
d
14,901
general
in a factory , an average of 70 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 68 sets / day . the average production per day for day last 5 days is ?
"production during these 5 days = total production in a month - production in first 25 days . = 30 x 68 - 25 x 70 = 290 ∴ average for last 5 days = 290 / 5 = 58 e"
a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 58
e
14,902
gain
if a large pizza has a radius that is 40 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
let the radius of medium pizza be r . then the radius of large pizza is 1.4 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.4 * r ) ^ 2 = 1.96 * pi * r ^ 2 , an increase of 96 % . the answer is c .
a ) 40 % , b ) 80 % , c ) 96 % , d ) 112 % , e ) 124 %
c
14,903
general
the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than a
"explanation : given that a + b = 16 + b + c = > a ? c = 16 + b ? b = 16 = > c is younger than a by 16 years answer : option b"
a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15
b
14,904
general
in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995
tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b
a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500
b
14,905
gain
on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
"explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r Γ£ β€” si ) / ( 2 Γ£ β€” 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r Γ£ β€” si ) / ( 2 Γ£ β€” 100 ) = 14 ( r Γ£ β€” 326 ) / ( 2 Γ£ β€” 100 ) = 14 r = 8.58 % answer : option c"
a ) 15 % , b ) 14.25 % , c ) 8.58 % , d ) 10.5 % , e ) 11.5 %
c
14,906
gain
if the compound interest on a certain sum of money for 7 years at 10 % per annum be rs . 993 , what would be the simple interest ?
"let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 7 yrs = ( 3000 x 10 x 7 ) / 100 = 2100 / - answer : d ."
a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 2100 , e ) none
d
14,907
gain
a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams . find the profit percent .
explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 940 100 + g / 100 + 0 = 1000 / 940 100 + g = 100 / 94 * 100 g = 6.38 answer : d
a ) 7.38 , b ) 5.38 , c ) 4.38 , d ) 6.38 , e ) 3.38
d
14,908
general
the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 40 cents more than the commodity y ?
"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a ."
a ) 2007 , b ) 2008 , c ) 2009 , d ) 2010 , e ) 2011
a
14,909
physics
two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 15 hr . if all pipes are opened simultaneously , then the cistern will be filled in
"solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 βˆ’ 1 / 15 = 7 / 60 hence , tank will be filled in 60 / 7 = 8.57 hour option ( c )"
a ) 7.5 hr , b ) 8 hr , c ) 8.57 hr , d ) 10 hr , e ) none of these
c
14,910
other
a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
"p ( both are red ) , = 3 c 2 / 8 c 2 = 6 c 213 c 2 = 3 / 28 c"
a ) 2 / 21 , b ) 3 / 41 , c ) 3 / 28 , d ) 3 / 31 , e ) 5 / 32
c
14,911
general
what is the sum of 100 consecutive integers from - 49 inclusive , in a increasing order ?
"from - 49 to - 1 - - > 49 nos . zero - - > 1 number from + 1 to + 49 - - > 49 nos . when we add up nos . from - 49 to + 49 sum will be zero . total 99 nos will be added . 100 th number will be 50 . sum of these 100 nos . = 50 . b is the answer ."
a ) - 29 , b ) 50 , c ) - 30 , d ) 30 , e ) 60
b
14,912
general
a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.5 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
"volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.5 = 300 answer : b"
a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 2,400
b
14,913
general
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 , - 4 ) , how many units is p from the y - axis ?
"the x - axis is 4 units from the point p . thus the y - axis is 8 units from the point p . the answer is c ."
a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
c
14,914
general
find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1568 ?
"1568 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1400 . answer : d"
a ) 1000 , b ) 2777 , c ) 2889 , d ) 1400 , e ) 2771
d
14,915
physics
cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 4 hours , how many minutes did it take cole to drive to work ?
first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 4 hrs therefore , 4 = d / 75 + d / 105 lcm of 75 and 105 = 525 4 = d / 75 + d / 105 = > 4 = 7 d / 525 + 5 d / 525 = > d = 525 / 3 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 3 x 75 ) = > t 1 = ( 7 x 60 ) / 3 - - in minutes = > t 1 = 140 minutes . e
a ) 66 , b ) 70 , c ) 95 , d ) 112 , e ) 140
e
14,916
gain
if the annual increase in the population of a town is 10 % and the present number of people is 12000 , what will the population be in 2 years ?
"the required population is = 12000 ( 1 + 10 / 100 ) ^ 2 = 12000 * 11 / 10 * 11 / 10 = 14520 answer is e"
a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 14520
e
14,917
physics
a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 4 miles per hour and 6 hours - 24 miles total 18 + 20 + 24 - 62 answer : option e .
a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
e
14,918
other
9 log 9 ( 5 ) = ?
"exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 5 ) = 5 correct answer d"
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
d
14,919
physics
beginning in town a , biker bob rides his bike 8 miles west , 5 miles north , 4 miles east , and then 15 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
"using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 8 - 4 = 4 m now this third side or the distance between town a and town b = 20 ^ 2 + 4 ^ 2 = sq root 416 = 20.4 miles answer : b"
a ) 25 miles , b ) 20.4 miles , c ) 30 miles , d ) 32 miles , e ) 33 miles
b
14,920
physics
a and b walk around a circular track . they start at 8 a . m from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 9 a . m
explanation : relative speed = ( 2 + 3 ) = 5 rounds per hour so , they cross each other 5 times in an hour hence , they cross 5 times before 9 a . m answer : option a
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
a
14,921
general
5 , 7 , 11 , 18 , 33 , ( . . . )
"explanation : 5 5 Γ— 2 - 3 = 7 7 Γ— 2 - 3 = 11 11 Γ— 2 - 3 = 18 18 Γ— 2 - 3 = 33 33 Γ— 2 - 3 = 63 answer : option d"
a ) 22 , b ) 35 , c ) 27 , d ) 63 , e ) 25
d
14,922
other
john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ?
let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d
a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000
d
14,923
general
the average of first 80 non - zero positive numbers is :
"explanation : sum of first n natural numbers = n ( n + 1 ) / 2 so , average of first n natural numbers = n ( n + 1 ) / 2 n = ( n + 1 ) / 2 required average = ( 80 + 1 ) / 2 = 81 / 2 = 40.5 . answer : d"
a ) 22.25 , b ) 31.25 , c ) 35 , d ) 40.5 , e ) none of these
d
14,924
general
find the value of x from this equation ? 7 ( x - 1 ) = 21
1 . divide both sides by 7 : 2 . simplify both sides : x - 1 = 3 3 . add 1 to both sides : x - 1 + 1 = 3 + 1 4 . simplify both sides : x = 4 b
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
b
14,925
other
in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those 3 teams , how many ny mets fans are there in this town ?
the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .
a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135
b
14,926
general
for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 5 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
"from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d ."
a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28350 , e ) $ 29160
d
14,927
geometry
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 y covered by the two roads ?
"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 y = 1000 + 600 - 25 = 1575 answer : option c"
a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
c
14,928
other
the h . c . f . of two numbers is 40 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
"the numbers are ( 40 x 11 ) and ( 40 x 15 ) . larger number = ( 40 x 15 ) = 600 . answer : b"
a ) 276 , b ) 600 , c ) 699 , d ) 722 , e ) 745
b
14,929
general
if the sum of two positive integers is 22 and the difference of their squares is 44 , what is the product of the two integers ?
"let the 2 positive numbers x and y x + y = 22 - - 1 x ^ 2 - y ^ 2 = 44 = > ( x + y ) ( x - y ) = 44 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 12 y = 10 product = 12 * 10 = 120 answer c"
a ) 108 , b ) 119 , c ) 120 , d ) 135 , e ) 143
c
14,930
general
10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 120000 , find the cost of a camel ?
"cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 120000 p = rs . [ ( 24 * 4 * 4 * 120000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 46080000 / 9600 ) = > p = rs . 4800 answer : d"
a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4800 , e ) s . 6880
d
14,931
general
subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 10 pages .
"subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 10 / 2.5 ) = 4 hrs answer : d"
a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 16
d
14,932
gain
a glass was filled with 10 ounces of water , and 0.06 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
"we are given that 0.06 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.06 by 20 . this gives us : 0.06 x 20 = 1.2 ounces finally , we are asked for β€œ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 1.2 / 10 ) x 100 % ( 12 / 100 ) x 100 % = 12 % answer d"
a ) 0.002 % , b ) 0.02 % , c ) 0.2 % , d ) 12 % , e ) 20 %
d
14,933
general
20 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
"1 st person will shake hand with 19 people 2 nd person will shake hand with 18 people 3 rd person will shake hand with 17 people . . . . . . total no . of handshakes = 19 + 18 + 17 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 190 or , if there are n persons then no . of shakehands = nc 2 = 20 c 2 = 190 answer : a"
a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230
a
14,934
physics
length of a rectangular plot is 32 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
"let breadth = x metres . then , length = ( x + 32 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 32 ) + x ] = 200 2 x + 32 = 100 2 x = 68 x = 34 . hence , length = x + 32 = 66 m b"
a ) 56 m , b ) 66 m , c ) 76 m , d ) 86 m , e ) 96 m
b
14,935
general
if a * b * c = 65 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
"explanation : a Γ’ Λ† β€” b Γ’ Λ† β€” c / b Γ’ Λ† β€” c Γ’ Λ† β€” d = 65 / 65 = > a / d = 1 d Γ’ Λ† β€” e Γ’ Λ† β€” f / c Γ’ Λ† β€” d Γ’ Λ† β€” e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 1 * 1 / 4 = 1 / 4 answer : b"
a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
b
14,936
physics
the distance between delhi and mathura is 150 kms . a starts from delhi with a speed of 25 kmph at 5 a . m . for mathura and b starts from mathura with a speed of 40 kmph at 6 p . m . from delhi . when will they meet ?
d = 150 – 25 = 125 rs = 40 + 25 = 65 t = 125 / 65 = 2 hours 6 a . m . + 2 = 8 a . m . . answer : c
a ) 11 , b ) 77 , c ) 8 , d ) 10 , e ) 12
c
14,937
geometry
the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side
explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a
['a ) rs . 200', 'b ) rs . 672', 'c ) rs . 546', 'd ) rs . 876', 'e ) none of these']
a
14,938
general
the instructions state that cheryl needs 4 / 9 square yards of one type of material and 2 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 18 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
"total bought = 4 / 9 + 2 / 3 left part 8 / 18 - - - > 4 / 9 so used part 4 / 9 + 2 / 3 - 4 / 9 = 2 / 3 answer : c"
a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
c
14,939
general
a jogger running at 9 km / hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e
a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 36 sec , e ) 32 sec
e
14,940
general
a batsman in his 10 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
"average score before 10 th innings = 85 - 3 Γ— 10 = 50 average score after 10 th innings = > 50 + 3 = 53 answer : b"
a ) 47 , b ) 53 , c ) 39 , d ) 43 , e ) 42
b
14,941
general
the average of first six prime numbers greater than 3 is ?
"5 + 7 + 11 + 13 + 17 + 19 = 72 / 6 = 12 answer : c"
a ) 16 , b ) 10 , c ) 12 , d ) 19 , e ) 17.8
c
14,942
physics
eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 460 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
"distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 460 km time taken by freddy = 4 hours average speed of freddy = 460 / 4 = 115 km / hour ratio of average speed of eddy to freddy = 200 / 115 = 40 / 23 answer e"
a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 40 / 23
e
14,943
gain
on a certain road , 40 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
"suppose there are x motorists . 40 % of them exceeded the speed limit and received the ticket , i . e . 2 x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = 2 x / 5 or y / x = 1 / 2 or y / x * 100 = 1 / 2 * 100 = 50 % e"
a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 50 %
e
14,944
gain
a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 46 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 54 in what ratio should he mix the water and milk ?
"water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.46 m = = > revenue = price x quantity = 0.54 ( m + w ) = = > profit = 0.54 ( m + w ) - 0.46 m = 0.2 * ( 0.46 m ) [ 20 % of cost ] = = > 0.54 m + 0.54 w - 0.46 m = 0.092 m = = > 0.012 m = 0.54 w = = > m / w = 0.54 / 0.012 = 45 - - or - - w / m = 1 / 45 d is correct ."
a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 45 , e ) 6 : 11
d
14,945
general
the denominator of a fraction is 1 less than twice the numerator . if the numerator and denominator are both increased by 1 , the fraction becomes 3 / 5 . find the fraction ?
let the numerator and denominator of the fraction be ' n ' and ' d ' respectively . d = 2 n - 1 ( n + 1 ) / ( d + 1 ) = 3 / 5 5 n + 5 = 3 d + 3 5 n + 5 = 3 ( 2 n - 1 ) + 3 = > n = 5 d = 2 n - 1 = > d = 9 hence the fraction is : 5 / 9 answer : d
a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 9 , e ) none of these
d
14,946
other
in a family 13 people eat only vegetarian , 7 people eat only non veg . , 8 people eat both veg and non veg . . how many people eat veg in the family ?
"total people eat veg = only veg + both veg and non veg total = 13 + 8 = 21 answer = e"
a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21
e
14,947
general
q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 60 , what is the greatest possible value of q minus r ?
"a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 60 . the greatest multiple of 9 which is less than 60 is 54 . the answer is b ."
a ) 52 , b ) 54 , c ) 55 , d ) 56 , e ) 58
b
14,948
other
in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ?
"required ratio = 500 : 500 = 1 : 1 answer a"
a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
a
14,949
physics
a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 6 km ?
"m = 4 s = 2 us = 4 - 2 = 2 d = 6 t = 6 / 2 = 3 answer : a"
a ) 3 , b ) 5 , c ) 6 , d ) 67 , e ) 7
a
14,950
physics
an aeroplane covers a certain distance at a speed of 240 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
"distance = ( 240 x 4 ) = 960 km . speed = distance / time speed = 960 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 960 x 3 / 5 ) km / hr = 576 km / hr answer c ) 576 km / hr"
a ) 520 , b ) 620 , c ) 576 , d ) 740 , e ) 720
c
14,951
gain
what quantity of water should be added to reduce 5 litres of 45 % acidic liquid to 25 % acidic liquid ?
"quantity of acid in 5 litres = 45 * 5 / 100 = 2.25 litres let x litres of water is added to the solution , then there is 2.25 litres of acid in ( 5 + x ) litres of liquid . 25 % of ( 5 + x ) = 2.25 , 25 / 100 * ( 5 + x ) = 2.25 x = 225 - 125 / 25 = 4 answer : d"
a ) 3 litres , b ) 2 litres , c ) 4 litres , d ) 4.5 litres , e ) 5 litres
d
14,952
general
how many 3 - digit numbers are completely divisible 6 ?
"3 - digit number divisible by 6 are : 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then tn = 996 . a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 number of terms = 150 . b )"
a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
b
14,953
gain
there were two candidates in an election . winner candidate received 62 % of votes and won the election by 408 votes . find the number of votes casted to the winning candidate ?
"w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 408 62 % - - - - - - - - ? = > 1054 answer : b"
a ) 288 , b ) 1054 , c ) 788 , d ) 298 , e ) 177
b
14,954
gain
solve the quickfire maths brain teaser √ 9 % = ?
"a 30 % √ 9 % = > √ 9 / √ 100 = > 3 / 10 = > 30 / 100 = > 30 %"
a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 29 %
a
14,955
gain
the banker Γ’ € β„’ s discount of a certain sum of money is rs . 42 and the true discount on the same sum for the same time is rs . 36 . the sum due is
"sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 42 * 36 / 42 - 36 ] = rs . [ 42 * 36 / 6 ] = rs . 252 answer a"
a ) 252 , b ) 280 , c ) 360 , d ) 450 , e ) none
a
14,956
physics
a train is running at a speed of 40 km / hr and it crosses a post in 18 seconds . what is the length of the train ?
speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 18 s distance covered , d = vt = ( 400 / 36 ) Γ— 18 = 200 m distance covered is equal to the length of the train = 200 m correct answer is 200 metres
a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
c
14,957
physics
a race course is 400 m long . aa and bb run a race and aa wins by 5 m . bb and cc run over the same course and bb win by 4 m . cc and dd run over it and dd wins by 16 m . if aa and dd run over it , then who would win and by how much ?
if aa covers 400 m , bb covers 395 m if bb covers 400 m , cc covers 396 m if dd covers 400 m , cc covers 384 m now if bb covers 395 m , then cc will cover 396400 Γ— 395 = 391.05396400 Γ— 395 = 391.05 m if cc covers 391.05 m , then dd will cover 400384 Γ— 391.05 = 407.24400384 Γ— 391.05 = 407.24 if aa and dd run over 400 m , then dd win by 7.2 m option b
a ) 7.1 m , b ) 7.2 m , c ) 8 m , d ) 9 m , e ) 11 m
b
14,958
physics
in what time will a train 600 meters long cross an electric pole , if its speed is 144 km / hr
"explanation : first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 600 / 40 = 15 seconds answer : d"
a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 15 seconds , e ) none of these
d
14,959
other
the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio o
"4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 = = > 6.5 answer a"
a ) 6 : 5 , b ) 4 : 7 , c ) 3 : 5 , d ) 5 : 7 , e ) 8 : 9
a
14,960
gain
the sale price sarees listed for rs . 400 after successive discount is 10 % and 5 % is ?
"400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 answer : c"
a ) 166 , b ) 178 , c ) 342 , d ) 199 , e ) 112
c
14,961
general
if you add all the numbers on your mobile phone except 9 , what is the answer ?
"we have to add 0 to 8 to find the answer . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 answer is d"
a ) 45 , b ) 28 , c ) 65 , d ) 36 , e ) 42
d
14,962
general
the contents of a certain box consist of 48 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
"apple = ( apple + kiwi + x ) * 0.3 48 = ( 30 + 48 + x ) * 0.3 x = 82 answer : c"
a ) 90 , b ) 72 , c ) 82 , d ) 54 , e ) 65
c
14,963
general
f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn βˆ’ 1 ( x ) ) fn ( x ) = f 1 ( fn βˆ’ 1 ( x ) ) for n β‰₯ β‰₯ 2 . find f 5 ( 2 )
answer : a
a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1
a
14,964
general
on dividinng 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 18 a
a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 17
a
14,965
general
the tax on a commodity is diminished by 14 % and its consumption increased by 15 % . the effect on revenue is ?
"100 * 100 = 10000 86 * 115 = 9890 - - - - - - - - - - - 10000 - - - - - - - - - - - 110 100 - - - - - - - - - - - ? = > 1.1 % decrease answer : e"
a ) 2.1 % , b ) 8.1 % , c ) 5.1 % , d ) 6.1 % , e ) 1.1 %
e
14,966
general
set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 8 ?
"points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
d
14,967
gain
a present value of a machine is $ 2500 . its value depletiation rate is 5 % per annum then find the machine value after 2 years ?
"p = $ 2500 r = 5 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 2500 * 19 / 20 * 19 / 20 = $ 2256 approximately answer is c"
a ) $ 2100 , b ) $ 2546 , c ) $ 2256 , d ) $ 2451 , e ) $ 2345
c
14,968
physics
a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
"net part filled in 1 hour = ( 1 / 5 - 1 / 8 ) = 3 / 40 the cistern will be filled in 40 / 3 hrs i . e . , 13.3 hrs . answer : b"
a ) 5.2 hrs , b ) 13.3 hrs , c ) 1.9 hrs , d ) 7.2 hrs , e ) 1.4 hrs
b
14,969
geometry
rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
the area of rectangle a is ab . c = 5 a / 3 and d = 5 b / 3 . the area of rectangle b is cd = 25 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 9 ) = 9 / 25 . the answer is c .
['a ) 5 / 3', 'b ) 9 / 5', 'c ) 9 / 25', 'd ) 3 / 5', 'e ) 25 / 9']
c
14,970
physics
81 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
"( 81 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 180 180 – 81 = 99 answer : a"
a ) a ) 99 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 88
a
14,971
general
how many real solutions does the equation x 5 + 2 x 3 + 8 x 2 + 16 = 0 have ?
note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
b
14,972
general
in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 60,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
"for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 60,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 420,000 - $ 160,000 = $ 220,000 . the correct answer is e ."
a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 220,000
e
14,973
physics
in what time will a train 150 m long cross an electric pole , it its speed be 144 km / hr ?
"speed = 144 * 5 / 18 = 40 m / sec time taken = 150 / 40 = 3.8 sec . answer : c"
a ) 2.5 sec , b ) 1.9 sec , c ) 3.8 sec , d ) 6.9 sec , e ) 2.9 sec
c
14,974
gain
a trader marked the selling price of an article at 40 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
sol . let c . p . = rs . 100 . then , marked price = rs . 140 , s . p . = rs . 99 . ∴ discount % = [ 11 / 140 * 100 ] % = 7.8 % answer b
a ) 10 % , b ) 7.8 % , c ) 11 % , d ) 12.5 % , e ) none
b
14,975
general
define a = the sum of digits of the number 7 ^ 100 and b = the sum of the digits of a . what is the sum of the digits of b ?
following approach will take you only couple of sec . \ ( 7 ^ { 100 } = ( 7 ^ { 50 } ) ^ 2 \ ) the sum of digits ( digital root ) of a perfect square can only be 1 , 4 , 7 or 9 . for example \ ( 7 ^ 2 = 49 \ ) = > dr = 4 + 9 = 13 = > 1 + 3 = 4 and etc . checking available options . answer a .
a ) 7 , b ) 16 , c ) 10 , d ) 11 , e ) can not be determined
a
14,976
physics
the distance from steve ' s house to work is 30 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
"time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 30 km = > speed = 15 kmph answer : d"
a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 , e ) 20 .
d
14,977
general
in a party , there are rows arranged with 1220 and 30 chairs and there were 3 left in all the cases . when there were 11 rows . there were no chair left . if 30 chairs were added . then what will be the reminder ?
lcm of 12 , 2030 is 120 . so the number is in the form of 120 x + 3 which is divisible by 11 , by placing x = 3 , we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363 . so the no . is 363 . so when 30 is added to it and is divided by 11 we get remainder as 8 answer : a
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
a
14,978
gain
the true discount on a bill of rs . 540 is rs . 90 . the banker ' s discount is :
"p . w . = rs . ( 540 - 90 ) = rs . 450 . s . i . on rs . 450 = rs . 90 . s . i . on rs . 540 = rs . ( 90 / 450 ) x 540 = rs . 108 . b . d . = rs . 108 . answer : b"
a ) rs . 60 , b ) rs . 108 , c ) rs . 110 , d ) rs . 112 , e ) rs . 122
b
14,979
physics
10 men do a work in 10 days . how many men are needed to finish the work in 5 days ?
"men required to finish the work in 5 days = 10 * 10 / 5 = 20 answer is b"
a ) 50 , b ) 20 , c ) 30 , d ) 10 , e ) 15
b
14,980
general
ab + ba ___ 202 in the addition problem above , a and b represent digits in two different two - digit numbers . what is the sum of a and b ?
two ways to do it . . 1 ) straight logic . . only 20 fits in . . d
a ) 6 , b ) 8 , c ) 9 , d ) 20 , e ) 14
d
14,981
gain
tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 63000 after completion of one year . what will be jose ' s share of profit ?
"sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 63000 = 35000 d"
a ) 20000 , b ) 10000 , c ) 25000 , d ) 35000 , e ) 30000
d