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Explain the solution process for the given equation.
a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 12 more blue balls than white balls , and six times as many red balls as blue balls , how many white balls does the box has ? a) 8 , b) 10 , c) 2 , d) 14 , e) 16
"x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 12 more blue balls than white balls . . . equation # 2 : y = 12 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 6 y solve equation # 2 for z : z = y - 12 now , we can replace both x and z with y in equation # 1 6 y + y + (y - 12) = 100 8 y - 12 = 100 5 y = 112 y = 14 there are 14 blue balls . this is 12 more than the number of white balls , so z = 2 . that' s the answer . just as a check , x = 84 , and 84 + 14 + 2 = 100 . answer = 2 , (c)"
Solve the problem systematically, showing each step clearly.
at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun' s age will be 36 years . what is the age of deepak at present ? a) 35 years , b) 25 years , c) 42 years , d) 39 years , e) 40 years
"let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak' s age = 7 x = 42 years answer is c"
Work through the equation methodically, ensuring clarity at each step.
the average weight of 8 person' s increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ? a) 56 kg , b) 80 kg , c) 85 kg , d) data inadequate , e) none of these
"b 80 kg total weight increased = (8 x 2.5) kg = 20 kg . weight of new person = (60 + 20) kg = 80 kg ."
Provide a detailed solution to the given mathematical problem.
what is the square root of 625 , divided by 5 ? a) 9 , b) 36 , c) 5 , d) 6 , e) 1
square root is a number times itself square root of 625 = 25 , 25 / 5 = 5 (c) 5
Explain the solution process for the given equation.
the ratio between the length and the breadth of a rectangular park is 1 : 4 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park (in sq . m) is ? ['a) 124545 m','b) 134561 m','c) 156787 m','d) 15450 m','e) 102400 m']
perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 4 x metres . then , 2 (1 x + 4 x) = 1600 or x = 160 . length = 160 m and breadth = 640 m . area = (160 x 640) m 2 = 102400 m e
Break down and solve the equation step by step.
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 / 6 . 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) 116 , b) 146 , c) 152 , d) 162 , e) 170
"the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ."
Provide a detailed solution to the given mathematical problem.
the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ? ['a) 10000','b) 10008','c) 10005','d) 10004','e) 10001']
100 * 100 = 10000 125 * 80 = 10000 no change answer : a
Solve the problem systematically, showing each step clearly.
a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ? a) 16 % , b) 32 % , c) 48 % , d) 84 % , e) 92 %
"16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d"
Work through the equation methodically, ensuring clarity at each step.
the average of 25 results is 24 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ? a) 740 , b) 228 , c) 690 , d) 780 , e) 458
"solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x (let) now , 12 * 14 + 12 * 17 + x = 25 * 24 or , x = 228 . answer : option b"
Work through the equation methodically, ensuring clarity at each step.
if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ? a) 20 % , b) 25 % , c) 18 % , d) 50 % , e) none of these
"here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d"
Break down and solve the equation step by step.
if n is a positive integer and n ^ 3 is a multiple of 550 , what is the least possible value of n ? a) 8 , b) 27 , c) 81 , d) 110 , e) 125
"cube of a number entails having 3 copies of the original prime factors . since 550 is a factor of n ^ 3 the least possible value of n is 5 (11) 2 = 110 the answer is d ."
Solve the problem systematically, showing each step clearly.
the maximum number of student amoung them 1080 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : a) 91 , b) 40 , c) 80 , d) 90 , e) none of these
"solution required number of student = h . c . f of 1080 and 920 = 40 . answer b"
Work through the equation methodically, ensuring clarity at each step.
the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is : a) 200 m , b) 230 m , c) 245 m , d) 250 m , e) 270 m
"let the length of the bridge : l the equation now is l + 145 / 12.5 m / s (45 km / hr or 12.5 m / s) = 30 solving , l = 230 m answer : b"
Work through the equation methodically, ensuring clarity at each step.
excluding stoppages , the speed of a bus is 80 kmph and including stoppages , it is 60 kmph . for how many minutes does the bus stop per hour ? a) 12 min , b) 20 min , c) 25 min , d) 30 min , e) 15 min
"due to stoppages , it covers 20 km less . time taken to cover 20 km = (20 / 80 x 60) min = 15 min answer : e"
Work through the equation methodically, ensuring clarity at each step.
in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ? a) 30 , b) 31 , c) 32 , d) 33 , e) 34
this is an example of a standard overlapping sets question . it has no' twists' to it , so you' ll likely find using the overlapping sets formula to be a fairly easy approach . if you' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + (# in neither group) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d
Work through the equation methodically, ensuring clarity at each step.
what is the units digit of 13 ^ 4 * 17 ^ 2 * 29 ^ 3 ? a) 9 , b) 7 , c) 5 , d) 3 , e) 1
"3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 7 3 ^ 4 = 1 , it is first digit 7 ^ 2 = 9 , it is second digit 9 ^ 3 = 9 , it is third digit 1 * 9 * 9 = 1 answer : e"
Break down and solve the equation step by step.
a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ? a) 36 , b) 40 , c) 44 , d) 48 , e) 52
"for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 (18) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48"
Work through the equation methodically, ensuring clarity at each step.
the average of 10 consecutive integers is 16 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ? a) 10.5 , b) 11 , c) 11.5 , d) 12 , e) 12.5
the total subtracted is (9 + 8 + . . . + 1) = (9 * 10) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is c .
Break down and solve the equation step by step.
in a kilometer race , a beats b by 80 meters or 10 seconds . what time does a take to complete the race ? a) 167 sec , b) 190 sec , c) 176 sec , d) 115 sec , e) 123 sec
"time taken by b run 1000 meters = (1000 * 10) / 80 = 125 sec . time taken by a = 125 - 10 = 115 sec . answer : d"
Break down and solve the equation step by step.
a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ? a) 3 / 8 , b) 9 / 10 , c) 1 / 2 , d) 3 / 5 , e) 3 / 4
"x * 6 / 100 * 1 + (20000 - x) * 10 / 100 * 1 = 1440 6 x - 8 x = 144000 - 200000 = > - 2 x = - 4000 = > x = 2000 so 18000 / 20000 = 9 / 10 answer - b"
Provide a detailed solution to the given mathematical problem.
by weight , liquid x makes up 0.5 percent of solution p and 1.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? a) 1.3 % , b) 1.2 % , c) 1.1 % , d) 1.0 % , e) 0.9 %
the number of grams of liquid x is 0.5 (200) / 100 + 1.5 (800) / 100 = 1 + 12 = 13 grams . 13 / 1000 = 1.3 % the answer is a .
Break down and solve the equation step by step.
what is the remainder when 2 ^ 20 is divided by 10 ? a) 0 , b) 2 , c) 4 , d) 6 , e) 8
"2 ^ 20 = 2 ^ 10 x 2 ^ 10 and 2 ^ 10 = 1024 4 * 4 = 16 , so the unit digit of this multiplication is 6 the remainder is 6 answer : d"
Work through the equation methodically, ensuring clarity at each step.
calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days , a) 6 days , b) 3 days , c) 4 days , d) 2 days , e) 5 days
"the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c"
Explain the solution process for the given equation.
the jogging track in a sports complex is 726 m in circumference . suresh and his wife start from the same point and walk in opposite direction at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ? a) 5.2 minutes , b) 5.21 minutes , c) 5.25 minutes , d) 5.28 minutes , e) 6 minutes
let both of them meet after tt min 4500 m are covered by suresh in 60 m . in tt min he will cover 4500 t 604500 t 60 likewise , in tt min suresh' s wife will cover 3750 t 603750 t 60 given , 4500 t 60 + 3750 t 60 = 7264500 t 60 + 3750 t 60 = 726 tt = 5.28 minutes option (d) is correct
Work through the equation methodically, ensuring clarity at each step.
calculate 469157 x 9999 = ? a) 4586970843 , b) 4686970743 , c) 4691100843 , d) 4586870843 , e) none
"answer 469157 x 9999 = 469157 x (10000 - 1) = 4691570000 - 469157 = 4691100843 . option : c"
Solve the problem systematically, showing each step clearly.
a candidate got 40 % of the votes polled and he lost to his rival by 2000 votes . how many votes were cast ? a) 10000 , b) 2028 , c) 2775 , d) 5496 , e) 6851
"40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 2000 100 % - - - - - - - - - ? = > 10000 answer : a"
Solve the problem systematically, showing each step clearly.
the average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive ? a) 5 , b) 8 , c) 10 , d) 15 , e) 20
"the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 (1 + 2 + . . . + n / 2) = 2 (n / 2) (n / 2 + 1) / 2 = (n / 2) (n / 2 + 1) the average is (n / 2) (n / 2 + 1) / (n / 2 + 1) = n / 2 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the average of the even numbers from 0 to 20 is 20 / 2 = 10 the answer is c ."
Work through the equation methodically, ensuring clarity at each step.
carol and jordan draw rectangles of equal area . if carol' s rectangle measures 12 inches by 15 inches and jordan' s rectangle is 6 inches long , how wide is jordan' s rectangle , in inches ? ['a) 24','b) 26','c) 28','d) 30','e) 32']
area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d
Break down and solve the equation step by step.
sony and johnny caught 40 fishes . sony caught 4 times as many as johnny . how many fishes did johnny catch ? a) 12 , b) 16 , c) 34 , d) 38 , e) 8
s + j = 40 s = 4 * j j = 8 answer : e
Break down and solve the equation step by step.
ravi can do a piece of work in 15 days while prakash can do it in 30 days . in how many days will they finish it together ? a) 11 days , b) 9 days , c) 8 days , d) 12 days , e) 10 days
"1 / 15 + 1 / 30 = 3 / 30 10 / 1 = 10 days answer : e"
Provide a detailed solution to the given mathematical problem.
if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y = a) 540 , b) 570 , c) 619 , d) 649 , e) 700
"before price increase price = y after 30 % price increase price = y + (30 / 100) * y = 1.3 y = 351 (given) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a"
Explain the solution process for the given equation.
bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ? a) $ 0.25 , b) $ 0.12 , c) $ 0.05 , d) $ 0.003 , e) $ 0.005
"cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e"
Break down and solve the equation step by step.
machine p and machine q are each used to manufacture 550 sprockets . it takes machine p 10 hours longer to produce 550 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? a) 5 , b) 15 , c) 55 , d) 95 , e) 125
"p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 550 / x = 550 / 1.1 x + 10 1.1 (550) = 550 + 11 x 11 x = 55 x = 5 the answer is a ."
Break down and solve the equation step by step.
in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ? a) 320 $ , b) 380 $ , c) 525 $ , d) 456 $ , e) 480 $
"total cost = (1.75 * 14) + (0.65 * 14 * 55) = 24.5 + 500.5 = > 525 hence answer will be (c) 525"
Solve the problem systematically, showing each step clearly.
how many positive integers less than 160 are there such that they are multiples of 13 or multiples of 12 but not both ? a) 18 , b) 19 , c) 20 , d) 23 , e) 25
"for 13 : 13 . . . 160 = 13 * 12 for 12 : 12 . . . 156 = 12 * 13 but there is one integer 13 * 12 . so n = (12 - 1) + (13 - 1) = 23 d"
Solve the problem systematically, showing each step clearly.
if the cost price of 60 articles is equal to the selling price of 50 articles , then what is the percent profit ? a) 10 % , b) 15 % , c) 20 % , d) 25 % , e) 30 %
"let x be the cost price of one article . let y be the selling price of one article . 50 y = 60 x y = 1.2 x the answer is c ."
Break down and solve the equation step by step.
the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ? a) 1 / 5 , b) 1 / 3 , c) 2 / 5 , d) 1 / 2 , e) 2 / 3
"let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ."
Solve the problem systematically, showing each step clearly.
a train 300 m long can cross an electric pole in 30 sec and then find the speed of the train ? a) 76 kmph , b) 54 kmph , c) 72 kmph , d) 36 kmph , e) 91 kmph
"length = speed * time speed = l / t s = 300 / 30 s = 10 m / sec speed = 10 * 18 / 5 (to convert m / sec in to kmph multiply by 18 / 5) speed = 36 kmph answer : d"
Work through the equation methodically, ensuring clarity at each step.
what is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45 ? a) 26 , b) 36 , c) 16 , d) 06 , e) 40
explanation : let' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = (1 + 44) + (2 + 43) + . . . . + (22 + 23) (22 pairs) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b
Explain the solution process for the given equation.
in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight a) 1 / 7 , b) 1 / 8 , c) 1 / 4 , d) 3 / 7 , e) 7 / 8
"good question . so we have a garden where all the flowers have two properties : color (green or yellow) and shape (straight or curved) . we' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr (yellow and straight) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr (a and b) = p (a) * p (b) . so we multiply the two probabilities , pr (yellow) * pr (straight) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."
Work through the equation methodically, ensuring clarity at each step.
the sale price sarees listed for rs . 400 after successive discount is 12 % and 5 % is ? a) 338 , b) 277 , c) 342 , d) 334.4 , e) 212
"400 * (88 / 100) * (95 / 100) = 334.4 answer : d"
Break down and solve the equation step by step.
of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ? a) 1000 , b) 1200 , c) 1400 , d) 1600 , e) 1800
"let x be the number of eggs that were laid . (2 / 5) (3 / 4) (1 / 3) x = 120 (6 / 60) x = 120 x = 1200 the answer is b ."
Explain the solution process for the given equation.
if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ? a) 3 , b) 9 , c) 15 , d) 19 , e) 28
"[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e"
Break down and solve the equation step by step.
the compounded ratio of (2 : 3) , (6 : 11) and (11 : 2) is : a) 1 : 2 , b) 5 : 9 , c) 2 : 1 , d) 11 : 24 , e) none
answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1
Provide a detailed solution to the given mathematical problem.
in a room with 9 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (assuming that friendship is a mutual relationship , i . e . if jane is paul' s friend , paul is jane' s friend) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ? a) 5 / 21 , b) 3 / 7 , c) 4 / 7 , d) 5 / 7 , e) 1
"(6 / 9) (7 / 8) + (5 / 9) (6 / 8) if you choose one of the 6 with one other friend , then you have a 7 / 8 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 8 chance of not picking one of their friends second . add them up . 42 / 72 + 30 / 72 72 / 72 = 1 e . 1"
Provide a detailed solution to the given mathematical problem.
the speed of a boat in still water is 12 kmph . what is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time ? a) 5 kmph , b) 6 kmph , c) 7 kmph , d) 4 kmph , e) 10 kmph
"x = the speed of the stream (12 + x) / (12 - x) = 2 / 1 12 + x = 24 - 2 x 3 x = 12 x = 4 km / hour if the speed of the stream is 4 km / hour , then the' downstream' speed of the boat is 12 + 4 = 16 km / hour and the' upstream' speed of the boat is 12 - 4 = 8 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 8 = 16 km downstream and 2 x 16 = 32 km / hour upstream . answer : d"
Work through the equation methodically, ensuring clarity at each step.
population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrement of 35 % and in 2007 there is an increment of 45 % , then find the population of city at theend of the year 2007 a) 2456789 , b) 3458009 , c) 3890043 , d) 3455048 , e) 1083875
"required population = p (1 + r 1 / 100) (1 - r 2 / 100) (1 + r 3 / 100) = p (1 + 15 / 100) (1 - 35 / 100) (1 + 45 / 100) = 1083875 e"
Break down and solve the equation step by step.
the calendar of the year 2080 can be used again in the year ? a) 2105 , b) 1955 , c) 1945 , d) 1935 , e) 2108
"explanation : given year 2080 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2080 + 28 = 2108 answer : e"
Explain the solution process for the given equation.
i flew my tiny seaplane to visit my mother . on the flight up , i flew at 130 mph . on the way home , i flew 88 mph . what was my average speed for the trip ? a) 198 mph , b) 110 mph , c) 88 mph , d) 100 mph , e) 109 mph
"(130 mph + 88 mph) / 2 = 109 mph correct answer is : e"
Break down and solve the equation step by step.
in the rectangular coordinate system point o has coordinates (0,0) and point b has coordinates (5,5) and if point a is equidistant from points o and b and the area of the triangle oab is 16 , which of the following are the possible coordinates of point a . ['a) (- 2,6)','b) (0,4)','c) (2 , - 6)','d) (2,6)','e) (4,0)']
area . pngsince a is equidistant from points o and b , then it must be somewhere on the green line (perpendicular bisector of ob) . (2 , - 6) and (2,6) are not on that line . if a is at (0,5) or (5,0) , then the area is 1 / 2 * 5 * 5 = 25 / 2 . thus a must be at (2,6) . answer : d .
Provide a detailed solution to the given mathematical problem.
the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 125 resolutions ? a) 794 m , b) 704 m , c) 454 m , d) 186 m , e) 176 m
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 125 resolutions . = 125 * 2 * 22 / 7 * 22.4 = 17600 cm = 176 m answer : e"
Explain the solution process for the given equation.
if the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is ? a) 18 , b) 26 , c) 14 , d) 12 , e) 9.3
"2 * 22 / 7 * 18 * x = 1056 = > x = 9.3 answer : e"
Work through the equation methodically, ensuring clarity at each step.
average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ? a) rs . 692.80 , b) rs . 820 , c) rs . 990 , d) rs . 1385 , e) none
"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 650 x 3 rs . = 990 rs . correct option : c"
Provide a detailed solution to the given mathematical problem.
if a 3 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? a) 40 % , b) 100 % , c) 150 % , d) 200 % , e) 300 %
"the area a of the large cube is 3 * 3 * 6 = 54 square cm . the area of the 27 small cubes is 27 * 6 = 54 * 3 = 3 a , an increase of 200 % . the answer is d ."
Explain the solution process for the given equation.
if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 92 . if $ 2000 is the total amount invested , how much is invested at 8 percent ? a) $ 600 , b) $ 700 , c) $ 800 , d) $ 900 , e) $ 1000
0.1 x = 0.08 (2000 - x) + 92 0.18 x = 252 x = 1400 then the amount invested at 8 % is $ 2000 - $ 1400 = $ 600 the answer is a .
Solve the problem systematically, showing each step clearly.
of the 400 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ? a) 65 , b) 100 , c) 115 , d) 130 , e) 260
"240 prefer x (group 1) ; 160 prefer y (group 2) . city y needs 300 people : letall 160 who prefer y (entire group 2) be relocated there , the rest 140 will be those who prefer x from group 1 ; city x needs 100 people : 240 - 140 = 100 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 160 + 100 = 260 . answer : e ."
Explain the solution process for the given equation.
the area of a triangle is with base 8.4 m and height 5.8 m ? a) 11.36 m 2 , b) 10.36 m 2 , c) 18.36 m 2 , d) 19.36 m 2 , e) 24.36 m 2
"1 / 2 * 8.4 * 5.8 = 24.36 m 2 answer : e"
Break down and solve the equation step by step.
if x , y , and z are positive real numbers such that x + y - z = 100 , y - z + x = 120 , and z - x + y = 50 , then find the x + y + z value ? a) 100 , b) 120 , c) 150 , d) 200 , e) 160
"x + y - z = 100 , - - - - - - 1) y - z + x = 120 , - - - - - - 2) z - x + y = 50 - - - - - - 3) from (1) & (2) 2 z = 20 z = 10 from (2) & (3) 2 y = 170 y = 85 then x = 100 - 75 = 25 x + y + z = 120 correct option is b"
Explain the solution process for the given equation.
population is 22000 . population increases by 10 % every year , then the population after 3 years is ? a) 26630 , b) 29282 , c) 36620 , d) 26620 , e) 26820
"population after 1 st year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24000 population after 2 nd year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26620 population after 3 rd year = 26620 * 10 / 100 = 2662 = = = > 26620 + 2662 = 29282 answer : b"
Explain the solution process for the given equation.
joan and karl each bought a telescopes and the sum of their purchases was $ 400 . if twice of what joan paid was $ 74 more than what karl paid , what did joan pay for her telescope ? a) $ 150 , b) $ 152 , c) $ 154 , d) $ 156 , e) $ 158
j + k = 400 so k = 400 - j 2 j = k + 74 2 j = (400 - j) + 74 3 j = 474 j = 158 the answer is e .
Solve the problem systematically, showing each step clearly.
the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ? a) 7 , b) 8 , c) 9 , d) 10 , e) 11
"14 n + 34 = 16 (n + 1) 2 n = 18 n = 9 the answer is c ."
Explain the solution process for the given equation.
at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 19.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ? a) 13.7 , b) 14.0 , c) 14.3 , d) 14.6 , e) 14.9
"let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 19.6 x ^ 2 = 1.96 x = 1.4 at 4 : 00 pm , the amount of bacteria was 10 (1.4) = 14 grams . the answer is b ."
Solve the problem systematically, showing each step clearly.
mr . kramer , the losing candidate in a two - candidate election , received 942568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ? a) 10 % , b) 12 % , c) 15 % , d) 29 % , e) 20 %
let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d .
Solve the problem systematically, showing each step clearly.
the lcm of two numbers is 2310 and hcf is 47 . if one of the numbers is 210 . then what is the other number ? a) 715 , b) 825 , c) 330 , d) 582 , e) 517
first number * second number = lcm * hcf other number = 2310 * 47 / 210 = 11 * 47 = 517 answer : e
Explain the solution process for the given equation.
in a 8 x 8 chess board what is the total number of squares . a) 238 , b) 204 , c) 678 , d) 169 , e) 161
ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares'' i . e . , n (n + 1) (2 n + 1) 6 n (n + 1) (2 n + 1) 6 so substituting 8 in the above formula we get 204 answer : b
Provide a detailed solution to the given mathematical problem.
two trains of equal length , running with the speeds of 60 and 40 kmph , take 60 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ? a) 10 sec , b) 16 sec , c) 12 sec , d) 67 sec , e) 13 sec
"rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 60 * 100 / 18 = 1000 / 3 rs = 60 + 40 = 100 * 5 / 18 t = 1000 / 3 * 18 / 500 = 12 sec answer : c"
Provide a detailed solution to the given mathematical problem.
find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg a) 2 : 0 , b) 3 : 4 , c) 2 : 1 , d) 2 : 2 , e) 2 : 8
"by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b"
Solve the problem systematically, showing each step clearly.
find the length of the longest pole that can be placed in an indoor stadium 24 m long , 18 m wide and 16 m high a) 31 , b) 32 , c) 33 , d) 34 , e) 35
"sqrt (1156) = 34 becoz max length is cuboid diagonal d = sqrt (l ^ 2 + b ^ 2 + h ^ 2) where l lenght b breadth & h height answer : d"
Work through the equation methodically, ensuring clarity at each step.
the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 72 of the area of the field . what is the length of the field ? a) 73 , b) 32 , c) 34 , d) 43 , e) 96
"explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e"
Break down and solve the equation step by step.
product of two natural numbers is 19 . then , the sum of reciprocals of their squares is a) 290 / 289 , b) 1 / 289 , c) 290 / 90 , d) 362 / 361 , e) none of these
explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 (2) + 1 / 19 (2) = 362 / 361 option d
Explain the solution process for the given equation.
after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ? a) 2160 , b) 2350 , c) 2000 , d) 2300 , e) 2400
"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e"
Solve the problem systematically, showing each step clearly.
the present population of a town is 1000 . population increase rate is 20 % p . a . find the population of town after 2 years ? a) 1440 , b) 1220 , c) 1400 , d) 1500 , e) 1620
"p = 1000 r = 20 % required population of town = p * (1 + r / 100) ^ t = 1000 * (1 + 20 / 100) ^ 2 = 1000 * (6 / 5) ^ 2 = 1440 (approximately) answer is a"
Provide a detailed solution to the given mathematical problem.
rs . 6000 is lent out in two parts . one part is lent at 4 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ? a) 5 : 1 , b) 5 : 7 , c) 5 : 2 , d) 5 : 8 , e) 5 : 2
"let the amount lent at 4 % be rs . x amount lent at 10 % is rs . (6000 - x) total interest for one year on the two sums lent = 4 / 100 x + 10 / 100 (6000 - x) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 2500 amount lent at 10 % = 3500 required ratio = 5 : 7 answer : b"
Solve the problem systematically, showing each step clearly.
in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.1 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ? a) 68.8 , b) 73.6 , c) 75.2 , d) 77.12 , e) 81.6
"degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = (7.5 + 8.1 + 8.5) = 24 point of value of the dive = 24.1 * 3.2 = 77.12 answer d"
Work through the equation methodically, ensuring clarity at each step.
express a speed of 56 kmph in meters per second ? a) 10.56 mps , b) 17.56 mps , c) 97.56 mps , d) 15.56 mps , e) 18.56 mps
"56 * 5 / 18 = 15.56 mps answer : d"
Break down and solve the equation step by step.
a survey was sent to 90 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ? a) 2 % , b) 6 % , c) 14 % , d) 28 % , e) 63 %
"case 1 : (7 / 90) = x / 100 x = 8 % case 2 : (9 / 63) = y / 100 y = 14 % so percent increase is = (y - x) = (14 - 8) % = 6 % answer is b"
Break down and solve the equation step by step.
if x + (1 / x) = 5 , what is the value of t = x ^ 2 + (1 / x) ^ 2 ? a) t = 21 , b) t = 22 , c) t = 23 , d) 24 , e) 27
"squaring on both sides , x ^ 2 + (1 / x) ^ 2 + 2 (x) (1 / x) = 5 ^ 2 x ^ 2 + (1 / x) ^ 2 = 23 answer : c"
Solve the problem systematically, showing each step clearly.
if a man lost 4 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 28 % ? a) 12 , b) 13 , c) 14 , d) 15 , e) 10
"96 % - - - - 16 128 % - - - - ? 96 / 128 * 16 = 12 answer : a"
Solve the problem systematically, showing each step clearly.
what is the least positive integer x for which (x ^ 2) + 164 is divisible by 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and 11 ? a) 27556 , b) 800 , c) 796 , d) 87 , e) 166
2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 so (x ^ 2) + 164 = (2 * 2 * 2 * 3 * 3 * 5 * 7 * 11) = 27720 . then (x ^ 2) = 27556 . then x = 166 , which is option e .
Solve the problem systematically, showing each step clearly.
a cyclist rides a bicycle 8 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 8 km / hr . what is the average speed for the entire trip ? a) 8.58 , b) 8.76 , c) 9.04 , d) 9.12 , e) 9.25
"distance = 19 km time = 8 / 11 + 11 / 8 = (64 + 121) / 88 = 185 / 88 hours average speed = (19 * 88) / 185 = 9.04 km / h the answer is c ."
Break down and solve the equation step by step.
300 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees a) 10 , b) 12 , c) 14 , d) 16 , e) 18
26 trees have 25 gaps between them , required distance (300 / 25) = 12 b
Work through the equation methodically, ensuring clarity at each step.
two trains 210 m and 260 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? a) 16.92 sec , b) 14.8 sec , c) 10.68 sec , d) 10.8 sec , e) 20.8 sec
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 210 + 260 = 470 m . required time = 470 * 9 / 250 = 16.92 = 16.92 sec . answer : a"
Break down and solve the equation step by step.
among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco' s sales staff . listco employs 90 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ? a) 46 , b) 42 , c) 56 , d) 32 , e) 40
"i' m going in on this one . so let' s say that we have the following so we know that l 1 = 90 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 90 = 110 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 60 = 40 . thus e is the correct answer choice"
Explain the solution process for the given equation.
the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ? a) 18.5 , b) 21.5 , c) 24.5 , d) 27.5 , e) 30.5
"the point of intersection is (- 7 , - 7) . the triangle has a base of length 7 and a height of 7 . area = (1 / 2) * base * height = (1 / 2) * 7 * 7 = 24.5 the answer is c ."
Provide a detailed solution to the given mathematical problem.
fox jeans regularly sell for $ 10 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ? a) 9 % , b) 10 % , c) 11 % , d) 12 % , e) 40 %
"x discount on pony jeans , (0.22 - x) discount on fox jeans . set the equation : 3 * 10 (0.22 - x) + 2 * 18 x = 9 - - > x = 0.4 = 40 % answer : e ."
Solve the problem systematically, showing each step clearly.
one ton has 2600 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ? a) 2080 , b) 1700 , c) 2350 , d) 2500 , e) 8000
"16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is (13 * 2600 * 16) / 260 = 2080 . answer : a ."
Work through the equation methodically, ensuring clarity at each step.
in a certain neighborhood , 60 percent of the student are going to school (a) , and the rest are going to school (b) . a new school (c) is opened , if 30 percent of student of school (a) and 40 percent of student of school (b) are expected to go to the new school (c) , what percent of student are expected to go to the new school (c) ? a) 30 % , b) 34 % , c) 38 % , d) 42 % , e) 46 %
say there are total of 100 students in the neighborhood , 60 students are going to school (a) and 40 student are going to school (b) 60 * 0.3 = 18 student of school (a) are expected to go to the new school (c) 40 * 0.4 = 16 student of school (b) are expected to go to the new school (c) thus total of 18 + 16 = 34 student are expected to go to the new school (c) , which is 34 % of students . answer : b .
Provide a detailed solution to the given mathematical problem.
the sector of a circle has radius of 18 cm and central angle 135 o . find its perimeter ? a) 78.4 cm , b) 11.5 cm , c) 91.8 cm , d) 92.5 cm , e) 99.5 cm
"perimeter of the sector = length of the arc + 2 (radius) = (135 / 360 * 2 * 22 / 7 * 18) + 2 (18) = 42.4 + 36 = 78.4 cm answer : a"
Work through the equation methodically, ensuring clarity at each step.
in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 80 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ? a) 8 % , b) 12 % , c) 16 % , d) 20 % , e) 24 %
"let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.8 x the number of students in beginner trigonometry is 4 / 5 * (2.5 x) - 0.8 x = 1.2 x the number of students in advanced trigonometry is 0.3 x the percentage in advanced trigonometry is 0.3 x / 2.5 x = 12 % the answer is b ."
Break down and solve the equation step by step.
if the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ? a) 4 / 15 , b) 1 / 3 , c) 2 / 15 , d) 4 / 5 , e) 7 / 6
"a : b = 2 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 2 : 15 answer c"
Break down and solve the equation step by step.
a metallic sheet is of rectangular shape with dimensions 48 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 3 m , the volume of the box (in m 3) is : a) 3780 , b) 5120 , c) 6420 , d) 8960 , e) 7960
"clearly , l = (48 - 6) m = 42 m , b = (36 - 6) m = 30 m , h = 8 m . volume of the box = (42 x 30 x 3) m 3 = 3780 m 3 . answer : option a"
Solve the problem systematically, showing each step clearly.
bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 19 left in his pocket . what was the value of n ? a) $ 36 , b) $ 44 , c) $ 52 , d) $ 60 , e) $ 68
"started to test answer d if he had 60 , then he spent 15 at hardware store now he was left with 45 $ he spent 7 dollars on cleaning , thus he remained with 38 $ he then spent 1 / 2 of 38 , or 19 , and was left with 19 . hence , the only option that can be right is a ."
Break down and solve the equation step by step.
an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ? a) 4 : 5 , b) 9 : 10 , c) 14 : 15 , d) 19 : 20 , e) 24 : 25
"let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 (3 x + 2 x) = 2 (y + y) 5 x = 2 y (5 / 2) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : (25 / 4) * x ^ 2 = 24 : 25 the answer is e ."
Solve the problem systematically, showing each step clearly.
a cylinder of height h is 7 / 8 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ? a) 25 % , b) 50 % , c) 69 % , d) 80 % , e) 100 %
"basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it' s height is 3 / 5 . original cylinder 7 / 8 new cylinder 3 / 5 so 3 / 5 / 7 / 8 = 3 / 5 * 8 / 7 = 0.69 or 69 % . answer c"
Explain the solution process for the given equation.
what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon) ? a) 1 / 2 , b) 1 / 3 , c) 1 / 4 , d) 1 / 6 , e) 1 / 9
"from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 6 = 1 / 3 . the answer is b ."
Solve the problem systematically, showing each step clearly.
a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ? a) 10 days , b) 12 days , c) 13 days , d) 9 days , e) 14 days
"b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a"
Provide a detailed solution to the given mathematical problem.
when magnified 1000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is a) 0.005 , b) 0.002 , c) 0.001 , d) 0.0003 , e) 0.0002
it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d
Solve the problem systematically, showing each step clearly.
each machine of type a has 3 steel parts and 2 chrome parts . each machine of type b has 2 steel parts and 4 chrome parts . if a certain group of type a and type b machines has a total of 50 steel parts and 66 chrome parts , how many machines are in the group a) 11 , b) 21 , c) 31 , d) 61 , e) 51
"look at the below representation of the problem : steel chrome total a 3 2 50 > > no . of type a machines = 50 / 5 = 10 b 2 4 66 > > no . of type b machines = 66 / 6 = 11 so the answer is 21 i . e b . hope its clear ."
Provide a detailed solution to the given mathematical problem.
a train running at the speed of 142 km / hr crosses a pole in 12 seconds . find the length of the train . a) 540 , b) 288 , c) 200 , d) 340 , e) 712
"speed = 162 * (5 / 18) m / sec = 45 m / sec length of train (distance) = speed * time 45 * 12 = 540 meter answer : a"
Work through the equation methodically, ensuring clarity at each step.
three unbiased coins are tossed . what is the probability of getting 1 heads and 1 tail ? a) 3 / 4 , b) 1 / 4 , c) 3 / 8 , d) 7 / 8 , e) 1 / 8
"let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { tht , hth } p (e) = n (e) / n (s) = 2 / 8 = 1 / 4 answer is b"