regisss/math_qa huggingface dataset:
Problem: a monkey start climbing up a tree 21 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 18 hrs it wil be 18 ft . but since the height of the tree is 21 ft , so if the monkey hops up the tree in the next hr i . e 19 th hr then it reaches at the top of the tree . hence it takes 19 hrs for monkey to reach at the top answer : c"
Answer: c
Problem: john makes $ 50 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 15 % , b ) 16.66 % , c ) 50 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 25 / 50 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c"
Answer: c
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 6400 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 2009 , e ) 22888
Rationale: "6400 * 9 / 8 * 9 / 8 = 8100 answer : a"
Answer: a
Problem: oil cans x and y are right circular cylinders and the height and radius of y are each thrice those of x . if the oil in can x filled to capacity sells for $ 4 , how much does the oil in y sell for if y is only 1 / 3 rd filled ?
Options: a ) $ 30 , b ) $ 25 , c ) $ 36 , d ) $ 40 , e ) $ 28
Rationale: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 27 * vy y when 1 / 3 rd filled will cost 9 times x so ans is c"
Answer: c
Problem: an alloy weighing 60 ounces is 20 percent copper . how many ounces of copper must be added to create an alloy that is 60 percent copper ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "an alloy of 60 oz which is 20 % copper means there is 12 oz of gold . to get to an alloy that is 60 % copper , let ' s use this expression : ( 12 + x ) / ( 60 + x ) = 0.60 with x representing the amount of pure copper that must be added to get to 60 % . the expression we are using represents the new total weight of pure copper over the new total weight of the alloy and this fraction should represent 60 % or 0.6 . you will see that 60 is the correct answer , as 72 / 120 = 0.6 choose c"
Answer: c
Problem: by selling 16 pens for a rupee a woman loses 5 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 13 , e ) 65
Rationale: d 95 % - - - 16 118 % - - - ? 95 / 118 * 16 = 13
Answer: d
Problem: a and b complete a work in 30 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1873 days , c ) 0.0673 days , d ) 0.0583 days , e ) 0.0773 days
Rationale: "1 / 30 + 1 / 40 = 0.0583 days answer : d"
Answer: d
Problem: an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1200 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 2700 , c ) 540 , d ) 640 , e ) 720
Rationale: "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1200 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1200 - - > { not on display } = 1800 . according to ( i ) 2 / 3 * { total } = 1800 - - > { total } = 2700 . answer : b ."
Answer: b
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12600 after a year ?
Options: a ) 3630 , b ) 3637 , c ) 3630 , d ) 3631 , e ) 3780
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12600 = 3780 answer : e"
Answer: e
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.45 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 7.30
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.45 ) = $ 6.3 ( as the charge is 0.45 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 6.3 = 7.3 answer is e ."
Answer: e
Problem: a and b together can do a work in 3 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 4 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 3 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 3 - ( 1 / 12 ) = 4 days answer : option a"
Answer: a
Problem: the distance from city a to city b is 180 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 120 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
Options: a ) 42 , b ) 45 , c ) 46 , d ) 48 , e ) 50
Rationale: "the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 4 hours for the trip . dan needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is b ."
Answer: b
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents c watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , c is 21 . d is the correct answer
Answer: d
Problem: find the lowest positive integer that can be divided by all the even numbers between 14 and 21 .
Options: a ) 4581 , b ) 5040 , c ) 3682 , d ) 1231 , e ) 1563
Rationale: the even numbers between 14 and 21 are 1416 , 1820 . find the lcm of these numbers lcm = 2 ^ 4 * 7 * 3 ^ 2 * 5 the answer is b )
Answer: b
Problem: by combining number of small cubes , a larger cube is produced . the ratio between volume of larger cube and small cube is 1000 : 8 then how many small cubes are required to produce a larger cube ?
Options: a ) 100
b ) 2
c ) 5
d ) 125
e ) 80
Rationale: the ratio is a 13 : a 23 = 1000 : 8 then number small cubes requiered is 1000 / 8 = 125 so the answre is d
Answer: d
Problem: jacob is now 12 years younger than michael . if 3 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 15 , d ) 21 , e ) 13
Rationale: "jacob = x years , mike = x + 12 years 3 years from now , 2 ( x + 3 ) = x + 15 2 x + 6 = x + 15 x = 9 x + 4 = 13 years answer e"
Answer: e
Problem: the area of a triangle will be when a = 2 m , b = 5 m , c = 7 m , a , b , c being lengths of respective sides ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 4
Rationale: "s = ( 2 + 5 + 7 ) / 2 = 7 answer : b"
Answer: b
Problem: in a certain circle there are 10 points . what is the number of the triangles connecting 2 points of the 10 points ?
Options: a ) 40 , b ) 45 , c ) 108 , d ) 120 , e ) 132
Rationale: "imo : b here we have to select 2 points out of 10 points . order is not important so the answer will be 10 c 2 = 45 answer b"
Answer: b
Problem: the length of the bridge , which a train 140 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 x = 235 m . answer : option a"
Answer: a
Problem: a 8000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 48
Rationale: in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 4,000 by that net inflow to get the minutes ) - 48 min . answer e .
Answer: e
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 124 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1800
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 4 yearned with the compound interest is the percent yearned on percent . so , $ 4 is yearned on $ 60 , which means that the interest = 15 % . this on the other hand means that half of the savings = 60 * 15 = $ 900 . twice of that = $ 1,800 . answer : e ."
Answer: e
Problem: abcd is a square where ab = â ˆ š 6000 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 6000 / 2 = 3000 . correct answer e"
Answer: e
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8410 / - . find out the amount that he borrowed .
Options: a ) s . 5266 , b ) s . 5269 , c ) s . 5461 , d ) s . 5218 , e ) s . 52192
Rationale: explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8410 = p + ( 54 p / 100 ) 8410 = ( 100 p + 54 p ) / 100 8410 = 154 p / 100 p = ( 8410 * 100 ) / 154 = rs . 5461.039 answer : c
Answer: c
Problem: the perimeter of a semi circle is 108 cm then the radius is ?
Options: a ) 17 , b ) 21 , c ) 19 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 108 = > r = 21 answer : b"
Answer: b
Problem: the length of a rectangle is one - sixth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1296 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 560 sq . units
b ) 360 sq . units
c ) 260 sq . units
d ) 460 sq . units
e ) 160 sq . units
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1296 = 36 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 36 * 10 = 360 sq . units answer : b
Answer: b
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 35 inclusive .
Options: a ) 288 , b ) 364 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 13 to 35 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 35 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 33 = 48 now we have proof that there is no middle term . we have 6 bunches of 48 . 6 ( 48 ) = 288 a"
Answer: a
Problem: the function f ( n ) is defined as the product of all the consecutive positive integers between 4 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 4 answer : d
Answer: d
Problem: in a shower , 5 cm of rain falls . the volume of water that falls on 1.5 hectares of ground is :
Options: a ) 75 cu . m
b ) 750 cu . m
c ) 7500 cu . m
d ) 75000 cu . m
e ) none of these
Rationale: solution area = ( 1.5 × 10000 ) m 2 = 45000 m 2 . depth = m = m . ∴ volume = ( area × depth ) = m 3 = 750 m 3 . answer b
Answer: b
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 200 ?
Options: a ) 48 , b ) 49 , c ) 50 , d ) 51 , e ) 52
Rationale: from first constraint 4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 200 4 n < 193 n < 48 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 48 ( 48 integers ) and n = - 1 and 0 so 50 integers . c is the answer
Answer: c
Problem: in the first 10 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 8.28 , c ) 6.11 , d ) 8.7 , e ) 8.11
Rationale: "required run rate = [ 282 - ( 2.1 * 10 ) ] / 30 = 261 / 30 = 8.70 answer : d"
Answer: d
Problem: 5216 x 51 = ?
Options: a ) 212016 , b ) 266016 , c ) 266436 , d ) 216314 , e ) 216318
Rationale: "normal way of multiplication may take time . here are one alternative . 5216 x 51 = ( 5216 x 50 ) + 5216 = ( 5216 x 100 ) / 2 + 5216 = 521600 / 2 + 5216 = 260800 + 5216 = 266016 answer is b"
Answer: b
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1857.14
Rationale: "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 70 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 70 = 1857.14 e is the answer"
Answer: e
Problem: a car takes 6 hours to cover a distance of 720 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 ) 60 , b ) 50 , c ) 80 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 720 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 720 / 9 = 80 kmph answer c ."
Answer: c
Problem: by selling 15 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 89 , e ) 81
Rationale: "85 % - - - 15 115 % - - - ? 15 / 115 * 15 = 11 answer : c"
Answer: c
Problem: the consumption of diesel per hour of a bus varies directly as square of its speed . when the bus is travelling at 50 kmph its consumption is 1 litre per hour . if each litre costs $ 50 and other expenses per hous is $ 50 , then what would be the minimum expenditure required to cover a distance of 500 km ?
Options: a ) 800 , b ) 950 , c ) 900 , d ) 1000 , e ) 1250
Rationale: "50 kmph consumption is 1 lt / hr so 500 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 50 so 10 lt costs $ 500 extra expenses for 1 hr - $ 50 10 hrs - $ 500 total expense - $ 500 + $ 500 = $ 1000 answer : d"
Answer: d
Problem: a man can row at 5 kmph in still water . if the velocity of current is 2 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.1 km , b ) 2.9 km , c ) 3.4 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 2 ) = 7 kmph speed upstream = ( 5 - 2 ) = 3 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 7 + x / 3 = 1 â ‡ ’ 3 x + 7 x = 21 â ‡ ’ 10 x = 21 â ‡ ’ x = 2.1 km answer : option a"
Answer: a
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: clearly d a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . 96 has more number of smaller prime factor thats the clue ! ! = d
Answer: d
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 24 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 24 ( 2 ^ 3 * 3 ) , sob = 2 ^ 3 or 2 ^ 3 * 3 ( 8 or 24 ) . combining 2 premises shows the answer is a ( 8 ) ."
Answer: a
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 7000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 28000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 7,000 * 2 ) * 2 = $ 28,000 ( after 9 years investment will become $ 7,000 * 2 = $ 14,000 and in another 9 years it ' ll become $ 14,000 * 2 = $ 28,000 ) . answer : a ."
Answer: a
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1480 ?
Options: a ) 228 , b ) 217 , c ) 100 , d ) 288 , e ) 772
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs . answer : c"
Answer: c
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of m + 2 n ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 25 , e ) 40
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 10 + 15 * 2 = 40 answer : e"
Answer: e
Problem: if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 14 , b ) 8 , c ) 12 , d ) 4 , e ) 18
Rationale: "let length of rectangle = l 4 ^ 2 = l * 4 = > l = 16 / 4 = 4 answer d"
Answer: d
Problem: what is the average ( arithmetic mean ) of the numbers 21 , 22 , 23 , 23 , 24 , and 25 ?
Options: a ) 23.0 , b ) 22.5 , c ) 21 , d ) 24 , e ) 23
Rationale: "{ 21 , 22 , 23 , 23 , 24 , 25 } = { 23 - 2,23 - 1 , 23 , 23,23 + 1,23 + 2 } - - > the average = 23 . answer : e ."
Answer: e
Problem: the average age of 28 students in a group is 16 years . when teacher â € ™ s age is included to it , the average increases by one . what is the teacher â € ™ s age in years ?
Options: a ) 45 , b ) 36 , c ) 41 , d ) 51 , e ) 48
Rationale: "sol . age of the teacher = ( 29 ã — 17 â € “ 28 ã — 16 ) years = 45 years . answer a"
Answer: a
Problem: a and b are two stations 390 km apart . a train starts from a at 10 a . m . and travels towards b at 65 kmph . another train starts from b at 11 a . m . and travels towards a at 35 kmph . at what time do they meet ?
Options: a ) 2.15 pm , b ) 1.15 pm , c ) 4.15 pm , d ) 3.15 pm , e ) 12.15 pm
Rationale: suppose they meet x hours after 10 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 390 . 65 x + 35 ( x - 1 ) = 390 = > 100 x = 425 = > x = 17 / 4 so , they meet 4 hrs . 15 min . after 10 a . m i . e . , at 2.15 p . m . answer a
Answer: a
Problem: in a group of cows and chickens , the number of legs was 16 more than twice the number of heads . the number of cows was :
Options: a ) 8 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 16 more than twice the number of heads . therefore , 2 × ( x + y ) + 16 = 4 x + 2 y . or , 2 x + 2 y + 16 = 4 x + 2 y . or , 2 x + 16 = 4 x [ subtracting 2 y from both sides ] . or , 16 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 16 = 2 x . or , x = 8 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 . correct answer : a ) 8"
Answer: a
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 5000 and b rs . 1000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 8160 , e ) 7291
Rationale: "5000 : 1000 = > 5 : 1 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 5 / 6 = 7200 + 960 = 8160 answer : d"
Answer: d
Problem: how much 90 % of 40 is greater than 80 % of 30 ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 18
Rationale: "( 90 / 100 ) * 40 – ( 80 / 100 ) * 30 36 - 24 = 12 answer : a"
Answer: a
Problem: an auction house charges a commission of 20 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 190,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.2 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 190,000 ( 20 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : b ."
Answer: b
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 3 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 1
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 3 ) = 36 / 12 = 3 / 1 . answer : e ."
Answer: e
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned ?
Options: a ) 19828.29 , b ) 19828.2 , c ) 19828.8 , d ) 19828.88 , e ) 19828.21
Rationale: "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : c"
Answer: c
Problem: a man took loan from a bank at the rate of 13 % p . a . s . i . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was ?
Options: a ) rs . 1846 , b ) rs . 18846 , c ) rs . 13846 , d ) rs . 2000 , e ) rs . 14846
Rationale: "principal = ( 100 * 5400 ) / ( 13 * 3 ) = rs . 13846 answer : c"
Answer: c
Problem: a sum amounts to rs . 4410 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) rs . 4000 , b ) rs . 5000 , c ) rs . 4500 , d ) rs . 4800 , e ) rs . 5800
Rationale: ci = 4410 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4410 = p [ 21 / 20 ] ^ 2 4410 [ 20 / 21 ] ^ 2 4000 answer : a
Answer: a
Problem: a man can row downstream at 18 kmph and upstream at 8 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 8 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 26 = > x = 13 , y = 5 . answer : b"
Answer: b
Problem: the compound ratio of 2 / 3 , 6 / 7 , 1 / 5 and 1 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 1 / 98 , d ) 3 / 350 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 1 / 5 * 1 / 8 = 12 / 1400 = 3 / 350 answer : d"
Answer: d
Problem: how many of the positive factors of 14 are not factors of 21 ?
Options: a ) 4 , b ) 3 , c ) 1 , d ) 2 , e ) 0
Rationale: "factors of 14 - 1 , 2 , 7 , 14 , factors of 21 - 1 , 3 , 7 , 21 , comparing both , we have three factors of 14 which are not factors of 21 - 2,14 the answer is c"
Answer: c
Problem: how much water must be added to 60 litres of milk at 1.5 litres for rs . 20 so as to have a mixture worth rs . 32 / 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) 21 litres
Rationale: c . p . of 1 litre of milk = rs . 20 × 2 / 3 = rs . 40 / 3 . c . p . of 1 litre of water = rs 0 . mean price = rs . 32 / 3 . by the rule of alligation , we have : c . p of 1 litre c . p of 1 litre of water of milk ( 0 ) ( rs . 40 / 3 ) \ / mean price ( rs . 32 / 3 ) / \ 40 / 3 − 32 / 3 32 / ( 3 − 0 ) 8 / 3 32 / 3 the ratio of water and milk = 8 / 3 : 32 / 3 . = 8 : 32 = 1 : 4 . thus , quantity of water to be added to 60 litres of milk : = ( 1 / 4 ) × 60 litres . = 15 litres . answer : c
Answer: c
Problem: a cricket bat is sold for $ 850 , making a profit of $ 255 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 43 %
Rationale: "255 / ( 850 - 255 ) = 255 / 595 = 51 / 119 = 43 % . answer : e ."
Answer: e
Problem: a car covers a distance of 624 km in 2 3 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 194 kmph , c ) 109 kmph , d ) 174 kmph , e ) 240 kmph
Rationale: 624 / 2 3 / 5 = 240 kmph answer : e
Answer: e
Problem: three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 30 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 36 square meters , c ) 42 square meters , d ) 45 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 30 = 90 sq m of the wallpaper overlaps in three layers . 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m . answer ( d ) ."
Answer: d
Problem: the average of first three prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50
Rationale: "23 + 29 + 31 = 83 / 3 = 27.7 answer : d"
Answer: d
Problem: if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 40 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 60 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ?
Options: a ) $ 50 , b ) $ 64 , c ) $ 75 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a"
Answer: a
Problem: the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ?
Options: a ) 120 cm , b ) 150 cm , c ) 160 cm , d ) 190 cm , e ) of these
Rationale: let the heights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 150 = > 5 k = 150 = > k = 30 therefore the height of the lightest boy = 4 k = 4 ( 30 ) = 120 cm . answer : a
Answer: a
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 29 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 15 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 29 = 61 - - > c = 5 / 9 * 29 = 16.11 . increase = 16.11 degrees . answer : b ."
Answer: b
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and auniform after 1 year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?
Options: a ) rs . 80 , b ) rs . 100 , c ) rs . 120 , d ) rs . 145 , e ) rs . 156
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Problem: the sale price of a trolley bag including the sale tax is rs . 1190 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 800 , b ) rs 820 , c ) rs 860 , d ) rs 850 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 1190 s . p . = rs . ( 1190 x 100 / 112 ) = rs . 1062.50 . c . p . = rs ( 100 / 125 x 1062.50 ) = rs 850 answer : d"
Answer: d
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 6 years hence ?
Options: a ) 22 , b ) 77 , c ) 70 , d ) 98 , e ) 72
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 6 years , their ages will be 46 and 26 . sum of their ages = 46 + 26 = 72 . answer : e"
Answer: e
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 5 m wide at the top and 3 m wide at the bottom and the area of cross - section is 3800 sq m , the depth of cannel is ?
Options: a ) 920 , b ) 930 , c ) 940 , d ) 950 , e ) 960
Rationale: "1 / 2 * d ( 5 + 3 ) = 3800 d = 950 answer : d"
Answer: d
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 74 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 74 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 70 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 70 / 10 = 7 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 7 = 28 + 4 = 32 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 32 / 4 = 8 hrs . . . answer e"
Answer: e
Problem: the two sides of a triangle are 32 and 68 . the area is 960 sq . cm . find the third side of triangle ?
Options: a ) 45
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: we see 68 ^ 2 - 32 ^ 2 = ( 68 + 32 ) * ( 68 - 32 ) = 100 * 36 = 60 ^ 2 now ( 1 / 2 ) * 60 * 32 = 960 ( match with given options ) ( i . e area of a right angled triangle whose sides are 32 , 60,68 ) third side = 60 answer : c
Answer: c
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 40 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 126 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 40 % = 90 * 1.2 = 126 thus ratio = 126 / 100 = 1.26 ( in % terms = 126 % ) . thus b is the correct answer ."
Answer: b
Problem: if 9 a - b = 10 b + 80 = - 12 b - 2 a , what is the value of 9 a - 11 b ?
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 80
Rationale: "this implies 9 a - b = 10 b + 80 , 9 a - b = - 12 b - 2 a , 10 b + 80 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = 10 b + 80 = = > 9 a - 11 b = 80 answer is e"
Answer: e
Problem: john makes $ 50 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 40 %
Rationale: "increase = ( 20 / 50 ) * 100 = 40 % . e"
Answer: e
Problem: the perimeter of one face of a cube is 48 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 625 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 48 / 4 = 12 cm volume = a * a * a = 12 * 12 * 12 = 1728 cm cube option e"
Answer: e
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 1 ) and ( 5 , 1 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 6 , d ) 3 , e ) 1 / 4
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 0.5 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 0.5 ) is 0.5 / 3 = 1 / 6 . the answer is c ."
Answer: c
Problem: on a game show , there are 3 tables . each table has 3 boxes ( one zonk ! , one cash prize , and one grand prize ) . the contestant can choose one box from each table for a total of 3 boxes . if any of the boxes are a zonk ! , the contestant loses everything . what is the probability of getting no zonk ! from any of the 3 boxes chosen ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 8 / 27 , d ) 1 / 27 , e ) 7 / 8
Rationale: no zonk ! : 1 st box = no zonk ! = 2 / 3 2 nd box = no zonk ! = 2 / 3 3 rd box = no zonk ! = 2 / 3 ( 2 / 3 ) ( 2 / 3 ) ( 2 / 3 ) = 8 / 27 8 / 27 is the probability of no zonk ! , so . . . answer : c
Answer: c
Problem: the average weight of a , b and c is 42 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 33 kg , b ) 31 kg , c ) 32 kg , d ) 40 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 42 x 3 ) = 126 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 40 . b ' s weight = 40 kg . d"
Answer: d
Problem: dividing by 3 ⁄ 8 and then multiplying by 5 ⁄ 9 is the same as dividing by what number ?
Options: a ) 31 ⁄ 5 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 40 / 27 , e ) 5 ⁄ 16
Rationale: say x / 3 / 8 * 5 / 9 = x * 8 / 3 * 5 / 9 = x * 40 / 27 d
Answer: d
Problem: how many integers n greater than and less than 100 are there such that , if the digits of n are reversed , the resulting integer is n + 9 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: ( 10 x + y ) = ( 10 y + x ) + 9 = > 9 x - 9 y = 9 = > x - y = 1 and only 8 numbers satisfy this condition and the numbers are 21,32 , 43,54 , 65,76 , 87,98 answer : d
Answer: d
Problem: a runs twice as fast as b and gives b a start of 50 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 50 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 50 m is 50 / 1 = 50 m so the total time taken by a and b to reach = 2 * 50 = 100 m answer : d"
Answer: d
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 12 % ?
Options: a ) 20 % , b ) 25 % , c ) 13 1 / 30 % , d ) 32 % , e ) 13 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 88 2 / 3 sp 1 = 88 sp 1 = 132 100 - - - 32 = > 32 % answer : d"
Answer: d
Problem: reeya obtained 65 , 67 , 76 , 80 and 95 out of 100 in different subjects , what will be the average
Options: a ) 76.6 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: explanation : ( 65 + 67 + 76 + 80 + 95 / 5 ) = 76.6 option a
Answer: a
Problem: an ant walks an average of 600 meters in 12 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 . , b ) 2.55 , c ) 2.775 . , d ) 3.2 . , e ) 3.5 .
Rationale: "the ant walks an average of 600 meters in 12 minutes 600 meters in 1 / 5 hours the beetle walks 15 % less distance = 600 - 90 = 510 meters in 12 minutes 0.510 km in 12 / 60 = 1 / 5 hours speed = 0.510 * 5 = 2.55 km / h correct answer b = 2.55"
Answer: b
Problem: an aeroplane covers a certain distance of 450 kmph in 4 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 490 , c ) 640 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 450 kmph distance travelled in 4 hours = 450 * 4 = 1800 km speed of aeroplane to acver 1800 km in 11 / 3 = 1800 * 3 / 11 = 490 km answer b ."
Answer: b
Problem: when the number 72 y 6139 is exactly divisible by 11 , then the smallest whole number that can replace y is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "the given number = 72 y 6139 sum of the odd places = 9 + 1 + y + 7 sum of the even places = 3 + 6 + 2 = 11 ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) ( 16 + y ) - ( 11 ) = divisible by 11 y � 5 = divisible by 11 . y must be 6 , to make given number divisible by 11 . d"
Answer: d
Problem: a 12 month project had a total budget of $ 42000 . after 8 months , the project had spent $ 23700 . at this point , how much was the project under budget ?
Options: a ) $ 4100 , b ) $ 4300 , c ) $ 4500 , d ) $ 4700 , e ) $ 4900
Rationale: each month , the project should spend $ 42,000 / 12 = $ 3500 . in 8 months , the project should spend 8 * $ 3500 = $ 28,000 . the project is under budget by $ 28,000 - $ 23,700 = $ 4300 . the answer is b .
Answer: b
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 4 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 16 , which also equals b . b is the second positive multiple of n , thus n = 16 / 2 = 8 . the answer is d ."
Answer: d
Problem: a cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm . find the total area of the wet surface .
Options: a ) 102 m sqaure , b ) 100 m sqaure , c ) 152 m sqaure , d ) 164 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 1.85 + 8 * 1.85 ) ] + 8 * 6 = 100 m square option b"
Answer: b
Problem: the ratio of buses to cars on river road is 1 to 13 . if there are 60 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 65 , b ) 60 , c ) 55 , d ) 40 , e ) 45
Rationale: "b / c = 1 / 13 c - b = 60 . . . . . . . . . > b = c - 60 ( c - 60 ) / c = 1 / 13 testing answers . clearly eliminate bcde put c = 65 . . . . . . . . . > ( 65 - 60 ) / 65 = 5 / 65 = 1 / 13 answer : a"
Answer: a
Problem: if a takes x days to do a work then b takes 2 x days to do the same work then with in how many day ' s a will alone complete this work ?
Options: a ) 27 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: 1 / x + 1 / 2 x = 1 / 18 = > 3 / 2 x = 1 / 18 = > x = 27 days . hence , a alone can finish the work in 27 days . answer : a
Answer: a
Problem: 62 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 154 , e ) 256
Rationale: "62 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 62 = 154 hence , d is the answer ."
Answer: d
Problem: if you throw two dice at a same time . can you find the probability of getting sum as 10 of the two numbers shown ?
Options: a ) 1 / 16 , b ) 2 / 14 , c ) 1 / 12 , d ) 1 / 19 , e ) 1 / 17
Rationale: c 1 / 12 all possible cases can be 36 ( 6 * 6 ) case we need : [ ( 4,6 ) , ( 5,5 ) , ( 6,4 ) ] = 3 probability = > 3 / 36 = 1 / 12
Answer: c
Problem: in an office , 30 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 480 , b ) 48 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 30 / 100 ) * workers = x + 16 = > x = 48 answer b"
Answer: b
Problem: the least number which must be subtracted from 820 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 1 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 820 by 9 , we get remainder = 1 therefore , required number to be subtracted = 1 answer : c"
Answer: c
Problem: can n and can в are both right circular cylinders . the radius of can n is twice the radius of can b , while the height of can n is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can n with the same brand of gasoline ?
Options: a ) $ 1
b ) $ 2
c ) $ 4
d ) $ 8
e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of n = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 120 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 27 % , e ) 40 %
Rationale: "total time for travelling 120 miles @ 60 mph = 120 / 60 = 2 hour = 120 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 120 minutes it will use = 3 gallons . thus , full tank = 3 + 8 = 11 gallons - - - > 3 / 11 = 27 % of the fuel used . d is the correct answer ."
Answer: d
Problem: if the sides of a triangle are 39 cm , 36 cm and 15 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 765 cm 2 , c ) 216 cm 2 , d ) 270 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 39 cm , 36 cm and 15 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : d"
Answer: d
Problem: what is the dividend . divisor 19 , the quotient is 7 and the remainder is 6
Options: a ) 136 , b ) 137 , c ) 138 , d ) 139 , e ) 140
Rationale: "d = d * q + r d = 19 * 7 + 6 d = 133 + 6 d = 139"
Answer: d
Problem: obra drove 120 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 18.75 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 120 π / 480 π = 25 % hence , answer is d ."
Answer: d
Problem: some persons can do a piece of work in 20 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "20 / ( 2 * 2 ) = 5 days answer : c"
Answer: c
Problem: if paint costs $ 3.20 per quart , and a quart covers 1200 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60
b ) $ 16.00
c ) $ 96.00
d ) $ 108.00
e ) $ 196.00
Rationale: total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 1200 = 0.5 cost will be 0.5 * 3.2 = $ 1.6 ans : a
Answer: a
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft
b ) 25 ft
c ) 750 ft
d ) 900 ft
e ) 1650 ft
Rationale: point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 33 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 50 . sub x = 50 either in ( x + 5 ) * 30 or in x * 33 to get the distance , which is 1650 . so the correct choice is e .
Answer: e
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length w of a cube whose surface area is equal to 6 z ?
Options: a ) w = 16 , b ) w = 8 √ 2 , c ) w = 8 , d ) w = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Problem: if 50 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 42.8 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 20 % of ( x + y ) 50 / 100 ( x - y ) = 20 / 100 ( x + y ) 3 x = 7 y required percentage = y / x * 100 = 3 y / 7 y * 100 = 42.85 % answer is b"
Answer: b