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Question: when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 2 / 3 of the remaining balance , what will be the final balance in her bank account ?
A.300.
B.375.
C.400.
D.500.
e ) 575D.
"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 2 / 3 of 300 = 200 total amount in her account = 500 answer d" | null |
Question: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?
A.2.
B.3.
C.5.
D.6.
e ) 8B.
"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b" | null |
Question: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .
['A.180 cm', 'B.220 cm', 'C.240 cm', 'D.270 cm', 'e ) 300 cm']C.
we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c . | null |
Question: two pipes a and b can fill a tank in 10 hours and 20 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
A.10 / 3.
B.20 / 3.
C.15 / 7.
D.11 / 17.
e ) 1 / 4B.
"part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 20 part filled by ( a + b ) in 1 hour = 1 / 10 + 1 / 20 = 3 / 20 both the pipes together fill the tank in 20 / 3 hours answer is b" | null |
Question: the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?
A.71.
B.62.
C.53.
D.35.
e ) 45B.
explanation : let the number be 10 x + y . β΄ x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 β΄ 9 ( x - y ) = 3 β΄ x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 β΄ number = 62 answer : option b | null |
Question: in one alloy there is 10 % chromium while in another alloy it is 6 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
A.7.2 %.
B.9 %.
C.9.2 %.
D.8.6 %.
e ) 8.4 %A.
"the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.06 * 35 = 3.6 kg , so the percentage is 3.6 / 50 * 100 = 7.2 % . answer : a ." | null |
Question: the food in a camp lasts for 10 men for 20 days . if 30 more men join , how many days will the food last ?
A.8 days.
B.4 days.
C.5 days.
D.10 days.
e ) 17 daysC.
"one man can consume the same food in 10 * 20 = 200 days . 30 more men join , the total number of men = 40 the number of days the food will last = 200 / 40 = 5 days . answer : c" | null |
Question: surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be
['A.4920 cm 2', 'B.4727 cm 2', 'C.9856 cm 2', 'D.19712 cm 2', 'e ) none']C.
sol . let the original radius be r . then , original surface area = 4 Ο r 2 = 2464 cm 2 ( given ) . new radius = 2 r . β΄ new surface area = 4 Ο ( 2 r ) 2 = 4 x 4 Ο r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c | null |
Question: how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?
A.15.8 sec.
B.14.9 sec.
C.12.4 sec.
D.10.8 sec.
e ) 11.8 secD.
"d 16.8 sec d = 100 + 80 = 180 m s = 60 * 5 / 18 = 50 / 3 t = 180 * 3 / 50 = 10.8 sec" | null |
Question: - 74 x 29 + 265 = ?
A.2436.
B.- 1881.
C.- 2801.
D.- 2071.
e ) none of themB.
"given exp . = - 74 x ( 30 - 1 ) + 265 = - ( 74 x 30 ) + 74 + 265 = - 2220 + 339 = - 1881 answer is b" | null |
Question: the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?
A.1134.
B.1238.
C.1348.
D.1500.
e ) 1249E.
population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e | null |
Question: if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 14 , what is the value of x ?
A.- 4.
B.- 1 / 4.
C.0.
D.1 / 4.
e ) 4D.
"we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d" | null |
Question: the radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
A.200.
B.250.
C.300.
D.330.
e ) none of theseB.
"radius of the wheel of bus = 70 cm . then , circumference of wheel = 2 Ο r = 140 Ο = 440 cm distance covered by bus in 1 minute = 66 β 60 Γ 1000 Γ 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm β΄ revolutions per minute = 6600000 / 60 Γ 440 = 250 answer b" | null |
Question: harry started a 4 - mile hike with a full 6 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?
A.1 / 3.
B.2 / 3.
C.3 / 4.
D.5 / 4.
e ) 4 / 3B.
no of cups leaked during the trip = 2 cups . no of cups harry drank = 3 cups . no of cups harry drank during the first 3 miles = 2 . drink / mile = 2 / 3 answer : b | null |
Question: in a room filled with 7 people , 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
A.5 / 21.
B.3 / 7.
C.4 / 7.
D.5 / 7.
e ) 16 / 21B.
"there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs β sssibl β g β ssand β ssviceversa ) β ss ( c β ssis β ssds β sssibl β g β ssand β ssviceversa ) β ss ( c β ssis β ssdssibl β gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 5 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 5 - - 5 c 2 = 10 total = 1 + 1 + 10 = 12 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 12 / 21 ( 21 is 7 c 2 ) = 1 - 12 / 21 = 9 / 21 = 3 / 7 ans b" | null |
Question: two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively . they are turned on at the same time . if the tap a is turned off after 4 minutes , how long will tap b take to fill the rest of the cistern ?
A.8 min ..
B.9 min ..
C.10 min ..
D.7 min ..
e ) none of theseA.
in one min , ( a + b ) fill the cistern = 1 β 12 + 1 β 18 = 5 β 36 th in 4 min , ( a + b ) fill the cistern = 5 β 36 Γ 4 = 5 β 9 th rest part = 1 - 5 β 9 = 4 β 9 th β΅ 1 β 18 th part is filled by b in one min . β΄ 4 β 9 th part is filled by b in 18 Γ 4 β 9 = 8 min answer a | null |
Question: how many digits are in ( 8 Γ 10 ^ 18 ) ( 10 Γ 10 ^ 10 ) ?
A.24.
B.25.
C.26.
D.27.
e ) 30E.
"the question simplfies to ( 8 Γ 10 ^ 18 ) ( 10 ^ 11 ) = > 8 * 10 ^ 29 = > will contain 29 zeros + 1 digit 8 = > 30 ans e" | null |
Question: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 3 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
A.340.
B.360.
C.380.
D.400.
e ) 420D.
"the relative speed of jack and christina is 3 + 3 = 6 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 6 = 40 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 40 = 400 feet . answer : d ." | null |
Question: the speed of a boat in still water is 60 kmph and the speed of the current is 17 kmph . find the speed downstream and upstream ?
A.77,43 kmph.
B.80,80 kmph.
C.80,42 kmph.
D.80,40 kmph.
e ) 83,40 kmphA.
speed downstream = 60 + 17 = 77 kmph speed upstream = 60 - 17 = 43 kmph . answer : a | null |
Question: a solution of 70 litres contains oil and water in the ratio 9 : x . if 6 litres of water is added to the solution , the ratio becomes 6 : 4 , find the value of x ?
A.6.
B.8.5.
C.9.
D.6.5.
e ) 5E.
exp . total new quantity = original sol + water = 70 + 6 = 76 new ratio = 6 : 4 , new quantity of oil = 6 / 10 * 76 = 45.6 lit , new quantity of water = 4 / 10 * 76 = 30.4 lit water present initially = ( 30.4 - 6 ) = 24.4 lit ratio = 45.6 / 24.4 = 9 / x there for x = 4.81 approx 5 answer : e | null |
Question: if an article is sold at 18 % profit instead of 11 % profit , then the profit would be $ 56 more . what is the cost price ?
A.$ 600.
B.$ 800.
C.$ 1000.
D.$ 1200.
e ) $ 1400B.
"7 % * cost price = $ 56 1 % * cost price = $ 56 / 7 = $ 8 the cost price is $ 800 . the answer is b ." | null |
Question: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?
A.2.
B.3.
C.4.
D.5.
e ) 6D.
"minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d" | null |
Question: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 17 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
A.1 / 3.
B.2 / 3.
C.2 / 5.
D.3 / 5.
e ) 4 / 5C.
"let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ." | null |
Question: the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
A.24.
B.32.
C.75.
D.28.
e ) 11A.
"a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a" | null |
Question: the area of a triangle is with base 2 m and height 3 m ?
A.11.
B.10.
C.787.
D.3.
e ) 12D.
"1 / 2 * 2 * 3 = 3 m 2 answer : d" | null |
Question: if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =
A.540.
B.570.
C.619.
D.649.
e ) 700A.
"before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a" | null |
Question: the purchase price of an article is $ 48 . in order to include 5 % of cost for overhead and to provide $ 12 of net profit , the markup should be
A.15 %.
B.25 %.
C.30 %.
D.40 %.
e ) 45 %C.
"cost price of article = 48 $ % of overhead cost = 5 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 5 = 30 % answer c" | null |
Question: a store reduced the price of all items in the store by 12 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
A.80.0.
B.79.2.
C.81.0.
D.81.1.
e ) 81.9B.
"consider price of the all items as $ 100 after a initial reduction of 12 % price becomes = 0.88 * 100 = $ 88 after the final reduction of 10 % price becomes = 0.9 * 88 = $ 79.2 price of all items on second day is 79.2 % of price on first day correct answer option b" | null |
Question: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
A.10.5.
B.15.
C.15.5.
D.30.
e ) 60C.
"the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 10 x = 15.5 minutes answer : c" | null |
Question: when the smallest of 3 consecutive odd integers is added to 4 times the largest , it produces a result 732 more than 4 times the middle integer . find the numbers ?
A.732.
B.678.
C.698.
D.710.
e ) 729A.
x + 4 ( x + 4 ) = 732 + 4 ( x + 2 ) solve for x and find all three numbers x + 4 x + 16 = 732 + 4 x + 8 x = 724 x + 2 = 726 x + 4 = 728 check : the smallest is added to four times the largest 724 + 4 * 728 = 3636 four times the middle 4 * 726 = 2904 3636 is more than 2904 by 3636 - 2904 = 732 a | null |
Question: in a particular city there are 100 homes numbered from 1 , 23 , . . , 100 . the city was build by a builder from chennai . there was 4 to 5 shops in the town which was build by a builder from mumbai . the 2 nd builder can build in 1 Β½ times as compared to time by 1 st builder . the 2 nd builder builds in 15 days , then how many 2 ' s are used by the builder from chennai in numbering the 100 homes ?
A.17.
B.18.
C.19.
D.20.
e ) 21D.
in the last line it should be given the builder from chennai in numbering the 100 homes ? then ans is 20 answer : d | null |
Question: p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
A.5 days.
B.10 days.
C.14 days.
D.20 days.
e ) 26 daysD.
"explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 8 days = 8 Γ£ β ( 1 / 40 ) = 1 / 5 remaining work = 1 Γ’ β¬ β 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 15 ) = 12 total days = 8 + 12 = 20 answer : option d" | null |
Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 2 of the remaining paint . how many gallons of paint has joe used ?
A.18.
B.225.
C.175.
D.216.
e ) 250B.
"total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 2 ) * 270 = 135 gallons total paint used = 225 gallons . option b" | null |
Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
A.$ 28.
B.$ 82.
C.$ 110.
D.$ 138.
e ) $ 195E.
by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me . | null |
Question: set s consists of integers { 7 , 8 , 10 , 12 , 13 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 10 % . what is the value of integer n ?
A.10.
B.12.
C.16.
D.22.
e ) 24C.
"the average of the numbers in set s is 10 . if we increase the mean by 10 % , the new mean is 11 . thus , on average , 5 numbers increase by 1 . therefore n = 11 + 5 = 16 the answer is c ." | null |
Question: the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?
A.31.
B.42.
C.29.
D.97.
e ) 27B.
total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b | null |
Question: the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 2000 for a computer table , then what was the cost price of the computer table ?
A.2789.
B.2772.
C.1250.
D.6725.
e ) 2099C.
"cp = sp * ( 100 / ( 100 + profit % ) ) = 1250 ( 100 / 160 ) = rs . 1250 . answer : c" | null |
Question: a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
A.1 / 250.
B.9 / 74.
C.1 / 11.
D.1 / 9.
e ) 1 / 3B.
"probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b" | null |
Question: 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 ?
A.A.1.
B.B.2.
C.C.4.
D.D.8.
e ) e ) 16D.
"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" | null |
Question: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 600 per sq . metre .
A.$ 12375.
B.$ 13575.
C.$ 16575.
D.$ 14575.
e ) $ 18575A.
"a area = 5.5 Γ 3.75 sq . metre . cost for 1 sq . metre . = $ 600 hence , total cost = 5.5 Γ 3.75 Γ 600 = $ 12375 a" | null |
Question: if n = 10 ^ 100 and n ^ n = 10 k what is the value of k ?
A.200.
B.10 ^ 100.
C.10 ^ 102.
D.100 ^ 100.
e ) 1000 ^ 10C.
"there is a simple logic to this question . ( a ^ m ) ^ n = a ^ mn so , ( 10 ^ 100 ) ^ ( 10 ^ 100 ) = 10 ^ ( 100 * ( 10 ^ 100 ) ) = 10 ^ ( ( 10 ^ 2 ) * ( 10 ^ 100 ) ) = 10 ^ ( 10 ^ 102 ) and this equals 10 ^ k so , k = 10 ^ 102 answer : c" | null |
Question: a bag contains 30 red jellybeans and 30 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
A.9 / 100.
B.2 / 19.
C.1 / 8.
D.1 / 20.
e ) 3 / 10D.
"method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 1 / 20 answer : option d" | null |
Question: what is the sum of the multiples of 4 between 63 and 151 inclusive ?
A.2240.
B.2250.
C.2310.
D.2330.
e ) 2332E.
"the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e" | null |
Question: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
A.10.5 %.
B.12.5 %.
C.15 %.
D.22 %.
e ) 25 %E.
"0.1 m = 0.40 e = > e / m = 1 / 4 * 100 = 25 % so answer is e . m - # of motorists e - # of motorists exceeding speed" | null |
Question: if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
A.4 : 9.
B.4 : 3.
C.3 : 7.
D.2 : 5.
e ) 1 : 6A.
"the ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9 . the ratio of apples to bananas to cucumbers is 4 to 3 to 9 . the answer is a ." | null |
Question: car dealership x , the total profit from sales increased by 12 percent over the previous years , while the number of cars sold decreased by 12 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
A.18 %.
B.20 %.
C.22 %.
D.27.27 %.
e ) 35 %D.
"let profit be x and cars sold be y originally profit / car = x / y now it is 1.12 x / 0.88 y = 112 / 88 ( x / y ) increase in profit per car = ( ( 24 / 88 ) ( x / y ) ) / ( x / y ) * 100 = 27.27 % answer = d" | null |
Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :
A.57.
B.68.
C.77.
D.87.
e ) 97B.
"explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . β΄ number of members = β ( 4624 ) = 68 . 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 15 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 .D.
"ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer" | null |
Question: for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 99 true ?
A.1.
B.3.
C.5.
D.7.
e ) 9B.
"answer c ( a + b ) ( a - b ) = 99 3 cases for ( a + b ) , ( a - b ) 99 , 1 33 , 3 11 , 9 answer b" | null |
Question: how many positive integers less than 100 are there such that they are multiples of 8 or multiples of 7 but not both ?
A.21.
B.22.
C.25.
D.24.
e ) 31D.
"for 8 : 8 . . . 100 = 8 * 12 for 7 : 7 . . . 98 = 7 * 14 but there is one integer 8 * 7 . so n = ( 12 - 1 ) + ( 14 - 1 ) = 24 d" | null |
Question: when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?
A.- 4.
B.- 2.
C.15.
D.13.
e ) 22C.
"the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer ." | null |
Question: if - 3 x + 5 y = 48 and 3 x - 2 y = 6 , what is the product of x and y ?
A.252.
B.428.
C.464 ..
D.200.
e ) 642A.
"given - 3 x + 5 y = 48 - - - eq 1 3 x - 2 y = 6 - - eq 2 sum both eqns we get 3 y = 54 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 6 . = > x = 14 now xy = 14 * 18 = 252 option a is correct answer ." | null |
Question: a can give b 60 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
A.148.94.
B.148.13.
C.148.22.
D.111.0.
e ) 111.12A.
"a runs 1000 m while b runs 940 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 940 = 851.06 m . b can give c = 1000 - 851.06 = 148.94 m . answer : a" | null |
Question: kim finds a 6 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
A.7 / 5.
B.1 / 2.
C.8 / 15.
D.2 / 5.
e ) 3 / 5E.
"3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is e" | null |
Question: how many prime numbers between 1 and 100 are factors of 143 ?
A.6.
B.5.
C.4.
D.2.
e ) 3D.
"factor of 143 = 11 * 13 - - - 2 prime numbers d" | null |
Question: a jar contains a mixture of ab in the ratio 3 : 2 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
A.12.
B.15.
C.16.
D.20.
e ) 36E.
"20 litres of mixture that is replaced will contain 12 litres of a and 8 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 12 ] / [ 2 k - 8 + 20 ] = 2 / 3 = > 9 k - 36 = 4 k - 16 + 40 = > 5 k = 60 solve for k which is k = 12 so initial volume of liquid a = 3 k = 36 litres answer : e" | null |
Question: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 3,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
A.850.
B.1,100.
C.1,800.
D.2,550.
e ) 3,400C.
"assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 3600 therefore x = 2400 / 4 = 600 price of 28 inch + 30 inch = 800 + 1000 = 1800 option c" | null |
Question: the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
A.100.
B.110.
C.115.
D.125.
e ) 140C.
"let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c" | null |
Question: if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is
A.15.
B.28.
C.33.
D.42.
e ) 60C.
"take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c ." | null |
Question: john and beth each drove from smallville to crown city by different routes . john drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than john to complete the trip . how many miles per hour was beth ' s average speed on this trip ?
A.24.
B.30.
C.48.
D.54.
e ) 75B.
speed = distance / time distance for john = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for john + 5 = 20 + 5 = 25 miles time taken by beth = time taken by john + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer . | null |
Question: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 100 ?
A.100.
B.200.
C.300.
D.600.
e ) 900B.
"prime factorization out is the way to go here ! 36 ^ 100 3 ^ 2 times 2 ^ 2 and both to the power of 100 [ ( 3 ^ 2 ) * ( 2 ^ 2 ) ] ^ 100 giving you the beautifully simplistic answer of 3 ^ 200 and 2 ^ 200 ans is 200 answer : b" | null |
Question: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 17 positive perfect squares ?
A.1,010.
B.1,164.
C.1,240.
D.1,316.
e ) 1,785E.
"first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 17 and c = 1 / 2 into the equation and simplify to get the answer 1785 . option e ." | null |
Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men Γ’ β¬ β’ s wages are ?
A.6 rs.
B.2 rs.
C.4 rs.
D.9 rs.
e ) 12 rsE.
"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e" | null |
Question: a train is 250 meter long is running at a speed of 36 km / hour . in what time will it pass a station of 200 meter length ?
A.28 seconds.
B.27 seconds.
C.45 seconds.
D.26 seconds.
e ) 18 secondsC.
"speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 250 + 200 = 450 meter time = distance / speed = 450 * ( 10 ) = 45 seconds answer : c" | null |
Question: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :
A.57.
B.67.
C.77.
D.85.
e ) 97D.
"explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . β΄ number of members = β ( 7225 ) = 85 . answer : d" | null |
Question: triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be
A.9 : 10.
B.17 : 16.
C.23 : 27.
D.13 : 17.
e ) 15 : 23B.
"let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2023 / 1792 ( x ^ 2 / y ^ 2 ) = ( 17 * 17 * 7 ) / ( 16 * 16 * 7 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 16 ^ 2 x / y = 17 / 16 ans = b you need to take a hint from given options to find factors of 2013 and 2527 ." | null |
Question: two trains each 120 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 85 km / h while the other travels at 65 km / h . how long will it take for them to pass each other completely .
A.11.07 sec.
B.10.07 sec.
C.13.07 sec.
D.12.07 sec.
e ) 14.07 secB.
"explanation : d = 120 m + 120 m = 240 m rs = 85 + 65 = 150 * 5 / 18 = 417 / 10 t = 420 * 10 / 417 = 10.07 sec answer : option b" | null |
Question: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 15,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
A.20000.
B.30000.
C.40000.
D.30301.5.
e ) 50000D.
"a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 15,000 ( 1 + 0.04 / 4 ) ^ 4 - 15,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 15,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 15,000 ( 1.0201 + 1 ) = 30301.5 hence answer is d ." | null |
Question: the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?
A.14 %.
B.15 %.
C.25 %.
D.30 %.
e ) 35 %C.
"sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c" | null |
Question: find the area of a parallelogram with base 10 cm and height 20 cm .
A.200.
B.384.
C.200.
D.244.
e ) 242C.
"area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c" | null |
Question: a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be .
A.60 kmph.
B.63 kmph.
C.57 kmph.
D.70 kmph.
e ) 61 kmphA.
time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer is a . | null |
Question: if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?
A.40 %.
B.50 %.
C.60 %.
D.70 %.
e ) 80 %B.
"can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b" | null |
Question: 200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?
A.40.
B.50.
C.60.
D.70.
e ) 80A.
n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a | null |
Question: the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
A.10 metres.
B.5 metres.
C.7.5 metres.
D.data inadequate.
e ) none of theseB.
"l Γ b = 15 Γ b β΄ l = 15 m and l β b = 10 β΄ b = 15 β 10 = 5 m answer b" | null |
Question: what could be the range of a set consisting of odd multiples of 9 ?
A.21.
B.24.
C.35.
D.72.
e ) 70D.
"range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 9 * ( 2 n + 1 ) where n is any positive integer . range = 9 * ( 2 m + 1 ) - 9 * ( 2 n + 1 ) = 9 * 2 * ( m - n ) = 18 * ( m - n ) . m , n - any positive integers the answer must be divisible by 18 , which is only 72 . the correct answer is d" | null |
Question: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 10 % p . a . was rs . 420 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
A.rs . 2530.
B.rs . 2430.
C.rs . 2420.
D.rs . 2410.
e ) rs . 2440C.
"let the sum be rs . p p { [ 1 + 10 / 100 ] 2 - 1 } = 420 p ( 10 / 100 ) ( 2 + 10 / 100 ) = 420 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 420 / ( 0.1 ) ( 2.1 ) = 2000 . amount = 2000 + 420 = rs . 2420 answer : c" | null |
Question: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 25 meters . what distance is she from the starting point and in which direction ?
A.35 m east.
B.35 m north.
C.30 m west.
D.45 m west.
e ) 45 m eastE.
the net distance is 20 + 25 = 45 meters to the east . the answer is e . | null |
Question: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 4 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
A.5 : 4.
B.7 : 6.
C.9 : 8.
D.11 : 10.
e ) 13 : 12D.
"3 b = 7 c and so b = 7 c / 3 7 a = 4 b and so a = 4 b / 7 = 4 c / 3 a + b = 4 c / 3 + 7 c / 3 = 11 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 11 : 10 the answer is d ." | null |
Question: a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
A.1.7.
B.1.4.
C.1.1.
D.1.5.
e ) 1E.
"m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e" | null |
Question: a man gains 30 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
A.130 %.
B.140 %.
C.150 %.
D.260 %.
e ) 170 %D.
"explanation : let the c . p . = x , then s . p . = ( 130 / 100 ) x = 13 x / 10 new s . p . = 2 ( 13 x / 10 ) = 26 x / 10 profit = 26 x / 10 - x = 26 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 26 x / 10 ) * ( 1 / x ) * 100 = 260 % option d" | null |
Question: a train traveled the first d miles of its journey it an average speed of 50 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train β s average speed over the total distance was 96 miles per hour , what is the value of y ?
A.68.
B.84.
C.90.
D.120.
e ) 160E.
"average speed = total distance traveled / total time taken 3 d / d / 50 + d / y + d / 160 = 96 solving for d and y , 15 y = 11 y + 480 3 y = 480 y = 160 answer e" | null |
Question: 2 persons can finish a job in 8 days . first person alone can finish the work in 24 days . how many days does the second person take to finish the job ?
A.10 days.
B.12 days.
C.14 days.
D.16 days.
e ) 18 daysB.
2 persons can do work in 1 day = 1 / 8 first person can do work in 1 day = 1 / 24 second person can do work in 1 day = 1 / 8 - 1 / 24 = 1 / 12 so second person can finish work in 12 days answer : b | null |
Question: a cistern is filled by pipe a in 12 hours and the full cistern can be leaked out by an exhaust pipe b in 18 hours . if both the pipes are opened , in what time the cistern is full ?
A.50 hrs.
B.60 hrs.
C.36 hrs.
D.80 hrs.
e ) 90 hrsC.
"time taken to full the cistern = ( 1 / 12 - 1 / 18 ) hrs = 1 / 36 = 36 hrs answer : c" | null |
Question: | x + 3 | β | 4 - x | = | 8 + x | how many x solutions will this equation have ?
A.0.
B.1.
C.2.
D.3.
e ) 4A.
"x = | x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a" | null |
Question: of the 100 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren β t full - time and haven β t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
A.20.
B.30.
C.50.
D.80.
e ) 100A.
"full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 20 answer : option a" | null |
Question: a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x β 0 ?
A.25 / 9.
B.3 / 7.
C.5 / 3.
D.3 / 5.
e ) 9 / 25B.
"sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b" | null |
Question: the list price of an article is rs . 70 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
A.10.85 %.
B.14.85 %.
C.15.85 %.
D.16.85 %.
e ) 17.85 %A.
"70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 10.85 % answer : a" | null |
Question: a man swims downstream 42 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
A.2.
B.8.
C.9.
D.6.
e ) 10E.
"42 - - - 3 ds = 14 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : e" | null |
Question: a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b Γ’ β¬ β’ s contribution in the capital ?
A.24887.
B.20778.
C.23788.
D.15750.
e ) 2811D.
"explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 Γ£ β 12 ) : ( 4 x ) = 2 : 3 Γ’ β‘ β x = 15750 answer : d" | null |
Question: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?
A.6.
B.8.
C.10.
D.9.
e ) 13D.
joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d ) | null |
Question: 5 20 380 144020 ?
A.20741616380.
B.20841616380.
C.21741616380.
D.22741616380.
e ) 20791616380A.
"if number = n , then next number = n * ( n - 1 ) so 5 , ( 5 * 4 = 20 ) , ( 20 * 19 = 380 ) , ( 380 * 379 = 144020 ) , ( 144020 * 144019 = 20741616380 ) answer : a" | null |
Question: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
A.s . 4538.
B.s . 6342.
C.s . 4518.
D.s . 4530.
e ) s . 4517B.
"area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b" | null |
Question: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds . the length of the faster train is
A.80 m.
B.100 m.
C.120 m.
D.180 m.
e ) 160 mB.
"relative speed = 81 km / h = 81 x 5 / 18 m / sec = 22.5 m / sec length of slower train = speed x time = 36 x 8 km / hr = 288 x 5 / 18 m / sec = 80 m / sec let length of faster train = b time cross to each other 8 = ( 80 + b ) x 18 / ( 81 x 5 ) = 3240 - 1440 = 18 b 1800 / 18 = b b = 100 m answer : b" | null |
Question: if the mean of numbers 28 , x , 42 , 78 and 104 is 62 , then what is the mean of 128 , 255 , 280 , 511 , 1023 and x ?
A.395.
B.375.8.
C.355.
D.415.
e ) 365B.
"the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 104 = 62 * 5 - - > x = 58 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 280 + 511 + 1023 + 58 ) / 6 = 375.8 . answer : b ." | null |
Question: the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?
A.73.
B.74.
C.75.
D.76.
e ) 77D.
let x be the number of students in the class . let p be the average of the rest of the class . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d . | null |
Question: the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1260 respectively . what is the rate of interest ?
A.5 %.
B.8 %.
C.11 %.
D.14 %.
e ) 18 %A.
"1260 - 1200 = 60 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 60 ) / ( 1200 ) = 5 % the answer is a ." | null |
Question: a fair 2 sided coin is flipped 7 times . what is the probability that tails will be the result at least twice , but not more than 7 times ?
A.119 / 128.
B.120 / 113.
C.114 / 210.
D.121 / 141.
e ) 104 / 117A.
"at least twice , but not more than 7 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 7 c 2 / 2 ^ 7 + 7 c 3 / 2 ^ 7 + 7 c 4 / 2 ^ 7 + 7 c 5 / 2 ^ 7 + 7 c 6 / 2 ^ 7 = 119 / 128 option : a" | null |
Question: in february wilson β s earnings were 40 percent of his family β s total income . in march wilson earned 25 percent less than in february . if the rest of his family β s income was the same in both months , then , in march , wilson β s earnings were approximately what percent q of his family β s total income ?
A.15 %.
B.17 %.
C.24 %.
D.30 %.
e ) 33 %E.
lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march q = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e | null |
Question: the s . i . on a certain sum of money for 2 years at 4 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
A.5250.
B.1267.
C.5750.
D.2267.
e ) 5262A.
"explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 5250 answer : a" | null |
Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
['A.6564', 'B.7372', 'C.8281', 'D.9331', 'e ) can not be determined']C.
let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c . | null |
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