Cheukting/mathqa huggingface dataset:
Question (gain): a man buy a book in rs 50 & sale it rs 60 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 60 profit = 60 - 50 = 10 % = 10 / 50 * 100 = 20 % answer : b"
Answer: b
Question (physics): a man complete a journey in 1010 hours . he travels first half of the journey at the rate of 2121 km / hr and second half at the rate of 2424 km / hr . find the total journey in km .
Options: a ) 121 km , b ) 242 km , c ) 224 km , d ) 112 km , e ) 110 km
Rationale: "solution 1 average speed = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr total distance = 22.4 ã — 10 = 224 km answer is c"
Answer: c
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 20 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 40 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 20 * x = 7 : 10 x = 40 answer : b"
Answer: b
Question (physics): pipe a fills a tank in 56 minutes . pipe b can fill the same tank 7 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a ' s rate is 1 / 56 and b ' s rate is 1 / 8 . the combined rate is 1 / 56 + 1 / 8 = 1 / 7 the pipes will fill the tank in 7 minutes . the answer is d .
Answer: d
Question (physics): a contractor undertakes to built a walls in 50 days . he employs 20 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 30 , e ) none of these
Rationale: 20 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 20 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 20 × 25 × 0.6 / 25 × 0.4 = 30 men answerd
Answer: d
Question (general): find the value for m ? 19 ( m + n ) + 17 = 19 ( - m + n ) - 135
Options: a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) - 4
Rationale: 19 m + 19 n + 17 = - 19 m + 19 n - 135 38 m = - 152 = > m = - 4 e
Answer: e
Question (other): there are 720 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 450 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 720 . hence 3 x + 5 x = 720 solve for x 8 x = 720 x = 90 number of boys 3 x = 3 × 90 = 270 number of girls 5 x = 5 × 90 = 450 c"
Answer: c
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2500 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 200
Rationale: "given that the area of the square = 2500 sq . units = > side of square = √ 2500 = 50 units the radius of the circle = side of the square = 50 units length of the rectangle = 2 / 5 * 50 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : option e"
Answer: e
Question (physics): convert 1.6 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.6 hectares in ares 1 hectare = 100 ares therefore , 1.6 hectares = 1.6 × 100 ares = 160 ares . answer - b"
Answer: b
Question (general): the average of 7 numbers is 15 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 90 , d ) d ) 85 , e ) e ) 75
Rationale: explanation : average of new numbers = 15 * 5 = 75 answer : option e
Answer: e
Question (physics): calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 15 km / hr downstream and 7 km / hr upstream .
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 11 kmph
Rationale: "speed in still water = ( 15 + 7 ) 1 / 2 kmph = 11 kmph . answer : e"
Answer: e
Question (physics): a and b go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 40 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 400 / ( 36 * 5 / 18 ) , 400 / ( 36 * 5 / 18 ) } = lcm ( 40 , 40 ) = 40 sec . answer : a"
Answer: a
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 108 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 9 + 14 + 10 + 29 + 8 ) = 30 % basic astrophysics . 30 % of 360 ° is 108 ° . answer : a ."
Answer: a
Question (general): a mixture of 40 liters of milk and water contains 10 % water . how much water should be added to this so that water may be 20 % in the new mixture ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 4 ltr - water 36 ltr - milk let x water be added then the new mixture must have 20 % water then 4 + x = 20 / 100 ( 40 + x ) x = 5 answer : c
Answer: c
Question (general): in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 50 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 20 , d ) 15 , e ) 25
Rationale: "you should notice that 50 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 4 = 20 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c"
Answer: c
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 5 x km .
Options: a ) 16 , b ) 18 , c ) 24 , d ) 40 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 5 x / ( x / 8 ) = 40 kmph answer : d"
Answer: d
Question (physics): riya and priya set on a journey . riya moves eastward at a speed of 21 kmph and priya moves westward at a speed of 22 kmph . how far will be priya from riya after 60 minutes
Options: a ) 43 kms , b ) 45 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 21 kmph * 1 hr = 21 km total westward distance = 22 kmph * 1 hr = 22 km total distn betn them = 21 + 22 = 43 km ans 43 km answer : a"
Answer: a
Question (general): a family had dinner in a restaurant and paid $ 30 for food . they also had to pay 9.5 % sale tax and 10 % for the tip . how much did they pay for the dinner ?
Options: a ) $ 35.83 , b ) $ 35.84 , c ) $ 35.85 , d ) $ 35.86 , e ) $ 35.87
Rationale: solution they paid for food , sales tax and tip , hence total paid = $ 30 + 9.5 % * 30 + 10 % * 30 = $ 35.85 answer c
Answer: c
Question (general): a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 88 years , d ) 66 years , e ) 24 years
Rationale: "let ' s son age is x , then father age is x + 26 . = > 2 ( x + 2 ) = ( x + 26 + 2 ) = > 2 x + 4 = x + 28 = > x = 24 years answer : e"
Answer: e
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 47.14 , b ) 45.15 , c ) 43.23 , d ) 41.44 , e ) 41.51
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 40 + 20 ) = 120 cm parameter of the square = 120 cm i . e . 4 a = 120 a = 30 diameter of the semicircle = 30 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 30 ) = 1 / 2 ( 22 / 7 ) ( 30 ) = 660 / 14 = 47.14 cm to two decimal places answer : a"
Answer: a
Question (physics): two trains 200 m and 300 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 ?
Options: a ) 18 , b ) 10.9 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 200 + 300 = 500 m . required time = 500 * 9 / 250 = 18 secs answer : a"
Answer: a
Question (general): the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 35 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 23.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) solve the equation . 262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) 9 , 199.75 + 3 , 104.35 x = 48980.75 + 1 , 399.45 x 9 , 199.75 + 1 , 704.9 x = 48980.75 1 , 704.9 x = 39,781 x ≈ 23.3 answer is b ."
Answer: b
Question (general): when n is divided by 15 , the remainder is 8 . what is the remainder when 5 n is divided by 6 ?
Options: a ) 2 , b ) 6 , c ) 3 , d ) 4 , e ) 1
Rationale: "let n = 8 ( leaves a remainder of 8 when divided by 48 ) 5 n = 5 ( 8 ) = 40 , which leaves a remainder of 4 when divided by 6 . answer d"
Answer: d
Question (general): a number x is 18 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 94.4 % , e ) 1 %
Rationale: "say y = 1 and x = 18 . then y = 1 is less than x = 18 by ( 18 - 1 ) / 18 * 100 = 17 / 18 * 100 = 94.4 % . answer : d ."
Answer: d
Question (general): a dozen eggs and 5 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 3 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 5 %
Rationale: say currently both a dozen eggs and 5 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 5 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 103 and the price of 5 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 5 pounds of oranges we ' ll need $ 209 . increase = 9 % . answer : b .
Answer: b
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Question (geometry): the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.60 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6072
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.60 ) = rs . 6072 . answer : e ) 6072"
Answer: e
Question (general): 3 years ago the average age of a class of 6 members was 19 years . a boy have been added , the average age of the class is the same today . what is the age of the boy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 6 * 22 = 132 7 * 19 = 133 ` 1 a
Answer: a
Question (gain): find the number of shares that can be bought for rs . 8200 if the market value is rs . 28 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 285.7 , e ) 111
Rationale: "explanation : cost of each share = ( 28 + 2.5 % of 28 ) = rs . 28.7 therefore , number of shares = 8200 / 28.7 = 285.7 answer : d"
Answer: d
Question (general): if ( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 29 ) x ^ 2 + 6 x + 9 = 6 x + 58 x ^ 2 - 49 = 0 ( x - 7 ) ( x + 7 ) = 0 x = 7 or x = - 7 the answer is d ."
Answer: d
Question (physics): a train 710 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 500 , d ) 297 , e ) 590
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 710 + x ) / 60 = 65 / 3 x = 590 m . answer : e"
Answer: e
Question (other): in a certain corporation , there are 300 male employees and 100 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 400 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 20 , b ) 1 / 10 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "in this corporation , there are 400 total employees . there are 100 women . of the 300 men , 20 % have advanced degrees — - 10 % of 300 must be 30 , so 20 % of 300 must be 60 . add the women and the men with advanced degrees : 100 + 60 = 160 . this is the or region , full set of individuals that satisfy the condition “ has an advanced degree or is female . ” of the 400 employees , what ’ s the probability of picking one of the 160 in this particular group ? p = 160 / 400 = 16 / 40 = 4 / 10 = 2 / 5 answer = d"
Answer: d
Question (general): the price of 24 apples is equal to that of 28 oranges . the price of 45 apples and 60 oranges together is rs . 1350 . the total price of 30 apples and 40 oranges is
Options: a ) 850 , b ) 900 , c ) 750 , d ) 950 , e ) 800
Rationale: let the price of one apple = a and price of one orange = b price of 24 apples is equal to that of 28 oranges 24 a = 28 b = > 6 a = 7 b ⇒ b = 6 a / 7 - - - - - ( equation 1 ) price of 45 apples and 60 oranges together is rs . 1350 = > 45 a + 60 b = 1350 = > 3 a + 4 b = 90 ⇒ 3 a + 4 ( 6 a ) / 7 = 90 ( ∵ substituted the value of b from equation 1 ) ⇒ a + 4 ( 2 a ) / 7 = 30 = > 7 a + 8 a = 30 × 7 = 210 = > 15 a = 210 ⇒ a = 21015 = 423 = 14 b = 6 a 7 = ( 6 × 14 ) / 7 = 6 × 2 = 12 total price of 30 apples and 40 oranges = 30 a + 45 b = ( 30 × 14 ) + ( 40 × 12 ) = 420 + 480 = 900 answer is b .
Answer: b
Question (probability): rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads .
Options: a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32
Rationale: exactly 4 heads out of 5 would be : hhhht , hhthh , or many other combinations . therefore , no . of possible combinations are 5 ! / 4 ! * 1 ! = 5 probability = 5 / 2 ^ 5 = 5 / 32 answer : a
Answer: a
Question (general): if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability r that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) r = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability r = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Question (physics): 25 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 30
Rationale: "binders books days 25 1400 21 x 1600 20 x / 25 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 30 answer : e"
Answer: e
Question (gain): the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 3 years is
Options: a ) rs . 9621 , b ) rs . 6921 , c ) rs . 9261 , d ) rs . 6261 , e ) rs . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 3 = 8000 ( 21 / 20 * 21 / 20 * 21 / 20 ) = rs 9261 answer : c"
Answer: c
Question (physics): the ratio of the capacity to do work of a and b is 3 : 2 . if they together can complete a work in 18 days , then how long does a take to complete the work alone ?
Options: a ) 45 , b ) 30 , c ) 24 , d ) 40 , e ) none of these
Rationale: llet a and b take 3 x and 2 x days to complete the work 1 / 3 x + 1 / 2 x = 1 / 18 ⇒ x = 15 so a will take 45 days . answer : a
Answer: a
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 14 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 77 , c ) 48 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 14 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 14 = 4 / 9 ( t - 14 ) 10 t = 1386 - 616 = > t = 77 . answer : b"
Answer: b
Question (general): the population of a town increased from 1 , 75000 to 2 , 97500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %
Rationale: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e
Answer: e
Question (gain): the workforce of company x is 40 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 480 , b ) 500 , c ) 520 , d ) 460 , e ) 440
Rationale: "let x be the total worker then 0.4 x = female worker and 0.6 x is male worker then 20 male worker added 04 x / ( 0.6 x + 20 ) = 50 / 100 or 40 x = 50 * ( 0.6 x + 100 ) = 30 x + 5000 or 10 x = 5000 , x = 500 total worker = 500 + 20 = 520 c"
Answer: c
Question (general): the ratio of kamla and nisha is 6 : 5 and the sum of their ages is 44 . what will be the ratio of their ages after 8 years .
Options: a ) 5 : 6 , b ) 7 : 8 , c ) 8 : 7 , d ) 12 : 11 , e ) 14 : 13
Rationale: answer : let age of kamla is 6 x and age of nisha is 5 x . then , 6 x + 5 x = 4411 x = 44 , x = 4 after 8 year the ratio of their ages = 6 x + 8 / 5 x + 8 = 8 : 7 answer c
Answer: c
Question (other): two identical cubes if one of them is painted pink on its 4 side and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting cube is 1 / 3 when we roll both the cube .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 0 faces should be painted pink i . e all faces blue answer : a
Answer: a
Question (physics): due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 11.79 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 25 = 9 * 12 / 5 = 21.6 time difference = 11.79 ans : a"
Answer: a
Question (gain): the cost price of a radio is rs . 2400 and it was sold for rs . 1980 , find the loss % ?
Options: a ) 17 % , b ) 12 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "2400 - - - - 420 100 - - - - ? = > 17 % answer : a"
Answer: a
Question (general): a couple spent $ 132 in total while dining out and paid this amount using a credit card . the $ 132 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 100 , b ) $ 104 , c ) $ 108 , d ) $ 112 , e ) $ 116
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 132 x = 100 the correct answer is a ."
Answer: a
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 28 , b ) 19 , c ) 22 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 14000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 56000 = x = 28 . answer : a"
Answer: a
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 52 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 6 ) ( b + 6 ) = m + 52 - - - - - - - - - > ( l + 6 ) ( b + 6 ) - 52 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 6 ) ( b + 6 ) - 52 lb + 2 l + 2 b + 4 = lb + 6 l + 6 b + 36 - 52 simplify 4 l + 4 b = 20 - - - - - - > 2 ( l + b ) = 10 ( check eq ( 1 ) ) answer is a"
Answer: a
Question (gain): uncle bruce is baking chocolate chip cookies . he has 50 ounces of dough ( with no chocolate ) and 40 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 30 % chocolate ?
Options: a ) 22.86 , b ) 23.86 , c ) 25 , d ) 26 , e ) 27
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 70 % * total = 40 = > ( 7 / 10 ) total = 40 = > total = 400 / 7 = > total = 57.14 oz , from there , you must find 30 % of the total 57.14 oz of the mixture . 30 % * total = > ( 3 / 10 ) ( 57.14 ) = 17.14 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 40 - 17.14 = 22.86 oz chocolate left over . answer : a"
Answer: a