Cheukting/mathqa huggingface dataset:
Question (physics): the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit y on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer ybis 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Question (geometry): in the rectangular coordinate system , points ( 4 , 0 ) and ( – 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 4 b"
Answer: b
Question (gain): on a map , 3 centimeters represents 33 kilometers . two cities 209 kilometers apart would be separated on the map by how many centimeters ?
Options: a ) 19 , b ) 7 , c ) 13 , d ) 110 , e ) 180
Rationale: "1 centimeter represents 11 kilometers ( 33 / 3 ) x = 209 / 11 = 19 answer : a"
Answer: a
Question (physics): a boat can travel with a speed of 5 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 100 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 10 hrs
Rationale: "speed downstream = ( 5 + 5 ) km / hr = 10 km / hr . time taken to travel 100 km downstream = 100 / 10 hrs = 10 hrs . answer : e"
Answer: e
Question (general): when f is divided by 5 , the remainder is 3 . when y is divided by 5 , the remainder is 4 . what is the remainder when f + y is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: in my view the answer should be c f / 5 has remainder = 3 - > f = 5 x q + 3 y / 5 has a remainder = 4 - > y = 5 x q + 3 combining both ( ( 5 x q 1 + 3 ) + ( 5 x q 2 + 3 ) ) / 5 = 5 ( q 1 + q 2 ) / 5 + 7 / 5 = q 1 + q 2 + 7 / 5 7 / 5 = 1 + 2 / 5 = > remainder 2 answer c
Answer: c
Question (geometry): the side of a rhombus is 24 m and length of one of its diagonals is 18 m . the area of the rhombus is ?
Options: a ) 410.47 , b ) 403.47 , c ) 420.47 , d ) 400.47 , e ) 300.47
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 24 ; p = 18 a = 1 / 2 * 18 * √ 4 ( 24 ) 2 - ( 18 ) 2 = 1 / 2 * 18 * √ 2304 - 324 = 1 / 2 * 18 * √ 1980 a = 400.47 answer : d"
Answer: d
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 21 , b ) 20 , c ) 22 , d ) 25 , e ) 40
Rationale: "let the total number of workers be x . then , 8000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 42000 = x = 21 . answer a"
Answer: a
Question (gain): one night a certain hotel rented 2 / 3 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 50 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: "the rooms which were not rented is 1 / 3 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 3 ) = 3 / 5 = 60 % the answer is b ."
Answer: b
Question (physics): a car travels at a speed of 55 miles per hour . how far will it travel in 5 hours ?
Options: a ) 425 miles , b ) 625 miles , c ) 325 miles , d ) 225 miles , e ) 275 miles
Rationale: "during each hour , the car travels 55 miles . for 5 hours it will travel 55 + 55 + 55 + 55 + 55 = 5 * 55 = 275 miles correct answer e"
Answer: e
Question (physics): every second saturday and all sundays are holidays . how many working days will be there in a month of 30 days beginning on a saturday ?
Options: a ) 24 , b ) 23 , c ) 18 , d ) 21 , e ) 22
Rationale: explanation : mentioned month has begins on a saturday and has 30 days sundays = 2 nd , 9 th , 16 th , 23 rd , 30 th = > total sundays = 5 second saturdays = 8 th and 22 nd total second saturdays = 2 total holidays = total sundays + total second saturdays = 5 + 2 = 7 total days in the month = 30 total working days = 30 - 7 = 23 answer : option b
Answer: b
Question (general): the present age of a father is 3 years more than 3 times the age of his son . 3 years hence , father ’ s age will be 10 years more than twice athe age of the son . find the present age of the father .
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: sol . let the son ’ s present age be x years . then , father ’ s present age = ( 3 x + 3 ) years . therefore ( 3 x + 3 + 3 ) = 2 ( x + 3 ) + 10 ‹ = › 3 x + 6 = 2 x + 16 ‹ = › x = 10 hence , father ’ s present age = ( 3 x + 3 ) = ( 3 x 10 + 3 ) years = 33 years . answer a
Answer: a
Question (gain): find number which is 60 % less than 80 .
Options: a ) 18 , b ) 32 , c ) 28 , d ) 26 , e ) 98
Rationale: "explanation : 60 % less is 40 % of the given number therefore , 40 % of 80 is 32 . answer : b"
Answer: b
Question (gain): a cricket bat is sold for $ 850 , making a profit of $ 230 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 37 % , e ) 40 %
Rationale: "230 / ( 850 - 230 ) = 230 / 620 = 23 / 62 = 37 % answer : d ."
Answer: d
Question (physics): a factory produces 5500 toys per week . if the workers at this factory work 4 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 2354 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 4 days ) by 4 . 5500 / 4 = 1375 toys correct answer e"
Answer: e
Question (geometry): if g is the smallest positive integer such that 3150 multiplied by g is the square of an integer , then g must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by g is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x g = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , g = 7 x 2 = 14 answer is e .
Answer: e
Question (general): the total age of a and b is 13 years more than the total age of b and c . c is how many year younger than a
Options: a ) a ) 11 , b ) b ) 12 , c ) c ) 13 , d ) d ) 14 , e ) e ) 15
Rationale: "explanation : given that a + b = 13 + b + c = > a – c = 13 + b – b = 13 = > c is younger than a by 13 years answer : option c"
Answer: c
Question (gain): ? % of 360 = 108.0
Options: a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) 30
Rationale: "? % of 360 = 108.0 or , ? = 108.0 × 100 / 360 = 30 answer e"
Answer: e
Question (other): two numbers are in the ratio of 1 : 2 . if 7 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 7 ) / ( y + 7 ) = 3 / 5 = > x = 14 and y = 28 answer : c"
Answer: c
Question (general): find the numbers which are in the ratio 3 : 2 : 1 such that the sum of the first and the second added to the difference of the third and the second is 16 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 12 , 8,4
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 1 given , ( a + b ) + ( c - b ) = 16 = > a + c = 16 = > 3 x + x = 16 = > x = 4 a , b , c are 3 x , 2 x , x a , b , c are 12 , 8 , 4 . answer : e"
Answer: e
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?
Options: a ) 40 , b ) 45 , c ) 49 , d ) 51 , e ) 43
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 175 × ( 9 / 35 ) = 5 × 9 = 45 answer is b ."
Answer: b
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 15 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 130.00 , b ) $ 145.60 , c ) $ 154.70 , d ) $ 182.00 , e ) $ 210.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 260 would be . . . . . ( $ 260 ) ( . 7 ) ( . 85 ) = ( $ 260 ) ( . 595 ) = 154.7 final answer : c"
Answer: c
Question (gain): a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 7.00 ?
Options: a ) 40 , b ) 84 , c ) 90 , d ) 120 , e ) 240
Rationale: cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 7 ( 1 / 12 ) * x = 7 x = 84 answer : b
Answer: b
Question (geometry): in a triangle abc , point d is on side ab and point e is on side ac , such that bced is a trapezium . de : bc = 3 : 5 . calculate the ratio of the area of triangle ade and the trapezium bced .
Options: a ) 9 / 16
b ) 8 / 16
c ) 7 / 16
d ) 6 / 16
e ) 5 / 16
Rationale: area of tri ( ade ) / area of tri ( abc ) = de ^ 2 / bc ^ 2 since tri ( ade ) - tri ( abc ) area of tri ( ade ) / area of tri ( abc ) = 9 / 25 area of tri ( abc ) / area of tri ( ade ) = 25 / 9 area of tri ( abc ) = area of tri ( ade ) + area of trap ( bcde ) ( area of tri ( ade ) + area of trap ( bcde ) ) / area of tri ( ade ) = 25 / 9 1 + area of trap ( bcde ) / area of tri ( ade ) = 25 / 9 take 1 on both sides area of trap ( bcde ) / area of tri ( ade ) = ( 25 / 9 ) - 1 = 16 / 9 since question is asking for area of tri ( ade ) / area of trap ( bcde ) = 9 / 16 answer : a
Answer: a
Question (general): 96 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 26682 , d ) 29973 , e ) 12312
Rationale: "x * ( 96 / 100 ) = 23040 x = 240 * 100 x = 24000 answer : b"
Answer: b
Question (general): solve the equation for x : 6 x - 87 + 3 x = 4 + 9 - x
Options: a ) 12 , b ) 5 , c ) 10 , d ) 9 , e ) 3
Rationale: "c 10 9 x + x = 13 + 87 10 x = 100 = > x = 10"
Answer: c
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 117 grams of water ?
Options: a ) 100 , b ) 102 , c ) 104 , d ) 106 , e ) 108
Rationale: "( 16 / 18 ) * 117 = 104 grams the answer is c ."
Answer: c
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1200 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 3890 , c ) 3300 , d ) 2789 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1300 * 21 - 1200 * 20 ) = rs . 3300 . answer : c"
Answer: c
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 141 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 141 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Question (general): there are 408 boys and 288 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 29
Rationale: explanation : hcf ( 408 , 288 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 288 / 24 = 17 + 12 = 29 answer : e
Answer: e
Question (general): what is the units digit of the expression 14 ^ 7 − 17 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 8 , e ) 6
Rationale: i think answer on this one should be d too . since we know that 14 ^ 7 > 17 ^ 4 , as will said one should always check if the number is positive .
Answer: d
Question (general): a certain experimental mathematics program was tried out in 2 classes in each of 42 elementary schools and involved 55 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 42 * 2 = 84 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 84 - 55 = 29 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 29 / 2 = 14.5 . so the greatest possible value of the # of teachers who had 3 classes is 14 . only answer b has this option ."
Answer: b
Question (general): if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 35
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 35 = 19008 / 35 = 543 , remainder = 3 b"
Answer: b
Question (general): if a ^ 4 + b ^ 4 = 100 , then the greatest possible value of b is between
Options: a ) 0 and 1 , b ) 1 and 2 , c ) 2 and 3 , d ) 3 and 4 , e ) 4 and 5
Rationale: for the greatest possible value of b ^ 4 , we must minimize the value of b ^ 4 i . e . lets say a ^ 4 = 0 then we need to find a number b such that b ^ 4 < 100 . 3 ^ 4 = 81 and 4 ^ 4 = 256 so we can say that the maximum possible value of b can be a little more than 3 hence answer = between 3 and 4 hence d
Answer: d
Question (gain): in how many years will a sum of money doubles itself at 5 % per annum on simple interest ?
Options: a ) 33 , b ) 20 , c ) 88 , d ) 66 , e ) 21
Rationale: "p = ( p * 5 * r ) / 100 r = 20 % answer : b"
Answer: b
Question (probability): how many different ways can 2 students be seated in a row of 7 desks , so that there is always at least one empty desk between the students ?
Options: a ) 2 , b ) 3 , c ) 30 , d ) 6 , e ) 12
Rationale: 15 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 15 x 2 = 30 c
Answer: c
Question (other): the ratio of 2 numbers is 5 : 2 and their h . c . f . is 20 . their l . c . m . is ?
Options: a ) 400 , b ) 300 , c ) 200 , d ) 100 , e ) 40
Rationale: "let the numbers be 5 x and 2 x their h . c . f . = 20 so the numbers are 5 * 20 , 2 * 20 = 100 , 40 l . c . m . = 200 answer is c"
Answer: c
Question (physics): what is the greatest possible length which can be used to measure exactly the lengths 180 m , 500 m and 15 m 20 cm ?
Options: a ) 80 cm , b ) 50 cm , c ) 40 cm , d ) 10 cm , e ) 100 cm
Rationale: required length = hcf of 18000 cm , 50000 cm , 1520 cm = 80 cm answer is a
Answer: a
Question (geometry): if radius of a circle is diminished by 10 % then its area is diminished by
Options: a ) 22
b ) 19
c ) 877
d ) 26
e ) 271
Rationale: explanation : let old radius = 10 units . new radius is diminshed by 10 % . so new radius = 90 % ( 10 ) = 9 units . old area = π × r 2 = 100 π new area = π × 92 = 81 π change = 19 π / 100 π × 100 = 19 % answer : b
Answer: b
Question (geometry): 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 4 : 3 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 9 : 10 , b ) 19 : 20 , c ) 29 : 30 , d ) 39 : 40 , e ) 49 : 50
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 4 y and 3 y . 2 ( 3 x + 2 x ) = 2 ( 4 y + 3 y ) 5 x = 7 y ( 5 / 7 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 4 y * 3 y = 6 x ^ 2 : 12 y ^ 2 = x ^ 2 : 2 y ^ 2 = x ^ 2 : 2 * ( 25 / 49 ) * x ^ 2 = 49 : 50 the answer is e ."
Answer: e
Question (geometry): the ratio of the areas of two squares , one having double its diagonal then the other is :
Options: a ) 2 : 1
b ) 1 : 2
c ) 2 : 3
d ) 1 : 4
e ) 4 : 1
Rationale: lenth of the diagonals be 2 x and x units . areas are 1 / 2 × ( 2 x ) power 2 and ( 1 / 2 × ( xpower 2 ) ) required ratio = 1 / 2 × 4 x 2 : 1 / 2 x 2 = 4 : 1 answer is e .
Answer: e
Question (other): a group of people participate in some curriculum , 25 of them practice yoga , 15 study cooking , 8 study weaving , 2 of them study cooking only , 7 of them study both the cooking and yoga , 3 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: both cooking and weaving = 15 - ( 2 + 3 + 7 ) = 3 so , the correct answer is c .
Answer: c
Question (general): a car travels first 160 km at 70 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 71.1 , d ) 74.66 , e ) 71.13
Rationale: "car travels first 160 km at 70 km / hr time taken to travel first 160 km = distancespeed = 160 / 70 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 160 / 80 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 70 + 160 / 80 average speed = total distance traveled / total time taken = 320 / ( 160 / 70 + 160 / 80 ) = 74.66 km / hr answer : d"
Answer: d
Question (gain): in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 347000 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 e )"
Answer: e
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 95 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 75 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )"
Answer: d
Question (general): john found that the average of 15 numbers is 40 . if 15 is added to each number then the mean of number is ?
Options: a ) 55 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 55 option a"
Answer: a
Question (general): 357 : 73 : : ?
Options: a ) 429 : 94 , b ) 201 : 21 , c ) 138 : 38 , d ) 93 : 39 , e ) 95 : 39
Rationale: "357 : 73 to get 2 nd number , middle digit is removed , 1 st & last interchanged their position of 1 st no . only option a ) match this . answer : a"
Answer: a
Question (general): scott ' s average ( arithmetic mean ) golf score on his first 4 rounds was 78 . what score does he need on his fifth round to drop his average score by 2 points ?
Options: a ) 68 , b ) 72 , c ) 78 , d ) 88 , e ) 312
Rationale: average score for first 4 rounds = 78 average score after 5 rounds = 76 score scott needs on his 5 th round to drop average score by 2 points = 78 - ( 2 * 5 ) = 68 answer a alternatively , sum of scores of first 4 rounds = 78 * 4 = 312 sum of scores after 5 rounds = 76 * 5 = 380 score scott needs on his 5 th round to drop average score by 2 points = 380 - 312 = 68 answer a
Answer: a
Question (probability): in 15 year ’ s time the combined age of my 4 brothers will be 107 . what will it be in the 6 year ’ s time ?
Options: a ) 61 , b ) 78 , c ) 71 , d ) 68 , e ) 94
Rationale: c 71 combined age in 15 years = 107 . 4 × 15 = 60 , therefore combined age now is 107 – 60 = 47 . in 6 years time , therefore , combined age will be 47 + 24 ( 4 x 6 ) = 71 .
Answer: c