Cheukting/mathqa huggingface dataset:
Question (geometry): the sides of a rectangle are in the ratio 4 : 3 and its area is 972 sq . m find the perimeter of rectangle
Options: a ) 120 m
b ) 122 m
c ) 124 m
d ) 126 m
e ) 128 m
Rationale: explanation : let 4 x and 3 x be sides of the rectangle we know that area of rectangle = l × b 4 x × 3 x = 972 12 x 2 = 972 x 2 = 81 x = 9 therefore length = 4 x = 4 × 9 = 36 m breadth = 3 x = 3 × 9 = 27 m therefore perimeter = 2 ( l + b ) = 2 ( 36 + 27 ) = 126 m answer : option d
Answer: d
Question (general): a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 14 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,240 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 14 : x + x - 2 = 14 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : a ."
Answer: a
Question (gain): a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 35 % . staff are allowed a further 30 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.555 d , b ) 0.765 d , c ) 0.455 d , d ) 0.785 d , e ) 0.805 d
Rationale: "effective discount = a + b + ab / 100 = - 35 - 30 + ( - 35 ) ( - 30 ) / 100 = - 54.5 sale price = d * ( 1 - 54.5 / 100 ) sale price = . 455 * d answer ( c )"
Answer: c
Question (general): the number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 84 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 6 and 28 = 84 answer c"
Answer: c
Question (general): if k ^ 3 is divisible by 336 , what is the least possible value of integer k ?
Options: a ) 56 , b ) 70 , c ) 84 , d ) 96 , e ) 120
Rationale: "k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c ."
Answer: c
Question (general): there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 40
Rationale: given the constraints of this question , we have to consider 6 possible outcomes . . . 1 green ball : 6 options grrrrr rgrrrr rrgrrr rrrgrr rrrrgr rrrrrg 2 green balls : 5 options ggrrrr rggrrr rrggrr rrrggr rrrrgg 3 green balls : 4 options gggrrr rgggrr rrgggr rrrggg 4 green balls : 3 options ggggrr rggggr rrgggg 5 green balls : 2 options gggggr rggggg 6 green balls : 1 option gggggg 6 + 5 + 4 + 3 + 2 + 1 = 21 options . b
Answer: b
Question (geometry): a man walked diagonally across a square lot . approximately , what was the percent saved by not walking along the edges ?
Options: a ) 20 %
b ) 30 %
c ) 40 %
d ) 50 %
e ) 55 %
Rationale: let the side of the square ( abcd ) be x metres . then , ab + bc = 2 x metres . ac = 2 x = ( 1.41 x ) m . saving on 2 x metres = ( 0.59 x ) m . saving % = ( 0.59 x ) / 2 x x 100 % = 30 % ( approx . ) b )
Answer: b
Question (gain): rs . 500 amounts to rs . 670 in 5 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 150 , b ) 550 , c ) 760 , d ) 450 , e ) 260
Rationale: ( 500 * 5 * 2 ) / 100 = 50 500 + 50 = 550 answer : b
Answer: b
Question (physics): the lcm and hcf of two numbers are 10000 and 1000 respectively . find the larger of the two numbers if their sum is 11000 .
Options: a ) 10000 , b ) 562 , c ) 352 , d ) 576 , e ) 594
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 10000 * 1000 = 10000000 so the answer which we are looking for has to be a factor of 10000000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 10000000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Question (physics): a cistern can be filled by a tap in 3 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 ?
Options: a ) 4.3 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 10 ) = 7 / 30 the cistern will be filled in 30 / 7 hrs i . e . , 4.3 hrs . answer : a"
Answer: a
Question (physics): a software engineer starts from home at 3 pm for every walk on a route which has level road for some distance and a then a hillock . he walks speed of 4 kmph on level ground and then at a speed of 3 kmph on the uphill and then down the hill at a speed of 6 kmph to the level ground and then at a speed of 4 kmph to the home if he reaches home at 9 pm . what is the distance one way of his route ?
Options: a ) 12 km , b ) 15 km , c ) 18 km , d ) 24 km , e ) data inadequate
Rationale: time = distance / speed so , let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so , ( x / 4 + y / 3 ) + ( y / 6 + x / 4 ) = 6 x + y = 12 km . answer : a
Answer: a
Question (general): a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 60 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 60 - c = 100 c = 20 option d ."
Answer: d
Question (general): there are 30 balls which are red , blue or green . if 11 balls are green and the sum of red balls and green balls is less than 25 , at most how many red balls are there ?
Options: a ) 14 , b ) 13 , c ) 16 , d ) 17 , e ) 8
Rationale: "r + g + b = 30 g = 11 r + g < 25 = > r + 11 < 25 = > r < 14 = > at most 13 red balls answer : b"
Answer: b
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 3000 resolutions ?
Options: a ) 2187 m , b ) 3704 m , c ) 4179 m , d ) 4224 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 3000 resolutions . = 3000 * 2 * 22 / 7 * 22.4 = 422400 cm = 4224 m answer : d"
Answer: d
Question (general): half a number plus 6 is 11 . what is the number ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 6 = 11 ( 1 / 2 ) x = 11 - 6 ( 1 / 2 ) x = 5 x = 10 correct answer is c
Answer: c
Question (general): n ^ ( n / 2 ) = 6 is true when n = 6 in the same way what is the value of n if n ^ ( n / 2 ) = 10 ?
Options: a ) 8 , b ) 12 , c ) 10 , d ) 16 , e ) 18
Rationale: n ^ ( n / 2 ) = 10 apply log n / 2 logn = log 10 nlogn = 2 log 10 = log 10 ^ 2 = log 100 logn = log 100 now apply antilog n = 100 / n now n = 10 . answer : c
Answer: c
Question (general): the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ?
Options: a ) 48 , b ) 50 , c ) 56 , d ) 62 , e ) 64
Rationale: 1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 550 = 56 c
Answer: c
Question (gain): after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6840 . find the actual price of the good .
Options: a ) rs . 6000 , b ) rs . 9000 , c ) rs . 10800 , d ) rs . 10000 , e ) rs . 9980
Rationale: "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6840 1 = 6840 / 68.4 100 = ( 6840 * 100 ) / 68.4 = rs . 10,000 . answer : option d"
Answer: d
Question (general): a rope of which a calf is tied is increased from 9 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 1212 , c ) 1408 , d ) 2707 , e ) 2591
Rationale: "π ( 232 – 92 ) = 1408 answer : c"
Answer: c
Question (general): what is the value of 3 x ^ 2 − 1.6 x + 0.3 for x = 0.8 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 0.94 , e ) 2.46
Rationale: "3 x ^ 2 - 1.6 x + 0.3 for x = 0.6 = 3 ( 0.8 * 0.8 ) - 2 * 0.8 * ( 0.8 ) + 0.3 = 0.8 * 0.8 + 0.3 = 0.94 correct option : d"
Answer: d
Question (gain): in a school of 900 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 144 , b ) 153 , c ) 162 , d ) 171 , e ) 180
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 900 * 18 / 100 = 162 the answer is c ."
Answer: c
Question (gain): if c is 14 % of a and 40 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "answer = d 14 a / 100 = 40 b / 100 b = 14 a / 40 = 35 a / 100 = 35 %"
Answer: d
Question (general): a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 7 / 15
Rationale: i think e - 7 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 2 x so old = x , new = x now 1 / 3 of x are occupied and 1 / 5 of x are occupied which simplifies to ( 1 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 1 / 5 of x occupied in the new ward . add them up to get 8 / 15 of x there are x beds in new tower so ratio is : ( 8 / 15 ) x / x = 8 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new towerb = 7 / 15 . e
Answer: e
Question (gain): cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 222 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 4.75
Rationale: "required run rate = 222 - ( 3.2 x 10 ) = 190 = 4.75 40 40 e"
Answer: e
Question (geometry): if the sum of a number and its square is 342 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 87 , e ) 18
Rationale: "explanation : let the integer be x . then , x + x 2 = 342 x 2 + x - 342 = 0 ( x + 19 ) ( x – 18 ) = 0 x = 18 answer : e"
Answer: e
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.6 , d ) 12 , e ) 12.5
Rationale: "mean = 16.2 two standard deviations is 2.3 + 2.3 = 4.6 there could be two calues for this . mean + two standard deviations = 20.8 mean - two standard deviations = 11.6 answer choice has 11.6 and so c is the answer ."
Answer: c
Question (general): a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 99 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "7 c + 6 p = 99 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 3 + 6 * 13 = 21 + 78 = 99 hence c is the answer"
Answer: c
Question (gain): p and q started a business investing rs . 85,000 and rs . 25,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 5
Rationale: "p : q = 85000 : 25000 = 17 : 5 . answer : e"
Answer: e
Question (gain): a shopkeeper has 280 kg of apples . he sells 40 % of these at 10 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 22 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: if the total quantity was 100 then 40 x 10 % + 60 x 30 % = 22 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer
Answer: a
Question (general): the simple interest on a sum of money will be rs . 600 after 10 years . if the principal is trebled after 5 years , what will be the total interest at the end of the tenth year ?
Options: a ) rs . 600 , b ) rs . 900 , c ) 1200 rupees , d ) rs . 1500 , e ) none
Rationale: solution 22.22 let the sum be rs . x . now , s . i . = rs . 600 , t = 10 years . rate = % = ( 100 x 600 / x x 10 ) % = ( 6000 / x ) % s . i . for first 5 years = rs . ( x x 5 x 6000 / x x 100 ) = rs . 300 . s . i . for first 5 years = rs . ( 3 x x 5 x 6000 / x x 100 ) = rs . 900 . ∴ total interest = rs . 1200 . answer c
Answer: c
Question (general): we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value w of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "w - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Question (general): out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: description : = > 8 x = 2 ( x + 2 ) + 5 + 3 ( x + 4 ) = > 3 x = 21 , x = 7 = > x + 4 = 11 x = 11 - 4 = 7 answer c
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 30 sec . what is the length of the train ?
Options: a ) 535 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 500 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 30 = 500 m answer : e"
Answer: e
Question (physics): a , b , c , d and e are 5 consecutive points on a straight line . if bc = 3 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 23
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 8 = 21 the answer is d ."
Answer: d
Question (general): what is the smallest number which when increased by 3 is divisible by 9 , 35 , 25 and 21 ?
Options: a ) 1572 , b ) 1782 , c ) 1992 , d ) 2122 , e ) 2342
Rationale: "when increased by 3 , the number must include at least 3 ^ 2 * 5 ^ 2 * 7 = 1575 the answer is a ."
Answer: a
Question (general): if | r + s | = | r - s | , then r * s must be equal to :
Options: a ) - 2 , b ) 2 , c ) 0 , d ) - 3 , e ) 3
Rationale: solution 1 : distance perspective | r - s | = | r + s | = = > the distance of r and s is equal to the distance of r and - s . < = = = = = = = ( - s ) = = = = = = = 0 = = = = = = = ( s ) = = = = = = > only 0 is the value that has a distance equal to s and - s . solution 2 : | r - s | = | r + s | ( square both ) r ^ 2 - 2 rs + s ^ 2 = r ^ 2 + 2 rs + s ^ 2 4 rs = 0 rs = 0 answer : c
Answer: c
Question (general): 8 cups of milk are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of milk should be poured into the 8 - cup bottle ?
Options: a ) 16 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 4 / 3 , e ) 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : a
Answer: a
Question (general): there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 6 were remaining . how many people were in total ?
Options: a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 91
Rationale: sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 6 x × 2 / 3 × 3 / 5 × 1 / 3 = 6 x = 6 × 5 × 3 / 2 = 45 answer : a
Answer: a
Question (other): in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 67 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) 1 : 1
Rationale: "required ratio = 500 : 500 = 3 : 1 answer e"
Answer: e
Question (gain): a 8 % stock yielding 10 % is quoted at :
Options: a ) 80 , b ) 110 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 8 , money invested = rs . ( 100 / 10 x 8 ) = rs . 80 . â ˆ ´ market value of rs . 100 stock = rs . 80 answer a"
Answer: a
Question (gain): if it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 50 % = 300 / 0.5 = 600 option e"
Answer: e
Question (gain): an error 8 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 26.64 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 8 + 8 + ( 8 × 8 ) / 100 ) % = 16.64 % answer : b"
Answer: b
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 15 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 7 + 16 x 7 ) ] = ( 225 - 210 ) = 15 years . answer c"
Answer: c
Question (general): car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ?
Options: a ) 10 . , b ) 25 . , c ) 30 . , d ) 38 , e ) 50 .
Rationale: total distance - 1000 km time ratio a : b - 3 : 1 speed ratio a : b - 3 : 1 so distance ( speed * time ) ratio will be - 3 * 3 : 1 * 1 - 9 : 1 so total distance traveled by b - 100 km time taken by b ( 18 : 00 - 16 : 00 = 2 ) - 2 hours speed of b - 50 kmph answer : e
Answer: e
Question (probability): there are 6 books on a shelf , of which 2 are paperbacks and 4 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
Options: a ) a ) 40 , b ) b ) 14 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Rationale: "approach 1 at - least 1 paper back = total - no paper back 6 c 4 - 4 c 4 = 14 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 4 c 3 + 2 c 2 * 4 c 2 = 14 answer is b"
Answer: b
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 931 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 931 96 + 225 + 490 + 6 x = 931 6 x = 120 = > x = 20 . answer : e"
Answer: e
Question (general): the average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 93 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 68 + 10 x 2.5 68 + 25 = 93 kg ans : ' b '"
Answer: b
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 176 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 154
Rationale: "set up equation : x = total number of workers 176 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 176 = 16 / 30 x x = 330 330 - 176 = 154 answer e"
Answer: e
Question (general): elena ’ s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 6 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 24
Rationale: "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 6 we get : 18 b + 24 f = 6 x therefore , we got 18 ounces of butter and 6 x amount of quantity when we use 24 ounces of floor . ans : e"
Answer: e
Question (geometry): in how many w ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: w = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Question (gain): suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 262.8 , d ) rs . 241.7 , e ) none
Rationale: solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 128 : 125 suganya ' s share = rs . ( 30570 ã — 2 / 253 ) = rs . 241.7 . answer d
Answer: d
Question (physics): a space shuttle orbits the earth at about 9 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 4,800 , d ) 28,800 , e ) 32,400
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 9 * 3600 = 32,400 answer : e"
Answer: e
Question (general): 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 17.5 % , b ) 17.8 % , c ) 18.1 % , d ) 18.4 % , e ) 18.7 %
Rationale: "the total amount of alcohol is 0.22 ( 7 ) + 0.11 ( 3 ) = 1.87 liters . the percentage is 1.87 / 10 = 18.7 / 100 which is 18.7 % the answer is e ."
Answer: e