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mathematics
A bakery opened yesterday with its daily supply of 60 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
[ "1", "2", "3", "4", "6" ]
answer is E ...6 dozens .... half sold by noon --> 30 dozens (30 *12 =360) remaining --> 30 dozens i.e 360 eggs... 80% sold --> 80*360/100 =288 eggs remaining 20 % --> 72 eggs (6 dozens ) --> answer The answer is: E
E
mathematics
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
[ "1", "2", "3", "4", "5" ]
DS = 6 US = 4 S = ? S = (6 - 4)/2 = 1 kmph Answer: A The answer is: A
A
mathematics
A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 8 more days. How many days would it have taken the second carpenter to do the complete job working alone?
[ "4 2/3", "7", "9", "14", "28" ]
A carpenter worked only 1 day on something that takes him 6 MORE days. Means; Carpenter finishes his work in 7 days. Let his buddy finish the same task in x days. Respective rates per day: 1/7 AND 1/x To complete 1 work: First guy worked for 5 days @ rate=1/7 per day. Second one worked for 8 days @ rate=1/x per day Expression: Days*Rate=Work 5*1/7+8*1/x=1 5x+56=7x 2x=56 x=28 days. Ans:E The answer is: E
E
mathematics
In how many years Rs 100 will produce the same interest at 5% as Rs. 600 produce in 4 years at 10%
[ "44", "52", "50", "46", "48" ]
Explanation: Clue: Firstly we need to calculate the SI with prinical 600,Time 4 years and Rate 10%, it will be Rs. 240 Then we can get the Time as Time = (100*240)/(100*5) = 48 Option E The answer is: E
E
mathematics
If the sum of 5 consecutive integers is 125, what is sum of the 5 consecutive integers preceding the former sequence?
[ "35", "25", "100", "105", "103" ]
1) least of each will have a difference of 5 and next least too will have a difference of 5 and so on... Therefore all 5 terms will have a term LESS by 5.. Sum = 125-(5*5) = 100 2.) if sum is 125, the average = median = 125/5 = 25. The median of previous 5 will be 25-5 = 20. And sum would be 20*5 = 100 Answer: C The answer is: C
C
mathematics
How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
[ "30", "20", "10", "45", "50" ]
Since each desired number is divisible by 5, so we much have 5 at the unit place. The hundreds place can now be filled by any of the remaining 4 digits . so, there4 ways of filling it. Required number of numbers = (1 * 5 * 4) = 20 Ans: B The answer is: B
B
mathematics
The profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?
[ "Rs. 40", "Rs. 50", "Rs. 49", "Rs. 59", "Rs.64" ]
S.P 1- C.P = C.P – S.P 2 86 - C.P = C.P - 42 2 C.P = 86 + 42; C.P = 128/2 = 64 ANSWER:E The answer is: E
E
mathematics
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
[ "2277", "2999", "1000", "2651", "1971" ]
X * (110/100) * (95/100) = 1045 X * (11/10) * (1/100) = 11 X = 1000 Answer: C The answer is: C
C
mathematics
A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day
[ "1\\5", "1\\6", "1\\7", "1\\8", "None of these" ]
Explanation: Please note in this quesƟon, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question So lets solve now, A's 1 day work = 1/18 B's 1 day work = 1/9 [because B take half Ɵme than A] (A+B)'s one day work = (118+19)=(1+218)=16 So in one day 1/6 work will be done Answer: B The answer is: B
B
mathematics
The average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
[ "120 kg", "130 kg", "137 kg", "190 kg", "None" ]
Solution Total weight increased = (10 x 7.2)kg = 72 kg. Weight of new person = (65 + 72)kg = 137 kg. Answer C The answer is: C
C
mathematics
A man jumps into a river from a overbridge ,at the same time a hat drops in the river which flows with the stream of the water. That man travels 10 minute upstream and returns back where he was asked to catch the hat. He catches hat at a distance of 1000 yard down at a second bridge . Find the speed of the river.
[ "50", "60", "55", "70", "75" ]
Explanation : Suppose x is the distance travelled by the man in 10 min upstream. Then => x/(v-u) = 10 where v is man's speed and u is river speed) Total time taken to swim by the man upstream and down stream is equal to the time taken by the hat to travel 1000 yards with the speed of river : => 1000/u = 10 + (x+1000) / (u+v) => now substitute x = 10(v-u) and simplify we will get, => 100v = 2uv => 2u = 100 => u = 50 yards per minute Hence (A) is the correct answer. Answer : A The answer is: A
A
mathematics
If the ratio of the roots of the equation x2+3px-6=0 is equal to that of the roots x2+6rx-12=0, then:
[ "5r=3p", "2p=r", "r=p", "2r=p", "None" ]
x2+3px-6=0 for this eqn... roots are R1=-3p R2=6 x2+6rx-12=0 for this eqn... roots are R3=-6r R4=12 As per Question, -3p/6=-6r/12 => r=p ANSWER:C The answer is: C
C
mathematics
On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 22% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
[ "10.5%", "12.8%", "15%", "22%", "30%" ]
Answer is B. This question is in the OG and thus well explained by ets. those who exceed : X so X = 10%+0,22X id est X = 12,8% The answer is: B
B
mathematics
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8463 for a computer table, then what was the cost price of the computer table?
[ "6825", "2977", "2871", "6725", "2981" ]
Explanation: CP = SP * (100/(100 + profit%)) = 8463(100/124) = Rs. 6825. Answer: A The answer is: A
A
mathematics
18! is equal to which of the following?
[ "6,402,373,705,728,125", "6,402,373,705,728,216", "6,402,373,705,728,624", "6,402,373,705,728,000", "6,402,373,705,728,989" ]
After 4!, the units digit of every factorial is 0. 5!=120 6!=720 etc... The answer is D. The answer is: D
D
mathematics
An empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed?
[ "70%", "85%", "80%", "75%", "65%" ]
Explanation: Let the weight of full bottle be 6kg. Therefore, weight of empty bottle is 1kg and that of water is 5kg. If x% of water is removed, the weight of the bottle becomes 2kg. Therefore, the amount of water removed is 4kg. % of water removed = 4/5 *100 = 80% ANSWER C The answer is: C
C
mathematics
Three seventh of a number is 12 more than 40% of that number. What will be the 10% of that number?
[ "A)148", "B)210", "C)21", "D)248", "E)258" ]
3/7 x – 40/100 x = 12 x = 35 * 12 35 * 12 * 10/100 = 42/2 = 21 ANSWER:C The answer is: C
C
mathematics
What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively
[ "56.25", "60", "52.5", "5.25", "None of these" ]
a +10d = 5.25, a+6d = 3.25, 4d = 2, d = ½ a +5 = 5.25, a = 0.25 = ¼, s 15 = 15/2 ( 2 * ¼ + 14 * ½ ) = 15/2 (1/2 +14/2 ) = 15/2 *15/2 =225/ 4 = 56.25 ANSWER:A The answer is: A
A
mathematics
Which is the smallest fraction:
[ "11/13", "9/11", "5/4", "5/7", "6/7" ]
11/13=.846 9/11=.818 5/4=1.25 5/7=.714 So smallest is 5/7 ANSWER:D The answer is: D
D
mathematics
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 768 as interest at the end of the loan period, what was the rate of interest?
[ "3.6", "6", "8", "24", "None of these" ]
Let rate = R% and time = R years. Then, (1200 x R x R)/100 = 768 12R2 = 768 R2 = 64 R = 8. Answer: Option C The answer is: C
C
mathematics
A rectangular table seats 6 people on each of two sides, with every person directly facing another person across the table. If 12 people choose their seats at random, what is probability that person P directly faces person Q?
[ "1/13", "1/12", "1/11", "1/10", "1/9" ]
Person P will be seated somewhere at the table. Each of the other 11 people has an equal chance of sitting opposite person P. The probability that person Q sits across is 1/11. The answer is C. The answer is: C
C
mathematics
In the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
[ "5", "4", "8", "12", "32" ]
Total = C + D + R - (CD + DR + CR) - 2CDR 60 = 32 + 40 + 10 - (12) - 2x x = 5 So, answer will be A The answer is: A
A
mathematics
IF 2+7=57 ; 3+6=63 ; 5+9=206 Then 5+8=?
[ "185", "186", "177", "168", "189" ]
2^3 + 7^2= 57 3^3 + 6^2=63 5^3 + 9^2=206 and 5^3 + 8^2=189 ANSWER:E The answer is: E
E
mathematics
An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time D will it take to fill the bucket to full capacity?
[ "7/18", "9/18", "2", "18/7", "18/5" ]
Solution - Work and Time are directly proportional. W1/W2=T1/T2 7/10 work in 6 mins 1 work in T mins (7/10)/1 = 6/T -> T = 60/7 mins. Remaining minutes to fill the tank D= 60/7 - 6 = 18/7 mins. ANS D. The answer is: D
D
mathematics
The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
[ "276", "280", "322", "345", "354" ]
Clearly, the numbers are (20 x 13) and (20 x 14). Larger number = (20 x 14) = 280. Answer: Option B The answer is: B
B
mathematics
Dhoni weighs twice as much as Nameetha. Nameetha's weight is 55% of Bima's weight. Dravid weighs 35% of Leela's weight. Leela weighs 30% of Dhoni's weight. Who among these 5 persons weighs the least?
[ "Dravid", "Dhoni", "Bima", "Nameetha", "Leela" ]
if Bima weight = x we get Nameetha's weight = 0.55x Dhoni's weight = 1.1x Leela's weight = 0.33x and Dravid's weight = 0.1155x Answer : A The answer is: A
A
mathematics
A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
[ "Rs. 150", "Rs. 144", "Rs. 138", "Rs. 132", "None of these" ]
Given that SP = Rs. 102 and loss = 15% CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120. To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144 ANSWER:B The answer is: B
B
mathematics
How many numbers are divisible by 4 between 1 and 100?
[ "25", "24", "23", "22", "20" ]
Numbers divisible by 4 till 100=(100/4)=25 But we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4. so answer is 24 numbers. Answer is option B The answer is: B
B
mathematics
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
[ "2", "5", "6", "7", "14" ]
3150*y = A^2 3 * 1050 * y = A^2 3*5*210*y = A^2 3*5*7*3*2*5*y = A^2 2*3^2*5^2*7*y = A^2 Concept: The factors of squared integer should occur in pair. So, the only numbers left are 2*7 Hence 14 ; ANSWER:E The answer is: E
E
mathematics
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 12, how many more dollars, in terms of x, will it cost per person?
[ "x/6", "x/16", "x/40", "3x/40", "3x/80" ]
Choose x as a multiple of 16, I chose 64: So for 10 people, that's 6.4 each and for 12 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is C. The answer is: C
C
mathematics
Of the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993?
[ "68.99%", "66.55%", "91.23%", "77.77%", "87.37%" ]
Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60 Number of families owning computer in 1998 = 60 * 150/100 = 90 Number of families in 1998 = 103 The percentage = 90/103 * 100 = 87.37%. ANSWER:E The answer is: E
E
mathematics
If the average marks of 3classes of 55, 60 and 45 students respectively is 50, 55, 60, then find the average marksof all the students is
[ "53", "53.5", "54.68", "55.6", "67.2" ]
Required average = 55 x 50 + 60 x 55 + 45 x 60 55 + 60 + 45 = 2750 + 3300 + 2700 160 = 8750 160 = 54.68 C The answer is: C
C
mathematics
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
[ "20/8 sec", "22/7 sec", "20/7 sec", "20/2 sec", "30/7 sec" ]
They are moving in opposite directions, relative speed is equal to the sum of their speeds. Relative speed = (54 + 72)*5/18 = 7*5 =35 mps. The time required = d/s = 100/35 =20/7 sec. Answer:C The answer is: C
C
mathematics
A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 36,000, what will be the amount A receives?
[ "15120", "14500", "14900", "14300", "14000" ]
Total amount invested = 50000 Assume that investment of C =x. Then investment of B =5000+x, Investment of A =4000+5000+x=9000+x x+5000+x+9000+x=50000 ⇒3x+14000=50000 ⇒3x=50000–14000=36000 ⇒x=36000/3=12000 Investment of C =x=12000 Investment of B =5000+x=17000 Investment of A =9000+x=21000 Ratio of the investment of A, B and C =21000:17000:12000 =21:17:12 Share of A = Total profit ×21/50 =36000×21/50=15,120 Answer is A. The answer is: A
A
mathematics
For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(102) – h(101)?
[ "102", "0", "101", "98", "100" ]
h(101) = 1*3*5*7*9*...*99*101 h(102) = 1*3*5*7*9*...*99*101 They are going to be the same. Hence their difference will be 0 hence:B The answer is: B
B
mathematics
Which of the following is the lowest positive integer that is divisible by 6, 7, 8, 9, and 10?
[ "2140", "2520", "2980", "3260", "3680" ]
The number needs to be divisible by 2*3, 7, 2^3, 3^2, and 2*5. The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520 The answer is B. The answer is: B
B
mathematics
If xy not equal 0 and x^2*y^2 -xy = 12, which of the following could be y in terms of x? I. 1/2x II. -4/x III. 3/x
[ "II and III", "II", "III", "IV", "I &II" ]
x2y2 - xy = 12 x2y2-xy-12 = 0 (xy-3)(xy+4)=0 xy = 3 or xy=-4 y = 3/x or y = -4/x II and III only A The answer is: A
A
mathematics
An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.30 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
[ "700,000", "300,000", "380,000", "400,000", "420,000" ]
Total royalties for first 100.000 books = .8*100,000= 80,000 Total royalties for the rest of the books = 260,000-80,000 = 180,000 Remaining books = 180,000/0.3 = 600,000 Total books = 600,000+100,000 = 700,000 Answer A The answer is: A
A
mathematics
Find the value of x from the below equation? : x^2+5x+25 = 0
[ "No answer", "25", "1", "0", "-2" ]
a = 1, b = 5, c = 25 x1,2 = (-5 ± √(5^2 - 4×1×25)) / (2×1) = (-5 ± √(25-100)) / 2 = (-5 ± √ -75) / 2 No real roots A The answer is: A
A
mathematics
A box contains 2 red, 3 black and 4 blue balls. 3 balls are randomly drawn from the box. If two balls are found to be different, what is the probability that the third ball is blue?
[ "8/3", "9/3", "5/3", "2/3", "1/3" ]
there are 6 ways to draw a blue ball at third attempt if first two balls are different. they are 1)RED BLACK BLUE 2)RED BLUE BLUE 3)BLACK RED BLUE 4)BLACK BLUE BLUE 5)BLUE RED BLUE 6)BLUE BLACK BLUE Probability of 1st way is (2/9)*(3/8)*(4/7) as at first attempt we got red which are two in number out of 9 and in second we got black which are 3 in number out of 8 (as first ball is removed)and in 3rd attempt we got blue which are 4 in number out of 7 balls left. similarly probability of other ways is as follows (2/9)*(4/8)*(3/7) (3/9)*(2/8)*(4/7) (3/9) *(4/8)*(3/7) (4/9)*(2/8)*(3/7) (4/9)*(3/8)*(3/7) total probability of getting a blue ball is sum of all above ways so p=(2/9)*(3/8)*(4/7)+(2/9)*(4/8)*(3/7)+(3/9)*(2/8)*(4/7)+(3/9) *(4/8)*(3/7)+(4/9)*(2/8)*(3/7)+(4/9)*(3/8)*(3/7)=1/3 so probability of ball to be blue is 1/3 Answer E The answer is: E
E
mathematics
The arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have?
[ "229", "-1", "-229", "90", "-90" ]
The Arithmetic Mean of 5 negative integers is (a+b+c+d+e)/5=-100 So, The sum of 5 negative integers would be a+b+c+d+e=-100*5 = -500 Similarly, The sum of 3 negative integers would be a+b+c= -90*3 = -270 Thus, the sum of the other 2 integers is -500 + 270= -230. Since we know that the integers are negative then the least one from these two can be -229, the other one being -1. Hence, the correct ans is C The answer is: C
C
mathematics
Tom planted vegetables in a rectangular garden that was 23 feet long and 15 feet wide. He used 1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
[ "155 sq. ft.", "156 sq. ft.", "161 sq. ft.", "168 sq. ft.", "179 sq. ft." ]
area of garden is 23 x 15 = 345 sq. ft. 1/3 x 345 = 115 sq. ft. for corn 1/5 x 345 = 69 sq. ft. for peas 115 + 69 = 184 sq. ft. used 345 - 184 = 161 sq. ft. left over correct answer C The answer is: C
C
mathematics
If you are given $4, and the amount doubles every day, how much money will you have after 8 days?
[ "$256", "$512", "$1024", "$65536", "$4096" ]
4^8=65536 The answer is D. The answer is: D
D
mathematics
A motorist knows six different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
[ "4", "8", "12", "24", "36" ]
Explanation: Total number of routes from Bristol to Carlisle = (6 x 3 x 2) = 36. Answer: E The answer is: E
E
mathematics
A certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
[ "79", "83", "85", "87", "88" ]
Consider 4 teams. Max possible games if a team is eliminated after 2 loses = 3 + 2 = 5 Similarly, if 5 teams are there, Max possible games = 4 + 3 = 7. So going forth we can play 15,17,19,21 max possible games for 9,10,11,12 teams respectively. Adding them up gives 72. Now there are two teams left in each group still. So four more games to give a winner in each team. So 72+ 4 = 76. Now of the four teams we can have max 3 games if its a knock out round. So 76 + 3 = 79. Answer A = 79. The answer is: A
A
mathematics
A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
[ "33", "878", "30", "10", "11" ]
C = 1/5 – 1/10 = 1/10 => 10 days Answer: D The answer is: D
D
mathematics
What is the 28th digit to the right of the decimal point in the decimal form of 5/11?
[ "3", "4", "5", "6", "7" ]
5/11 = 0.45454545... The even numbered positions in the decimal expansion are all 5. The answer is C. The answer is: C
C
mathematics
A man sells two articles for Rs.3250 each and he gains 40% on the first and loses 40% on the next. Find his total gain or loss?
[ "19%loss", "12%loss", "16%loss", "18%loss", "11%loss" ]
Explanation: (40*40)/100 = 16%loss Answer:C The answer is: C
C
mathematics
60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $200 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
[ "12", "18", "32", "40", "44" ]
Lets take numbers here. Assume that the total number of movie theaters in the town = 100 Then number of movie theaters with 3 screens or less = 60 => Number of movie theaters with 4 screens or more = 40 Movie theaters with 3 screens or less selling popcorn at more than $200 = 20% of 60 = 12 Number of movie theaters selling popcorn at $300 or less = 56 => Number of movie theaters selling popcorn at more than $300 = 100-56 = 44 Of these 44 theaters, 12 are those with 3 screens or less Therefore 18 (44-12) must be those with four screens or more B is the answer The answer is: B
B
mathematics
0.35 represents what percent of 0.7?
[ "0.05%", "0.5%", "50%", "500%", "5000%" ]
One more method 0.35 represents what percent of 0.7? Adjusting the decimal 3.5 represents what percent of 7? Divide by 7 0.5 represents what percent of 1? Answer = 0.5*100 = 50% = C The answer is: C
C
mathematics
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 2 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
[ "23 years", "22 years", "25 years", "26 years", "27 years" ]
EXPLANATION Let the average age of the whole team by x years. 11x – (26 + 28) = 9(x -1) 11x – 9x = 45 2x = 45 x = 22. So, average age of the team is 22 years. Answer B The answer is: B
B
mathematics
A certain high school has 500 students. Of these students, 20 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
[ "430", "440", "450", "460", "470" ]
We're given a series of facts to work with: 1) A certain high school has 500 students. 2) Of these students: X are taking music, Y are taking art, and Z are taking BOTH music and art. We're asked how many students are taking NEITHER music nor art? Let's TEST X = 20 Y = 20 Z = 10 So, we have 20 students taking music, 20 taking art and 10 taking BOTH music and art. That 10 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is... 10 student taking JUST music 10 student taking JUST art 10 student taking BOTH music and art Total = 30 students We're asked for the total number of students who are taking NEITHER Course. That is 5000 - 30 = 470. E The answer is: E
E
mathematics
If the radius of a circle that centers at the origin is 5, how many M points on the circle have integer coordinates?
[ "4", "8", "12", "15", "20" ]
I understand this might not be required but I used the equation of a circle. Since the origin is at 0, x^2+y^2=5^2. X,Y could be +/- (0,5 or 5,0) - 4 possibilities. X,Y could be +/- (3,4 or 4,3) - 8 possibilities. Ans: M=C The answer is: C
C
mathematics
[1+(1/5)]^n=2? What is the value of n?
[ "1.999", "2.999", "3.88", "4.88", "5.88" ]
1+1/5 = 6/5 = 1.2 1.2*1.2 = 1.44 *1.2 = 1.728 *1.2 = 2.0736 so if N is integer, N=4. if not, N = 3.8 (1.2)^3.8 = 1.999 ANSWER:C The answer is: C
C
mathematics
If x and y are non-zero integers, and 64x^4 – 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
[ "2y^2", "2y", "2y^2/8", "2y^2-1/8", "2y^2+1/8" ]
64x^4 – 4y^4 = 8x^2 + 2y^2 (8x^2 + 2y^2) (8x^2 - 2y^2) = 8x^2 + 2y^2 8x^2 - 2y^2 = 1 8x^2 = 2y^2+1 x^2 = 2y^2+1/8 Answer : E The answer is: E
E
mathematics
You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7. What is the probability that you get a sum of 4 before the sum of 7?
[ "5/6", "4/5", "2/5", "1/8", "4/4" ]
C 2/5 This problem can be solved with different approaches. Let us not go into the complicated generic stuff to avoid confusion and try to solve it with simpler means. Let us find the results separately. There can be 4 different results that give the sum of 5 and there can be 6 different results that give the sum of 7. Thus, the probability that we get the sum of 4 before the sum of 7 will be: 4/(4+6) = 4/10 = 2/5. The answer is: C
C
mathematics
There are 720 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
[ "75", "100", "120", "175", "225" ]
Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 720. Hence, we have m+f= 720 Now, we have that half the female participants and one-quarter of the male participants are Democrats. Let d equal the number of the Democrats. Then we have the equation f/2 + m/4 =d Now, we have that one-third of the total participants are Democrats. Hence, we have the equation d = 720/3 = 240 Solving the three equations yields the solution f = 240,m= 480, and d= 240. The number of female democratic participants equals half the female participants equals 240/2 = 120. ANSWER:C The answer is: C
C
mathematics
The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?
[ "179 cm and 172 cm", "181 cm and 169 cm", "173 cm and 178 cm", "176 cm and 176 cm", "174 cm and 177 cm" ]
Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm. Answer: B The answer is: B
B
mathematics
96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
[ "66", "77", "42", "88", "12" ]
x/7 = y/9 => x:y = 7:9 7/16 * 96 = 42.Answer: C The answer is: C
C
mathematics
A, B and C started a shop by investing Rs. 4,000, Rs. 12,000 and Rs. 8,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 1,000, then the total profit was :
[ "3,000", "60,000", "80,000", "120,000", "None" ]
Sol. A : B : C = 4000 : 12000 : 8000 = 1: 3 : 2. so, C’s share : Total Profit = 2 : 6 Let the total profit be Rs. x. Then, 2/6 = 1000/x or x = 1000 * 6/ 2 = 3000. Answer A The answer is: A
A
mathematics
If ab - 2c = a(b - c), which of the following must be true?
[ "a=2 and c=0", "a=1/2 and b=2", "b=1 and c=0", "a=1 or b=0", "a=1/2 or c=0" ]
ab-2c = a (b-c) ab - 2c = ab - ac 2c= ac ac-2c = 0 c(a-2) = 0 Either c = 0; or a = 2 A is the answer The answer is: A
A
mathematics
If there are 80 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
[ "1/25", "2/25", "3/25", "4/25", "21/25" ]
30 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3 So, 5x=80 ---> x=16 Red marbles = 2*x = 2*16 = 32 Blue marbles = 3*x = 3*16 = 48 Prob to select a red marble = 32/80 = 2/5 Prob to select 2 red marbles with replacement = 2/5*2*5 = 4/25 Hence, answer will be D. The answer is: D
D
mathematics
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?
[ "0.096", "0.128", "0.488", "0.512", "0.64" ]
Re-phrasing the question: What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain Probablity of rain = 0.6 Therefore, probability of no rain = 0.4 0.4*0.4*0.6 = 0.096 Hence A The answer is: A
A
mathematics
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 588, what was his profit?
[ "s. 64", "s. 69", "s.108", "s.75", "s.90" ]
C.P. = Rs. (100/122.5)x588 = Rs. (1000/1225)x588 = Rs. 480 Profit = Rs. (588 - 480) = Rs. 108. Answer:C The answer is: C
C
mathematics
A truck covers a distance of 392 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 70 km more than that travelled by the truck ?
[ "6 hours", "5 hours", "7 hours", "8 hours", "None" ]
Explanation : Speed of the truck = Distance/time = 392/8 = 49 kmph Now, speed of car = (speed of truck + 18) kmph = (48 + 18) = 66 kmph Distance travelled by car = 392 + 70 = 462 km Time taken by car = Distance/Speed = 462/66 = 7 hours. Answer – C The answer is: C
C
mathematics
2 men catch 2 fish in 2 minutes. At this rate, how many men could catch 500 fish in 500 minutes?
[ "2", "4", "6", "500", "0" ]
2 men.....there are no other!!!! The answer is: A
A
mathematics
At Veridux Corporation, there are 215 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
[ "50", "20", "25", "30", "35" ]
Well, first let’s take care of the “totals”. The numbers in the “totals” row must add up. If 90 are females, the other 215 – 90 = 125 must be males. Similarly, the numbers in the “totals” column must add up. If 40 are managers, then the other 215 – 40 = 175 must be associates. Now, in the “associate” row, 135 + E = 175, which means E = 40— the other 40 associates must be female. Now, to find B, which is what the question is asking, we need only look at the sum in the “female” column: B + 40 = 90, which means B = 50. There are fifteen female managers in this company. Thus, the answer = 50(A). The answer is: A
A
mathematics
Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 14 inches on a side and costs $10, and a large pizza that measures 21 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
[ "5 square inches", "10 square inches", "49 square inches", "25 square inches", "350 square inches" ]
In the first case each can buy one pizza of $10 and one pizza of $20. In square inches that would be (14*14=196) for the small pizza and (21*21=441) for the large pizza. In total sq inches that would be (196+441)*2= 1274 sq inches. In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*441= 1323 sq inches. Hence, the difference is 49 square inches more (1323-1274). The correct answer is C The answer is: C
C
mathematics
A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
[ "5", "4", "7", "3", "5.1" ]
M = 5.5 S = 1.5 DS = 7 US = 4 AS = (2 * 7 * 4) /11 = 5.1 Answer: E The answer is: E
E
mathematics
It was calculated that 75 men could complete a piece of work in 10 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
[ "10 days.", "20 days.", "25 days.", "12.5 days.", "15 days." ]
One day work = 1 / 10 One man’s one day work = 1 / ( 10 * 75) Now: No. Of workers = 50 One day work = 50 * 1 / ( 10 * 75) The total no. of days required to complete the work = (75 * 10) / 50 = 15 Answer:E The answer is: E
E
mathematics
If the number 653 xy is divisible by 90, then (x + y) = ?
[ "2", "3", "4", "6", "5" ]
90 = 10 x 9 Clearly, 653xy is divisible by 10, so y = 0 Now, 653x0 is divisible by 9. So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4. Hence, (x + y) = (4 + 0) = 4. Answer: C The answer is: C
C
mathematics
If sy + z = s(y + z), which of the following must be true?
[ "x = 0 and z = 0", "s= 1 and y = 1", "s = 1 and z = 0", "s = 1 or y = 0", "s = 1 or z = 0" ]
sy + z = sy + sz z = sz case 1: z not= 0, s = z/z = 1 case 2: z = 0, 0 = s0 = 0 Combining 2 cases: s = 1 or z =0 E. is the answer. The answer is: E
E
mathematics
Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 15 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
[ "20", "40", "60", "80", "100" ]
Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam. After 40 minutes Annie is 2 km ahead. In the next 15 minutes, Sam rides 3 km so Sam will be 1 km ahead. It will take Annie 20 minutes to catch Sam. The answer is A. The answer is: A
A
mathematics
The average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student. The weight of the student is
[ "62 kg", "60 kg", "70 kg", "72 kg", "None of these" ]
Explanation : Let the weight of student be x kg. Given, Difference in average weight = 3 kg => (80-x)/6 = 3 => x = 62 Answer : A The answer is: A
A
mathematics
Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
[ "30", "36", "70", "80", "150" ]
Method I: the rates solution “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time: T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36 BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums. Answer = B. The answer is: B
B
mathematics
Roy opened a shop investing Rs.20000. Alex joined him 8 months later, investing Rs.34000. They earned a profit of Rs.32000 after completion of two years. What will be Roy's share of profit?
[ "18000", "19000", "20000", "15000", "17000" ]
SoL = ~s- So Roy's share = [15/32] x 32000 = 15000 Answer : D The answer is: D
D
mathematics
A certain boxer has agreed to pay his opponent a fee of 3% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in seven pounds over the specified limit, what was the boxer's purse?
[ "$65,625", "$105,000", "$125,000", "$183,750", "$1,050,000" ]
.03*7 = .21 26250/.21 = $125,000 Answer: C The answer is: C
C
mathematics
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
[ "7 sec", "6 sec", "4 sec", "2 sec", "1 sec" ]
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr [66 * 5/18] m/sec = [55/3] m/sec. Time taken to pass the man = [110 * 3/55] sec = 6 sec Answer: B The answer is: B
B
mathematics
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 12 o’clock in the afternoon?
[ "120°", "90°", "180°", "320°", "None of these" ]
Sol. Angle traced by the hour hand in 4 hours = [360/12 * 4]° = 120° Answer A The answer is: A
A
mathematics
A boy traveled from the village to the post-office at the rate of 12.5 kmph and walked back at the rate of 2 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.
[ "5 km", "7 km", "9 km", "10 km", "12 km" ]
Explanation : Solution: Average speed = 2xy/(x+y) km/hr = (2*12.5*2)/(12.5+2) km/hr = 50/14.5 km/hr. Total distance = (50/14.5 * 29/5) km. = 20 km. Required distance = 20/2 = 10 km. Answer : D The answer is: D
D
mathematics
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 80 sq. feet, how many feet of fencing will be required?
[ "28", "40", "68", "88", "78" ]
We have: l = 20 ft and lb = 80 sq. ft. So, b = 4 ft. Length of fencing = (l + 2b) = (20 + 8) ft = 28 ft. ANSWER:A The answer is: A
A
mathematics
A man spent 1/5 of his loan amount on house construction and 1/4 of the remaining on his office renovation. How much fraction of the loan amount is he left with after spending on house and office renovation?
[ "3/5", "2/6", "5/4", "1/5", "4/3" ]
The man spent 1/5 his loan amount on house construction, remaining amount is 4/5 He spent 1/4 of the remaining amount for office renovation, 1/4*4/5=4/20 Total loan amount spent on house and office renovation =1/5+4/20 To get a common denominator we use 20, so 1/5 is 4/20 4/20+4/20=8/20 is the total amount spent on house construction and office renovation. remaining 12/20 is left with the man, 3/5 Answer is A The answer is: A
A
mathematics
In a college students can play cricket or basketball. 500 play cricket.220 played both and 600 played basketball. What is the total strength of college?
[ "800", "880", "920", "950", "980" ]
P(C)= 500 P(B)=600 P(C n B) =220 P(C U B)= P(C)+ P(B) - P(C n B) = 500+600-220= 880 ANSWER:B The answer is: B
B
mathematics
A milk man has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
[ "20%", "25%", "33.33%", "18%", "None of these" ]
Explanation: when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk. Therefore, profit percentage = 25 %. Answer: B The answer is: B
B
mathematics
Mrs. Rodger got a weekly raise of $135. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
[ "$ 145.", "$ 146", "$ 135", "$ 148", "None" ]
Solution: Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 135. So after completing the 1st week she will get $ (x+135). Similarly after completing the 2nd week she will get $ (x + 135) + $ 135. = $ (x + 135 + 135) = $ (x + 270) So in this way end of every week her salary will increase by $ 135. Answer C The answer is: C
C
mathematics
The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability T that exactly two visitors will buy a pack of candy?
[ "0.343", "0.147", "0.189", "0.063", "0.027" ]
3C2 * (3/10)^2 * 7/10 = 3 * 9/100 * 7/10 = 189/1000 = 0.189=T Answer - C The answer is: C
C
mathematics
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $55,000?
[ "$38,796.", "$40,000.", "$38,976.", "$39,679.", "$53,592." ]
55,000 *1.16*.84= 53,592 Answer E The answer is: E
E
mathematics
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
[ "150 m", "350 m", "300 m", "240 m", "none" ]
Speed =(54 x5/18m/sec) = 15 m/sec. Length of the train = (15 x 20)m =300 m. Let the length of the platform be x metres. Then,x + 300/36= 15 x + 300 = 540 x = 240 m Answer: D The answer is: D
D
mathematics
If 1 + 9 + 11 = 1, Then what is the value of 12 + 11 + 9 = ?
[ "12", "7", "11", "9", "10" ]
E Explanation: Equation 1 + 9 + 11 = 1 can be derived from One (o) + nine (n) + eleven (e) = one => 1 Similarly for equation, 12 + 11 + 9 Twelve (t) + eleven (e) + nine (n) => ten (10) The answer is: E
E
mathematics
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 72 sec. The length of each train is?
[ "50", "26", "27", "28", "100" ]
Let the length of each train be x m. Then, distance covered = 2x m. Relative speed = 46 - 36 = 10 km/hr. = 10 * 5/18 = 25/9 m/sec. 2x/72 = 25/9 => x = 100. Answer: E The answer is: E
E
mathematics
A certain Maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight. A certain green paint contains 10 percent blue pigment and 90 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
[ "1.5", "2", "2.5", "3", "3.5" ]
10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.3 =1.5 Grams of red pigment The answer is: A
A
mathematics
Raman mixed 48 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
[ "129", "287", "195", "188", "112" ]
Explanation: CP per kg of mixture = [48(150) + 36(125)]/(48 + 36) = Rs. 139.28 SP = CP[(100 + profit%)/100] = 139.28 * [(100 + 40)/100] = Rs. 195 Answer:C The answer is: C
C
mathematics
A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be
[ "7744", "2388", "3778", "2992", "2888" ]
Explanation: length of wire = {\color{Blue}2 \Pi r}= 2 *(22/7 )*56 = 352 cm side of the square = 352/4 = 88cm area of the square = 88*88 = 7744sq cm Answer: A) 7744 The answer is: A
A
mathematics
A store raised the price of an item by exactly 20 percent. Which of the following could NOT be the resulting price of the item?
[ "6", "12", "18", "24", "58" ]
If it raised the value by 20% then the resulting price is 1.2 times the original price. So the final answer has to be a multiple of 1.2. Check the answers. 6 - Yes 12 - Yes 18 - Yes 24 - Yes 58 - No Answer : E The answer is: E
E
mathematics
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 60 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
[ "17 1/4 min", "28 1/7 min", "15 min", "17 1/8 min", "17 5/7 min" ]
1/20 + 1/30 - 1/60 = 4/60 = 1/15 15/1 = 15 Answer:C The answer is: C
C
mathematics
The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
[ "11 years", "12 years", "13 years", "18 years", "10 years" ]
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years. Answer: A The answer is: A
A
mathematics
If both a and b belongs to the set {1,2,3,4 }, then the number of equations of the form ax2 + bx + 1 = 0 having real roots is
[ "10", "7", "6", "12", "15" ]
Explanation : ax2 + bx + 1 = 0 . For real roots => b2 -4ac ≥ 0 . i.e b2 - 4a(1) ≥ 0 . i.e b2 ≥ 4a. For a = 1, 4a = 4, ∴ b = 2, 3, 4 a = 2, 4a = 8, ∴ b = 3, 4 a = 3, 4a = 12, ∴ b = 4 a = 4, 4a = 16, ∴ b = 4 ∴ Number of equations possible = 7. Harsh Mishra a year ago 0 upvotes Answer : B The answer is: B
B
mathematics
The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new man.
[ "69", "72", "75", "71", "None of them" ]
Total weight increased =(1.8 x 10) kg =18 kg. :. Weight of the new man =(53 + 18) kg =71 kg. Answer is D The answer is: D
D
mathematics
Samantha is driving from City A to City B. The distance between the two cities is 88 miles. She is driving at a constant speed of 22 miles per hour, and has been travelling for half an hour after starting from City A. What percent of the total distance she is yet to cover?
[ "87", "87.5", "88", "90", "97.5" ]
She is driving at the rate of 22 miles per hour for half an hour. Means the distance she has covered so far is = speed x time = 22 miles per hour x 0.5 hour = 11 miles. Therefore, the distance she is yet to cover is 88 - 11 = 77 miles. We want to know 77 miles is what percent of the total distance (88 miles). Let it be x % of the total distance. This means x % of 88 = 77 Solving we get, x = 87.5 Ans B The answer is: B
B
mathematics
A train covers a distance at a speed of 240kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of?
[ "516", "840", "560", "720", "920" ]
Distance = 240*5 = 1200km Required speed = 1200*3/5 = 720 km/hr Answer is D The answer is: D
D