Cheukting/mathqa huggingface dataset:
Question (gain): by selling an article at rs . 900 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 540 , e ) s . 550
Rationale: "sp = 900 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 900 * [ 100 / 125 ] = 720 loss = 25 % = 25 % of 720 = rs . 180 sp = cp - loss = 720 - 180 = rs . 540 answer : d"
Answer: d
Question (physics): a train 220 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 9
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 220 * 3 / 55 ] sec = 12 sec answer : option d"
Answer: d
Question (general): assume that f ( 1 ) = 0 and f ( m + n ) = f ( m ) + f ( n ) + 4 ( 9 mn - 1 ) . for all natural numbers ( integers > 0 ) m and n . what is the value of f ( 17 ) ?
Options: a ) 4832 , b ) 4855 , c ) 4825 , d ) 4895 , e ) 4862
Rationale: explanation : f ( 1 ) = 0 f ( 2 ) = f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 4 ( 9 × 1 × 1 – 1 ) = 0 + 0 + 4 × 8 = 32 f ( 4 ) = f ( 2 + 2 ) = f ( 2 ) + f ( 2 ) + 4 ( 9 × 2 × 2 – 1 ) = 32 + 32 + 4 × 35 = 204 f ( 8 ) = f ( 4 + 4 ) = f ( 4 ) + f ( 4 ) + 4 ( 9 × 4 × 4 – 1 ) = 204 + 204 + 4 × 143 = 980 f ( 16 ) = f ( 8 + 8 ) = f ( 8 ) + f ( 8 ) + 4 ( 9 × 8 × 8 – 1 ) = 980 + 980 + 4 × 575 = 4260 f ( 17 ) = f ( 1 + 16 ) = f ( 16 ) + f ( 1 ) + 4 ( 9 × 16 × 1 – 1 ) = 4260 + 0 + 4 × 143 = 4832 answer : a
Answer: a
Question (physics): allay ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning allay makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?
Options: a ) 15 , b ) 24 , c ) 25 , d ) 26 , e ) 13
Rationale: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now allay can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional paymentsi . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c
Answer: c
Question (general): the smallest value of n , for which n + 3 is not a prime number , is
Options: a ) 1 , b ) 2 , c ) 6 , d ) 8 , e ) 3
Rationale: "( 1 + 3 ) = 3 . ( 2 + 3 ) = 5 . ( 3 + 3 ) = 6 . ( 4 + 3 ) = 7 . which is not prime , n = 3 . answer : e"
Answer: e
Question (physics): a man swims downstream 72 km and upstream 45 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 2.28 , b ) 2.24 , c ) 2.27 , d ) 2.25 , e ) 2.23
Rationale: "72 - - - 6 ds = 12 ? - - - - 1 45 - - - - 6 us = 7.5 ? - - - - 1 s = ? s = ( 12 - 7.5 ) / 2 = 2.25 answer : d"
Answer: d
Question (general): if ( 2 ^ 16 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 23
Rationale: given 2 ^ 16 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 16 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans d on comparing the power of 2 = > m = 16
Answer: d
Question (general): 90 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 91 , e ) 81
Rationale: "explanation : 90 + 5 * 12 / ( 180 / 3 ) = 90 + 5 * 12 / ( 60 ) = 90 + ( 5 * 12 ) / 60 = 90 + 1 = 91 . answer : d"
Answer: d
Question (gain): if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
Answer: c
Question (physics): a can finish a work in 20 days , b in 15 days and c in 12 days . b and c start the work but are forced to leave after 2 days . the remaining work was done by a in :
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "( b + c ) ’ s one day ’ s work = 1 / 15 + 1 / 12 = 3 / 20 work done by b and c in 2 days = 3 * 2 / 20 = 3 / 10 remaining work = 1 - 3 / 10 = 7 / 10 1 / 20 work is done by a in 1 day . so , 7 / 10 work is done by a in 20 * 7 / 10 = 14 days answer : e"
Answer: e
Question (general): when positive integer n is divided by positive integer j , the remainder is 8 . if n / j = 150.25 , what is value of j ?
Options: a ) 16 , b ) 26 , c ) 32 , d ) 132 , e ) 20
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 150.25 here 150 is the quotient . given that remainder = 8 so , 150.25 = 150 + 8 / j so , j = 32 answer : c"
Answer: c
Question (general): a welder received an order to make a 1 million liter cube - shaped tank . if he has only 2 x 3 meter sheets of metal that can be cut , how many metal sheets will be required for this order ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 100
Rationale: the question say : a welder received an order to make a 1 million liter cube - shaped tank . ( 1 cubic meter = 1,000 liters ) in other words , the tank is going to have a volume of 1000 cubic meters . that would equal 1 million liters . a cube with a volume of 1000 cubic meters must be ( 10 meters ) x ( 10 meters ) x ( 10 meters ) . the question does n ' t specify whether this tank should have a closed top or an open top . ( the real gmat is good about specifying things like that . ) here , we are going to assume a closed top , only because if the top is open , we do n ' t use enough metal - - - we get an answer smaller than any of the answer choices . a closed - top cube , a full cube , has 6 sides , each of which is ( 10 meters ) x ( 10 meters ) . that ' s a total surface area of 600 sq m . the question tells us : he has only 2 x 3 meter sheets of metal that can be cut . each sheet has an area of 6 sq m . how many of these need to fill up 600 sq m ? 600 / 6 = 100 . he needs 100 sheets . answer = e
Answer: e
Question (physics): if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is .
Options: a ) 18 , b ) 21 , c ) 24 , d ) 28 , e ) 30
Rationale: explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x = > 140 * 30 * x = 100 * 18 * 42 = > or x = 18 answer : a
Answer: a
Question (general): when x is multiplied by 3 , the result is 10 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) 9 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 10 = 26 - x or , 4 x = 36 or , x = 9 . b answer ."
Answer: b
Question (physics): if the l . c . m of two numbers is 560 and their product is 42000 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 75 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 42000 / 560 = 75 . answer : c"
Answer: c
Question (general): 1,000 ^ 2 + 1,001 ^ 2 + 1,002 ^ 2 + 1,003 ^ 2 + 1,004 ^ 2 =
Options: a ) 6 , 030,053 , b ) 6 , 030,054 , c ) 6 , 030,055 , d ) 6 , 020,030 , e ) 6 , 030,057
Rationale: interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 . . . 1004 ^ 2 - > 16 total - > * 30 answer d .
Answer: d
Question (general): in a room filled with 6 people , all 6 people have exactly 1 sibling in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 5 / 6 , d ) 5 / 12 , e ) 7 / 12
Rationale: the 6 people consist of three sets of 2 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the second group of siblings is 2 c 2 = 1 . the number of ways to choose 2 from the third group of siblings is 2 c 2 = 1 . the number of ways to choose 2 people who are siblings is 1 + 1 + 1 = 3 . the number of ways to choose 2 people who are not siblings is 15 - 3 = 12 . p ( the two people are not siblings ) = 12 / 15 = 4 / 5 the answer is b .
Answer: b
Question (general): find the least number of complete years in which a sum of money put out at 50 % compound interest will be more than double of itself ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 2 years answer : a
Answer: a
Question (general): excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 18 min , b ) 17 min , c ) 19 min , d ) 20 min , e ) 21 min
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 60 - 40 ) km i . e 20 km at 60 km / hr . stoppage time = 20 / 60 hrs = 20 min . answer : d"
Answer: d
Question (gain): in an office , 50 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 8 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: ( 10 / 100 ) workers = 16 = > number of workers = 160 ( 50 / 100 ) * workers = x + 16 = > x = 8 answer a
Answer: a
Question (general): a certain roller coaster has 6 cars , and a passenger is equally likely to ride in any 1 of the 6 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 6 times , what is the probability that the passenger will ride in each of the 6 cars ?
Options: a ) 3 / 1944 , b ) 1 / 96 , c ) 2 / 96 , d ) 1 / 1944 , e ) 1
Rationale: if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 6 * 6 * 6 * 6 * 6 * 6 = 46656 now the number of ways if he is to choose a different car each time is = 6 * 5 * 4 * 3 * 2 * 1 = 720 so the probability is = 720 / 46656 = 3 / 1944 answer : a
Answer: a
Question (physics): bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many d hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in d = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Question (general): the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?
Options: a ) 96 , b ) 200 , c ) 128 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 8 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 640 = 200 answer : b"
Answer: b
Question (geometry): a 9 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 2 / 9 , d ) 1 / 3 , e ) 2 / 5
Rationale: "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 1 meters from either end . the probability of this is 2 / 9 . the answer is c ."
Answer: c
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 17 , the how old is b ? a . 7 b . 8 c . 9 d . 10 explanation :
Options: a ) 6 , b ) 7 , c ) 9 , d ) 10 , e ) 11
Rationale: let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 17 5 x = 15 x = 3 . hence , b ' s age = 2 x = 6 years . answer : option a
Answer: a
Question (physics): two pipes can fill a tank in 12 minutes and 20 minutes respectively . both pipes are opened together and after some time the first pipe is closed and the tank is full in totally 10 minutes . for how many minutes was first pipe open ?
Options: a ) 8 minutes , b ) 6 minutes , c ) 7 minutes , d ) 10 minutes , e ) 9 minutes
Rationale: second pipe is opened for 10 minutes . so , part of tank filled by the second pipe = 10 / 20 = 1 / 2 . so , 1 - 1 / 2 = 1 / 2 tank is filled by first pipe . first pipe can fill 1 / 2 of tank in 1 * 12 / 2 = 6 minutes . so , the first pipe is opened for 6 minutes . answer : b
Answer: b
Question (general): what is the area inscribed by the lines y = 6 , x = 3 , y = 2 x - 4 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
Rationale: "first , let ' s graph the lines y = 6 and x = 3 at this point , we need to find the points where the line y = 2 x - 4 intersects the other two lines . for the vertical line , we know that x = 3 , so we ' ll plug x = 3 into the equation y = 2 x - 4 to get y = 2 ( 3 ) - 4 = 2 perfect , when x = 3 , y = 2 , so one point of intersection is ( 3,2 ) for the horizontal line , we know that y = 6 , so we ' ll plug y = 6 into the equation y = 2 x - 4 to get 6 = 2 x - 4 . solve to get : x = 5 so , when y = 6 , x = 5 , so one point of intersection is ( 5,6 ) now add these points to our graph and sketch the line y = 2 x - 4 at this point , we can see that we have the following triangle . the base has length 2 and the height is 4 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 4 ) = 4 answer : c"
Answer: c
Question (geometry): the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and three - fourths of the females in the class ?
Options: a ) 186 , b ) 192 , c ) 198 , d ) 204 , e ) 210
Rationale: "1 / 4 * 2 / 5 + 3 / 4 * 3 / 5 = 2 / 20 + 9 / 20 = 11 / 20 the number of degrees is 11 / 20 * 360 = 198 degrees the answer is c ."
Answer: c
Question (general): the average of 50 numbers id 20 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.75 , b ) 33.25 , c ) 22.25 , d ) 11.75 , e ) 18.75
Rationale: "explanation : total of 50 numbers = ( 50 × 20 ) = 1000 total of 48 numbers = ( 1000 - ( 45 + 55 ) ] = 900 required average = 900 / 48 = 18.75 answer : e"
Answer: e
Question (geometry): the area of a triangle is with base 10 m and height 10 m ?
Options: a ) 11 , b ) 10 , c ) 50 , d ) 122 , e ) 12
Rationale: "1 / 2 * 10 * 10 = 50 m 2 answer : c"
Answer: c
Question (physics): in what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 40 / 36 * 18 / 5 = 4 sec answer : b"
Answer: b
Question (general): find remainder if ( 67 ^ 67 + 67 ) is divided by 68
Options: a ) 60 , b ) 62 , c ) 66 , d ) 72 , e ) 78
Rationale: = > ( 6767 + 1 ) is divisible by ( 67 + 1 ) = > ( 6767 + 1 ) is divisible by 68 = > ( 6767 + 1 ) ÷ 68 gives a remainder of 0 = > [ ( 6767 + 1 ) + 66 ] ÷ 68 gives a remainder of 66 = > ( 6767 + 67 ) ÷ 68 gives a remainder of 66 c
Answer: c
Question (gain): last year a worker saved 6 % of her annual salary . this year , she made 20 % more money than last year and she saved 5 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 90 % , b ) 100 % , c ) 110 % , d ) 120 % , e ) 130 %
Rationale: let x be the worker ' s salary last year . last year , she saved 0.06 x . this year , she saved 0.05 ( 1.2 x ) = 0.06 x 0.06 x / 0.06 x = 100 % the answer is b .
Answer: b
Question (physics): a walks at 10 kmph and 4 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 80 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 4 hours . x / 10 - x / 20 = 4 x = 80 km answer is c"
Answer: c
Question (physics): a and b can do a piece of work in 10 days and 10 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 40 days , c ) 50 days , d ) 60 days , e ) 70 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 10 + 1 / 10 ] = 10 [ 1 + 1 / 10 ] = 2 a complete remaining work in 2 * 10 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Question (physics): one hour before john started walking from p to q , a distance of 33 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 21 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 33 - 3 = 30 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 30 miles so it will take them 30 / 5 = 6 hours to meet . in 6 hrs , ann would have covered 6 hrs * 3 miles per hour = 18 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 18 = 21 miles . answer ( e )"
Answer: e
Question (physics): kim finds a 2 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 3 / 5 , b ) 2 / 5 , c ) 7 / 5 , d ) 1 / 2 , e ) 8 / 15
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is a"
Answer: a
Question (gain): two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 216 marks in the second test and failed by 36 marks in that test . find the pass mark in the first test ?
Options: a ) 277 , b ) 266 , c ) 111 , d ) 121 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 36 marks in the second test . pass mark in the second test = 216 + 36 = 252 45 / 100 m = 252 pass mark in the first test = 40 / 100 m = 40 / 45 * 252 = 224 . answer : e"
Answer: e
Question (general): a man can swim in still water at 12 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 1.7 , b ) 2.67 , c ) 1.2 , d ) 1.5 , e ) 4
Rationale: "m = 12 s = x ds = 12 + x us = 12 + x 12 + x = ( 12 - x ) 2 12 + x = 24 - 2 x 3 x = 12 x = 4 answer : e"
Answer: e
Question (other): nitin ranks 24 th in a class of 58 students . what is rank from the last ?
Options: a ) 33 , b ) 34 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 58 - 24 ) = 34 nitin is 34 nd from the last answer : b ) 34"
Answer: b
Question (general): a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 4 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if average of 3 is 4 so sum of 3 should be 12 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 5 and 5 so a has to be 2 a
Answer: a
Question (general): 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 12 days . how many additional pipes q , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: this is an inverse proportional problem . . . . . . 5 pipes in 12 days ; so for 4 days , it will be = 12 x 5 / 4 = 15 so , q = 15 - 5 = 10 . c
Answer: c
Question (general): set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 3 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 3 , e ) e ) 16
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is d"
Answer: d
Question (gain): a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 45 % . staff are allowed a further 40 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.35 d , b ) 0.76 d , c ) 0.65 d , d ) 0.77 d , e ) 0.33 d
Rationale: effective discount = a + b + ab / 100 = - 45 - 40 + ( - 45 ) ( - 40 ) / 100 = - 67 sale price = d * ( 1 - 67 / 100 ) sale price = . 33 * d answer ( e )
Answer: e
Question (physics): convert 300 miles into km ?
Options: a ) 360 km , b ) 480 km , c ) 510 km , d ) 320 km , e ) 500 km
Rationale: "1 mile = 1.6 km approximately 300 mile = 300 * 1.6 = 480 km answer is b"
Answer: b
Question (general): difference of 2 numbers is 100 . if 5 % of one number is 10 % of the other number , find the addition of 2 numbers ?
Options: a ) 150 , b ) 300 , c ) 210 , d ) 290 , e ) 180
Rationale: "let the numbers be x and y 5 % of x = 10 % of y x = 2 y x - y = 100 2 y - y = 100 y = 100 x = 2 y = 200 x + y = 300 answer is b"
Answer: b
Question (general): in a room with 6 people , 4 people have exactly 1 friend in the room and 3 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 ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 15
Rationale: "( 4 / 6 ) ( 5 / 5 ) + ( 3 / 6 ) ( 4 / 5 ) if you choose one of the 4 with one other friend , then you have a 5 / 5 chance of not picking their friend 2 nd . if you choose one of the 3 with 2 friends , you have a 4 / 5 chance of not picking one of their friends second . add them up . 20 / 30 + 12 / 30 32 / 30 = 16 / 15 e . 16 / 15"
Answer: e