regisss/math_qa huggingface dataset:
Problem: a tank can be filled by a tap in 20 minutes and by another tap in 60 minutes . both the taps are kept open for 10 minutes and then the first tap is shut off . after this , the tank will be completely filled in what time ?
Options: a ) 10 mins , b ) 15 mins , c ) 20 mins , d ) 25 mins , e ) 30 mins
Rationale: explanation : how we can solve this question ? first we will calculate the work done for 10 mins , then we will get the remaining work , then we will find answer with one tap work , as part filled by tap a in 1 min = 1 / 20 part filled by tap b in 1 min = 1 / 60 ( a + b ) ' s 10 mins work = 10 ∗ ( 1 / 20 + 1 / 60 ) = 10 ∗ 4 / 60 = 2 / 3 remaining work = 1 − 2 / 3 = 1 / 3 method 1 = > 1 / 60 : 1 / 3 = 1 : x = > x = 20 method 2 1 / 60 part filled by b in = 1 min 1 / 3 part will be filled in = 1 / 3 / 1 / 60 = 60 / 3 = 20 option c
Answer: c
Problem: renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 6 = 1 / 6 suma can do it alone in 6 days . answer : a"
Answer: a
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 50 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 75 , d ) d . 68 , e ) e . 60
Rationale: "50 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 50 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 125 thus , more men needed to finish the task = 125 - 50 = 75 hence answer is c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 876 m , d ) 200 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 12 ) m = 200 m . answer : d"
Answer: d
Problem: a is twice as fast as b . if b alone can do a piece of work in 24 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 12 , c ) 6 , d ) 2 , e ) 8
Rationale: a can do the work in 24 / 2 i . e . , 12 days . a and b ' s one day ' s work = 1 / 12 + 1 / 24 = ( 2 + 1 ) / 24 = 1 / 8 so a and b together can do the work in 8 days . answer : e
Answer: e
Problem: the owner of a furniture shop charges his customer 32 % more than the cost price . if a customer paid rs . 5400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 4090 , b ) rs . 4067 , c ) rs . 6290 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5400 ( 100 / 132 ) = rs . 4090 . answer : a"
Answer: a
Problem: in the coordinate plane , a circle centered on point ( - 3 , - 4 ) passes through point ( - 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π
b ) 18 π
c ) 29 π
d ) 37 π
e ) 41 π
Rationale: r ^ 2 = ( - 3 + 1 ) ^ 2 + ( - 4 - 1 ) ^ 2 = 4 + 25 = 29 area of circle = π r ^ 2 = 29 π answer : c
Answer: c
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 00 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 00 pm + 2 hrs = 7 : 00 pm answer : e . 7 : 00"
Answer: e
Problem: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price b per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: correct answer : a explanation : the relevant formula for this problem is average b = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility .
Answer: a
Problem: a cylinder is 6 cms in diameter and 6 cms in height . if spheres of the same size are made from the material obtained , what is the diameter of each sphere ?
Options: a ) 5 cms
b ) 2 cms
c ) 3 cms
d ) 4 cms
e ) 6 cms
Rationale: since the sphere is made out of the cylinder material their volume will be same volume of cylinder = pi * 3 ^ 2 * 6 volume of one sphere = 4 / 3 * pi * r ^ 3 ( where r is radius of sphere ) so if there are n such sphere ' s equating the volumes , pi * r ^ 2 * h = n * ( 4 / 3 ) * pi * r ^ 3 n is the number of spheres , substituting the , r and h 9 * 6 = n * ( 4 / 3 ) * ( d / 2 ) ^ 3 d is the diameter of a sphere , n = ( 9 * 6 * 3 * 8 ) / ( 4 * d ^ 3 ) n = 324 / d ^ 3 now substitute the given answers for d and find the values for n , since a n has to be an integer only value fit for d is 3 , answer : c
Answer: c
Problem: a number x is 8 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 8 . then y = 1 is less than x = 8 by ( 8 - 1 ) / 8 * 100 = 7 / 8 * 100 = 87.5 % . answer : b ."
Answer: b
Problem: if 20 typists can type 44 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 198 , d ) 216 , e ) 400
Rationale: "20 typists can type 44 letters , so 30 typists can type = 44 * 30 / 20 44 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 44 * 30 * 60 / 20 * 20 = 198 c is the answer"
Answer: c
Problem: if ( 1 / 5 ) ^ m * ( 1 / 2 ) ^ 5 = 1 / ( ( 10 ) ^ 5 ) , then m =
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 / 5 ) ^ m ( 1 / 2 ) ^ 5 = 1 / { ( 10 ) ^ 5 } ( 10 ) ^ 5 / 2 ^ 5 = 5 ^ m [ ( 2 ^ 5 ) ( 5 ^ 5 ) ] / [ 2 ^ 5 ] = 5 ^ m 5 ^ 5 = 5 ^ m m = 5 e"
Answer: e
Problem: amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is :
Options: a ) rs . 4250 , b ) rs . 4288 , c ) rs . 4227 , d ) rs . 4218 , e ) rs . 4219
Rationale: "explanation : amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } { 6 } = 4250 answer : a"
Answer: a
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 105 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.28 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 105 ( multiplying factor is 7 : ( 105 / 15 ) ) then typical dosage would be 2 * 7 = 14 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 14 ) * 100 = 14.28 % e is the answer ."
Answer: e
Problem: a discount electronics store normally sells all merchandise at a discount of 5 percent to 45 percent off the suggested retail price . if , during a special sale , an additional 2 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 215.00 , b ) $ 200.00 , c ) $ 215.80 , d ) $ 182.00 , e ) $ 215.60
Rationale: "original price : 400 $ max first discount = - 45 % thus : 400 â ˆ — ( 1 â ˆ ’ 45 / 100 ) = 220 second discount on the discounted price = - 2 % thus : 220 â ˆ — ( 1 â ˆ ’ 2 / 100 ) = 215.60 answer e"
Answer: e
Problem: a man sold 20 articles for $ 40 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 67.5
Rationale: "production cost per article : $ 40 * ( 100 % - 20 % ) / 20 = $ 1.6 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 1.6 = 67.5 thus , solution e is correct ."
Answer: e
Problem: two trains are moving in the same direction at 162 kmph and 18 kmph . the faster train crosses a man in the slower train in 33 seconds . find the length of the faster train ?
Options: a ) 1300 , b ) 1310 , c ) 1320 , d ) 1330 , e ) 1340
Rationale: "relative speed = ( 162 - 18 ) * 5 / 18 = 8 * 5 = 40 mps . distance covered in 33 sec = 33 * 40 = 1320 m . the length of the faster train = 1320 m . answer : c"
Answer: c
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served only for 9 months and receiveduniform and rs . 650 , find the price of the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 130 , d ) rs . 170 , e ) rs . 190
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Problem: 500 x 223 + 500 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 150000 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 500 x 300 = 150000 answer is c"
Answer: c
Problem: how many factors of 220 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 220 has 4 prime factors . of these prime factors 2 are odd and 2 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 1 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Problem: in xyz business school , 88 % are taking their specialization as finance at the same time 76 % taking their specialization as marketing . if 90 % are taking their specialization as finance then , what is % of marketing specialization students ?
Options: a ) 55 , b ) 75 , c ) 43 , d ) 52 , e ) 45
Rationale: percentage of finance specialization = 88 ; percentage of marketing specialization = 75 % ; total = 90 * 100 ; percentage of finance specialization = 90 - 88 = 2 ; percentage of marketing specialization = 100 - 75 = 25 ; then percentage of marketing specialization = 0.75 * 24 = 18 . then total percentage of marketing specialization = 25 + 18 = 43 . answer : c
Answer: c
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: ? % 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a , b and c have rs . 600 between them , a and c together have rs . 250 and b and c rs . 450 . how much does c have ?
Options: a ) 70 , b ) 90 , c ) 120 , d ) 100 , e ) 140
Rationale: "a + b + c = 600 a + c = 250 b + c = 450 - - - - - - - - - - - - - - a + b + 2 c = 700 a + b + c = 600 - - - - - - - - - - - - - - - - c = 100 answer : d"
Answer: d
Problem: a store reduced the price of all items in the store by 15 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 76.5 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 15 % price becomes = 0.85 * 100 = $ 85 after the final reduction of 10 % price becomes = 0.9 * 85 = $ 76.5 price of all items on second day is 76.5 % of price on first day correct answer option a"
Answer: a
Problem: find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 9 cm and 6 cm ?
Options: a ) 189 cm 2
b ) 300 cm 2
c ) 127 cm 2
d ) 177 cm 2
e ) 187 cm 2
Rationale: 1 / 2 * 40 ( 9 + 6 ) = 300 cm 2 answer : b
Answer: b
Problem: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters k long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = k , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 25 % solution ?
Options: a ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 20 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 25 / 100 40 + 4 x = 100 + x 3 x = 60 x = 20 answer is d"
Answer: d
Problem: my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 140 years . can you tell me my age in years ?
Options: a ) 80 , b ) 90 , c ) 85 , d ) 84 , e ) 89
Rationale: let the age of the man = x years so according to the given condition age of my grandson = x / 12 years and age of my son = x 30 / 52 = 15 x / 26 and x + ( x / 12 ) + ( 15 x / 26 ) = 140 or ( 156 x + 13 x + 90 x ) / 156 = 140 or 259 x = 156 * 140 or x = 156 * 140 / 259 = 84 answer : d
Answer: d
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 15,500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 120,000
Rationale: answer equals e in 48 years . i thought by 50 th year it would reach 120,000 . options should have been separated more widely for clarity .
Answer: e
Problem: there are 361 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ?
Options: a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 181
Rationale: "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 361 = 209 answer : a"
Answer: a
Problem: 20 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33.33 , b ) 34.01 , c ) 26.32 , d ) 28.33 , e ) 19.21
Rationale: "explanation : let the two parts be ( 20 - x ) and x . then , 10 ( 20 - x ) + 22 x = 780 = > 12 x = 580 = > x = 48.33 . bigger part = ( 20 - x ) = 28.33 . answer : d ) 28.3"
Answer: d
Problem: a chartered bank offers a 5 - year escalator guaranteed investment certificate . in successive years it pays annual interest rates of 4 % , 4.5 % , 5 % , 5.5 % , and 6 % , respectively , compounded at the end of each year . the bank also offers regular 5 - year gics paying a fixed rate of 5 % compounded annually . calculate and compare the maturity values of $ 1000 invested in each type of gic . ( note that 5 % is the average of the 5 successive one - year rates paid on the escalator gic . )
Options: a ) 1276.28 , b ) 1276.22 , c ) 1276.29 , d ) 1276.21 , e ) 1276.23
Rationale: explanation : fv = $ 1000 ( 1.04 ) ( 1.045 ) ( 1.05 ) ( 1.055 ) ( 1.06 ) = $ 1276.14 the maturity value of the regular gic is fv = $ = $ 1276.28 answer : a ) 1276.28
Answer: a
Problem: on a trip covering 350 km , a bicyclist travels the first 200 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 15.5 , b ) 16.0 , c ) 17.5 , d ) 19.0 , e ) 18.5
Rationale: "time 1 = 200 / 20 = 10 hours time 2 = 150 / 15 = 10 hours total time = 20 hours average speed = 350 / 20 = 17.5 km / hr the answer is c ."
Answer: c
Problem: how many seconds will a 1200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 26 sec , b ) 65 sec , c ) 55 sec , d ) 19 sec , e ) 72 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 1200 * 3 / 50 = 72 sec . answer : e"
Answer: e
Problem: the ratio of two quantities is 3 to 4 . if each of the quantities is increased 4 and 3 respectively , what is the ratio of these two new quantities ?
Options: a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given
Rationale: "3 / 4 = 3 x / 4 x we need to find out ( 3 x + 4 ) / ( 4 x + 3 ) off course we can not solve this to arrive at any rational number hence e ."
Answer: e
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.30 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 865.8 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.3 = 865.8 answer : c"
Answer: c
Problem: 25 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 8 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 10 days
Rationale: "1 women ' s 1 day work = 1 / 175 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 175 + 10 / 140 ) = 1 / 10 5 women and 10 children will complete the work in 10 days . answer : e"
Answer: e
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 5 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 300 kmph , b ) 360 kmph , c ) 600 kmph , d ) 720 kmph , e ) none
Rationale: "explanation : distance = ( 240 x 5 ) = 1200 km . speed = distance / time speed = 1200 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 1200 x 3 / 5 km / hr = 720 km / hr . answer : option d"
Answer: d
Problem: in arun ' s company 60 % of the employees earn less than $ 50000 a year , 60 % of the employees earn more than $ 40000 a year , 11 % of the employees earn $ 43000 a year and 5 % of the employees earn $ 49000 a year . what is the median salary for the company ?
Options: a ) 43.0 , b ) 45.5 , c ) 46.0 , d ) 49.0 , e ) 50.0
Rationale: in arun ' s company 60 % of the employees earn less than $ 50,000 a year , 50 and 51 employee will be each 43 k . hence median = ( 43 k + 43 k ) / 2
Answer: a
Problem: 50 square stone slabs of equal size were needed to cover a floor area of 72 sq . m . find the length of each stone slab ?
Options: a ) 120 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 72 / 50 m 2 = 1.44 m 2 length of each slab √ 1.44 = 1.2 m = 120 cm"
Answer: a
Problem: a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 90 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 36 % , c ) 30 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 190 , so from 2003 to 2005 it increased by ( 190 - 140 ) / 140 = 50 / 140 = ~ 29 % . answer : b"
Answer: b
Problem: the number of the members of a club is more than 20 and less than 50 . when 5 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 8 - people groups , how many people will be left ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the number of members is 7 k + 5 = 6 j + 5 the only number in this range which satisfies this is 47 . 47 / 8 = 5 ( 8 ) + 7 the answer is e .
Answer: e
Problem: a train 300 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 19 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 300 m at 50 / 3 m / sec = 300 * 3 / 50 sec = 18 sec answer : d ."
Answer: d
Problem: at the store opening , larry ' s grocery had 50 lemons and 60 oranges . by closing , the store at 20 lemons and 40 oranges left . by approximately what percent did the ratio of lemons to orange decrease from opening to closing .
Options: a ) 50.0 % , b ) 40.0 % , c ) 30.0 % , d ) 20.0 % , e ) 10.0 %
Rationale: opening : lemons / oranges = 50 / 60 = 100 / 120 closing : lemons / oranges = 20 / 40 = 60 / 120 aside : it ' s useful to write both ratios with the same denominator . this allows us to ignore the denominator and focus solely on the numerators . so , our ratio went from 100 / 120 to 60 / 120 ignoring the denominators , we went from 100 to 60 the percent change = 100 ( difference in values ) / ( original value ) = ( 100 ) ( 100 - 60 ) / 100 = ( 100 ) ( 40 ) / 100 ) = 40 answer : b
Answer: b
Problem: what is the 27 th digit to the right of the decimal point in the decimal form of 5 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 11 = 0.45454545 . . . the odd numbered positions in the decimal expansion are all 4 . the answer is b ."
Answer: b
Problem: if x is a positive integer with fewer than 3 digits , what is the probability that z x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability z that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Problem: the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 108 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c"
Answer: c
Problem: if y is 40 % greater than x , than x is what % less than y ?
Options: a ) 24.4 % , b ) 28.6 % , c ) 32.3 % , d ) 36.5 % , e ) 40.9 %
Rationale: "y = 1.4 x x = y / 1.4 = 10 y / 14 = 5 y / 7 x is 2 / 7 less which is 28.6 % less than y . the answer is b ."
Answer: b
Problem: a luxury liner , queen marry ii , is transporting several cats as well as the crew ( sailors , a cook , and one - legged captain ) to a nearby port . altogether , these passengers have 16 heads and 41 legs . how many cats does the ship host ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 7 , e ) 8
Rationale: sa ' s + co + ca + cats = 16 . sa ' s + 1 + 1 + cats = 16 or sa ' s + cats = 14 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 41 sa ' s * 2 + cats * 4 = 38 or sa ' s + cats * 2 = 19 or 14 - cats + cat * 2 = 19 then cats = 5 a
Answer: a
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.85 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 420 $ , c ) 582 $ , d ) 650 $ , e ) 780 $
Rationale: 12 * 1.75 + 0.85 * 12 * 55 = 582 hence - c
Answer: c