regisss/math_qa huggingface dataset:
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 4 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.76 % , c ) 14.14 % , d ) 13.13 % , e ) 12.12 %
Rationale: "( 100 % + 4 % ) * ( 100 % - 19 % ) = 1.04 * . 81 = 0.8424 . 1 - 0.8424 = 15.76 % lost = - 15.76 % the answer is b the organization has lost 15.76 % of its total volunteers from fall to spring ."
Answer: b
Problem: find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 0.81 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 2.5 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.81 ) + ( √ 0.81 ) / ( √ 0.49 ) 11 / 9 + 9 / 7 = > 2.50 answer is b"
Answer: b
Problem: a cubical tank is filled with water to a level of 3 feet . if the water in the tank occupies 48 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "the volume of water in the tank is h * l * b = 48 cubic feet . since h = 3 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 48 / 64 = 3 / 4 the answer is c ."
Answer: c
Problem: a and b began business with rs . 6000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 273 , d ) 877 , e ) 361
Rationale: "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 13 / 30 * 630 = 273 answer : c"
Answer: c
Problem: there are 18 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Rationale: there are 18 balls in a jar . you take out 3 blue balls without putting 3 blue balls + 15 / 5 = 6 answer : e
Answer: e
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 45 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: 45 % is 15 % - points above 30 % and 15 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 1 : 1 . 1 / 2 * 70 % = 35 % the answer is c .
Answer: c
Problem: in august , a cricket team that played 120 matches won 20 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
Options: a ) 40 , b ) 52 , c ) 68 , d ) 80 , e ) 98
Rationale: "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 24 + x by solving we get x = 80 answer : d"
Answer: d
Problem: dacid obtained 72 , 45 , 72 , 77 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 68 , c ) 87 , d ) 26 , e ) 75
Rationale: "average = ( 72 + 45 + 72 + 77 + 75 ) / 5 = 341 / 5 = 68 . answer : b"
Answer: b
Problem: find the area of a parallelogram with base 24 cm and height 16 cm .
Options: a ) 379 , b ) 384 , c ) 345 , d ) 342 , e ) 376
Rationale: "area of a parallelogram = base * height = 24 * 16 = 384 cm 2 area of a parallelogram = base * height = 24 * 16 = 384 cm 2 answer : option b"
Answer: b
Problem: two pipes a and b can fill a tank in 30 hours and 45 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 18 hours , b ) 15 hours , c ) 10 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 30 part filled by b in 1 hour = 1 / 45 part filled by ( a + b ) in 1 hour = 1 / 30 + 1 / 45 = 5 / 90 = 1 / 18 both the pipes together fill the tank in 18 hours answer is a"
Answer: a
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 d 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 d = ( 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 certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 120,000 and variables costs averaging $ 8 per item . if the manufacturer ’ s selling price per item is $ 12 , how many items the manufacturer produce and sell to earn an annual profit of $ 140,000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 21,429 , d ) 35,000 , e ) 65,000
Rationale: "let the items manufactured or sold bex 120000 + 8 x = 12 x - 140000 4 x = 260000 x = 65000 ans : e"
Answer: e
Problem: there are 20 poles with a constant distance between each pole . a car takes 24 seconds to reach the 12 th pole . how much time will it take to reach the last pole ?
Options: a ) 25.25 s , b ) 17.45 s , c ) 35.75 s , d ) 41.45 s , e ) none of these
Rationale: let the distance between each pole be x m . then , the distance up to 12 th pole = 11 xm speed = 11 x ⁄ 24 m / s time taken to covers the total distance of 19 x = 19 x × 24 / 11 x = 41.45 s answer d
Answer: d
Problem: in a group of 90 students , 36 are taking history , and 32 are taking statistics . if 57 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 25 , d ) 27 , e ) 31
Rationale: number of students taking history = h = 36 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 57 number of students taking neither history nor statistics = n = 90 - 57 = 33 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 32 + 33 - x or x = 11 now , number of students taking only history will be h - x or 36 - 11 = 25 answer : - c
Answer: c
Problem: if a - b = 4 and a 2 + b 2 = 18 , find the value of ab .
Options: a ) 9 , b ) 1 , c ) 2 , d ) 18 , e ) 19
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 18 - 16 = 2 ab = 1 . answer : b"
Answer: b
Problem: one computer can upload 100 megabytes worth of data in 5 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 40 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 5 seconds then in 5 * 8 = 40 seconds it can upload 8 * 100 = 800 megabytes worth of data , hence the second computer in 40 seconds uploads 1300 - 800 = 500 megabytes worth of data . the second computer can upload 100 megabytes of data in 8 seconds . answer : b ."
Answer: b
Problem: a batsman makes a score of 88 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 40 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 88 = 17 x therefore x = 40 answer : c"
Answer: c
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 2 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 2 days = 2 ( 1 / 18 ) = 1 / 9 . answer d"
Answer: d
Problem: find the area between two concentric circles defined by x 2 + y 2 - 2 x + 4 y + 1 = 0 x 2 + y 2 - 2 x + 4 y - 11 = 0
Options: a ) 11 pi , b ) 12 pi , c ) 13 pi , d ) 14 pi , e ) 15 pi
Rationale: rewrite equations of circles in standard form . hence equation x 2 + y 2 - 2 x + 4 y + 1 = 0 may be written as ( x - 1 ) 2 + ( y + 2 ) 2 = 4 = 22 and equation x 2 + y 2 - 2 x + 4 y - 11 = 0 as ( x - 1 ) 2 + ( y + 2 ) 2 = 16 = 42 knowing the radii , the area of the ring is pi ( 4 ) 2 - pi ( 2 ) 2 = 12 pi correct answer is b ) 12 pi
Answer: b
Problem: stacy has a 63 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 8.5 , e ) 21
Rationale: "63 / 3 = 21 answer : e"
Answer: e
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 10 . what is the percent decrease ?
Options: a ) 90 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 10 = 90 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a"
Answer: a
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 3000 m 3 , b ) 4580 m 3 , c ) 18500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 2000 * 2 * 45 ) / 60 = 3000 m 3 answer : option a"
Answer: a
Problem: the sale price sarees listed for rs . 400 after successive discount is 20 % and 5 % is ?
Options: a ) 338 , b ) 277 , c ) 342 , d ) 882 , e ) 304
Rationale: "400 * ( 80 / 100 ) * ( 95 / 100 ) = 304 answer : e"
Answer: e
Problem: calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 5 , 8 , 11 and 15 seconds . ?
Options: a ) 1310 , b ) 1320 , c ) 1322 , d ) 1323 , e ) 1312
Rationale: lcm of 5 , 8 , 11 and 15 is 1320 lcm = 1320 answer : b
Answer: b
Problem: the price of 3 pants and 6 t - shirts is rs . 2250 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 1300 , b ) 1100 , c ) 1000 , d ) 1200 , e ) 800
Rationale: "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 2250 . . . . ( i ) and x + 12 y = 2250 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 750 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 2250 ( - ) x + 2 y = 750 - - - - - - - - - - - - - - - - 10 y = 1500 - - - - - - - - - - - - - - - - y = 150 cost of 8 t - shirts = 8 * 150 = 1200 answer : d"
Answer: d
Problem: a train running at the speed of 30 km / hr crosses a pole in 24 seconds . what is the length of the train ?
Options: a ) 200 m , b ) 250 m , c ) 300 m , d ) 350 m , e ) 400 m
Rationale: "speed = ( 30 * 5 / 18 ) m / sec = ( 25 / 3 ) m / sec length of the train = ( speed x time ) = ( 25 / 3 * 24 ) m = 200 m . answer : a"
Answer: a
Problem: - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 190 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 210 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 190 students answered yes only for subject m , then the remaining 310 students who answered yes for subject m , also answered yes for subject r . so , 310 students answered yes for both subjects . if 310 students answered yes for both subjects , then 400 - 310 = 90 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 90 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 90 + 300 ) = 210 students did not answer yes for either subject . answer : b ."
Answer: b
Problem: in may mrs lee ' s earnings were 45 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 50 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 45 in may rest of the family ' s income = 55 in june mrs lees income = 45 * 120 / 100 = 54 in june total income = 54 + 55 = 109 % of mrs lee ' s income = 54 / 109 = 49.54 ( a )"
Answer: a
Problem: 217 * 217 + 183 * 183
Options: a ) 70578 , b ) 82578 , c ) 80578 , d ) 80568 , e ) 89045
Rationale: "explanation : 1 / 2 × 2 ( a 2 + b 2 ) = 1 / 2 × [ ( a + b ) 2 + ( a − b ) 2 ] = 1 / 2 × [ ( 217 + 183 ) 2 + ( 217 − 183 ) 2 ] = 80578 option c"
Answer: c
Problem: the length of a bridge in meters , which a train 100 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 225 , b ) 245 , c ) 275 , d ) 325 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 100 = 375 meters x = 275 meters the answer is c ."
Answer: c
Problem: reema took a loan of rs 800 with simple interest for as many years as the rate of interest . if she paid rs . 632 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 8.62 % , b ) 8.88 % , c ) 8.32 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 800 ∗ r ∗ r / 100 = 632 = > r 2 = 79 = > r = 8.88 % option b"
Answer: b
Problem: pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 3 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 32 / 7 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 32 / 5 minutes
Rationale: pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 3 times fasterthan pipe a - - > the rate of b = 1 / 32 + 3 / 32 = 4 / 32 tank / minute . their combined rate = 1 / 32 + 4 / 32 = 5 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 5 minutes . answer : e
Answer: e
Problem: a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 49 km / hr , b ) 50 km / hr , c ) 45 km / hr , d ) 65 km / hr , e ) 87 km / hr
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : a"
Answer: a
Problem: divide $ 1000 among a , b in the ratio 1 : 4 . how many $ that b get ?
Options: a ) $ 500 , b ) $ 800 , c ) $ 1000 , d ) $ 200 , e ) $ 750
Rationale: "sum of ratio terms = 1 + 4 = 5 a = 1000 * 4 / 5 = $ 800 answer is b"
Answer: b
Problem: the positive number z is divisible by 4 . what is the remainder of dividing z ( 2 + 4 + z ) + 3 by 2 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: when we solve any of these equations : 28 + 3 ( z = 4 ) or 56 + 3 ( z = 8 ) we end up with numbers to which we have to subtract 1 to end up with a number that is exactly divisible by 2 . this is why we know that every result we get is going to have 1 as a remainder . hence answer is b .
Answer: b
Problem: an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is :
Options: a ) 2 , b ) 4 , c ) 8 , d ) 3 , e ) 1
Rationale: "5 / 8 * 16 = 10 3 / 8 * 16 = 6 ( 10 + x ) / 6 = 3 / 1 = 8 answer : c"
Answer: c
Problem: what is the value of ( 2 ) ^ - 6 ?
Options: a ) 1 / 62 , b ) 1 / 64 , c ) 1 / 65 , d ) 1 / 66 , e ) 1 / 67
Rationale: "2 ^ - 6 = 1 / ( 2 ) ^ 6 = 1 / 64 answer : b"
Answer: b
Problem: the population of a village is 7800 . it increases annually at the rate of 18 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 13000 , d ) 10860 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7800 × 118 / 100 × 118 / 100 = 10860 d"
Answer: d
Problem: find the numbers which are in the ratio 5 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 18 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 10 , 4,8 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 5 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 21 = > 5 x + 4 x = 18 = > x = 2 a , b , c are 5 x , 2 x , 4 x a , b , c are 10 , 4 , 8 . answer : c"
Answer: c
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 168 and for 36 kgs of apples is 186 then the cost of first 20 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 100 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 168 30 l + 6 q = 186 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 30 l = 150 = > l = 5 then we get l = 5 cost of 20 kgs of apples = 20 x 5 = 100 answer : d"
Answer: d
Problem: two trains 200 m and 160 m long run at the speed of 68 kmph and 40 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12 sec , e ) 15 sec
Rationale: "relative speed = 68 + 40 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 200 + 160 = 360 m required time = 360 * 1 / 30 = 12 sec answer is d"
Answer: d
Problem: the total age of a and b is 11 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 11 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 11 a - c = 11 answer is c"
Answer: c
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Answer: a
Problem: s = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set s and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs s , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 3 of the juniors is equal to 4 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 2 , d ) 2 / 7 , e ) 4 / 5
Rationale: "let total number of juniors = j total number of seniors = s ( 1 / 3 ) j = ( 4 / 3 ) s = > s = 1 / 4 j total number of students = j + s = ( 5 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 5 / 4 ) j ] = 4 / 5 answer e"
Answer: e
Problem: how many 7 in between 1 to 130 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 , 117,127 23 7 ' s between 1 to 130 answer : d"
Answer: d
Problem: given that 100.48 = x , 100.70 = y and xz = y ² , then the value of z is close to
Options: a ) 1.2 , b ) 1.45 , c ) 2.2 , d ) 2.9 , e ) none
Rationale: sol . xz = y ² ⇔ ( 10 0.48 ) z ( 100.70 ) 2 ( 10 0.48 z ) = 10 ( 2 × 0.70 ) = 101.40 ⇔ 0.48 z = 1.40 ⇔ z = 140 / 48 = 35 / 12 = 2.9 ( approx ) . answer d
Answer: d
Problem: the number of stamps that p and q had were in the ratio of 7 : 4 respectively . after p gave q 8 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: p started with 7 k stamps and q started with 4 k stamps . ( 7 k - 8 ) / ( 4 k + 8 ) = 6 / 5 35 k - 24 k = 48 + 40 11 k = 88 k = 8 p has 7 ( 8 ) - 8 = 48 stamps and q has 4 ( 8 ) + 8 = 40 stamps . the answer is b .
Answer: b
Problem: a certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water . if between 8 and 15 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 85 % = 291.55 so vol above water , between 68.6 and 51.45 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 85 % = 54.4 vol above water between 12.8 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 85 % = 106.25 vol above water between 18.75 - 25 ( sides are 4 cubic centimeters ) b"
Answer: b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 10 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 21
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 4.4 , so radius is 2.2 new area = 4.84 π increase in area is 0.84 π % increase in area = 0.84 / 4 * 100 so , % increase is 21 % answer will be ( e )"
Answer: e
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 25 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 20 , b ) 18 , c ) 21.4 , d ) 16 , e ) 10
Rationale: "step 1 ) took lcm of 20 and 25 . . came as 100 . step 2 ) 100 distance between b to c . . . do 100 / 25 hence 4 gallons used step 3 ) twice distance . . hence 100 * 2 = 200 . . . do as above . . 200 / 20 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 100 + 200 = 300 miles hence . . average of whole journey = 300 / 14 which comes to 21.4 answer : c"
Answer: c
Problem: the market value of a certain machine decreased by 20 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 4,800
Rationale: "e . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 20 / 100 ) = 8000 - 1600 = $ 6400 market value in 1984 = market value in 1983 - ( 20 % of $ 8000 ) = 6400 - 1600 = $ 4800"
Answer: e
Problem: sum of the squares of 3 no . ' s is 267 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 23 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = √ 529 = 23 d"
Answer: d
Problem: the average age of 10 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 30 , b ) 26 , c ) 28 , d ) 29 , e ) 45
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 10 ) = 26 years answer : b"
Answer: b
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability w that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . w = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 17 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 11 , b ) 444 , c ) 2881 , d ) 287 , e ) 456
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 17 + 21 = 38 t = 12 d = 38 * 12 = 456 answer : e"
Answer: e
Problem: in a college , 70 % of total 100 arts students are locals . 50 % of students from 200 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce .
Options: a ) 56 , b ) 86.7 , c ) 25.7 , d ) 66 , e ) 64.7
Rationale: "locals from arts = 70 % of 100 = 70 locals from science = 50 % of 200 = 100 locals from commerce = 85 % of 120 = 102 total local percentage = ( 70 + 100 + 102 ) / ( 100 + 200 + 120 ) = 272 / 420 = 0.647 e"
Answer: e
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` cow ' ' ?
Options: a ) 120 , b ) 123 , c ) 126 , d ) 129 , e ) 132
Rationale: "` ` cow ' ' = ( 3 + 15 + 23 ) * 3 = 123 . the answer is b ."
Answer: b
Problem: if the population of a certain country increases at the rate of 1 person every 60 seconds , by how many persons does the population increase in 2 hours ?
Options: a ) 120 , b ) 80 , c ) 100 , d ) 150 , e ) 140
Rationale: "answer = 1 * 120 ( 2 hour = 120 minutes ) = 120 answer = a"
Answer: a
Problem: a straight line in the xy - plane has y - intercept of 79 and slope of 6 . on this line the y - coordinate of the point is 14 , then what is the x - coordinate of the point ?
Options: a ) 11 , b ) - 10.83 , c ) 71 , d ) 20.83 , e ) - 12
Rationale: "eq of line = y = mx + c c = 79 m = 6 y = 14 substitute given : x = ( y - c ) / m = ( 14 - 79 ) / 6 = - 65 / 6 = - 10.83 correct option is b"
Answer: b
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area t covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads t = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Problem: 3 candidates in an election and received 5136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 48 % , c ) 57 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 5136 + 7636 + 11628 ) = 24400 so , required percentage = 11628 / 24400 * 100 = 48 % b"
Answer: b
Problem: 3550 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 3500 , d ) 2981 , e ) none of these
Rationale: "3550 - 50 = 3500 answer : c"
Answer: c
Problem: two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of z crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of z ?
Options: a ) z / 2 , b ) z , c ) 3 z / 2 , d ) 2 z , e ) 3 z
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( z ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Problem: a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 135 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 435 = 135 answer : a"
Answer: a
Problem: a waiter ' s salary consists of his salary and tips . during one week his tips were 3 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 3 / 7 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 3 / 4 = s * 7 / 4 tips = s * 3 / 4 fraction of his income came from tips = ( s * 3 / 4 ) / ( s * 7 / 4 ) = 3 / 7 answer : a"
Answer: a
Problem: the least number which must be subtracted from 509 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 5 , e ) e ) 6
Rationale: on dividing 509 by 9 , we get remainder = 5 therefore , required number to be subtracted = 5 answer : c
Answer: c
Problem: if x / y = 9 / 8 , then ( 8 x + 7 y ) / ( 8 x â € “ 7 y ) = ?
Options: a ) 8 , b ) 7 , c ) 10 , d ) 9 , e ) 6
Rationale: "answer dividing numerator as well as denominator by y , we get given exp . = ( 8 x + 7 y ) / ( 8 x â € “ 7 y ) = ( 8 x / y + 7 ) / ( 8 x / y â € “ 7 ) since x / y = 9 / 8 this implies that = [ ( 8 * 9 ) / 8 + 7 ] / [ ( 8 * 9 ) / 8 - 7 ) ] = ( 9 + 7 ) / ( 9 - 7 ) = 8 option : a"
Answer: a
Problem: a train 140 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 sec , b ) 16 sec , c ) 18 sec , d ) 11 sec , e ) 8 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 140 * 2 / 35 = 8 sec answer : e"
Answer: e
Problem: a person borrows rs . 8000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 8000 * 6 * 2 ) / 100 ] - [ ( 8000 * 4 * 2 ) / 100 ] 960 - 640 = 320 gain in 1 year = ( 320 / 2 ) = 160 rs answer : c"
Answer: c
Problem: the ages of two persons differ by 16 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,9 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 16 ) years . 5 ( x - 5 ) = ( x + 16 - 5 ) or 4 x = 36 or x = 9 . their present ages are 25 years and 9 years option c"
Answer: c
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 %
Rationale: "as everything is either fraction or percentage , the given figure 18360 is just a false alarm . we can do this by assuming that originally the branch had 100 volumes . originally : total - 100 fiction - 30 transferred : total - 33 ( one third of original total ) fiction - 11 ( one third of those transferred ) remaining : total - 100 − 33 = 67100 − 33 = 67 fiction - 30 − 11 = 1930 − 11 = 19 to find : 19 is what percent of 67 28.3 option c"
Answer: c
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 1 p . m . and travels towards b at 100 km / hr . another starts from b at 2 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 6 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 1 p . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 1 + 5 = 6 p . m . answer is b"
Answer: b
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 50 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 12 , b ) 10 , c ) 9 , d ) 8 , e ) 11
Rationale: the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 50 5 x - 10 = 50 5 x = 40 x = 8 answer : d
Answer: d
Problem: if 17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x , what is the units digit of x ?
Options: a ) 8 , b ) 3 , c ) 6 , d ) 7 , e ) 9
Rationale: "17 ^ 4 * 13 ^ 4 * 9 ^ 4 * 8 ^ 4 = x units digit of x will be 7 ^ 4 * 3 ^ 4 * 9 ^ 4 * 8 ^ 4 = 1 * 1 * 1 * 6 = 6 therefore , units digit of x = 6 answer c"
Answer: c
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.15 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 15 - cent increment ) and the the difference in sequential prices of the pots is 15 cents , the largest pot probably has a price that is a 15 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.75 1 1.15 1.3 1.45 1.6 1.75 total = $ 8.25 so this must be the answer . a"
Answer: a
Problem: a pipe can fill a cistern in 66 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 6 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 66 minutes 1 / 11 part filled in = 66 * 1 / 11 = 6 minutes answer is c"
Answer: c
Problem: a train crosses a platform of 160 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 110 , b ) 887 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 160 / 15 = x + 250 / 20 20 x + 3200 = 15 x + 3750 5 x = 550 x = 110 m answer : a"
Answer: a
Problem: if a = 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 + a ^ 6 ) ?
Options: a ) - 14 , b ) - 4 , c ) 0 , d ) 4 , e ) - 5
Rationale: "if a = - 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) + ( 1 ^ 6 ) ] = - [ 1 + 1 + 1 + 1 + 1 ] = - 5 answer = e = - 5"
Answer: e
Problem: a positive number x is multiplied by 2 , and this product is then divided by 5 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 3 / 2 because x is positive , x = 3 / 2 . the answer is b ."
Answer: b
Problem: if the number 892 , 132,26 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 132,24 x sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 6 = 18 ( ii ) ( i ) - ( ii ) = 15 + x - 18 = x - 3 hence x should be = 3 to make this a multiple of 11 ( 0 ) option c"
Answer: c
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.75 km and 1.10 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 66 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.75 + 1.10 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : d"
Answer: d
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 210 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 45 , c ) 39 : 40 , d ) 39 : 41 , e ) 39 : 42
Rationale: "3 : 4 a = 3 / 7 * 210 = 90 390 : 400 39 : 40 answer : a"
Answer: a
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 = › x - 153 = 22.50 = › x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer c"
Answer: c
Problem: if a and b are integers and ( a * b ) ^ 5 = 144 y , y could be :
Options: a ) 40 , b ) 48 , c ) 56 , d ) 62 , e ) 54
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 144 y find the prime factorization of 144 . this is 2 ^ 4 * 3 ^ 2 . we need 2 ^ 1 and 3 ^ 3 i . e 2 * 27 = 54 the answer is e ."
Answer: e
Problem: on dividing 23 by a number , the quotient is 4 and the remainder is 3 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "d = ( d - r ) / q = ( 23 - 3 ) / 4 = 20 / 4 = 5 d"
Answer: d
Problem: the diagonal of a rectangle is 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18 cm
b ) 28 cm
c ) 30 cm
d ) 38 cm
e ) 42 cm
Rationale: l 2 + b 2 = 41 . also , lb = 20 . ( l + b ) 2 = ( l 2 + b 2 ) + 2 lb = 41 + 40 = 81 ( l + b ) = 9 . perimeter = 2 ( l + b ) = 18 cm . a )
Answer: a
Problem: a boy is travelling from his home to school at 12 km / hr and reached 7 min late . next day he traveled at 16 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 12 km , b ) 13 km , c ) 14 km , d ) 15 km , e ) 16 km
Rationale: "let the distance be x t 1 = x / 12 hr t 2 = x / 16 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 12 - x / 16 = 1 / 4 x / 48 = 1 / 4 x = 12 km answer is a"
Answer: a
Problem: if a and b get profits of rs . 15,000 and rs . 5,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 1 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 15000 / 5000 = 3 : 1 answer : c"
Answer: c
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.4 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5
b ) 3.0
c ) 4.0
d ) 6.4
e ) 8.0
Rationale: let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.4 x = 6.4 alternate solution : try to backsolve . initial volume = 6.4 after one hour - - > ( 1 / 4 ) 6.4 = 1.6 after two hours - - > ( 1 / 4 ) 1.6 = 0.4 answer : d
Answer: d
Problem: the speed of a car is 10 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 85 kmph , c ) 35 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 10 + 60 ) / 2 = 35 kmph answer : c"
Answer: c
Problem: how many integers between 324,700 and 436,600 have tens digit 1 and units digit 3 ?
Options: a ) 327 , b ) 645 , c ) 987 , d ) 1119 , e ) 1339
Rationale: "the integers are : 324,713 324,813 etc . . . 436,513 the number of integers is 4366 - 3247 = 1119 the answer is d ."
Answer: d
Problem: plaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Options: a ) 54 , b ) 72 , c ) 96 , d ) 144 , e ) 432
Rationale: plaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a .
Answer: a
Problem: in town x , 64 percent of the population are employed , and 55 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 14 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 55 are employed males , hence 9 % are employed females . ( employed females ) / ( total employed people ) = 9 / 64 = 14 % answer : a ."
Answer: a
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 30 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 32 % , e ) 60 %
Rationale: "in the first plot 30 % of 300 seeds germinated , so 0.3 x 300 = 90 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 90 + 70 = 260 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 160 / 500 ) x 100 % , or 32 % . answer : d ."
Answer: d
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of a + b ?
Options: a ) 110 , b ) 100 , c ) 190 , d ) 200 , e ) 210
Rationale: "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 a + b = 110 + 100 = 210 ans : e"
Answer: e
Problem: a car takes 6 hours to cover a distance of 540 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 35 kmph , b ) 48 kmph , c ) 52 kmph , d ) 54 kmph , e ) 60 kmph
Rationale: "time = 6 distance = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph e )"
Answer: e
Problem: how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 50 * 4 = 200 m time taken = 200 * 3 / 10 = 60 sec answer is c"
Answer: c
Problem: a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 th innings ?
Options: a ) 28 , b ) 27 , c ) 12 , d ) 37 , e ) 01
Rationale: "explanation : 16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"
Answer: d
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 5 such machines produce in 4 minutes ?
Options: a ) 900 , b ) 1,800 , c ) 2,700 , d ) 10,800 , e ) 64,800
Rationale: "6 machines produce 270 bottles per minute ; 1 machine produces 270 / 6 = 45 bottles per minute ; 5 machines produce 45 * 5 = 225 bottles per minute ; in 4 minutes 10 machines produce 225 * 4 = 900 bottles . answer : a ."
Answer: a
Problem: when a train travels at a speed of 70 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 37.5 km , b ) 50.5 km , c ) 60 km , d ) 85.5 km , e ) 95 km
Rationale: "let x be the time reached with the speed 70 km / h 50 km / h - - - - > x + 15 distance is equal so 70 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 70 x = 50 x + 750 so the would be in km and x = 37.5 answer : a"
Answer: a
Problem: p , q and r have $ 9000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 3600 , c ) 3998 , d ) 2539 , e ) 1930
Rationale: "b 3600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 ."
Answer: b
Problem: if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is - .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 7 / 8 , d ) 3 / 4 , e ) 7 / 3
Rationale: "answer : option b the number of exhaustive outcomes is 36 . let e be the event of getting an even number on one die and an odd number on the other . let the event of getting either both even or both odd then = 18 / 36 = 1 / 2 p ( e ) = 1 - 1 / 2 = 1 / 2 ."
Answer: b
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 2 years hence ?
Options: a ) 58 , b ) 59 , c ) 64 , d ) 70 , e ) 74
Rationale: "explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 2 years , their ages will be 42 and 22 . sum of their ages = 42 + 22 = 64 . c )"
Answer: c
Problem: what is the units digit of the expression 13 ^ 27 + 1 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 8 , e ) 9
Rationale: "power of 3 follows repetition pattern of = 3 , 9 , 7 , 1 , 3 , 9 , 7 , 1 . . . . repetition after 4 powers = ( 3 , 9 , 7 , 1 ) 13 ^ 27 = 27 th power = 24 + 3 24 / 4 = 6 ( 6 repetitions ) + 3 = ` ` 7 ' ' 7 + 1 = 8 answer d"
Answer: d