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Question: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 40 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A.A.5.61.
B.B.3.69.
C.C.10.
D.D.15.
e ) e ) 24B.
"old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 40 = 9 * 3 / 2 = 13.5 time difference = 3.69 ans : b" | null |
Question: how many figures are required to number the pages the pages of a book containing 2200 pages ?
A.7593.
B.6693.
C.7693.
D.7793.
e ) 7893C.
"1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 to 2200 = 1201 * 4 = 4804 - - - - - - - - - - - 7693 answer : c" | null |
Question: there are two cars . one is 100 miles north of the other . simultaneously , the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 15 miles per hour . how many miles apart are the cars after 3 hours ?
A.125.
B.150.
C.200.
D.225.
e ) 250A.
"here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 75 and a height of 100 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 75 lines up with the ' 3 ' and the 100 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 25 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 75 / 100 / 125 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : a" | null |
Question: what decimal fraction is 90 ml of a litre ?
A.. 9.
B.. 009.
C.. 09.
D.0.09.
e ) none of theseC.
answer required fraction = 90 / 1000 = 9 / 100 = . 09 correct option : c | null |
Question: what is the smallest integer k for which 64 ^ k > 4 ^ 20 ?
A.4.
B.5.
C.6.
D.7.
e ) 8D.
"64 ^ k > 4 ^ 20 4 ^ ( 3 k ) > 4 ^ 20 3 k > 20 k = 7 the answer is d ." | null |
Question: a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 210 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
A.5 mph.
B.10 mph.
C.20 mph.
D.30 mph.
e ) 40 mphD.
"solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i . e . r 2 = 20 mph answer : d" | null |
Question: a cistern 8 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
A.62 m 2.
B.50 m 2.
C.53.5 m 2.
D.55 m 2.
e ) 57 m 2A.
"area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : option a" | null |
Question: if 2994 Γ£ Β· 14.5 = 179 , then 29.94 Γ£ Β· 1.45 = ?
A.17.1.
B.17.3.
C.17.5.
D.17.7.
e ) 17.9E.
29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 179 in the place of 2994 / 14.5 ] = 179 / 10 = 17.9 answer is e . | null |
Question: ( β 27 + β 243 ) / β 75 = ?
A.2 β 2.
B.2 β 3.
C.3 β 2.
D.3 β 3.
e ) 12 / 5E.
"( β 27 + β 243 ) / β 75 = ( 3 β 3 + 9 β 3 ) / 5 β 3 = 12 β 3 / 5 β 3 = 12 / 5 . hence , the correct answer is e" | null |
Question: a set s = { x , - 8 , - 7 , - 6 , 6 , 8 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
A.1.
B.0.
C.2.
D.- 1.
e ) can not be determinedC.
median of the set = ( - 6 + 6 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 23 - 21 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c | null |
Question: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 10 hours and 8 hours respectively . the ratio of their speeds is
A.4 : 9.
B.4 : 3.
C.4 : 12.
D.4 : 8.
e ) 4 : 5E.
let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 10 = 4 : 5 . answer : e | null |
Question: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 8 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
A.400.
B.625.
C.1,250.
D.2,500.
e ) 312E.
"total fish = x percentage of second catch = ( 8 / 50 ) * 100 = 16 % so , x * 16 % = 50 x = 312 ans . e" | null |
Question: what is the sum of the digits of integer k , if k = ( 10 ^ 45 - 46 )
A.356.
B.366.
C.363.
D.396.
e ) 408D.
"there are 46 digits in 10 ^ 45 when we subtract 46 from it , there will be 45 digits left . 10 ^ 45 can be written as 9999999 . . . . ( 45 times ) + 1 so , 10 ^ 45 - 46 = 9999999 . . . . ( 45 times ) + 1 - 46 = 9999999 . . . . ( 45 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 43 and the last two digits are 54 the sum of the digits will be ( 43 * 9 ) + 5 + 4 = 396 answer : - d" | null |
Question: if 5 a = 3125 , then the value of 5 ( a - 3 ) is :
A.25.
B.125.
C.625.
D.1625.
e ) none of theseA.
solution 5 a = 3125 β 5 a = 5 a β a = 5 . β΄ 5 ( a - 3 ) = 5 ( 5 - 3 ) = 52 = 25 . answer a | null |
Question: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 130 marks , the no of questions he attempts correctly is :
A.33.
B.38.
C.99.
D.27.
e ) 71B.
"let the number of correct answers be x . number of incorrect answers = ( 60 β x ) . 4 x β ( 60 β x ) = 130 = > 5 x = 190 = > x = 38 answer : b" | null |
Question: there are 27 different 3 - digit integers that can be formed using only the digits 3 , 4 and 5 . if all 27 of the integers were listed , what would their sum be ?
A.11,888.
B.11,988.
C.12,088.
D.12,188.
e ) 12,288B.
there must be nine 3 ' s in the hundreds place , nine 3 ' s in the tens place , and nine 3 ' s in the units place . this is also true for the 4 ' s and 5 ' s . then the sum is : 9 ( 333 + 444 + 555 ) = 9 * ( 1332 ) = 11,988 . the answer is b . | null |
Question: if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 4 k , what is one possible value for k ?
A.2.
B.3.
C.4.
D.6.
e ) 8C.
"first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 5 or k = 4 . all the answers are positive , so we choose k = 4 . answer = c" | null |
Question: what is the units digit of 2222 ^ ( 555 ) * 3333 ^ ( 222 ) ?
A.0.
B.2.
C.4.
D.6.
e ) 8B.
"each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 2 . final answer : b" | null |
Question: a is half good a work man as b and together they finish a job in 20 days . in how many days working alone b finish the job ?
A.98 days.
B.30 days.
C.17 days.
D.18 days.
e ) 19 daysB.
"wc = 1 : 2 2 x + x = 1 / 20 = > x = 1 / 60 2 x = 1 / 60 = > 30 days answer : b" | null |
Question: what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?
A.47.
B.25.
C.37.
D.33.
e ) 29B.
"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ." | null |
Question: if log 4 x + log 4 ( 1 / 6 ) = 1 / 2 then the value of x is ?
A.18.
B.24.
C.16.
D.12.
e ) 10D.
log 4 x + log 4 ( 1 / 6 ) = 1 / 2 = > log 4 [ x x 1 / 6 ] = 1 / 2 = > log 4 [ x / 6 ] = 1 / 2 = > 41 / 2 = x / 6 = > 2 = x / 6 therefore , x = 12 answer : d | null |
Question: what quantity of water should taken out to concentrate 27 liters of 40 % acidic liquid to 60 % acidic liquid ?
A.5 liters.
B.10 liters.
C.15 liters.
D.9 liters.
e ) 6 litersD.
"required answer is = 27 ( 60 - 40 ) / 60 = 9 liters answer is d" | null |
Question: marts income is 30 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
A.124 %.
B.B.120 %.
C.C.78 %.
D.D.80 %.
e ) e ) 64 %C.
"m = ( 130 / 100 ) t t = ( 60 / 100 ) j = > m = ( 78 / 100 ) j answer c ." | null |
Question: there is a 5 - digit number . the fifth digit is one fourth of the third digit and one half of the fourth digit . third digit is one half of the first digit . second digit is 5 more than the fifth digit . what is that 5 - digit number ?
A.86421.
B.86424.
C.89421.
D.96421.
e ) 76421A.
we can prove it as follows suppose number is pqrst , now t = ( 1 / 4 ) r = ( 1 / 2 ) s . . . . . . ( 1 ) , r = ( 1 / 2 ) p . . . . . ( 2 ) , q = t + 5 . . . . ( 3 ) now from ( 1 ) 4 t = r = 2 s = k ( suppose ) . . . . ( 4 ) from ( 2 ) 2 r = p . . . ( 5 ) now ( 4 ) * 2 then we get 8 t = 2 r = 4 s = k ( again some integer ) . . . . ( 6 ) from ( 5 ) and ( 6 ) 8 t = 2 r = 4 s = p = k . . . . . . . . . ( 7 ) now we have to choose the value of k 1 ) if choose k = 0 then it is worthless number will be 00000 ( not a answer ) 2 ) for k = 1 to 7 and for k = 9 digits will be in fractions 3 ) for k = 8 we get p = 8 , s = 2 , r = 4 , t = 1 and q = 6 and number is pqrst = 86421 answer : a | null |
Question: what is the tens digit of 6 ^ 10 ?
A.7.
B.3.
C.5.
D.1.
e ) 9A.
"( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 10 ( dont actually calculate full values ) and answer is a : 7" | null |
Question: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
A.7000.
B.2787.
C.2799.
D.2699.
e ) 2790A.
"let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 36 x / 100 - 24 x / 100 = 840 = > 12 x / 100 = 840 = > x = 7000 . answer : a" | null |
Question: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.15 β 6.15 * ?
A.1.5.
B.0.15.
C.6.25.
D.0.25.
e ) 6.0B.
"since z * is defined as the greatest positive even integer less than or equal to z , then 6.15 * = 6 ( the greatest positive even integer less than or equal to 6.15 is 6 ) . hence , 6.15 β 6.15 * = 6.15 - 6 = 0.15 answer : b ." | null |
Question: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.15 , what is the value of y ?
A.96.
B.60.
C.48.
D.25.
e ) 12B.
"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.15 and remainder is 9 so . 15 x y = 9 hence y = 60 ans b" | null |
Question: the cost of the paint is rs . 40.00 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 10 feet each side
A.rs . 1200.
B.rs . 672.
C.rs . 546.
D.rs . 876.
e ) none of theseA.
"explanation : surface area of a cube = 6 x 10 ^ 2 = 600 s q . ft quantity of paint required = ( 600 / 20 ) = 30 kg cost of painting = 40 x 30 = rs . 1200 answer : a" | null |
Question: what is the perimeter of a rectangular field whose diagonal is 10 m and length is 3 m ?
['A.12 m', 'B.5 m', 'C.10 m', 'D.8 m', 'e ) 6 m']D.
sol : breadth of the rectangular plot is = 10 ^ 2 - 3 ^ 2 = 1 m therefore , perimeter of the rectangular plot = 2 ( 3 + 1 ) = 8 m d ) 8 m | null |
Question: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
A.2 : 9.
B.2 : 7.
C.1 : 7.
D.1 : 4.
e ) 1 : 3C.
2 % is 1 % - point below 3 % and 10 % is 7 % - points above 3 % . the ratio of a : b should be 1 : 7 . the answer is c . | null |
Question: a man can row at 5 kmph in still water . if the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
A.2.4 km.
B.2.9 km.
C.3.4 km.
D.4.4 km.
e ) 1.6 kmE.
"explanation : speed in still water = 5 kmph speed of the current = 3 kmph speed downstream = ( 5 + 3 ) = 8 kmph speed upstream = ( 5 - 3 ) = 2 kmph let the required distance be x km total time taken = 1 hour Γ’ β‘ β x / 8 + x / 2 = 1 Γ’ β‘ β x + 4 x = 8 Γ’ β‘ β 5 x = 8 Γ’ β‘ β x = 1.6 km answer : option e" | null |
Question: a 120.00001 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
A.220 meter.
B.225 meter.
C.380 meter.
D.435 meter.
e ) none of theseC.
"explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 120 / 9 = 500 / 9 = > x + 120 = 500 = > x = 380 so the length of the train is 380 meters option c" | null |
Question: the ratio between the length and the breadth of a rectangular plot is 7 : 5 . if the perimeter of the plot is 288 metres , what is its area ?
['A.1320 sq . metres', 'B.3260 sq . metres', 'C.4280 sq . metres', 'D.5040 sq . metres', 'e ) none of these']D.
let the length and breadth be 7 x and 5 x respectively . then , p = 2 ( 7 x + 5 x ) = 288 Γ’ β‘ β x = 12 area = 7 Γ£ β 12 Γ£ β 5 Γ£ β 12 = 5040 sq . m . answer d | null |
Question: during the first two weeks of january , the total rainfall in springdale was 20 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
A.5 inches.
B.6 inches.
C.9 inches.
D.10 inches.
e ) 12 inchesE.
"total rainfall in 2 weeks = 20 inches . assume the rainfall in second week = 1.5 x rainfall in first week = x total rainfall = 2.5 x = 20 inches x = 8 and 1.5 x = 12 rainfall during second week = 12 inches option e" | null |
Question: the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 3 or 4 as its largest number ?
A.3 / 4.
B.3 / 8.
C.3 / 16.
D.5 / 16.
e ) 3 / 32B.
the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . of the remaining 8 subsets , 3 is an element in 4 of them . thus 3 is the largest number in 4 subsets of s . the probability that 3 or 4 is the largest number is 12 / 32 = 3 / 8 . the answer is c . | null |
Question: an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 80 % is a passing grade , what is the probability that brian passes ?
A.1 / 16.
B.37 / 256.
C.1 / 2.
D.219 / 256.
e ) 125 / 256E.
"if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 β¦ . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 125 / 256 . e" | null |
Question: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 4 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
A.40.
B.46.
C.52.
D.62.
e ) 85E.
"the probability of survival for each of the first 3 months of life is 1 - 1 / 4 = 3 / 4 , so of 200 newborn 200 * 3 / 4 * 3 / 4 * 3 / 4 = ~ 85 is expected to survive . answer : e ." | null |
Question: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 4 , and the digit 2 can be used only once ?
A.20.
B.150.
C.225.
D.300.
e ) 320C.
"4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 3 options for the fourth digit : 0 , 4 , 8 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 3 = 240 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 3 = 15 . thus there are 240 - 15 = 225 such numbers . answer : c ." | null |
Question: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 390 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
A.120.
B.180.
C.260.
D.280.
e ) 320C.
"3 x = 390 x = 130 therefore , the salesman sold 130 kg in the morning and 2 β
130 = 260 kg in the afternoon . so answer is c ." | null |
Question: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability q that this product will be a multiple of 45 ?
A.1 / 32.
B.1 / 28.
C.1 / 24.
D.1 / 16.
e ) 1 / 14C.
"there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability q = 1 / 24 . answer c ." | null |
Question: a certain high school has 500 students . of these students , 20 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
A.430.
B.440.
C.450.
D.460.
e ) 470E.
"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 20 y = 20 z = 10 so , we have 20 students taking music , 20 taking art and 10 taking both music and art . that 10 person has been counted twice though ( once in the music ' group ' and once in the art ' group ' ) , so what we really have is . . . 10 student taking just music 10 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 5000 - 30 = 470 . e" | null |
Question: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.15 ?
A.980.
B.1120.
C.1260.
D.1420.
e ) 1670E.
"the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.15 - $ 0.65 = $ 1.50 the charge for the next 1400 grams is $ 1.40 which leaves a charge of $ 0.10 the weight is somewhere between 1650 and 1750 . the answer is e ." | null |
Question: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 1 year the amount to be paid is ?
A.3377.
B.2688.
C.2688.
D.7800.
e ) 1268D.
"a = 7500 ( 26 / 25 ) ^ 1 = 7800 answer : d" | null |
Question: a shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
A.40 %.
B.90 %.
C.33 %.
D.35 %.
e ) 30 %A.
"the total number of mangoes bought by the shopkeeper be 35 . if he buys 7 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 7 profit = sp - cp = 7 - 5 = 2 profit percent = 2 / 5 * 100 = 40 % answer : a" | null |
Question: the difference between a number and its two - fifth is 510 . what is 12 % of that number ?
A.58.
B.110.
C.76.
D.102.
e ) 86D.
"let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 12 % of 850 = 102 . answer : d" | null |
Question: a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
A.96.
B.100.
C.104.
D.108.
e ) 112A.
"originally , the distance the car could go on a full tank was 12 * 24 = 288 miles . after it has been modified , the car can go 24 / 0.75 = 32 miles per gallon . on a full tank , the car can go 32 * 12 = 384 miles , thus 96 miles more . the answer is a ." | null |
Question: the h . c . f . of two numbers is 15 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
A.225.
B.300.
C.299.
D.322.
e ) 345A.
"the numbers are ( 15 x 11 ) and ( 15 x 15 ) . larger number = ( 15 x 15 ) = 225 . answer : a" | null |
Question: in a dance competition the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . ashita participated in several rounds in the competition and the product of her score was 50000 . in how many rounds did she participate ?
A.3.
B.2.
C.1.
D.5.
e ) can not be determinedE.
correct answer is e because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 15 rounds out of only 5 rounds were there in which she was awarded some points . | null |
Question: a metallic sheet is of rectangular shape with dimensions 46 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
A.4830.
B.5120.
C.6420.
D.4800.
e ) 8960D.
"l = ( 46 - 16 ) m = 30 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 30 x 20 x 8 ) m 3 = 4800 m 3 . answer : option d" | null |
Question: in an election between two candidates , one got 60 % of the total valid votes , 30 % of the votes were invalid . if the total number of votes was 9000 , the number of valid votes that the other candidate got , was :
A.2500.
B.2520.
C.3000.
D.3100.
e ) none of theseB.
"explanation : number of valid votes = 70 % of 9000 = 6300 . valid votes polled by other candidates = 40 % of 6300 ( 40 / 1006300 ) = 2520 . harsh mishra a year ago 0 upvotes answer : b" | null |
Question: on a certain road , 10 % 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 ?
A.10.5 %.
B.12.5 %.
C.15 %.
D.22 %.
e ) 30 %B.
suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . 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 = x / 10 or y / x = 1 / 8 or y / x * 100 = 1 / 8 * 100 = 12.5 % answer : b | null |
Question: x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 30 km / hr . his average speed during the whole journey in km / hr . is :
A.34.
B.43.
C.40.
D.38.
e ) 29C.
"solution : average speed = 2 xy / x + y = 2 * 60 * 30 / 60 + 30 = 40 answer : c" | null |
Question: a drink vendor has 20 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
A.135.
B.137.
C.142.
D.130.
e ) 133E.
"the number of liters in each can = hcf of 20 , 144 and 368 = 4 liters . number of cans of maaza = 20 / 4 = 5 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 5 + 36 + 92 = 133 cans . answer : e" | null |
Question: jonathan can type a 40 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
A.5 minutes.
B.10 minutes.
C.15 minutes.
D.18 minutes.
e ) 20 minutesB.
"you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 40 / 40 + 40 / 30 + 40 / 24 = 40 / x if you solve this equation , you get the same answer b ( 10 )" | null |
Question: find the least number must be subtracted from 62575 so that remaining number is divisible by 99 .
A.93.
B.7.
C.54.
D.9.
e ) 6B.
on dividing 62571 by 99 we get the remainder 7 , so 7 should be subtracted . answer is b | null |
Question: a man is 12 years older than his brother . in two years , his age will be twice the age of his brother . the present age of his brother is :
A.10.
B.21.
C.22.
D.23.
e ) 24A.
let the brother ' s present age be x years . then , man ' s present age = ( x + 12 ) years . ( x + 12 ) + 2 = 2 ( x + 2 ) x + 14 = 2 x + 4 x = 10 . answer : a | null |
Question: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 280 pounds of the mixture ?
A.200.
B.84.
C.40.
D.28.
e ) 20A.
"almonds : walnuts = 5 : 2 total mixture has 7 parts in a 280 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 280 = 200 pounds answer ( a )" | null |
Question: how many 4 - digit numbers that do not contain the digits 2 , 3 , 4 , 5 , 6 , or 7 are there ?
A.168.
B.176.
C.184.
D.192.
e ) 200D.
the 1 st digit can be filled up by the numbers : { 1 , 8,9 } = 3 ways the 2 nd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 3 rd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 4 th digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the total number of such four - digit numbers is 3 * 4 * 4 * 4 = 192 the answer is d . | null |
Question: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
A.5600.
B.6000.
C.6400.
D.7200.
e ) noneC.
"solution number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 / 25 x 11.25 x 6 ) = 6400 . answer c" | null |
Question: the average weight of 6 person ' s increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg . what might be the weight of the new person ?
A.73 kg.
B.79.8 kg.
C.86 kg.
D.data inadequate.
e ) none of theseB.
"total weight increased = ( 6 x 1.8 ) kg = 10.8 kg . weight of new person = ( 69 + 10.8 ) kg = 79.8 kg . answer : option b" | null |
Question: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 7200 interest . the principal amount borrowed by him was .
A.rs 14000.
B.rs 15000.
C.rs 16000.
D.rs 20000.
e ) none of theseD.
"explanation : s . i . = p Γ’ Λ β r Γ’ Λ β t / 100 = > p = s . i . Γ’ Λ β 100 / r Γ’ Λ β t = > p = 7200 Γ’ Λ β 100 / 12 Γ’ Λ β 3 = rs 20000 option d" | null |
Question: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?
A.2003.
B.2004.
C.2005.
D.2006.
e ) 2007D.
"she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d ." | null |
Question: i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been
A.2000.
B.3000.
C.4000.
D.5000.
e ) 6000C.
explanation : total amount = rs . 10000 let money lent a = rs . x and money lent to b = rs . ( 10000 x ) x = rs . 6000 . so the amount of money lent to b = rs . 4000 answer : c | null |
Question: what percent is 320 gm of 1 kg ?
A.25 %.
B.40 %.
C.10 %.
D.8 %.
e ) 32 %E.
"1 kg = 1000 gm 320 / 1000 Γ£ β 100 = 32000 / 1000 = 32 % answer is e" | null |
Question: to be considered for β movie of the year , β a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy β s 785 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for β movie of the year β ?
A.191.
B.197.
C.193.
D.212.
e ) 213B.
"total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . ." | null |
Question: the number 0.5 is how much greater than 1 / 3 ?
A.1 / 6.
B.2 / 10.
C.1 / 50.
D.1 / 500.
e ) 2 / 500A.
"let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a" | null |
Question: the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .
A.26 %.
B.33 %.
C.34 %.
D.35 %.
e ) 24 %A.
quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a | null |
Question: there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
A.50.78 kg.
B.49.32 kg.
C.61.67 kg.
D.69.15 kg.
e ) 70.89 kgC.
"total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c" | null |
Question: a number is increased by 20 % and then decreased by 20 % . find the net increase or decrease per cent .
A.9 %.
B.8 %.
C.7 %.
D.3 %.
e ) 4 %E.
"let the number be 100 . increase in the number = 20 % = 20 % of 100 = ( 20 / 100 Γ£ β 100 ) = 20 therefore , increased number = 100 + 20 = 120 this number is decreased by 20 % therefore , decrease in number = 20 % of 120 = ( 20 / 100 Γ£ β 120 ) = 2400 / 100 = 24 therefore , new number = 120 - 24 = 96 thus , net decreases = 100 - 96 = 4 hence , net percentage decrease = ( 4 / 100 Γ£ β 100 ) % = ( 400 / 100 ) % = 4 % answer : e" | null |
Question: if x ^ 2 β 3 x = 18 , then one possible value of x β 4 =
A.- 9.
B.- 5.
C.- 3.
D.- 1.
e ) 2E.
x ^ 2 β 3 x = 18 i . e . x ^ 2 β 3 x - 18 = 0 i . e . x ^ 2 β 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e | null |
Question: if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?
A.23.
B.3.
C.15.
D.52 / 7.
e ) 60 / 7A.
4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a | null |
Question: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 11 cm .
A.335 cm 2.
B.209 cm 2.
C.285 cm 2.
D.825 cm 2.
e ) 725 cm 2B.
"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 11 ) = 209 cm 2 answer : b" | null |
Question: working alone , a can complete a certain kind of job in 3 hours . a and d , working together at their respective rates , can complete one of these jobs in 2 hours . in how many hours can d , working alone , complete one of these jobs ?
A.2.
B.4.
C.6.
D.8.
e ) 10C.
let total time taken by d to complete the job = d total time taken by a to complete the job = 3 work done by a in an hour 1 / a = 1 / 3 working together a and d can complete the job in 2 hours 1 / a + 1 / d = 1 / 2 = > 1 / d = 1 / 2 - 1 / a = 1 / 2 - 1 / 3 = 1 / 6 = > d = 6 hours answer c | null |
Question: a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?
A.37.
B.38.
C.27.
D.29.
e ) 11A.
explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37 | null |
Question: what number must be added to 6 , 16 and 8 to get an average of 13 ?
A.23.
B.22.
C.44.
D.33.
e ) 55B.
b 22 | null |
Question: the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
A.46.
B.55.
C.43.
D.39.
e ) 54A.
"explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a" | null |
Question: if x = the product of 7 distinct prime numbers , how many factors does x have besides 1 and itself ?
A.108.
B.114.
C.120.
D.126.
e ) 132D.
since x has 7 distinct prime factors , x has a total of 2 ^ 7 = 128 factors . besides 1 and itself , x has 126 factors . the answer is d . | null |
Question: how many integers n are prime numbers in the range 200 < n < 220 ?
A.1.
B.2.
C.3.
D.4.
e ) 5A.
to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a | null |
Question: a sum of $ 800 amounts to $ 920 in 3 years at simple interest . if the interest rate is increased by 3 % it would amount to how much ?
A.$ 506.
B.$ 774.
C.$ 992.
D.$ 854.
e ) $ 1021C.
s . i = 920 - 800 = 120 p = $ 800 t = 3 years r = 100 * 120 / 800 * 3 = 5 % new rate = 5 + 3 = 8 % new s . i . = 800 * 8 * 3 / 100 = $ 192 new amount = 800 + 192 = $ 992 answer is c | null |
Question: a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 65 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
A.3,000.
B.2,700.
C.4,500.
D.5,400.
e ) 324,000A.
"together the two machines make 35 + 65 = 100 copies per minute . so , in half an hour they will make 100 * 30 = 3,000 copies . answer : a ." | null |
Question: what will be the compound interest on a sum of rs . 28,000 after 3 years at the rate of 12 % p . a . ?
A.s . 10123.77.
B.s . 10123.21.
C.s . 10123.20.
D.s . 10123.28.
e ) s . 11337.98E.
"amount = [ 28000 * ( 1 + 12 / 100 ) 3 ] = 28000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 39337.984 c . i . = ( 39337.984 - 28000 ) = rs . 11337.98 answer : e" | null |
Question: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ?
A.5.
B.9.
C.10.
D.20.
e ) 30C.
"what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ? 9 ^ 5 = ( 3 ^ 2 ) ^ 5 = 3 ^ 10 c . 10" | null |
Question: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?
A.7349.
B.6300.
C.6325.
D.6939.
e ) 2989C.
"x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c" | null |
Question: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?
A.w = 200.
B.w = 600.
C.w = 800.
D.w = 1600.
e ) w = 50D.
"original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600" | null |
Question: if a car went the first third of the distance at 80 kmh , the second third at 30 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
A.36 kmh.
B.40 kmh.
C.42 kmh.
D.45 kmh.
e ) 50 kmhD.
assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 30 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 30 * t 2 = 8 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 16 hrs d = rt ( 240 * 3 ) = r * 16 r = 45 answer : d | null |
Question: a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
A.30.
B.40.
C.50.
D.60.
e ) 80C.
"let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50" | null |
Question: the compound ratio of 2 / 3 , 6 / 7 , 4 / 3 and 1 / 8 is given by ?
A.2 / 21.
B.1 / 48.
C.1 / 98.
D.1 / 96.
e ) 1 / 68A.
"2 / 3 * 6 / 7 * 4 / 3 * 1 / 8 = 48 / 504 = 2 / 21 answer : a" | null |
Question: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > x or x > 0 ?
A.7 / 8.
B.5 / 6.
C.3 / 8.
D.1 / 2.
e ) 3 / 4A.
"the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points to the right of the y - axis satisfy the condition that x > 0 . the union of these two areas is 7 / 8 of the circle . the answer is a ." | null |
Question: reema took a loan of rs 900 with simple interest for as many years as the rate of interest . if she paid rs . 729 as interest at the end of the loan period , what was the rate of interest .
A.5 %.
B.6 %.
C.7 %.
D.8 %.
e ) 9 %E.
"explanation : let rate = r % then time = r years . = > 900 β r β r / 100 = 729 = > r 2 = 81 = > r = 9 % option e" | null |
Question: of the 20 members of a kitchen crew , 17 can use the meat - cutting machine , 18 can use the bread - slicing machine , and 15 can use both machines . if one member is chosen at random , what is the probability that the member chosen will be someone who can not use either machine ?
A.0.
B.1 / 10.
C.1 / 7.
D.1 / 4.
e ) 1 / 3A.
you know how to solve for total number of people who can use at least one machine : total = n ( a ) + n ( b ) - n ( a and b ) total people who can use at least one machine = 17 + 18 - 15 = 20 so all 20 people know how to use at least one machine . hence , if you pick anyone , the probability is 0 that he would n ' t know how to use any machine . answer a | null |
Question: the average of first 9 natural numbers is ?
A.1.5.
B.2.5.
C.3.5.
D.4.5.
e ) 5.5D.
"sum of 10 natural no . = 90 / 2 = 45 average = 45 / 10 = 4.5 answer : d" | null |
Question: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 20 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
A.36.
B.72.
C.132.
D.144.
e ) 180C.
1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 132 min c | null |
Question: a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
A.7.
B.8.
C.9.
D.10.
e ) 12E.
"xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e" | null |
Question: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
A.1 : 4.
B.16 : 9.
C.2 : 3.
D.1 : 2.
e ) 2 : 5B.
the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 8 dollars - - > the loss from one mango = 1 / 5 - 1 / 8 = 3 / 40 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 40 / 3 = 16 / 9 b | null |
Question: if an investor puts $ 800 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
A.$ 878.
B.$ 880.
C.$ 882.
D.$ 884.
e ) $ 886C.
"1.05 * 1.05 * 800 = $ 882 the answer is c ." | null |
Question: in an election between two candidates , one got 55 % of the total valid votes . 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ?
A.2800.
B.2700.
C.2100.
D.2500.
e ) 3000B.
"total no of votes = 7500 20 % invalid = > 80 % valid tot valid votes = 7500 * 80 / 100 = > valid for 2 nd candidate got 7500 * 80 / 100 * 45 / 100 = 2700 answer b" | null |
Question: the average of first five multiples of 6 is ?
A.6.
B.18.
C.9.
D.5.
e ) 7B.
"average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 = 18 . answer : b" | null |
Question: indu gave bindu rs . 625 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
A.1.
B.2.
C.7.
D.4.
e ) 9A.
"625 = d ( 100 / 4 ) 2 d = 1 answer : a" | null |
Question: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
A.2 / 7.
B.3 / 5.
C.3 / 11.
D.1 / 4.
e ) 7 / 16C.
"total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 3 c 1 * 5 c 1 * 4 c 1 = 3 * 5 * 4 = 60 probability = 60 / 220 = 3 / 11 answer is c" | null |
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