regisss/math_qa huggingface dataset:
Problem: what is the total number of prime numbers less than 70 ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: solution prime numbers less than 70 are = 12 . 2,3 , 5,7 , 11,13 , 17,19 , 23,29 , 31,37 , 41,43 , 47,53 , 59,61 , and 67 their number is 19 . answer c
Answer: c
Problem: 3 / 5 of all married couples have more than one child . 1 / 2 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 7 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 3 / 5 of 100 couples have more than one child = 60 couples . 1 / 2 of 100 couples have more than 3 kids = 50 couples . this implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples , which equals 40 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 60 - 50 = 10 . fraction will be 10 / 100 = 1 / 10 . option b"
Answer: b
Problem: at a special sale , 6 tickets can be purchased for the price of 3 tickets . if 6 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 6 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 50 % , e ) 66.6 %
Rationale: let the price of a ticket be rs . 100 , so 3 tickets cost 300 & 6 tickets cost 600 6 tickets purchased at price of 3 tickets ie . , for 300 , so amount saved s rs . 300 , % of 6 tickets = ( 300 / 600 ) * 100 = 50 % answer : d
Answer: d
Problem: a 4 - digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1 , 2 , 4 , and 6 at all . if repeated digits are allowed , what is the probability that it has at least one even digit ?
Options: a ) 23 / 24 , b ) 31 / 36 , c ) 55 / 64 , d ) 65 / 81 , e ) 75 / 121
Rationale: p ( no even digits ) = 2 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 16 / 81 p ( at least one even digit ) = 1 - 16 / 81 = 65 / 81 the answer is d .
Answer: d
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 15 % ?
Options: a ) 228 , b ) 480 , c ) 267 , d ) 288 , e ) 544
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 96 sp = cp - loss = 640 - 96 = rs . 544 answer : e"
Answer: e
Problem: the speed of a train is 120 kmph . what is the distance covered by it in 10 minutes ?
Options: a ) 26 kmph , b ) 20 kmph , c ) 28 kmph , d ) 30 kmph , e ) 40 kmph
Rationale: "120 * 10 / 60 = 20 kmph answer : b"
Answer: b
Problem: from a total of 4 boys and 4 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 36 , c ) 60 , d ) 120 , e ) 240
Rationale: "answer = b = 36 no of 4 person committees that can be formed = 4 c 2 * 4 c 2 = 36 answer b"
Answer: b
Problem: if an article is sold at 20 % profit instead of 14 % profit , then the profit would be rs . 180 more . what is the cost price ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 3000 , d ) rs . 4000 , e ) rs . 5200
Rationale: "explanation : let the cost price of an article be rs . x . ( 20 % of x ) - ( 14 % of x ) = 180 20 x / 100 - 14 x / 100 = 105 = > 6 x = 180 * 100 = > x = 3000 cost price = rs . 3000 answer : c"
Answer: c
Problem: find the greatest number that exactly divides 35 , 91 and 840 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the greatest number that exactly divides 35 , 91 and 840 is the hcf of the three numbers . so , calculating hcf we get the answer 7 . answer : c"
Answer: c
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 3 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 168 , b ) 144 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 3 ) * 360 = 120 gallons . remaning paint = 240 gallons paint used in the second week = ( 1 / 5 ) * 240 = 48 gallons total paint used = 168 gallons . option a"
Answer: a
Problem: find the probability that a non leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Rationale: "there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e ."
Answer: e
Problem: when a number is divided by 6 & then multiply by 12 the answer is 11 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 6
Rationale: "if $ x $ is the number , x / 6 * 12 = 11 = > 2 x = 11 = > x = 5.5 c"
Answer: c
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 2400 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 100 , c ) 125 , d ) 988 , e ) 271
Rationale: "3 x * 2 x = 2400 = > x = 20 2 ( 60 + 40 ) = 200 m 200 * 1 / 2 = rs . 100 answer : b"
Answer: b
Problem: if 3 x + 4 y = 60 and 6 x - 4 y = 12 , what is the product of x and y ?
Options: a ) 80 , b ) 54 , c ) 54 , d ) 72 , e ) 12
Rationale: given 3 x + 4 y = 60 - - - eq 1 6 x - 4 y = 12 - - eq 2 sum both eqns we get 9 x = 72 = > x = 8 sum 6 x in eq 2 = > 48 - 4 y = 12 . = > y = 9 now xy = 8 * 9 = 72 option d is correct answer .
Answer: d
Problem: a rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm . how many times can it go round a cylinder having radius 20 cm ?
Options: a ) 49 rounds
b ) 42 rounds
c ) 54 rounds
d ) 52 rounds
e ) none of these
Rationale: explanation : let the required number of rounds be x more radius , less rounds ( indirect proportion ) hence we can write as radius 14 : 20 } : : x : 70 ⇒ 14 × 70 = 20 x ⇒ 14 × 7 = 2 x ⇒ x = 7 × 7 = 49 . answer : option a
Answer: a
Problem: a seller of used cars has 18 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 18 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 18 / 3 = 6 but since every car is being selected three times so no . of clients must be thrice as well = 6 * 3 = 18 answer : option d"
Answer: d
Problem: what percent of 120 are 90 ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 33 % , e ) 30 %
Rationale: "explanation : ( ? % / 100 ) * 120 = 90 ? = 75 % answer is c"
Answer: c
Problem: vijay sells a cupboard at 12 % below cost price . had he got rs . 1650 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 7400 , d ) 6875 , e ) none of these
Rationale: "explanation : cost price = 1650 / ( 0.12 + 0.12 ) = 2086 / 0.24 = rs . 6875 answer d"
Answer: d
Problem: a hostel had provisions for 250 men for 48 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 48 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 48 250 × 48 = 200 x 5 × 48 = 4 x x = 5 × 12 = 60 answer d"
Answer: d
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 12 such machines to perform the same job ?
Options: a ) 6 hours , b ) 8.75 hours , c ) 12 hours , d ) 4 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 3 machines 12 units of work ( 12 machines ) - - - > 1 hour for 48 units of work 12 * 4 - - - > 1 * 4 hours d 4 hours"
Answer: d
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 70 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 1 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 70 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 1 ) x = 130 ans c"
Answer: c
Problem: if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 50 , how much more remains to be paid ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "95 % remains to be paid so the remaining amount is 19 * 50 = $ 950 . the answer is e ."
Answer: e
Problem: john buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods .
Options: a ) rs . 6876.10 , b ) rs . 4500 , c ) rs . 4600 , d ) rs . 3400 , e ) rs . 7500
Rationale: rebate = 6 % of rs . 6650 = rs . 6 x 6650 = rs . 399 . 100 sales tax = 10 % of rs . ( 6650 - 399 ) = rs . 10 x 6251 = rs . 625.10 100 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 correct answer - a
Answer: a
Problem: the ratio of the adjacent angles of a parallelogram is 4 : 11 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 132 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 4 x + 11 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 48 ° and 132 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 48 ° + 84 ° = 132 ° answer : a
Answer: a
Problem: a and b start a business , with a investing the total capital of rs . 25000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 250 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 22500 , b ) b ) 33500 , c ) c ) 22510 , d ) d ) 33510 , e ) e ) 11500
Rationale: "interest received by a from b = 10 % of half of rs . 25000 = 10 % * 12500 = 1250 . amount received by a per annum for being a working partner = 250 * 12 = rs . 3000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 1250 + 3000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 1250 + 3000 + p ) = 2 ( p ) p = 4250 total profit = 2 p + 3000 = 2 * 4250 + 3000 = 11500 answer : e"
Answer: e
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 38 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 152 , d ) 128 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 38 4 / x = 1 / 38 = > x = 152 min . answer : c"
Answer: c
Problem: a circular dartboard of radius 1 foot is at a distance of 20 feet from you . you throw a dart at it and it hits the dartboard at some point q in the circle . what is the probability that q is closer to the center of the circle than the periphery ?
Options: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58
Rationale: radius of inner dartboard / overall radius of dartboard ( ( r / 2 ) ^ 2 ) / ( r ^ 2 ) = 1 / 4 = 0.25 answer : c
Answer: c
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 76 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 76 / 25 = 3 . . . . so the max is 3 76 / 20 = 3 . . . so the max is 3 76 - 75 = 1 answer : b"
Answer: b
Problem: a , b and c have rs . 700 between them , a and c together have rs . 300 and b and c rs . 600 . how much does c have ?
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: "a + b + c = 700 a + c = 300 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 900 a + b + c = 700 - - - - - - - - - - - - - - - - c = 200 answer : a"
Answer: a
Problem: a and b together can do a work in 7 days . if a alone can do it in 14 days . in how many days can b alone do it ?
Options: a ) 14 , b ) 10 , c ) 21 , d ) 20 , e ) 25
Rationale: "a 14 1 / 7 â € “ 1 / 14 = 1 / 14 = > 14"
Answer: a
Problem: a and b start walking towards each other at 7 am at speed of 12 kmph and 13 kmph . they were initially 25 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 am , c ) 7 am , d ) 10 am , e ) 8 am
Rationale: "time of meeting = distance / relative speed = 25 / 13 + 12 = 25 / 25 = 1 hr after 7 pm = 8 am answer is e"
Answer: e
Problem: find the lowest common multiple of 24 , 36 and 42 .
Options: a ) 360 , b ) 504 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 7 = 504 . answer is b"
Answer: b
Problem: if a / b = 1 / 7 , b / c = 3 , c / d = 2 / 3 , d / e = 2 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 72 / 21 , b ) 27 / 85 , c ) 34 / 47 , d ) 13 / 81 , e ) 16 / 21
Rationale: "say a = 1 . then : a / b = 1 / 7 - - > b = 7 ; b / c = 3 - - > c = 7 / 3 ; c / d = 2 / 3 - - > d = 7 / 2 ; d / e = 2 - - > e = 7 / 4 ; e / f = 1 / 2 - - > f = 7 / 2 . abc / def = ( 1 * 7 * 7 / 3 ) / ( 7 / 2 * 7 / 4 * 7 / 2 ) = 16 / 21 . answer : e ."
Answer: e
Problem: what is the least value of x . so that 43 x 87 is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 6 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + 3 + x + 8 + 7 = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . c"
Answer: c
Problem: 675.987 - ? + 56.84 = 289.654
Options: a ) a ) 443.173 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) of these
Rationale: "explanation : 443.173 answer : option a"
Answer: a
Problem: if shares of two persons in profits are rs . 800 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 800 / 600 = 4 : 3 answer : c"
Answer: c
Problem: if 7 / 10 of a pencil is green , 4 / 5 of the remaining is gold and the remaining 1 / 2 is white , what is the total length of the pencil ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 4 , e ) 2
Rationale: green is 7 / 10 gold is 4 / 5 which can also be written as 8 / 10 white is 1 / 2 which can also be written as 5 / 10 7 / 10 + 8 / 10 + 5 / 10 = 2 answer is e ) 2
Answer: e
Problem: what is the smallest no . that should be added to 41381 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 4 + 1 + 3 + 8 + 1 = 17 , the next multiple of 9 is 18 . 1 must be added to 41381 to make it divisible by 9 a"
Answer: a
Problem: a takes twice as much time as b & c takes thrice as much time as b to finish a piece of work . working together they can finish the work in 18 days . the no . of days need for b to do the work alone is ?
Options: a ) 30 days , b ) 31 days , c ) 33 days , d ) 41 days , e ) 52 days
Rationale: let a takes x days to complete the work , then b takes x / 2 days and c takes 3 x / 2 days to complete the work . a , b and c together complete the work in 18 days in 1 day , all they together can do = > 1 / x + 2 / x + 2 / 3 x = 1 / 18 3 + 6 + 2 / 3 x = 1 / 18 3 x 23 x 2 = 18 x = 66 days the number of days b alone takes to finish the work = x / 2 = 33 days c
Answer: c
Problem: a man can row his boat with the stream at 20 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 6 kmph , d ) 5 kmph , e ) 4 kmph
Rationale: "ds = 20 us = 8 s = ? s = ( 20 - 8 ) / 2 = 6 kmph answer : c"
Answer: c
Problem: what will be the compound interest on rs . 25000 after 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 25000 × ( 1 + 12 / 100 ) 3 ) = > 25000 × 28 / 25 × 28 / 25 × 28 / 25 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 option a"
Answer: a
Problem: a certain airline ' s fleet consisted of 70 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x be the number of years . 4 x > 70 - 3 x 7 x > 70 x > 10 the answer is e ."
Answer: e
Problem: the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 2898 sq m
b ) 1788 sq m
c ) 4312 sq m
d ) 7656 sq m
e ) 1786 sq m
Rationale: let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 352 s = 264 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1762 / ∏ 2 - 1322 / ∏ 2 } = 1762 / ∏ - 1322 / ∏ = ( 176 - 132 ) ( 176 + 132 ) / ∏ = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c
Answer: c
Problem: a man buys rs . 60 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 45
Rationale: "dividend on rs . 60 = rs . 9 / 100 x 60 = rs . 5.4 . rs . 12 is an income on rs . 100 . rs . 5.4 is an income on rs . 100 / 12 x 5.4 = rs . 45 . answer : option e"
Answer: e
Problem: a number of 53 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 16 * 3 + 1 * 5 = 53 - - > 16 + 1 = 17 . answer : e ."
Answer: e
Problem: the rhombus ( afce ) is inscribed in rectangle ( abcd ) . the length of bf = de . if the rectangle has a width of 20 yards and a length of 25 yards , what would be the total length ( the perimeter ) of a fence along the sides defined by afce ?
Options: a ) 80 yards , b ) 82 yards , c ) 84 yards , d ) 85 yards , e ) 90 yards
Rationale: the definition of a rhombus states that every side is of equal length . this definition is the key to solving this question . 1 ) we state that the hypotenuse of either side triangle is x . for this solution , i will be working with the left triangle . 2 ) we state that the bottom and top sides of the rhombus are also x , due to the definition of a rhombus . 3 ) we will define the bottom of the left triangle as y . that is , for the rectangle bottom itself , we can define it as 25 = y + x , where x is a side for the rhombus and y is the bottom part of the left triangle . 4 ) from ( 1 ) , we know that x = 202 + y 2 − − − − − − − √ 202 + y 2 . 5 ) from ( 3 ) , we know x = 25 - y . 6 ) from ( 4 ) and ( 5 ) , we have the equation 202 + y 2 − − − − − − − √ = 25 − y 202 + y 2 = 25 − y 7 ) solving for y , we get 4.5 . 8 ) 25 - 4.5 = 20.5 = x 9 ) since all sides of the rhombus are the same , 20.5 * 4 = 41 * 2 = 82 . the answer is b , 82
Answer: b
Problem: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 %
Rationale: "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.4 * 4 = 9.6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 9.6 % , answer : e"
Answer: e
Problem: a can do a piece of work 60 days . b can do work in 20 days . in how many days they will complete the work together ?
Options: a ) 12 days , b ) 16 days , c ) 15 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 60 , ratio = 60 : 20 = 3 : 1 no of days = 60 / ( 3 + 1 ) = 90 / 4 = 15 days answer : c"
Answer: c
Problem: if there are 10 apples and 20 oranges , what is the ratio of apples to oranges ?
Options: a ) 10 : 20 , b ) 2 : 4 , c ) 1 : 2 , d ) 4 : 8 , e ) it can not be determined from the information given
Rationale: a ratio should be reduced to the lowest common denominator . 10 : 20 means 10 x : 20 x which can be written as 1 ( 10 ) : 2 ( 10 ) . . . answer : c
Answer: c
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 9500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 700 , d ) rs . 1500 , e ) rs . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 9500 = 38000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 6000 salary of may is rs . 6500 salary of january = rs . 500 answer : a"
Answer: a
Problem: what two - digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5 ?
Options: a ) 94 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 10 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 10 x ^ 2 + y ^ 2 - 2 xy = 15 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 94 thus the answer is a"
Answer: a
Problem: last week david spent 20 percent of his wages on recreation . this week , his wages are 30 percent less than last week ʼ s wages and he spent 20 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 75 % , b ) 72 % , c ) 70 % , d ) 73 % , e ) 74 %
Rationale: "say david ' s wages last week were $ 100 , so he spent 0.20 * 100 = $ 20 on recreation ; this week ' s wages is 0.70 * 100 = $ 70 , so he spends 0.2 * 70 = $ 14 on recreation ; 14 / 20 = 0.70 , hence the amount he spends on recreation this week is 70 % of the amount he spent on recreation last week : 20 * 0.7 = 14 answer : c"
Answer: c
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 180 votes . find the total number of valid votes ?
Options: a ) 450 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 180 = > 4 x / 10 = 180 = > 4 x = 1800 = > x = 450 . answer : a"
Answer: a
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 10 liters of milk , the can would be full and the ratio of milk and water would become 5 : 2 . find the capacity of the can ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: let c be the capacity of the can . ( 4 / 7 ) * ( c - 10 ) + 10 = ( 5 / 7 ) * c 4 c - 40 + 70 = 5 c c = 30 the answer is d .
Answer: d
Problem: a car runs at the speed of 55 km per hour when not serviced and runs at 90 kmph when serviced . after servicing the car covers a certain distance in 3 hours . how much time will the car take to cover the same distance when not serviced ?
Options: a ) 8 hours , b ) 6 hours , c ) 9 hours , d ) 7 hours 12 minutes , e ) none
Rationale: explanation : time = 90 * 3 / 45 = 6 hours answer â € “ b
Answer: b
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 24 kmph , find the speed of the stream ?
Options: a ) 18 kmph , b ) 6 kmph , c ) 8 kmph , d ) 10 kmph , e ) 12 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 24 / 3 = 8 kmph . answer : c"
Answer: c
Problem: a began business with rs . 27000 and was joined afterwards by b with rs . 36000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1.5 , b ) 6.5 , c ) 7.5 , d ) 8 , e ) 2
Rationale: "27 * 12 : 36 * x = 2 : 1 x = 4.5 12 - 4.5 = 7.5 answer : c"
Answer: c
Problem: a certain kind of fuel is 1515 high octane and 4545 regular octane . if high octane costs 3 times as much as regular octane , what fraction of the cost of the fuel is due to the high octane ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 3 / 7 , d ) 3 / 5 , e ) 4 / 5
Rationale: let x be the amount of fuel high octane = x / 5 regular = 4 x / 5 price of regular = y price of high octante = 3 y cost of high octane in the fuel = 3 y * x / 5 total cost = 3 y * x / 5 + 4 x / 5 * y % = cost of high octante / total cost = 3 / 7 answer is c
Answer: c
Problem: 8 coins are tossed . whats is the probability that one and only one turns up head ?
Options: a ) 1 / 256 , b ) 1 / 32 , c ) 1 / 64 , d ) 1 / 128 , e ) 1 / 189
Rationale: explanation : possible outcomes ( sample space ) when 8 coins are tossed are : ( h , h , h , h , h , h , h , h ) , ( h , h , h , h , h , h , h , t ) , ( h , h , h , h , h , h , t , h ) , ( h , h , h , h , h , h , t , t ) , . . . . . . . ( t , t , t , t , t , t , t , t ) = 28 required outcomes : ( h , t , t , t , t , t , t , t ) , ( t , h , t , t , t , t , t , t ) , ( t , t , h , t , t , t , t , t ) , ( t , t , t , h , t , t , t , t ) , ( t , t , t , t , h , t , t , t ) , ( t , t , t , t , t , h , t , t ) , ( t , t , t , t , t , t , h , t ) , ( t , t , t , t , t , t , t , h ) = 8 so the required probability = 8 / 28 = 1 / 32 answer : b
Answer: b
Problem: a rectangular lawn of dimensions 110 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) s . 3988 , b ) s . 4800 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
Rationale: "area = ( l + b – d ) d ( 110 + 60 – 10 ) 10 = > 1600 m 2 1600 * 3 = rs . 4800 answer : b"
Answer: b
Problem: if you multiply all the numbers on your mobile phone , what is the answer ?
Options: a ) 2 , b ) 6 , c ) 1 , d ) 0 , e ) 7
Rationale: d 0 their is a zero in your phone .
Answer: d
Problem: if x is 20 percent greater than 12 , then x =
Options: a ) 10.2 , b ) 12.1 , c ) 8.1 , d ) 15.6 , e ) 14.4
Rationale: "x is 20 % greater than 12 means x is 1.2 times 12 ( in other words 12 + 20 / 100 * 12 = 1.2 * 12 ) therefore , x = 1.2 * 12 = 14.4 answer : e"
Answer: e
Problem: if 7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ ( 7 ^ 9 ) - 7 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 3 ^ 10 , e ) 7 ^ 11 - 1
Rationale: "7 ^ k + 7 ^ k = ( 7 ^ 9 ) ^ 7 ^ 9 - 7 ^ k 7 * ( 7 ^ k ) = 7 ^ ( 49 * 7 ^ 9 ) = 7 ^ ( 7 ^ 2 * 7 ^ 9 ) = 7 ^ ( 7 ^ 11 ) 7 ^ k + 1 = 7 ^ ( 7 ^ 11 ) so k + 1 = 7 ^ 11 so k = 7 ^ 11 - 1 answer is e"
Answer: e
Problem: find the probability in a group of 10 students sitting in a row , two of them always sit next to each other
Options: a ) 0.5 , b ) 0.4 , c ) 0.3 , d ) 0.2 , e ) 0.1
Rationale: assume that these 2 students are 1 and then u can sit is 9 ! and these 2 students can sit by 2 ways then total ways are 9 ! * 2 and the probability is 9 ! * 2 / 10 ! = 1 / 5 = 0.2 answer : d
Answer: d
Problem: a student got 74 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 66 % , b ) 67 % , c ) 68 % , d ) 69 % , e ) 70 %
Rationale: "74 + 81 + x = 3 * 75 x = 70 the answer is e ."
Answer: e
Problem: a leak in the bottom of a tank can empty the full tank in 3 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 1440 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 3 - 1 / 12 ) = 1 / 4 work done by the inlet in 1 min . = ( 1 / 4 × 1 / 60 ) = 0.004167 volume of 0.004167 part = 6 litres . therefore , volume of whole = 0.004167 x 6 ‹ = › 1440 litres . answer d"
Answer: d
Problem: the ratio of 2 numbers is 4 : 6 and their h . c . f . is 8 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 52 , d ) 96 , e ) 60
Rationale: "let the numbers be 4 x and 6 x their h . c . f . = 8 so the numbers are 4 * 8 , 6 * 8 = 32,48 l . c . m . = 96 answer is d"
Answer: d
Problem: when positive integer n is divided by 4 , the remainder is 1 . when n is divided by 7 , the remainder is 5 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 19 , e ) 20
Rationale: "when positive integer n is divided by 4 , the remainder is 1 i . e . , n = 4 x + 1 values of n can be one of { 1 , 5 , 9 , 13 , 17 , . . . . . . . . . . . 29 , 33 , 37 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 7 , the remainder is 5 . . i . e . , n = 7 y + 5 values of n can be one of { 5 , 12 , 19 , 26 , 33 , 40 , . . . . . . . . } combining both the sets we get n = { 5,33 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 35 or 35 x in case of n = 33 p = 2 so for min value of p , we take min value of n . b is the answer ."
Answer: b
Problem: sam invested rs . 12000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 13230.0 , b ) 12300.02 , c ) 16537.5 , d ) 15000.0 , e ) 16537.11
Rationale: "p = rs . 12000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 12000 * ( 1 + 5 / 100 ) 2 ] = ( 12000 * 21 / 20 * 21 / 20 ) = rs . 13230.00 answer : a"
Answer: a
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 18 , what was the price before the first discount ?
Options: a ) $ 32 , b ) $ 34.31 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 65.23
Rationale: let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 18 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 18 solve for x x = $ 32 correct answer a
Answer: a
Problem: the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 16 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 36 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 16 = 36 km apart , they take 1 hour to be 1000 m apart , they take 36 * 1000 / 1000 = 36 min . answer is e"
Answer: e
Problem: a cube of edge 5 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 10 cm * 5 cm , find the rise in water level ?
Options: a ) 2.5 cm , b ) 3.6 cm , c ) 5 cm , d ) 6.43 cm , e ) 7.56 cm
Rationale: "increase in volume = volume of the cube = 5 * 5 * 5 cm ^ 3 rise in water level = volume / area = 5 * 5 * 5 / 10 * 5 = 2.5 cm answer is a"
Answer: a
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 15 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 5 ) = 2 / 15 answer : b ) 2 / 15"
Answer: b
Problem: 4 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days . the ratio between the efficiencies of a man and boy is ?
Options: a ) 18 : 19 , b ) 17 : 19 , c ) 15 : 19 , d ) 18 : 14 , e ) 18 : 11
Rationale: "4 m + 12 b - - - - - 4 days 7 m + 6 b - - - - - - - 5 days 16 m + 48 b = 35 m + 30 b 18 b = 19 m = > 5 m = 6 b m : b = 18 : 19 answer : a"
Answer: a
Problem: a boatman trying to cross the river . the width of the river is 400 m . he is selling boat with 10 m / sec . he takes 50 sec to cross the river due to flow of water . calculate the drift .
Options: a ) 500 , b ) 400 , c ) 300 , d ) 200 , e ) 100
Rationale: the distance boatman travel to cross the river = 50 * 10 = 500 m he sell the boat diagonally . so height = 400 m , base be x and hypotenuse = 500 m so by pythagoras theorem , square of 400 + square of x = square of 500 so , square of x = 250000 - 160000 x = â ˆ š 250000 - 160000 , x = â ˆ š 90000 = 300 drift = 300 m answer c
Answer: c
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 60 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 25 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 60 ounces of a substance has a volume of ( 48 / 112 ) * 60 = 25 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 60 will have a volume a little more than 24 , that is 25 c"
Answer: c
Problem: the average speed of a train is 87 kmph . the train was scheduled to start at 9 am in bangalore , and as per schedule it has to reach a destination of 348 km away from bangalore at 1 : 45 pm same day and a halt was scheduled onthe way . for how long was the halt scheduled ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 60 minutes , e ) none of these
Rationale: speed of train = 87 kmph and distance it covers is 348 km . time taken to cover the distance = distance / speed = 348 / 87 = 4 hours . but total time taken by train to reach destination is = 1 : 45 pm – 9 a . m = 4 hours 45 minutes . time of halt = total time – take taken without halt = 4 hours 45 minutes – 4 hours = 45 minutes a )
Answer: a
Problem: the height of the wall is 4 times its width and length of the wall is 3 times its height . if the volume of the wall be 10368 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 4 x and length = 12 x 12 x ã — 4 x ã — x = 10368 x = 6 answer : c"
Answer: c
Problem: a courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm . the total number of bricks required is :
Options: a ) 6000 , b ) 8000 , c ) 8960 , d ) 2000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2400 ã — 1400 / 25 ã — 15 ) = 8960 option c"
Answer: c
Problem: rajan and rakesh started a business and invested rs . 20,000 and rs . 25,000 respectively . after 4 months rakesh left and mukesh joined by investing rs . 15,000 . at the end of the year there was a profit of rs . 4,600 . what is the share of rajan ?
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: ratio of share of rajan , rakesh nd mukesh = > 20000 : 25000 : 15000 = > 4 : 5 : 3 = > 4 * 12 : 5 * 4 : 3 * 8 [ since rakesh left after 4 months nd mukesh joined after 4 months . . . ] = > 12 : 5 : 6 share of rajan = > 4600 * 12 / 23 = 2400 answer : e
Answer: e
Problem: when a = x + ( 3 / x ) and b = x - ( 3 / x ) , ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 4096
Rationale: "- - > ( 2 ^ a ^ 2 ) / ( 2 ^ b ^ 2 ) = { ( 2 ) ^ ( a ^ 2 - b ^ 2 ) } = 2 ^ ( a - b ) ( a + b ) . since a - b = 6 / x and a + b = 2 x , 2 ^ ( a - b ) ( a + b ) = 2 ^ ( 6 / x ) ( 2 x ) = 2 ^ 12 = 4096 therefore , the answer is e"
Answer: e
Problem: 20 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 90 %
Rationale: to maximize the percentage of companies offering both , let ' s assume that all 20 % of companies which offer wireless internet also offer snacks . the answer is a .
Answer: a
Problem: in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 54 km / hr ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: speed = 54 * 5 / 18 = 15 m / s time = 180 / 15 = 12 seconds the answer is b .
Answer: b
Problem: if 20 typists can type 40 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 180 , e ) 400
Rationale: "20 typists can type 40 letters , so 30 typists can type = 40 * 30 / 20 40 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 40 * 30 * 60 / 20 * 20 = 180 d is the answer"
Answer: d
Problem: there are 4 people who has to cross a stretch of 300 km . they normally run at a speed of 10 kmph . one of them has a bike that travels at 50 kmph . the bike first takes one person alone and crosses the stretch while the other two keep running . then he comes back without wasting time and picks up another person from the way , drives him across the stretch , and does the same for the last person . how long does this whole process take ?
Options: a ) 24 hrs , b ) 16 hrs , c ) 56 / 3 hrs , d ) 58 / 3 hrs , e ) 18 hrs
Rationale: expl : time taken to carry 2 nd person = 300 / 50 = 6 hrs . time taken to meet 3 rd person = ( 300 - 6 * 10 ) / ( 50 + 10 ) = 4 hrs time taken to carry 3 rd person = 4 hours time taken to meet 4 th person = ( 300 – 140 ) / 60 = 8 / 3 total time = 6 + 4 + 4 + 8 / 3 + 8 / 3 = 58 / 3 hours answer : d
Answer: d
Problem: a courtyard is 18 meter long and 12 meter board is to be paved with bricks of dimensions 15 cm by 13 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18078 , c ) 11076 , d ) 11456 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 1800 ã — 1200 / 15 ã — 13 ) = 11076 option c"
Answer: c
Problem: if one length of a square is tripled , and the original parameter is 4 y . what is the new length of one of the sides ?
Options: a ) 12 y / 3
b ) 2 y / 2
c ) 6 y / 3
d ) 12 y / 4
e ) 4 y / 3
Rationale: if the original parameter is 4 y , each length of the square is 4 y / 4 . if the parameter is tripled , then each length becomes 3 ( 4 y ) / 4 . this is 12 y / 4 . answer option d .
Answer: d
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 1 , d ) 8 : 2 , e ) 8 : 4
Rationale: "let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b"
Answer: b
Problem: 80 % of a number is added to 20 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 270 , d ) 100 , e ) 281
Rationale: ( 80 / 100 ) * x + 20 = x 4 x + 100 = 5 x x = 100 answer : : d
Answer: d
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 780 grams per kg , what is his percent ?
Options: a ) 28 % , b ) 25 % , c ) 55 % , d ) 28 % , e ) 28.2 %
Rationale: "780 - - - 220 100 - - - ? = > 28.2 % answer : e"
Answer: e
Problem: angelina walked 840 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 16 , e ) 30
Rationale: "let the speed be x . . . so time taken from home to grocery = 840 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 840 / x - 240 / x = 40 . . 600 / x = 40 . . x = 15 m / secs . . so grocery to gym = 2 * 15 = 30 m / s . . . e"
Answer: e
Problem: david obtained 74 , 65 , 82 , 67 and 90 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) a ) 87 , b ) b ) 99 , c ) c ) 68 , d ) d ) 82 , e ) e ) 76
Rationale: "average = ( 74 + 65 + 82 + 67 + 90 ) / 5 = 380 / 5 = 76 . answer : e"
Answer: e
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.8 % , d ) 18 % , e ) 19.5 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many e acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn e = 4 * 94 = 376 correct option - c"
Answer: c
Problem: at an elementary school , 70 % of the faculty members are women and 60 % of the faculty members are married . if 2 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 20 - - - - - 20 - - - - - - - - - 40 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 10 / 30 = 1 / 3 c"
Answer: c
Problem: when n is divided by 24 , the remainder is 5 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6 , e ) 7
Rationale: "let n = 5 ( leaves a remainder of 5 when divided by 24 ) 4 n = 4 ( 5 ) = 20 , which leaves a remainder of 4 when divided by 8 . answer c"
Answer: c
Problem: question : a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 180 . the cost for 1 bat and 6 balls is $ 190 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 195 for the purchase ? options :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: imo it should be c that is c reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 180 1 b + 6 c = 190 solving both we get b that is bat = 40 and c that is ball = 25 new equation 195 to be divided in equal 3 b + 3 c = 195 3 * 40 + 3 * 25 = 195 120 + 75 = 195
Answer: c
Problem: a train 400 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 277 m , b ) 700 m , c ) 900 m , d ) 187 m , e ) 1678 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 400 + x ) / 60 = 65 / 3 x = 900 m . answer : c"
Answer: c
Problem: ramu bought an old car for rs . 42000 . he spent rs . 8000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 29.8 % , b ) 16 % , c ) 18 % , d ) 82 % , e ) 23 %
Rationale: "total cp = rs . 42000 + rs . 8000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : a"
Answer: a
Problem: machine p and machine q are each used to manufacture 990 sprockets . it takes machine p 10 hours longer to produce 990 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 990 / x = 990 / 1.1 x + 10 1.1 ( 990 ) = 990 + 11 x 11 x = 99 x = 9 the answer is e ."
Answer: e
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 40 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 105 , e ) 110
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 40 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 40 = ( 2 ^ 2 * 5 ^ 2 ) ^ 40 = 2 ^ 80 * 5 ^ 80 answer : a"
Answer: a
Problem: if the product of 2 integers is negative , at most how many of the integers can be negative ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the product of 2 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 1 correct option : a"
Answer: a
Problem: what will be the difference between simple and compound interest @ 10 % per annum on the sum of rs 1000 after 4 years
Options: a ) rs 62.10 , b ) rs 63.10 , c ) rs 64.10 , d ) rs 65.10 , e ) none of these
Rationale: explanation : s . i . = 1000 ∗ 10 ∗ 4 / 100 = 400 c . i . = [ 1000 ( 1 + 10 / 100 ) 4 − 1000 ] = 464.10 so difference between simple interest and compound interest will be 464.10 - 400 = 64.10 option c
Answer: c
Problem: find k if 16 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 16 / k = 4 and 16 / 4 = 4 , then k = 4 correct answer d"
Answer: d
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 sq . ft , how much will it cost to paint outside of a cube having 8 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 82 = 384 sq . ft quantity of paint required = ( 384 / 16 ) = 24 kg cost of painting = 36.5 x 24 = rs . 876 answer : d"
Answer: d