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Provide a detailed solution to the given mathematical problem. | find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 a ) 26 , b ) 22 , c ) 25 , d ) 30 , e ) 29 | "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 3 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 3 = 2 ^ 22 x 7 ^ 5 x 11 ^ 3 total number of prime factors = ( 22 + 5 + 3 ) = 30 . answer is d ." |
Explain the solution process for the given equation. | if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ? a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01 | answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest num... |
Provide a detailed solution to the given mathematical problem. | if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 5 ] ] ? a ) 39 , b ) 9 , c ) 15 , d ) 19 , e ) 25 | "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 5 ] ] = 5 ^ 2 + 2 * 5 + 4 = 39 . option a" |
Explain the solution process for the given equation. | a professional athlete was offered a 3 - year contract to play with team k that provided for an annual salary of $ 100000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and a bonus of $ 50000 on signing . team l offered a 3 - year contract providing for an annua... | team k' s contract = $ 100,000 + $ 100,000 * 1.2 + $ 100,000 * 1.2 * 1.2 + $ 50,000 = $ 414,000 team l' s contract = $ 150,000 + $ 150,000 * 1.2 + $ 150,000 * 1.2 * 1.2 = $ 546,000 the difference = $ 132,000 . answer : a . |
Provide a detailed solution to the given mathematical problem. | a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ? a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5 | "the table you made does n' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ... |
Solve the problem systematically, showing each step clearly. | if a 2 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? a ) 50 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 250 % | "the area a of the large cube is 2 * 2 * 6 = 24 square cm . the area of the 8 small cubes is 8 * 6 = 48 = 2 a , an increase of 100 % . the answer is b ." |
Solve the problem systematically, showing each step clearly. | carina has 115 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ? a ) 5 , b ) 7 , c ) 6 , d ) 4 , e ) 3 | "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 115 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 105 / 15 . = 7 b" |
Work through the equation methodically, ensuring clarity at each step. | the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ? ['a ) 32 cm','b ) 48 cm','c ) 50 cm','d ) 28 cm','e ) 30 cm'] | ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b |
Explain the solution process for the given equation. | find a two digit number , given that the sum of the digits is 13 and the difference of the digits is 5 . ? a ) 74 , b ) 82 , c ) 95 , d ) 76 , e ) 94 | "using elimination method find which of the options fit the description of the number . . . from the option only 94 meets this description sum of digits - - - 9 + 4 = 13 difference of digits - - - 9 - 4 = 5 answer e ." |
Provide a detailed solution to the given mathematical problem. | a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food . a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72 | "explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e" |
Solve the problem systematically, showing each step clearly. | in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ? a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e )... | "let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ." |
Provide a detailed solution to the given mathematical problem. | a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ? a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet | "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b" |
Work through the equation methodically, ensuring clarity at each step. | a man can do a job in 20 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ? a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2 | "1 day work of the three persons = ( 1 / 20 + 1 / 20 + 1 / 25 ) = 7 / 50 so , all three together will complete the work in 300 / 47 = 7.1 days . answer : c" |
Break down and solve the equation step by step. | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 16 . the larger of the two numbers is : a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 368 | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 16 ) . larger number = ( 23 x 16 ) = 368 . answer : option e" |
Solve the problem systematically, showing each step clearly. | if k ^ 3 is divisible by 162 , what is the least possible value of integer k ? a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36 | "k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ." |
Break down and solve the equation step by step. | if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ? a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + o... |
Solve the problem systematically, showing each step clearly. | there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90 | "20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct" |
Solve the problem systematically, showing each step clearly. | john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ? a ) 30 , b ) 40 , c ) 5... | "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a" |
Provide a detailed solution to the given mathematical problem. | a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 1.8 kilometer long bridge , at the same speed ? a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min | s = 600 / 40 = 15 mps s = 1800 / 15 = 120 sec = 2 min . answer : b |
Work through the equation methodically, ensuring clarity at each step. | at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 30 males did not bring gifts to the party , how many females did bring gifts ? a ) 18 , b ) 28 , c ) 40 , d ) 68 , e ) 70 | "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 30 are males , so remaining 90 - 30 = 60 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 60 , 100 % = 60 * 100 / 60 = 100 . ans 40 % of 100 = 40 c" |
Provide a detailed solution to the given mathematical problem. | linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ? a ) $ 900 , b ) $ 800 , c ) $ 1000 , d ) $ 920 , e ) $ 1500 | "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d" |
Provide a detailed solution to the given mathematical problem. | if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is ? a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) rs . 9000 | "explanation : a = 7500 ( 26 / 25 ) 2 = 8112 answer is d" |
Explain the solution process for the given equation. | if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ? a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9 | "28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 =... |
Break down and solve the equation step by step. | a watch was sold at a loss of 10 % . if it was sold for rs . 540 more , there would have been a gain of 8 % . what is the cost price ? a ) 1000 , b ) 2998 , c ) 3000 , d ) 2788 , e ) 2991 | "90 % 108 % - - - - - - - - 18 % - - - - 540 100 % - - - - ? = > rs . 3000 answer : c" |
Provide a detailed solution to the given mathematical problem. | calculate how much time could be saved if the train would run at its usual speed , given that it ran at 5 / 7 of its own speed and got to its destination in 15 hours ? a ) 1.29 hrs , b ) 2.29 hrs , c ) 4.29 hrs , d ) 5.29 hrs , e ) 3.29 hrs | "new speed = 5 / 7 of usual speed new time = 5 / 7 of usual time 5 / 7 of usual time = 15 hrs usual time = 15 * 5 / 7 = 10.71 hrs time saved = 15 - 10.71 = 4.29 hrs answer is c" |
Provide a detailed solution to the given mathematical problem. | convert 0.35 in to a vulgar fraction ? a ) 18 / 50 , b ) 16 / 50 , c ) 7 / 20 , d ) 19 / 50 , e ) none | "answer 0.35 = 35 / 100 = 7 / 20 correct option : c" |
Provide a detailed solution to the given mathematical problem. | 5 n + 2 > 17 and 7 n - 5 < 44 ; n must be between which numbers ? a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9 | "5 n > 15 - - > n > 3 7 n < 49 - - > n < 7 3 < n < 7 answer : d" |
Work through the equation methodically, ensuring clarity at each step. | the grade point average of one third of the classroom is 54 ; the grade point average of the rest is 45 . what is the grade point average of the whole class ? a ) 52 , b ) 54 , c ) 48 , d ) 58 , e ) 60 | "let n = total students in class total points for 1 / 3 class = 54 n / 3 = 18 n total points for 2 / 3 class = 45 * 2 n / 3 = 30 n total points for whole class = 18 n + 30 n = 48 n 48 n total class points / n total students = 48 grade point average for total class answer : c" |
Provide a detailed solution to the given mathematical problem. | in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108 | total students = 420 boys = 312 , girls = 108 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 108 - 35 = 73 . correct option : b |
Work through the equation methodically, ensuring clarity at each step. | from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 60 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ? a ) 3... | "1.15 x = 60 - - > 23 / 20 * x = 60 - - > x = 60 * 20 / 23 = 1200 / 23 = ~ 52 . answer : e ." |
Explain the solution process for the given equation. | a box contains 6 pairs of shoes ( 12 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? a ) 1 / 11 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9 | the problem with your solution is that we do n' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first o... |
Solve the problem systematically, showing each step clearly. | the average of first 25 prime numbers is ? a ) 9.9 , b ) 8.8 , c ) 5.6 , d ) 11.9 , e ) 11.11 | "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 / 9 = 100 / 9 = 11.11 ( approx ) answer is e" |
Work through the equation methodically, ensuring clarity at each step. | of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ? a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you ... |
Work through the equation methodically, ensuring clarity at each step. | a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 10.50 less , he would have gained 30 % . find the cost of the article . a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70 | let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 10.50 when c . p = ( 100 * 10.50 ) / 21 = 50 answer : c |
Break down and solve the equation step by step. | what is the least possible value of expression e = ( x - 1 ) ( x - 3 ) ( x - 4 ) ( x - 6 ) + 10 for real values of x ? a ) 1 , b ) 10 , c ) 9 , d ) 0 , e ) 8 | explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a |
Provide a detailed solution to the given mathematical problem. | in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ? ['a ) 56','b ) 88','c ) 112','d ) 116','e ) 120'] | ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer |
Solve the problem systematically, showing each step clearly. | a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ? a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km | difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a ) |
Break down and solve the equation step by step. | 1370 , 1320 , 1070 , - 180 ? a ) - 6430 , b ) - 6530 , c ) - 6630 , d ) - 6730 , e ) - 6830 | 1370 , 13201070 , - 180 , ? 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a . |
Work through the equation methodically, ensuring clarity at each step. | if x is less than y by 45 % then y exceed x by : a ) 33.33 % , b ) 25 % , c ) 81.81 % , d ) 66.66 % , e ) none of these | "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 45 / ( 100 - 45 ) * 100 = 81.81 % answer : c" |
Work through the equation methodically, ensuring clarity at each step. | the ratio between the present ages of a and b is 4.5 : 3 respectively . the ratio between a' s age 4 years ago and b' s age 4 years hence is 1 : 1 . what is the ratio between a' s age 4 years hence and b' s age 4 years ago ? a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 7 : 3 , e ) 3 : 7 | "let the present ages of a and b be 4.5 x and 3 x years respectively . then , ( 4.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1.5 x = 8 = > x = 5.33 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 28 : 12 = 7 : 3 . answer : d" |
Break down and solve the equation step by step. | two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25 | "part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b" |
Solve the problem systematically, showing each step clearly. | there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visi... | "9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ." |
Explain the solution process for the given equation. | how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ? a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58 | "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x... |
Provide a detailed solution to the given mathematical problem. | if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 11.00 / day for each additional week , how much does it cost to stay for 23 days ? a ) $ 160 , b ) $ 176 , c ) $ 282 , d ) $ 302 , e ) $ 286 | "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 11 = 16 * 11 = 176 $ total charge = 126 + 176 = 302 $ answer d" |
Work through the equation methodically, ensuring clarity at each step. | a certain number of men can finish a piece of work in 10 days . however , if there were 10 less men it will take 10 days more for the work to be finished . how many men were there originally ? a ) 10 men , b ) 30 men , c ) 40 men , d ) 20 men , e ) none of these | "let x be the number of men originally thus , 10 x = ( 10 + 10 ) ( x - 10 ) 10 x = 20 ( x - 10 ) x = 2 ( x - 10 ) x = 20 answer : d" |
Break down and solve the equation step by step. | in a family 15 people eat only vegetarian , 8 people eat only non veg . , 11 people eat both veg and non veg . . how many people eat veg in the family ? a ) 20 , b ) 11 , c ) 23 , d ) 26 , e ) 21 | "total people eat veg = only veg + both veg and non veg total = 15 + 11 = 26 answer = d" |
Solve the problem systematically, showing each step clearly. | a math teacher has 24 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles . a ) 7 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 24 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at l... |
Explain the solution process for the given equation. | excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hour ? a ) 20 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 11 min | "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( 18 / 54 ) x 60 = 20 min answer : a" |
Explain the solution process for the given equation. | what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ? a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920 | when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer . |
Provide a detailed solution to the given mathematical problem. | if x is equal to the sum of the integers from 30 to 50 , inclusive , and y is the number of even integers from 30 to 50 , inclusive , what is the value of x + y ? a ) 810 , b ) 811 , c ) 830 , d ) 850 , e ) 851 | since the integers from 30 - 50 are consecutive we can use the ` ` median x # of terms formula'' to determine x . there are 21 terms and the median is 40 . this gives a total of 21 x 40 = 840 . there are 11 even integers from 30 - 50 = y . therefore , x + y = 851 . answer : e |
Work through the equation methodically, ensuring clarity at each step. | a man has some hens and cows . if the number of heads be 50 and the number of feet equals 144 , then the number of hens will be a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28 | "explanation : let number of hens = h and number of cows = c number of heads = 50 = > h + c = 48 - - - ( equation 1 ) number of feet = 144 = > 2 h + 4 c = 144 = > h + 2 c = 72 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 72 - 50 = > c = 22 substituting the value of c in equation 1 , we get h + 2... |
Work through the equation methodically, ensuring clarity at each step. | for how many values of q , is | | | q - 5 | - 10 | - 5 | = 2 ? ( those ls are mods ) a ) 0 , b ) 2 , c ) 4 , d ) 8 , e ) more than 8 | i think its 8 | | | q - 5 | - 10 | - 5 | = 2 let | q - 5 | = a which makes above | | a - 10 | - 5 | = 2 let | a - 10 | = b which makes | b - 5 | = 2 now for the above b can take 3 , 7 for every b = 3 a can have 13 , 7 and for b = 7 a can have 17 and 3 so' a' has four solutions 13 , 7 , 17 and 3 for a = 13 ; q has 18 or... |
Work through the equation methodically, ensuring clarity at each step. | the size of a television screen is given as the length of the screen' s diagonal . if the screens were flat , then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ? a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 76 | "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e ." |
Provide a detailed solution to the given mathematical problem. | if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 54 kmh , what was the average speed of the car for the entire trip ? a ) 36 kmh , b ) 40 kmh , c ) 41 kmh , d ) 44 kmh , e ) 50 kmh | "assume d / 3 = 2160 ( this number is convenient because it is divisible by 80 , 24 and 54 ) so : 2160 = 80 * t 1 = 27 hrs 2160 = 24 * t 2 = 90 hrs 2160 = 54 * t 3 = 40 hrs t = t 1 + t 2 + t 3 = 157 hrs d = rt ( 240 * 3 ) = r * 157 r = 41.27 answer : c" |
Provide a detailed solution to the given mathematical problem. | if | 20 x - 10 | = 90 , then find the product of the values of x ? a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 20 | "| 20 x - 10 | = 90 20 x - 10 = 90 or 20 x - 10 = - 90 20 x = 100 or 20 x = - 80 x = 5 or x = - 4 product = - 4 * 5 = - 20 answer is e" |
Provide a detailed solution to the given mathematical problem. | how many even integers n , such that 20 < = n < = 180 are of the form 3 k + 4 , where k is any natural number ? a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36 | the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b . |
Explain the solution process for the given equation. | find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 13 cm . a ) 335 cm 2 , b ) 885 cm 2 , c ) 285 cm 2 , d ) 247 cm 2 , e ) 725 cm 2 | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 13 ) = 247 cm 2 answer : d" |
Break down and solve the equation step by step. | the length of a bridge in meters , which a train 80 - meters long and traveling at 45 km / hr can cross in 30 seconds is ? a ) 215 , b ) 235 , c ) 255 , d ) 275 , e ) 295 | "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 80 = 375 meters x = 295 meters the answer is e ." |
Explain the solution process for the given equation. | an empty wooden vessel weighs 14 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled . a ) 6 / 13 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5 | "an empty wooden vessel weighs 14 % of its total weight when filled with paint : vessel = 0.14 ( vessel + paint ) ; 14 v = v + p ( so the weight of completely filled vessel is 14 v ) p = 13 v ( so the weight of the paint when the vessels is completely filled is 13 v ) . the weight of a partially filled vessel is one ha... |
Break down and solve the equation step by step. | tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 8 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ? a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4.5 mph , e ) 0.5 mph | "( 1 mph + 8 mph ) / 2 = 4.5 mph correct option is : d" |
Explain the solution process for the given equation. | how many 3 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 121 . a ) 90 , b ) 610 , c ) 729 , d ) 900 , e ) 1000 | "take the task of building palindromes and break it intostages . stage 1 : select the hundreds digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the tens digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways im... |
Work through the equation methodically, ensuring clarity at each step. | a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 6.7 hrs , e ) 8.6 hrs | "net part filled in 1 hour = ( 1 / 4 - 1 / 10 ) = 3 / 20 the cistern will be filled in 20 / 3 hrs i . e . , 6.7 hrs . answer : d" |
Work through the equation methodically, ensuring clarity at each step. | the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ? a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680 | "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c" |
Solve the problem systematically, showing each step clearly. | a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 350 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 220 | "orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer... |
Work through the equation methodically, ensuring clarity at each step. | the area of an isosceles trapezoid with sides of length 5 and bases of length 8 and 14 is ? a ) 22 , b ) 32 , c ) 44 , d ) 55 , e ) 56 | "we can divide the trapezoid into two triangles and a rectangle sides of triangle , t 1 - - > h 1 = 5 , b 1 = 3 , s 1 = root ( 25 - 9 ) = 4 = s 2 of triangle t 2 area of triangle = ( 1 / 2 ) * 4 * 3 = 6 side of the rectangle = 8 * 4 = 32 total area of the trapezoid = 32 + 6 + 6 = 44 answer : c" |
Provide a detailed solution to the given mathematical problem. | if 20 % of a number = 1000 , then 120 % of that number will be ? a ) 20 , b ) 120 , c ) 360 , d ) 6000 , e ) 820 | "let the number x . then , 20 % of x = 1000 x = ( 1000 * 100 ) / 20 = 5000 120 % of x = ( 120 / 100 * 5000 ) = 6000 . answer : d" |
Solve the problem systematically, showing each step clearly. | two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 26 seconds . the ratio of their speeds is ? a ) 3 / 1 , b ) 9 / 1 , c ) 3 / 3 , d ) 3 / 5 , e ) 5 / 2 | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 26 = = > 27 x + 17 y = 26 x + 26 y = = > 1 x = 9 y = = > x / y = 9 / 1 . answer : b" |
Break down and solve the equation step by step. | a train covers a distance of 9 km in 6 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ? a ) 100 , b ) 105 , c ) 110 , d ) 120 , e ) 125 | "speed = ( 9 / 6 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 5 = 125 m . answer : option e" |
Solve the problem systematically, showing each step clearly. | a watch was sold at a loss of 12 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ? a ) s . 1000 , b ) s . 875 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002 | "explanation : 88 % 104 % - - - - - - - - 16 % - - - - 140 100 % - - - - ? = > rs . 875 answer : b" |
Provide a detailed solution to the given mathematical problem. | a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ? a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59 | "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c" |
Break down and solve the equation step by step. | a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ? a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these | train overtakes a bike means that we are talking about total length of the train . ( train' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d ... |
Explain the solution process for the given equation. | 25.25 / 1500 is equal to : a ) 1.012526333 , b ) 0.012625333 , c ) 0.125263333 , d ) 0.126253333 , e ) 0.016833333 | "25.25 / 2000 = 2525 / 200000 = 0.016833333 answer : e" |
Explain the solution process for the given equation. | the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 200 liters of water , how many liters of detergent will ... | "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 200 dnew = wnew / 5 = 200 / 5 = 40 so , answer will be e" |
Work through the equation methodically, ensuring clarity at each step. | the difference of two numbers is 11 . one third of their sum is 7 . what are the two numbers ? a ) 21,10 , b ) 16,5 , c ) 3,14 , d ) 11,10 , e ) 7,14 | "let the two numbers be x and y . equation ( i ) : x - y = 11 equation ( ii ) : ( x + y ) / 3 = 7 solve system of equations : x + y = 21 x - y = 11 ( add equations together ) - - - 2 x = 32 - - - x = 16 16 - y = 11 - - - y = 5 since x = 16 and y = 5 , answer b ( 16,5 ) is correct ." |
Work through the equation methodically, ensuring clarity at each step. | rahim bought 65 books for rs . 1150 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ? a ) rs . 17 , b ) rs . 18 , c ) rs . 12 , d ) rs . 11 , e ) rs . 10 | "average price per book = ( 1150 + 920 ) / ( 65 + 50 ) = 2070 / 115 = rs . 18 answer : b" |
Work through the equation methodically, ensuring clarity at each step. | if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters , what is the length of the rectangle , in centimeters ? a ) 4 , b ) 8 , c ) 2 , d ) 16 , e ) 18 | "let length of rectangle = l 4 ^ 2 = l * 8 = > l = 16 / 8 = 2 answer c" |
Provide a detailed solution to the given mathematical problem. | if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 10 men in 3 days ? a ) 65 mtr . , b ) 28 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr . | "20 men is 6 days can build 112 metres 10 men in 3 days can build = 112 * ( 10 / 20 ) x ( 3 / 6 ) = 28 meters answer : b ." |
Provide a detailed solution to the given mathematical problem. | the average age of 39 students in a group is 14 years . when teacher' s age is included to it , the average increases by one . what is the teacher' s age in years ? a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) none of these | "explanation : age of the teacher = ( 40 * 15 - 39 * 14 ) years = 54 years . answer : d" |
Provide a detailed solution to the given mathematical problem. | the cost price of 12 articles is equal to the selling price of 10 articles . what is the profit percent ? a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 % | "10 * sp = 12 * cp sp = 1.2 * cp the profit percent is 20 % . the answer is b ." |
Solve the problem systematically, showing each step clearly. | on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays in... | "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.2 * 4 = 8.8 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 8.8 % answer : e ." |
Provide a detailed solution to the given mathematical problem. | suppose you work for a manufacturing plant that pays you $ 12.50 an hour and $ . 16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 800 ( before payroll deductions ) ? a ) 1800 , b ) 1825 , c ) 1850 , d ) 1855 , e ) 1875 | "hourly = $ 12.50 / hour totalhours = 40 piecework = $ 0.16 / widget totalpieces = ? ? ? ? total pay = ( hourly * totalhours ) + ( piecework * totalpieces ) so , put it all together : $ 800 = ( $ 12.50 * 40 ) + ( $ 0.16 * total pieces ) totalpieces = ( $ 800 - ( $ 12.50 * 40 ) ) / $ 0.16 = 1875 widgets e . 1875" |
Work through the equation methodically, ensuring clarity at each step. | gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ? a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5 | "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b" |
Break down and solve the equation step by step. | if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6 | we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the ... |
Solve the problem systematically, showing each step clearly. | two employees m and n are paid a total of $ 616 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ? a ) $ 270 , b ) $ 280 , c ) $ 290 , d ) $ 300 , e ) $ 310 | "1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ." |
Work through the equation methodically, ensuring clarity at each step. | with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 4 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ? a ) 347 , b ) 480 , c ) 288 , d ) 278 , e ) 131 | "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 4 2 x / 15 - x / 8 = 4 = > x = 480 km . answer : b" |
Break down and solve the equation step by step. | if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ? a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4 | "( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ." |
Solve the problem systematically, showing each step clearly. | a man can row downstream at the rate of 16 km / hr and upstream at 8 km / hr . find man' s rate in still water and the rate of current ? a ) 12,4 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these | "explanation : rate of still water = 1 / 2 ( 16 + 8 ) = 12 km / hr rate of current = 1 / 2 ( 16 - 8 ) = 4 km / hr answer : option a" |
Work through the equation methodically, ensuring clarity at each step. | find the ones digit of 73 ^ 352 a ) 1 , b ) 5 , c ) 6 , d ) 7 , e ) 9 | "the units digit of 73 ^ 352 will be the same as the units digit of 3 ^ 352 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units d... |
Explain the solution process for the given equation. | - 64 x 29 + 165 = ? a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 1601 , e ) none of them | "given exp . = - 64 x ( 30 - 1 ) + 165 = - ( 64 x 30 ) + 64 + 165 = - 1830 + 229 = - 1601 answer is d" |
Explain the solution process for the given equation. | a watch was sold at a loss of 10 % . if it was sold for rs . 168 more , there would have been a gain of 4 % . what is the cost price ? a ) s : 1000 , b ) s : 1067 , c ) s : 1200 , d ) s : 1028 , e ) s : 1027 | "90 % 104 % - - - - - - - - 14 % - - - - 168 100 % - - - - ? = > rs : 1200 answer : c" |
Explain the solution process for the given equation. | how many integers are divisible by 5 between 10 ! and 10 ! + 20 inclusive ? a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | a - 7 10 ! is divisible by 5 there are 4 numbers between 10 ! and 10 ! + 20 that are divisible by 5 . hence 5 |
Explain the solution process for the given equation. | in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr . | "e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr ." |
Provide a detailed solution to the given mathematical problem. | martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.60 , how many discounted tickets did he buy ? a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.6 0.4 x = 1.6 = > x = 4 discounted tickets = 10 - x = 6 ans : d" |
Solve the problem systematically, showing each step clearly. | a man can do a piece of work in 5 days , but with the help of his son , he can do it in 3 days . in what time can the son do it alone ? a ) 13 / 2 , b ) 7 , c ) 15 / 2 , d ) 8 , e ) 9 | "son' s 1 day' s work = ( 1 / 3 ) - ( 1 / 5 ) = 2 / 5 the son alone can do the work in 15 / 2 days answer is c" |
Break down and solve the equation step by step. | a cycle is bought for rs . 670 and sold for rs . 780 , find the gain percent ? a ) 70 % , b ) 20 % , c ) 16 % , d ) 19 % , e ) 80 % | "explanation : 670 - - - - 110 100 - - - - ? = > 16 % answer : c" |
Solve the problem systematically, showing each step clearly. | in a certain corporation , there are 300 male employees and 150 female employees . it is known that 10 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female... | p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.1 * 300 / 450 = 30 / 450 = 1 / 15 the sum of the probabilities is 6 / 15 = 2 / 5 the answer is c . |
Explain the solution process for the given equation. | if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 10 ) , what is the value of x ? a ) 9 , b ) 11 , c ) 13 , d ) 12 , e ) 17 | "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 10 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 10 hence x = 12 . answer is d" |
Work through the equation methodically, ensuring clarity at each step. | a worker' s daily wage is increased by 50 % and the new wage is $ 51 per day . what was the worker' s daily wage before the increase ? a ) $ 28 , b ) $ 32 , c ) $ 34 , d ) $ 35 , e ) $ 40 | "let x be the daily wage before the increase . 1.5 x = $ 51 x = $ 34 the answer is c ." |
Break down and solve the equation step by step. | the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 20 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal ... | "assume the manager bought 100 tomatoes . cost price = 80 given : 20 % are damaged - - > available tomatoes to sell = 80 80 * x - 80 = 0.08 * 80 80 x - 80 = 6.4 80 x = 86.64 x = 86.64 / 80 = 87 / 80 ( approx ) = 1.0875 x is slightly under 1.0875 = 1.09 answer : e" |
Explain the solution process for the given equation. | consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ? a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these | "explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > al... |
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