Cheukting/mathqa huggingface dataset:
Question (physics): each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 40 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 55 minutes , e ) 35 minutes
Rationale: "as they arrived 40 minutes earlier than usual , they saved 40 minutes on round trip from home to station ( home - station - home ) - - > 20 minutes in each direction ( home - station ) - - > wife meets husband 20 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 20 minutes = 40 minutes . answer : c"
Answer: c
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio a of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) a = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Question (general): if ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) , what is the value of y ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: ( 8000 ) ( 6000 ) = ( 480 ) ( 10 ^ y ) = > ( 8000 ) ( 6000 ) / 480 = 10 ^ y = > 100000 = 100 ^ y = > 10 ^ 5 = 10 ^ y since , base is same so powers will be same too . so , y = 5 answer will be a
Answer: a
Question (general): if ( 5 + k ) ( 5 - k ) = ( 5 ^ 2 ) - ( 2 ^ 3 ) , then what is the value of k ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 2 , e ) 6
Rationale: obviously , it is in the formula a ^ 2 - b ^ 2 = ( a + b ) ( a - b ) so k is 2 option d
Answer: d
Question (physics): a train consists of 48 boxcars pulled by 2 engines . the boxcars are 15 meters long and the two engines are each 20 meters long . it crosses over a highway 24 meters wide at a speed of 14 m / s . how long does it take for the entire train to cross ?
Options: a ) 56 sec , b ) 63 sec , c ) 72 sec , d ) 81 sec , e ) 88 sec
Rationale: a 56 sec d = 48 * 15 m + 2 * 20 m + 24 m = 784 m t = 784 m / 14 m / s = 56 s
Answer: a
Question (general): the average age of 40 students in a class is 10 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 59 , b ) 55 , c ) 61 , d ) 51 , e ) 36
Rationale: "total age of 50 students = 40 * 10 = 400 total age of 51 persons = 41 * 11 = 451 age of teacher = 451 - 400 = 51 years answer is d"
Answer: d
Question (general): a store reported total sales of $ 416 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 30 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 416 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 416 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 416 – 320 ) / 320 ] x 100 = 30 % the answer is c ."
Answer: c
Question (geometry): the ratio of the radius of two circles is 2 : 5 , and then the ratio of their areas is ?
Options: a ) 4 : 25 , b ) 2 : 9 , c ) 1 : 9 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 2 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 25 answer : a"
Answer: a
Question (gain): a , b and c start a business each investing 20,000 . after 5 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 69,900 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7 = 205000 : 212000 : 282000 = 205 : 212 : 282 . b ’ s share = ( 69900 × 212 ⁄ 699 ) = 21200 ; answer c"
Answer: c
Question (general): of the families in city x in 2000 , 30 percent owned a personal computer . the number of families in city x owning a computer in 2004 was 20 percent greater than it was in 1994 , and the total number of families in city x was 10 percent greater in 2004 than it was in 2000 . what percent of the families in city x owned a personal computer in 1998 ?
Options: a ) 55.42 % , b ) 52.25 % , c ) 56.23 % , d ) 30.70 % , e ) 32.72 %
Rationale: "say a 100 families existed in 2000 then the number of families owning a computer in 2000 - 30 number of families owning computer in 2000 = 30 * 120 / 100 = 36 number of families in 2004 = 110 the percentage = 36 / 110 * 100 = 32.72 % . option : e"
Answer: e
Question (gain): raman mixed 48 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?
Options: a ) 129 , b ) 287 , c ) 195 , d ) 188 , e ) 112
Rationale: "explanation : cp per kg of mixture = [ 48 ( 150 ) + 36 ( 125 ) ] / ( 48 + 36 ) = rs . 139.28 sp = cp [ ( 100 + profit % ) / 100 ] = 139.28 * [ ( 100 + 40 ) / 100 ] = rs . 195 answer : c"
Answer: c
Question (other): how many odd factors does 460 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 460 = 2 * 5 * 23 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 460 . answer : b ."
Answer: b
Question (general): how many integers between 50 and 100 can be evenly divided by neither 3 nor 5 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "divisible by 3 between 50 and 100 = 17 ( 51 , 54,57 , 60,63 , 66,69 , 72,75 , 78,81 , 84,87 , 90,93 , 96,99 ) divisible by 5 between 50 and 100 = 9 ( 55 , 60,65 , 70,75 , 80,85 , 90,95 ) common divisible for 5 and 3 = 3 ( 60 , 75 , 90 ) total divisible by 5 and 3 between 50 and 100 = 17 + 9 - 3 = > 23 there are 49 numbers between 50 to 100 i . e 51 to 99 so the integers that are not divisible by 3 and 5 = > 49 - 23 = > 26 answer : c"
Answer: c
Question (other): a certain high school has 500 students . of these students , 30 are taking music , 10 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "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 = 30 y = 10 z = 10 so , we have 30 students taking music , 10 taking art and 10 taking both music and art . 20 student taking just music 0 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 500 - 30 = 470 . e"
Answer: e
Question (physics): in what time will a train 100 metres long cross an electric pole , if its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) none
Rationale: solution speed = ( 144 x 5 / 18 ) m / sec = 40 m / sec time taken = ( 100 / 40 ) sec = 2.5 sec . answer a
Answer: a
Question (physics): in a garden , there are 10 rows and 13 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 13 plants . there are 12 gapes between the two corner trees ( 12 x 2 ) metres and 1 metre on each side is left . therefore length = ( 24 + 2 ) m = 26 m . answer : d"
Answer: d
Question (general): how many 3 - digit even numbers are possible such that if one of the digits is 3 , the next / succeeding digit to it should be 7 ?
Options: a ) 495 , b ) 305 , c ) 365 , d ) 405 , e ) 5
Rationale: 370 , 572 , 374 , 376 , and 378 , so total 5 . hence option e .
Answer: e
Question (gain): a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 70 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 21 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 170 , so from 2003 to 2005 it increased by ( 170 - 140 ) / 140 = 30 / 140 = ~ 21 % . answer : e ."
Answer: e
Question (physics): a start walking from a place at a uniform speed of 4 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 4.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 4 + 5 / 9 = 4.55 answer b"
Answer: b
Question (physics): 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 ?
Options: a ) a ) 5.61 , b ) b ) 3.69 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "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"
Answer: b
Question (general): how many figures are required to number the pages the pages of a book containing 2200 pages ?
Options: a ) 7593 , b ) 6693 , c ) 7693 , d ) 7793 , e ) 7893
Rationale: "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"
Answer: c
Question (physics): 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 ?
Options: a ) 125 , b ) 150 , c ) 200 , d ) 225 , e ) 250
Rationale: "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"
Answer: a
Question (physics): what decimal fraction is 90 ml of a litre ?
Options: a ) . 9 , b ) . 009 , c ) . 09 , d ) 0.09 , e ) none of these
Rationale: answer required fraction = 90 / 1000 = 9 / 100 = . 09 correct option : c
Answer: c
Question (general): what is the smallest integer k for which 64 ^ k > 4 ^ 20 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 20 4 ^ ( 3 k ) > 4 ^ 20 3 k > 20 k = 7 the answer is d ."
Answer: d
Question (physics): 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 ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "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"
Answer: d
Question (physics): 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 :
Options: a ) 62 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) 57 m 2
Rationale: "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"
Answer: a
Question (general): if 2994 ã · 14.5 = 179 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.9
Rationale: 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 .
Answer: e
Question (general): ( √ 27 + √ 243 ) / √ 75 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 12 / 5
Rationale: "( √ 27 + √ 243 ) / √ 75 = ( 3 √ 3 + 9 √ 3 ) / 5 √ 3 = 12 √ 3 / 5 √ 3 = 12 / 5 . hence , the correct answer is e"
Answer: e
Question (general): 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 | ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) - 1 , e ) can not be determined
Rationale: 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
Answer: c
Question (physics): 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
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 8 : 10 = 4 : 5 . answer : e
Answer: e
Question (gain): 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 ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 312
Rationale: "total fish = x percentage of second catch = ( 8 / 50 ) * 100 = 16 % so , x * 16 % = 50 x = 312 ans . e"
Answer: e
Question (general): what is the sum of the digits of integer k , if k = ( 10 ^ 45 - 46 )
Options: a ) 356 , b ) 366 , c ) 363 , d ) 396 , e ) 408
Rationale: "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"
Answer: d
Question (general): if 5 a = 3125 , then the value of 5 ( a - 3 ) is :
Options: a ) 25 , b ) 125 , c ) 625 , d ) 1625 , e ) none of these
Rationale: solution 5 a = 3125 ⇔ 5 a = 5 a ⇔ a = 5 . ∴ 5 ( a - 3 ) = 5 ( 5 - 3 ) = 52 = 25 . answer a
Answer: a
Question (physics): 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 :
Options: a ) 33 , b ) 38 , c ) 99 , d ) 27 , e ) 71
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 130 = > 5 x = 190 = > x = 38 answer : b"
Answer: b
Question (general): 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 ?
Options: a ) 11,888 , b ) 11,988 , c ) 12,088 , d ) 12,188 , e ) 12,288
Rationale: 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 .
Answer: b
Question (general): if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 4 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "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"
Answer: c
Question (general): what is the units digit of 2222 ^ ( 555 ) * 3333 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "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"
Answer: b
Question (physics): 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 ?
Options: a ) 98 days , b ) 30 days , c ) 17 days , d ) 18 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 20 = > x = 1 / 60 2 x = 1 / 60 = > 30 days answer : b"
Answer: b
Question (general): what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "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 ."
Answer: b
Question (general): if log 4 x + log 4 ( 1 / 6 ) = 1 / 2 then the value of x is ?
Options: a ) 18 , b ) 24 , c ) 16 , d ) 12 , e ) 10
Rationale: 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
Answer: d
Question (gain): what quantity of water should taken out to concentrate 27 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 9 liters , e ) 6 liters
Rationale: "required answer is = 27 ( 60 - 40 ) / 60 = 9 liters answer is d"
Answer: d
Question (general): 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
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 78 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 130 / 100 ) t t = ( 60 / 100 ) j = > m = ( 78 / 100 ) j answer c ."
Answer: c
Question (general): 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 ?
Options: a ) 86421 , b ) 86424 , c ) 89421 , d ) 96421 , e ) 76421
Rationale: 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
Answer: a