Cheukting/mathqa huggingface dataset:
Question (physics): working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 10 x boxes ?
Options: a ) 13 minutes , b ) 14 minutes , c ) 15 minutes , d ) 16 minutes , e ) 20 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 10 x / 5 x * 10 = 6 min ans : e"
Answer: e
Question (general): if y > 0 , ( 1 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 35 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to y / 20 + 3 y / 10 = 7 y / 20 = 35 % a"
Answer: a
Question (other): how many of the positive factors of 25 , 15 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 25 - 1 , 5 , and 25 factors of 15 - 1 , 3 , 5 and 15 comparing both , we have three common factors of 45,16 - 2 answer b"
Answer: b
Question (gain): a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 5 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 17.5 % , b ) 26 % , c ) 30 % , d ) 35 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.05 = 126 increase in 1993 from 1991 = 126 - 100 = 26 answer : b"
Answer: b
Question (general): of the 17,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 28.6 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . d"
Answer: d
Question (physics): an electric pump can fill a tank in 10 hours . because of a leak in the tank , it took 20 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 20 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 10 - 1 / 20 = 1 / 20 the leak will empty the tank in 20 hours answer is c"
Answer: c
Question (general): for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 36 ) ?
Options: a ) 2 , b ) 5 , c ) 11 , d ) 17 , e ) 23
Rationale: "f ( 36 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 * 32 * 34 * 36 the greatest prime factor in this list is 17 . the answer is d ."
Answer: d
Question (physics): pipe a can fill a tank in 10 hours . due to a leak at the bottom , it takes 15 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 76 , b ) 84 , c ) 56 , d ) 75 , e ) 30
Rationale: let the leak can empty the full tank in x hours 1 / 10 - 1 / x = 1 / 15 = > 1 / x = 1 / 10 - 1 / 15 = ( 3 - 2 ) / 30 = 1 / 30 = > x = 30 . answer : e
Answer: e
Question (physics): 5 women can do a work in two days . 10 men can complete the same work in five days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: "explanation : ( 5 ã — 2 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 10 ( 10 ã — 5 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 50 so , required ratio = 1 / 10 : 1 / 50 = 1 : 5 answer : b"
Answer: b
Question (general): what is the positive difference between the sum of the squares of the first 8 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 161 , b ) 162 , c ) 163 , d ) 164 , e ) 165
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 8 ^ 2 = 204 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 204 is 163 . so the answer is ( c ) ."
Answer: c
Question (general): the average age of 19 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 9 , b ) 71 , c ) 85 , d ) 92 , e ) 90
Rationale: "age of the 15 th student = 19 * 15 - ( 14 * 5 + 16 * 9 ) = 285 - 214 = 71 years answer is b"
Answer: b
Question (gain): a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 40.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 22.40 , d ) $ 16.00 , e ) $ 18.00
Rationale: "for retail price = $ 40 first maximum discounted price = 40 - 30 % of 40 = 40 - 12 = 28 price after additional discount of 20 % = 28 - 20 % of 28 = 28 - 5.6 = 22.4 answer : option c"
Answer: c
Question (geometry): the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 45 , then how long is the base of isosceles triangle ?
Options: a ) 5 units , b ) 10 units , c ) 15 units , d ) 20 units , e ) 25 units
Rationale: "the base of the isosceles triangle is 45 - 20 - 20 = 5 units the answer is a ."
Answer: a
Question (geometry): a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 80 inches . find b .
Options: a ) 8
b ) 16
c ) 24
d ) 32
e ) 48
Rationale: from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 80 ( 2 ^ 4 * 5 ) , sob = 2 ^ 4 or 2 ^ 4 * 5 ( 16 or 80 ) . combining 2 premises shows the answer is b ( 16 ) .
Answer: b
Question (general): calculate the ratio between x and y if 25 % of x equal to 40 % of y ?
Options: a ) 5 : 8 , b ) 5 : 9 , c ) 5 : 7 , d ) 5 : 6 , e ) 5 : 4
Rationale: "explanation : 25 x = 40 y x : y = 25 : 40 = 5 : 8 answer : a"
Answer: a
Question (general): . 003 / ? = . 01
Options: a ) . 3 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 003 / x = . 01 ; then x = . 003 / . 01 = . 3 / 1 = . 3 answer is a"
Answer: a
Question (general): if √ 10 = 3.16 , find the value of if √ 5 / 2
Options: a ) 1.3 , b ) 1.58 , c ) 2.03 , d ) 2.15 , e ) 3.15
Rationale: explanation : √ ( 5 / 2 ) = √ ( 5 × 2 / 2 × 2 ) = √ ( 10 ) / 2 = 3.16 / 2 = 1.58 answer : b
Answer: b
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 7420 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 300 , d ) 400 , e ) 80
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 7420 [ 4 l - 40 ] = 7420 / 26.50 = 280 4 l = 320 l = 320 / 4 = 80 meters . answer : e"
Answer: e
Question (physics): 30 men can do a work in 40 days . when should 12 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 18 days , b ) 10 days , c ) 55 days , d ) 44 days , e ) 22 days
Rationale: "total work to be done = 30 * 40 = 1200 let 12 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 12 * 40 ) = 1200 40 p = 720 = > p = 18 days answer : a"
Answer: a
Question (general): carrie likes to buy t - shirts at the local clothing store . they cost $ 9.65 each . one day , she bought 12 t - shirts . how much money did she spend ?
Options: a ) $ 115.8 , b ) $ 248.75 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.65 * 12 = $ 115.8 . answer is a .
Answer: a
Question (physics): a train 110 m long is running with a speed of 30 km / h . in how many seconds will the train pass a man who is running at 3 km / h in the direction opposite to that in which the train is going ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "the speed of the train relative to the man = 30 + 3 = 33 km / h . 33000 m / h * 1 h / 3600 s = ( 330 / 36 ) m / s ( 110 m ) / ( 330 / 36 m / s ) = ( 110 * 36 ) / 330 = 36 / 3 = 12 seconds the answer is d ."
Answer: d
Question (gain): kanul spent $ 3000 in buying raw materials , $ 1000 in buying machinery and 30 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 5825.16 , b ) $ 5725.26 , c ) $ 5714.28 , d ) $ 5912.52 , e ) $ 5614.46
Rationale: "let the total amount be x then , ( 100 - 30 ) % of x = 3000 + 1000 70 % of x = 4000 70 x / 100 = 4000 x = $ 40000 / 7 x = $ 5714.28 answer is c"
Answer: c
Question (general): a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 204 , what is the fewest number of $ 3 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 52 , e ) 2
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 204 x = 64 - y 3 ( 64 - y ) + 4 y = 204 192 - 3 y + 4 y = 204 y = 12 x = 64 - 12 = 52 d"
Answer: d
Question (physics): two trains 110 meters and 200 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.69 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 110 + 200 ) / ( 80 + 65 ) * 18 / 5 t = 7.69 answer : b"
Answer: b
Question (general): how many 1 / 10 s are there in 37 1 / 2 ?
Options: a ) 375 , b ) 475 , c ) 500 , d ) 670 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 10 ) = ( 75 / 2 x 10 / 1 ) = 375 . answer : a"
Answer: a
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 12 % microphotonics ; 24 % home electronics ; 15 % 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 ) 43 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 12 + 24 + 15 + 29 + 8 = 88 % . so remaining 12 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 12 % will be 43 degrees . . imo option a ."
Answer: a
Question (gain): how much interest will $ 10,000 earn in 3 months at an annual rate of 6 % ?
Options: a ) $ 250 , b ) $ 150 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: "soln : - 6 months = 1 / 4 of year ; 6 % = 6 / 100 = 3 / 50 ; $ 10,000 ( principal ) * 3 / 50 ( interest rate ) * 1 / 4 ( time ) = $ 150 . answer : b"
Answer: b
Question (general): how many different values of positive integer x , for which | x + 9 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer c i opted to put the random value option . i used 0 , 9 , - 9 and the the extreme of 10 and - 10 . . i was able to solve it in 1 : 09 c"
Answer: c
Question (general): if the average of 10 consecutive integers is 21.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 26 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 21 , integer 6 = 22 . counting up to the tenth integer we get 26 . answer : d"
Answer: d
Question (general): in a box of 8 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 2 / 10 , b ) 3 / 11 , c ) 4 / 13 , d ) 5 / 14 , e ) 6 / 17
Rationale: "p ( neither pen is defective ) = 5 / 8 * 4 / 7 = 5 / 14 the answer is d ."
Answer: d
Question (physics): in filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be ?
Options: a ) 100 cu . m
b ) 1000 cu . m
c ) 10000 cu . m
d ) 100000 cu . m
e ) 10000000 cu . m
Rationale: 100 * 10 * 10 = 10000 answer : c
Answer: c
Question (physics): a train passes a station platform in 30 sec and a man standing on the platform in 12 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 240 , c ) 200 , d ) 178 , e ) 270
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 12 = 180 m . let the length of the platform be x m . then , ( x + 180 ) / 30 = 15 = > x = 270 m . answer : e"
Answer: e
Question (geometry): a right triangle is inscribed in a circle . the legs of the triangle have lengths 6 and 8 . what is the diameter of the circle ?
Options: a ) 8
b ) 8 π
c ) 9 √ 3
d ) 10
e ) 12
Rationale: property of a right triangle inscribed in a circle is that when an angle is made from diameter of the circle , it is a right triangle . or if a right triangle is made inscribed in a circle , its its longest side is the diameter of the circle . hence diameter = ( 6 ^ 2 + 8 ^ 2 ) ^ 1 / 2 = 10 d is the answer
Answer: d
Question (gain): what is 15 percent of 64 ?
Options: a ) 7.2 , b ) 8.4 , c ) 9.6 , d ) 10.4 , e ) 11.8
Rationale: "( 15 / 100 ) * 64 = 9.6 the answer is c ."
Answer: c
Question (general): each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 55 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?
Options: a ) 15 , b ) 28 , c ) 18 , d ) 24 , e ) 21
Rationale: "let x be the number of 55 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 55 x = 15 ( x + 30 ) 30 x = 450 x = 15 ans - a"
Answer: a
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 181 ?
Options: a ) 3820 , b ) 5740 , c ) 6580 , d ) 7360 , e ) 9200
Rationale: "100 + 102 + . . . + 180 = 100 * 41 + ( 2 + 4 + . . . + 80 ) = 100 * 41 + 2 * ( 1 + 2 + . . . + 40 ) = 100 * 41 + 2 ( 40 ) ( 41 ) / 2 = 100 * 41 + 40 * 41 = 140 ( 41 ) = 5740 the answer is b ."
Answer: b
Question (general): a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 800 more than that by the previous schema , his sales were worth ?
Options: a ) s . 4,000 , b ) s . 12,000 , c ) s . 30,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 800 x = 4000 answer : a"
Answer: a
Question (general): if k is an integer and 0.0010101 x 10 ^ k is greater than 10 , what is the least possible value of k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "0.0010101 * 10 ^ k > 10 we need to move the decimal point to the right 4 places to get 10.101 this is equivalent to multiplying by 10 ^ 4 . the answer is c ."
Answer: c
Question (general): if a and b are positive integers and ( 3 ^ a ) ^ b = 3 ^ 3 , what is the value of 3 ^ a * 3 ^ b ?
Options: a ) 3 , b ) 9 , c ) 81 , d ) 27 , e ) 243
Rationale: 3 ^ ab = 3 ^ 3 therefore ab = 3 either a = 1 or 3 or b = 3 or 1 therefore 3 ^ a * 3 ^ b = 3 ^ ( a + b ) = 3 ^ 4 = 81 c
Answer: c
Question (probability): a gardener is going to plant 2 red rosebushes and 2 white rosebushes . if the gardener is to select each of the bushes at random , one at a time , and plant them in a row , what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) ½
Rationale: we are asked to find the probability of one particular pattern : wrrw . total # of ways a gardener can plant these four bushes is the # of permutations of 4 letters wwrr , out of which 2 w ' s and 2 r ' s are identical , so 4 ! / 2 ! 2 ! = 6 ; so p = 1 / 6 answer : b .
Answer: b
Question (other): a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 138 , b ) 140 , c ) 142 , d ) 145 , e ) 148
Rationale: "1 c 5 * 2 c 8 = 5 * 28 = 140 the answer is ( b )"
Answer: b
Question (physics): what will be the lcm of 8 , 24 , 36 and 54
Options: a ) 54 , b ) 108 , c ) 216 , d ) 432 , e ) none of these
Rationale: explanation : lcm of 8 - 24 - 36 - 54 will be 2 * 2 * 2 * 3 * 3 * 3 = 216 answer : option c
Answer: c
Question (general): a number exceeds by 35 from its 3 / 8 part . then the number is ?
Options: a ) a ) 56 , b ) b ) 35 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: "x – 3 / 8 x = 35 x = 56 answer : a"
Answer: a
Question (general): if 0.75 : x : : 5 : 6 , then x is equal to :
Options: a ) 1.12 , b ) 1.16 , c ) 1.2 , d ) 0.9 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 6 ) x = 4.5 / 5 = 0.9 answer : d"
Answer: d
Question (physics): two trains of equal lengths take 10 sec and 14 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 11.7 , e ) 15
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 14 = 8.6 m / sec . relative speed = 12 + 8.6 = 20.6 m / sec . required time = ( 120 + 120 ) / 20.6 = 11.7 sec . answer : option d"
Answer: d
Question (geometry): four equal circles are described about the four corners of a square so that each touches two of the others . if a side of the square is 14 cm , then the area enclosed between the circumferences of the circles is :
Options: a ) 24 cm 2
b ) 42 cm 2
c ) 154 cm 2
d ) 196 cm 2
e ) none of these
Rationale: the shaded area gives the required region . area of the shaded region = area of the square – area of four quadrants of the circles = ( 14 ) 2 - 4 × 1 ⁄ 4 π ( 7 ) 2 = 196 - 22 ⁄ 7 × 49 = 196 - 154 = 42 cm 2 answer b
Answer: b
Question (general): in the coordinate plane , line a has a slope of - 1 and an x - intercept of 1 . line b has a slope of 4 and a y - intercept of - 4 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - x + 1 the equation of line b is y = 4 x - 4 4 x - 4 = - x + 1 x = 1 y = 0 the point of intersection is ( 1,0 ) and then a + b = 1 . the answer is b ."
Answer: b
Question (gain): if the annual increase in the population of a town is 10 % and the present number of people is 10000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 10002
Rationale: "the required population is = 10000 ( 1 + 10 / 100 ) ^ 2 = 10000 * 11 / 10 * 11 / 10 = 12100 answer is a"
Answer: a
Question (physics): the sum of two consecutive integers is 41 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 20,21 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 41 2 n + 1 = 41 2 n = 40 n = 20 answer : d"
Answer: d
Question (physics): calculate the circumference of a circular field whose radius is 10 centimeters .
Options: a ) 20 π cm , b ) 19 π cm , c ) 28 π cm , d ) 25 π cm , e ) 30 π cm
Rationale: "circumference c is given by c = 2 π r = 2 π * 10 = 20 π cm answer : a"
Answer: a