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mathematics
A university needs to select a nine-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?
[ "44", "55", "66", "77", "88" ]
student government + the student advisory board consists of 9 + 8 = 17 members. 6 students hold membership in both, so they were counted twice. The total number of people to choose from is 17 - 6 = 11 The number of ways to choose 9 members from 11 is 11C9 = 55 The answer is B. The answer is: B
B
mathematics
when W is divided by 13, the reminder is 0. if W is one lesser than it value and when divided by 5 its remainder is 0. what is the value of W ?
[ "13", "25", "26", "52", "65" ]
W is divided by 13 so that is multiple of 14 as 13,26,39... W-1 is divided by 5 the remainder is 0 so it is divisible by 5. Consider from option let us take the number is 13 it is divisible by 13 but 13-1 is not divisible by 5 so it is not answers so let us take 2nd option 25 which is not divisible by 13 in 3rd option 26 is divisible by 13 and 26-1 is divisible by 5 so ans is C The answer is: C
C
mathematics
A shop owner sells 60mtr of cloth and gains SP of 10 mtrs. Find the gain %?
[ "20%", "40%", "50%", "60%", "70%" ]
Here, selling price of 10 m cloth is obtained as profit. Profit of 10 m cloth = (S.P. of 60 m cloth) – (C.P. of 60 m cloth) Selling price of 50 m cloth = Selling Price of 60 m of cloth Let cost of each metre be Rs. 100. Therefore, cost price of 50 m cloth = Rs. 5000 and S.P. of 50 m cloth = Rs. Rs. 6000 Profit% = 10/50 × 100 = 20% 20 Profit of 20% was made by the merchant. A The answer is: A
A
mathematics
An Olympic diver received the following scores: 4, 3, 7, 6, and 5. The standard deviation of her scores is in which of the following ranges?
[ "2.4 to 2.8", "1.4 to 1.8", "3.4 to 3.8", "4.4 to 4.8", "5.4 to 5.8" ]
4+3+7+6+5/5 = 5 |4-5| = 1 1^2 = 0 |3-5| = 2 2^2 = 4 |7-5| = 2 2^2 = 4 |6-5| = 1 1^2 = 1 |5-5| = 0 0^2 = 0 SD = sqrt 10/5 =1.41 Answer : B The answer is: B
B
mathematics
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
[ "49", "50", "12", "13", "67" ]
Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr. Answer: Option B The answer is: B
B
mathematics
A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 50 days as before. How many of them left?
[ "400", "288", "266", "121", "158" ]
2000 ---- 50 2000 ---- 40 x ----- 50 x*50 = 2000*40 x=1600 2000 ------- 400 Answer: A The answer is: A
A
mathematics
A person covers a distance in 12 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
[ "8 m/s", "4 m/s", "15 m/s", "10 m/s", "5 m/s" ]
Explanation: T = 12 m Spees = 12 kmph = 12 x 5/18 = 10/3 m/s Let new speed be "x" 12 x (10/3) = 5x x = 8 m/s Answer: Option A The answer is: A
A
mathematics
A plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?
[ "11.40 p.m.", "12.40 p.m.", "1.40 p.m.", "2.40 p.m.", "4.40 p.m." ]
Time difference between places will be 4*(40+40) minutes = 320 min = 5 hrs 20 min as change of 1 degree in longitude cause change of 4 minutes in time. and that change is 80 degrees here. so when plane land. time will be = 10.00 + 8.00 -5.20 = 12.40 p.m. ANSWER:B The answer is: B
B
mathematics
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 3?
[ "180", "288", "286", "284", "324" ]
We have to find the total number of 3-digit odd numbers not having 3 as a digit. Units digits will be among 1,5,7,9 Tenth digits will be among 0,1,2,5,4,6,7,8,9 Hundredth digits will be among 1,2,5,4,6,7,8,9 So total numbers = 4*9*8 =288 Answer : B The answer is: B
B
mathematics
A can do a job in 20 days and B can do it in 30 days. A and B working together will finish thrice the amount of work in ------- days?
[ "22 days", "22 days", "36 days", "72 days", "24 days" ]
1/20 + 1/30 =5/60 = 1/12 12/1 = 12 *3= 36 days Answer: C The answer is: C
C
mathematics
If selling price is doubled, the profit triples. Find the profit percent.
[ "20%", "25%", "30%", "60%", "100%" ]
Let C.P. be Rs. x and S.P. be Rs. y. Then, 3(y - x) = (2y - x) y = 2x. Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x. Profit % = x x 100 % = 100% x E) The answer is: E
E
mathematics
A jar contains 9 marbles consisting of an equal number of red, green, and blue marbles. Three marbles are removed from the jar and discarded. What is the probability that only two colors will remain in the jar after the Three marbles have been removed?
[ "1/49", "1/16", "1/28", "1/3", "1/2" ]
Jar contains {3-red, 3-green, 3-blue} marbles. We are asked to find the probability that after removing 3 marbles only 2 colours remain in the jar, i.e., the probability of removing EITHER red, OR green, OR blue. Sample space = 9C3 = 84. Probability of choosing 3 red = 3C3/9C3 = 1/84. Probability of choosing 3 green = 3C3/9C3 = 1/84. Probability of choosing 3 blue = 3C3/9C3 = 1/84. Required probability = 1+1+1/84 = 3/84 = 1/28. Ans (C). The answer is: C
C
mathematics
The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
[ "Rs.1718", "Rs.1729", "Rs.1750", "Rs.1724", "Rs.1723" ]
C.I. = [4000 * (1 + 10/100)2 - 4000] = (4000 * 11/10 * 11/10 - 4000) = Rs. 840. Sum = (420 * 100)/(3 * 8) = Rs.1750 Answer:C The answer is: C
C
mathematics
A box contains 11 apples, 10 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
[ "3", "4", "5", "6", "7" ]
P(choosing a red apple 6 times in a row) = 10/11*9/10*8/9*7/8*6/7*5/6 = 5/11 < 0.5 The answer is D. The answer is: D
D
mathematics
The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.
[ "60", "59", "62", "66", "58" ]
6th result = (58*6+63*6-60*11)=66 Answer is D The answer is: D
D
mathematics
15.03 × 0.01 = ?
[ "0.1503", "0.001503", "1.503", "0.001503", "None of these" ]
15.03 × 0.01 = ? or,? = 0.1503 Answer A The answer is: A
A
mathematics
FOG + FOG + FOG + FOG = 1460. If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
[ "11", "12", "13", "14", "15" ]
given,FOG + FOG + FOG + FOG = 1460 4(FOG)=1460 =>FOG=365 Face value of F is:3 Face value of O is:6 Face value of G is:5 so F+O+G=3+6+5=14 ANSWER:D The answer is: D
D
mathematics
Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 45 marks. How many sums did Sandy get correct?
[ "18", "21", "24", "27", "28" ]
Let x be the correct sums and (30-x) be the incorrect sums. 3x - 2(30-x) = 45 5x = 105 x = 21 The answer is B. The answer is: B
B
mathematics
If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
[ "67%.", "70%.", "60%.", "68%.", "80%." ]
Given ratio = 1/8 : 1/5 = 5 : 8 Let first number be 5x and the second number be 8x. The second number is more than first number by 3x. Required percentage = 3x/5x * 100 = 60%. Answer: C The answer is: C
C
mathematics
A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 700 m long?
[ "28 sec", "89 sec", "95 sec", "16 sec", "15 sec" ]
Speed = 250/25 = 10 m/sec. Required time = (250 + 700)/10 = 95 sec. Answer:C The answer is: C
C
mathematics
Which one of the following is the sum of the numbers 1, 3, 5, 7, 9…. up to nth number?
[ "N2 + 1", "N2 - 1", "N(N + 1)/2", "N2", "N(N + 1)" ]
Explanation: N2 Answer: D The answer is: D
D
mathematics
I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
[ "25", "37", "54", "65", "75" ]
when divided 2,3,4 leaves remainder 1 and leaves remainder 0 while dividing 5 ANSWER:A The answer is: A
A
mathematics
In a certain store, the profit is 320% of the cost. If the cost increases by 35% but the selling price remains constant, approximately what percentage of the selling price is the profit
[ "68%", "80%", "90%", "100%", "None of above" ]
Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 135% of Rs. 100 = Rs. 135 New S.P. = Rs. 420. Profit = Rs. (420 - 135) = Rs. 285 Required percentage = (285/420) * 100 = 68%(approx) Answer: A The answer is: A
A
mathematics
A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?
[ "60 miles / hour", "50 miles / hour", "80 miles / hour", "90 miles / hour", "40 miles / hour" ]
We first convert the time of 4 hours 41 minutes in minutes 4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes Average speed S is given by distance / time. Hence S = 281 miles / 281 minutes = 1 mile / minute = 60 miles / hour correct answer A The answer is: A
A
mathematics
A feed shop sells two varieties of birdseed: Product A, which is 40% millet and 60% sunflower, and Product B, which is 65% millet and 35% safflower. If a customer purchases a mix of the both types of birdseed that is 50% millet, what percent of the mix is Product A?
[ "50%", "55%", "60%", "40%", "45 %" ]
Yes there is a simple method : Consider the following method Product A : 40% millet and 60% sunflower Product B : 65% millet and 35% safflower Mix : 50% millet Here the weighted average is 50%, Now Product A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I Similarly, Product B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II Now, both Product A and Product B are combined to give a 50% mix containing millet, so equate I and II implies, 0.10 A = 0.15 B Therefore A/B = 0.15/0.10 = 3/2 A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5 We have to find, percent of the mix is Product A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 % Here is a pictorial representation : Product A= 40%------------------------10% or 0.10 below average, A times-----------------Total below = - 0.10 A ----------------------------------------------------------------------------------------Average = 50% or 0.50 Product B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B Since the amount below the average has to equal the average above the average; therefore, 0.10 A = 0.15 B A/B = 3/2 A:B: Total = 3:2:5 A/Total = 3:5 = 60 % Answer: C The answer is: C
C
mathematics
Twelve machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?
[ "2", "3", "4", "6", "8" ]
Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original. So 3/2*12 =18 So we need 18-12 = 6 more machines. Answer : D The answer is: D
D
mathematics
If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 200 units?
[ "50 hours", "40 hours", "25 hours", "12 hours", "8 hours" ]
Here, we're told that 5 machines can produce 20 units in 10 hours.... That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units. 20 units/5 machines = 4 units are made by each machine every 10 hours Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to... 10 hours/4 units = 2.5 hours per unit when 1 machine is working. The prompt asks us how long would it take 20 machines to produce 200 units. If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 200 units is '10 times' 20, we need '10 times' more TIME. (2.5 hours)(10 times) = 25 hours Final Answer: [Reveal]Spoiler: C The answer is: C
C
mathematics
Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
[ "Rs.2166.67", "Rs.2187.67", "Rs.2188", "Rs.2200", "Rs.2234.7" ]
Now, in this numerical, there is no common loss and gain %. Hence, solve it making equations. Let cost price of camel be x. As cost of camel and carriage = Rs 5000 Cost of carriage = Rs. (5000 – x) After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%. Therefore, 20% of x – 10 % of (5000 – x) = 3 % of 5000 20 × x – 10 × (5000 – x) = 3 × 5000 100 100 100 x – (5000 – x) = 150 5 10 10x – (5000 – x) × 10 = 150 × 10 5 10 2x-5000+x=1500 3x=1500+5000 x=2166.67 The cost of camel = Rs.2166.67 Option (A) is the correct answer The answer is: A
A
mathematics
A can do a piece of work in 8 days. B can do it in 12 days. With the assistance of C they completed the work in 4 days. Find in how many days can C alone do it?
[ "87 days", "20 days", "16 days", "24 days", "36 days" ]
C = 1/4 - 1/8 - 1/12 = 1/24 => 24 days Answer:D The answer is: D
D
mathematics
Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
[ "1", "4", "5", "6", "8" ]
2: 5: 13 2x 5x 13x 15 7.5 2.5 30x + 37.5x + 32.5x = 100x/20x Average = 5 Answer: C The answer is: C
C
mathematics
Car A runs at the speed of 50km/hr & reaches its destination in 8hr. Car B runs at the speed of 25 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
[ "4 : 1", "11 : 8", "13 : 7", "15 : 7", "16 : 9" ]
Sol. Distance travelled by Car A = 50 × 8 = 400 km Distance travelled by Car B = 25 × 4 =100 km Ratio = 400/100 = 4 : 1 Answer : A The answer is: A
A
mathematics
The cost of producing x tools by a company is given by C(x) = 1200 x + 5500 (in $) a) What is the cost of 100 tools?
[ "125500 $", "125800 $", "125900 $", "126500 $", "122500 $" ]
Solution C(100) = 1200*100 + 5500 = 125500 $ Answer A The answer is: A
A
mathematics
A train traveled the first d miles of its journey it an average speed of 60 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 90 miles per hour, what is the value of y?
[ "68", "84", "90", "110", "135" ]
Average speed=Total distance traveled /Total time taken 3d/d/60+d/y+d/160=90 Solving for d and y, 15y=11y+480 4y=440 y=110 Answer D The answer is: D
D
mathematics
A furniture store owner decided to drop the price of her recliners by 20% to spur business. By the end of the week she had sold 50% more recliners. What is the percentage increase of the gross?
[ "10%", "15%", "20%", "25%", "50%" ]
Say a recliner is actually worth $100 If she sells 100 recliners then she earns $10000 After the discount of 20%, she will earn $80 per recliner and she sells 50% more ie.,150 recliners Hence her sales yields 150*80=$12000 Increase in sales=12000-10000=$2000 So% increase = 2000*100/10000 =20% C is the answer The answer is: C
C
mathematics
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
[ "8", "2", "7", "5", "3" ]
45*12 : 54*x = 2: 1 x = 5 12 -5 = 7 Answer: C The answer is: C
C
mathematics
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 3 buckles is how many times that of 5 buckles and 6 buttons?
[ "7/15.", "4/9.", "6/11.", "5/9.", "8/15." ]
2buttons + 2buckles = 1/3(11buckles + 3buttons) 6buttons + 6buckles = 11buckles + 3buttons 3buttons = 5buckles Weight of 3buttons and 3buckles = 5buckles + 3buckles = 8buckles Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles (3buttons and 2buckles) = x * (6buttons and 5buckles) 8 = x*15 x = 8/15 Answer: E The answer is: E
E
mathematics
A large tank can filled by A and B in 30 minutes and 45 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
[ "30min", "20min", "25min", "40min", "45min" ]
Part filled by A+B in 1 minute = 1/30 + 1/45 = 1/45 Suppose the tank is filled in x minutes Then, x/2(1/45 + 1/45) = 1 x/2 * 2/45 = 1 x = 45 min Answer is E The answer is: E
E
mathematics
How many two-element subsets of {2,4,6,8} are there that do not contain the element 4?
[ "1", "2", "3", "4", "5" ]
Required subsets are = {2,6}, {2,8}, {6,8}= 3 Answer: C The answer is: C
C
mathematics
The below sequence is a bit tricky. Can you solve it to find the next number? 8, 28, 328, 4328, ?
[ "29816", "38291", "54325", "38290", "54328" ]
See the pattern. With every digit, the previous numbers are added after that digit So the next number in the series is 54328 Answer : E The answer is: E
E
mathematics
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?
[ "6.25", "6.28", "6.11", "6.19", "6.21" ]
Required run rate = [282 - (3.2 * 10)]/40 = 250/40 = 6.25 Answer:A The answer is: A
A
mathematics
How many times will the hands of a clock coincide in a day?
[ "24", "22", "23", "44", "42" ]
solution The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day so Answer is B The answer is: B
B
mathematics
If a 10 percent deposit that has been paid toward the purchase of a certain product is $120, how much more remains to be paid?
[ "$880", "$990", "$1,000", "$1,100", "$1,080" ]
10/100P = 120 >> p= 120*100/10 = 1200 1200 - 120 = 1080 ANSWER:E The answer is: E
E
mathematics
The arithmetic mean of the scores of a group of students in a test was 42. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
[ "A)61.4.", "B)51.7", "C)33.18", "D)51.1", "E)51.2" ]
Let the required mean score be x. Then, 20 * 80 + 25 * 31 + 55 * x = 42 * 100 = 1600 + 775 + 55x = 4200 = 55x = 1825 = x = 33.18 Answer:C The answer is: C
C
mathematics
The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 40 more than the number who did not, and if receipts for registration and lunch totaled $39,480, how many people paid just for registration at the meeting?
[ "700", "800", "300", "1,500", "1,800" ]
Hope this might be useful to you. Let the number of people who have opted only to register = x Now since the registration cost is 50$ per person, the total amount sums to = 50x $ As per the information given in the question, the number of registrants who paid for lunch was 40 more than the number who did not. That means, total number of people who registered and paid for lunch = 40 + x. For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $. Total amount in this case sums to = 72(40 + x) = 2880 + 72x Now, total amount received was 39480 Thus, from the above data, 50x + 2880 + 72x = 39480 122x = 39480 - 2880 122x = 36600 x = 300. Hence the correct Ans is C The answer is: C
C
mathematics
The food in a camp lasts for 20 men for 50 days. If twenty more men join, how many days will the food last?
[ "22 days", "25 days", "28 days", "16 days", "27 days" ]
one man can consume the same food in 20*50 = 1000 days. 20 more men join, the total number of men = 40 The number of days the food will last = 1000/40 = 25 days. Answer:B The answer is: B
B
mathematics
A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by e meteres, What is the area of the rug in square meters?
[ "mn - p(m+n)", "mn – 2p(m+n)", "mn – p^2", "(m - p)(n - p)", "(m - 2p)(e - 2p)" ]
The answer must be E. Plug in M 100 N 50 e 10. The answer is: E
E
mathematics
In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one of each type of coin must be included?
[ "49", "69", "73", "91", "99" ]
I. Case I = Four Quarters = this is impossible, because if we already have a dollar in quarters, then we cannot have any dimes. We can't have all four coins represented if we have four quarters. II. Case II = Three Quarters (75 cents) This allows for two or one dime. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels. Subcase 1 = 3 Q, 2 D (95 cents) 1) one nickel (N) and 5 pennies (P) (2 nickels would not allow for any pennies) Subcase 2 = 3 Q, 1 D (85 cents) 2) 3 N and 5 P 3) 2 N and 10 P 4) 1 N and 15 P Case II allows for a total of four ways. III. Case III = Two Quarters (50 cents) This allows for 1-4 dimes. Subcase 1 = 2 Q, 4 D (90 cents) (2 ways) we could have 1-2 nickels Subcase 2 = 2 Q, 3 D (80 cents) (4 ways) we could have 1-4 nickels Subcase 3 = 2 Q, 2 D (70 cents) (6 ways) we could have 1-6 nickels Subcase 4 = 2 Q, 1 D (60 cents) (8 ways) we could have 1-8 nickels Case III allows for a total of 20 ways IV. Case IV = One Quarter (25 cents) This allows for 1-7 dimes Subcase 1 = 1 Q, 7 D (95 cents) (1 way) we could have 1 nickel Subcase 2 = 1 Q, 6 D (85 cents) (3 ways) we could have 1-3 nickels Subcase 3 = 1 Q, 5 D (75 cents) (5 ways) we could have 1-5 nickels Subcase 4 = 1 Q, 4 D (65 cents) (7 ways) we could have 1-7 nickels Subcase 5 = 1 Q, 3 (55 cents) (9 ways) we could have 1-9 nickels Subcase 6 = 1 Q, 2 D (45 cents) (11 ways) we could have 1-11 nickels Subcase 7 = 1 Q, 1 D (35 cents) (13 ways) we could have 1-13 nickels Case IV allows for a total of 49 ways. There's no other case, because we have to have at least one quarter and one dime. The total over the cases equals Total = 4 + 20 + 49 =73 ways. OA =(C) The answer is: C
C
mathematics
Kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?
[ "3500", "1500", "2500", "4500", "None of them" ]
Let the no of fifty rupee notes be x Then,no of 100 rupee notes =(85-x) 50x+100(85-x)=5000 x+2(85-x)=100 x=70 so, required amount=Rs.(50*70)= Rs.3500 Answer is A. The answer is: A
A
mathematics
By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
[ "42 6/8%", "42 8/7%", "482 6/7%", "42 6/7%", "42 1/7%" ]
SP = CP + g 50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? => 42 6/7% Answer:D The answer is: D
D
mathematics
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
[ "337", "375", "297", "266", "291" ]
CP1 = 100 SP1 = 120 CP2 = 80 SP2 = 80 * (125/100) = 100 20 ----- 100 75 ----- ? => 375 Answer: B The answer is: B
B
mathematics
What is the greatest prime factor of 8^11 - 2^30?
[ "2", "3", "5", "7", "11" ]
8^11 - 2^30 =(2^3)^11 - 2^30 = 2^33 - 2^30 = 2^30 (2^3 -1) = 2^30 * (8-1) = 2^30 * 7 The greatest prime factor is 7. The answer is D. The answer is: D
D
mathematics
If 6 (A's capital) = 8 (B's capital) = 12 (C's capital). Then the ratio of their capitals is?
[ "20:15:16", "4:3:1", "4:3:2", "20:15:11", "20:15:19" ]
6A = 8B = 12 C A:B:C = 1/6:1/8:1/12 = 4:3:2 Answer: C The answer is: C
C
mathematics
Mohan purchased 15 kgs of rice at the rate of Rs.20 per kg and 8 kgs of pulses at the rate of Rs.20 per kg. Whaat is the total amount that he paid to the shopkeeper?
[ "A)Rs.598", "B)Rs.594", "C)Rs.460", "D)Rs.595", "None of these" ]
Explanation: Price of 15 kgs of rice at Rs.20/kg = 15x20 = Rs.300 Price of 8 kgs of pulses at Rs.20/kg = 8x20 = Rs.160 Therefore, Total amount = Rs.300+Rs.160 = Rs.460 Answer: Option C The answer is: C
C
mathematics
A clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?
[ "38", "11", "237", "29", "112" ]
Time from 5 a.m. on a day to 10 p.m. on 4th day = 89 hours. The faulty clock shows only 1424 min for 24 hours in correct clock. So 1 minute of the faulty clock = 24/1424 hours 1 hour of the faulty clock = 24/1424 × 60 hours 89 hours of the faulty clock = 24/1424 × 60 × 89 = 90 hours. So true time is 1 hour more than 10 pm. i.e., 11 pm.AnswerB The answer is: B
B
mathematics
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
[ "2288", "2778", "8297", "8112", "3241" ]
A = 7500(26/25)2 = 8112.Answer: D The answer is: D
D
mathematics
A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 50 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
[ "79", "89", "95", "77.27", "97.2" ]
Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6 A1+A2+A3+A4+A5+A6 = 100*6 = 600 The year before , the 5 courses be B1, B2 , B3 , B4 , B5 B1+B2+B3+B4+B5 = 50*5 = 250 Student's average = (600+250)/11 = 77.27 Answer D The answer is: D
D
mathematics
If The GCD of two numbers (not equal, both integers, greater than 1) is 2, then which of the following can be true? A. They are prime. B. They are even. C. They do not have a common prime factor. D. They do not have a common factor other than 2.
[ "Only A", "Only B", "Only C", "Only D", "Only B and D" ]
The GCD of two numbers (not equal, both integers, greater than 1) is 2 means that they don't share factors other than 1 and 2. This also means that both numbers are even ( divisible by 2.) A. They are not prime. 2 is the only even number that is prime, so one number can be prime but the other number cannot be. B. They are even. Since they are divisible by 2, they are even.. C. They have a common prime factor. The question defines the numbers as having a GCD of 2, which is prime. D. They have a common factor other than 2. Both numbers have common factors of 2 and 1. For example: The factors of 4 are 1 and 2, the factors of 6 are 1, 2, and 3. Therefore, (B) is the only correct answer. The answer is: B
B
mathematics
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
[ "5/34", "3/37", "9/42", "5/41", "7/43" ]
The probability that first toy shows the even number, =1021=1021 Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left. Hence, probability that second toy shows the even number, =920=920 Required probability, =(1021)×(920)=(1021)×(920) =9/42 C The answer is: C
C
mathematics
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability W that all three secretary are assigned at least one report?
[ "8/9", "64/81", "4/9", "16/81", "5/9" ]
I got the same answer: Here's my reasoning First Report you have 3 choices Second Report you have 2 choices Third Report you have 1 choice Fourth report 3 choices again Then total number of ways is: 3*2*1*3=3^2*2 This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases. The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36 Required probability W= 36/81.C The answer is: C
C
mathematics
The labeled price of a table is Rs. 6,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
[ "Rs. 4956", "Rs. 6195", "Rs. 6425", "Rs. 7200", "None of these" ]
Explanation: Labeled price = Rs. 6,000 By giving 5% discount on labeled price, the selling price is = 95 / 100 * 6,000 = Rs. 5700 By earning 15% profit on the selling of price Rs. 5700 the cost price is = 100 / 115 * 5700 = Rs. 4956 Therefore, approximate cost is 4956 ANSWER A The answer is: A
A
mathematics
Joshua and Jose work at an auto repair center with 1 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
[ "1/15", "1/12", "1/9", "1/6", "1/3" ]
Two Methods 1) Probability of chosing Josh first = 1/3 Probability of chosing Jose second = 1/2 total = 1/6 Probability of chosing Jose first = 1/3 Probability of chosing Josh second = 1/2 Total = 1/6 Final = 1/6 + 1/6 = 1/3 E The answer is: E
E
mathematics
Local kennel has cats and dogs in the ratio of 6:12. If there are 24 fewer cats than dogs, how many dogs are in the kennel?
[ "50", "48", "52", "54", "56" ]
Lets work with the data given to us. We know that there ratio of cats to dogs is 6:12 or cats 6 dogs 12 we can write number of cats as 6x and number of dogs as 12x and we know that 12x-6x= 24(therefore 6x = 24 => x=4) Then # of dogs = 12x4= 48 Answer is B The answer is: B
B
mathematics
If 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 Then 12 = ? Hint: Its a logic Riddle not a mathematical riddle
[ "1", "2", "3", "4", "5" ]
B 2 As stated 2=12 => 12=2 Answer is B The answer is: B
B
mathematics
At what rate percent on simple interest will a sum of money double itself in 60 years?
[ "3 1/3%", "3 1/9%", "1 2/3%", "3 2/3%", "3 6/3%" ]
P = (P*60*R)/100 R = 1 2/3% Answer: C The answer is: C
C
mathematics
Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
[ "1", "2", "4", "5", "6" ]
Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years. (4x + 8) = 5 (x + 8) 2 8x + 16 = 5x + 40 3x = 24 x = 8. Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2. B The answer is: B
B
mathematics
A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 5 seconds. Find the length of the train and its speed.
[ "5.6 m/sec", "15 m/sec", "18 m/sec", "9 m/sec", "25 m/sec" ]
If length of train is l and speed of train is s, then l/s = 5 (l+180)/s = 20 (l+180)/l = 20/5 =4 l+180 =5*l 4*l=180 l=45 mtrs s= l/5 = 45/5 = 9 m/sec ANSWER:D The answer is: D
D
mathematics
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
[ "40", "45", "70", "12", "25" ]
Answer: Option C a + b = 60, a = 2b 2b + b = 60 => b = 20 then a = 40. 5 years, their ages will be 45 and 25. Sum of their ages = 45 + 25 = 70. The answer is: C
C
mathematics
A Cuban cigar would cost 1 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
[ "16.7$.", "23$.", "25.5$.", "35$.", "37.4$." ]
The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each. From the given data we know French cigar < Cuban cigar < Arabic cigar and each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer. Therefore A is the answer The answer is: A
A
mathematics
If 70 percent of 600 is 40 percent of x, then x=?
[ "105", "168", "342", "660", "1050" ]
Given: 0.7*600=0.4x --> 420=4/10*x --> x=1,050. Answer: E. The answer is: E
E
mathematics
Mary has 1803 dollars with her. What is the amount that she should keep with her inorder to distribute the same among nine kids equally?
[ "3", "0", "10", "2", "6" ]
The answer is 3. (1803-3=1800). 1800 is divisible by nine which gives an answer of 20.So,she will be distributing 20 each for the nine kids and the remaining 3 will be left with her. So the answer is A=3 The answer is: A
A
mathematics
How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
[ "360", "560", "760", "840", "1260" ]
The most restrictive case. We should have a two. No repetition. Numbers range from 1 to 8. = 1*7*6*5 = 210 ways we can write if '2' is in the first position. = 4*(210) =840 ways. Another method. Without restriction for 8 digits- 8*7*6*5 = 1680 Ways we can write. Without restriction for 7 digits- 7*6*5*4 = 840 Ways. With restriction = 1680 - 840 = 840 Ways. ANSWER:D The answer is: D
D
mathematics
A is a set containing 8 different positive odd numbers. B is a set containing 7 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
[ "The range of B is even.", "The mean of A is even.", "The mean of B is even.", "The range of A is equal to the range of B.", "The median of B is equal to the mean of B." ]
Given: A is a set containing 8 different positive odd numbers Easily inferred: B is a set containing 7 differentoddnumbers (A) The range of B is even. - Always even, since it is a difference of two odd numbers (B) The mean of A is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number (C) The mean of B is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even. (D) The range of A is equal to the range of B. (E) The median of B is equal to the mean of B Option C. The answer is: C
C
mathematics
Two men are going along a track rail in the opposite direction. One goods train crossed the first person in 20 sec. After 10 min the train crossed the other person who is coming in opposite direction in 18 sec .After the train has passed, when the two persons will meet?
[ "95 minutes", "90 minutes", "88 minutes", "95 minutes", "None of these" ]
Explanation : Let us consider that speed of train , first man and second man are respectively t, f and s. According to first given condition goods train crossed the first person moving in same direction in 20 sec. So length of the will be 20(t-f) Similarly train crossed the second man in 18 sec. So length of the train will be 18(t+s) on comparing these two equations, we get 20(t-f) = 18(t+s) => 2t = 20f + 18s => t = 10f + 9s Now it is given that After 10 min the train crossed the other person who is coming in opposite direction. So,If we consider this way of train as L then the next equation will be L = 600t (here 600 is used for 10 minutes) Finally as asked in the question the time required to meet the two man after the train has passed will be given by Time = (L-600 f)/(f+s) {here 600f is used for the distance traveled by first man in 10 minutes} => = (600t-600f) / (f+s) => = [600(10f+9s)-600f] / (f+s) => = 600(10f+9s-f) / (f+s) = 600 * 9(f+s) / (f+s) => =600*9 seconds => = 600*9/60min => = 90 minutes Hence (B) is the correct answer. Answer : B The answer is: B
B
mathematics
The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than
[ "14 years", "12 years", "56 years", "66 years", "11 years" ]
Given that A+B = 11 + B + C => A – C = 11 + B – B = 11 => C is younger than A by 11 years Answer:E The answer is: E
E
mathematics
In how many different number of ways 4 boys and 2 girls can sit on a bench such that girls always sit together.
[ "A)720", "B)240", "C)740", "D)780", "E)790" ]
240 Option 'B' The answer is: B
B
mathematics
A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
[ "230", "997", "266", "289", "179" ]
Relative speed = 120 + 80 = 200 km/hr. = 200 * 5/18 = 500/9 m/sec. Let the length of the other train be x m. Then, (x + 270)/9 = 500/9 => x = 230. Answer: A The answer is: A
A
mathematics
If a > 1, which of the following is equal to (2a + 4)/(a^2 + 2a - 3)?
[ "2(a+2)/(a+3)(a-1)", "a + 3", "2/(a - 1)", "2a/(a - 3)", "(a - 1)/2" ]
Here's the algebraic approach: (2A + 4)/(A^2 + 2A - 3) can be rewritten as... 2(A + 2)/(A+3)(A-1) We can simplify the fraction, which leaves us with... Ans : A The answer is: A
A
mathematics
Sam purchased 20 dozens of toys at t he rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
[ "3.5", "4.5", "5.6 percent", "6.5", "None" ]
Solution C.P of 1 toy = Rs.(375/12) = Rs.31.25 S.P of 1 toy = Rs.33. Therefore,Profit = (1.75/31.25×100)% =(28/5)% =5.6%. Answer C The answer is: C
C
mathematics
The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
[ "27", "29", "30", "34", "35" ]
The total of seven numbers = 7X18 = 126 The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99 So, the middle number is (126 - 99 ) = 27 A The answer is: A
A
mathematics
A certain car uses 12 gallons of gasoline in traveling 120 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
[ "2", "4", "6", "8", "10" ]
120/10 = 12. The difference is 12- 10 = 2. Answer A The answer is: A
A
mathematics
9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 42 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
[ "6", "7", "8", "12", "14" ]
If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle. Side 1 = 8 m/h --> 4 m in 1/2 hr Side 2 = 10 m/h --> 5 m in 1/2 hr to complete this right angle triangle d^2 = 4^2 + 5^2 d^2 = 41 = ~ 6 Answer option A The answer is: A
A
mathematics
Ayesha's father was 58 years of age when she was born while her mother was 42 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
[ "6", "40", "50", "10", "20" ]
Mother's age when Ayesha's brother was born = 42 years. Father's age when Ayesha's brother was born = (58 + 4) years = 62 years. Required difference = (62 - 42) years = 20 years. Answer:E The answer is: E
E
mathematics
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
[ "5", "6", "7", "4", "32" ]
US = 25 DS = 35 M = (35 - 25)/2 = 5 Answer: A The answer is: A
A
mathematics
On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles?
[ "5.2", "7.4", "13.7", "21.2", "28.7" ]
Z inches necessary to represent a distance of 383.6 miles = 383.6/28 = 13.7 Answer C The answer is: C
C
mathematics
hat should come in place of question mark (?) in the following equation ? 197 × ? + 16(2) = 2620
[ "22", "12", "14", "16", "None of these" ]
? = 2620−256 /197=12 Answer B The answer is: B
B
mathematics
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
[ "90", "99", "92", "94", "97" ]
The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600; The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275. From above, the total score of the 5 largest scores = 600 - 275 = 325. Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively: a + b + c + d + e = 55 + 56 +57 + 58 + e = 325; e = 99. Answer: B. The answer is: B
B
mathematics
Today is Thursday. A person wants to meet a lawyer and as that lawyer is busy he asks him to come three days after the before day of the day after tomorrow? On which day the lawyer asks the person to come?
[ "SUNDAY", "MONDAY", "TUESDAY", "WEDNESDAY", "FRIDAY" ]
Today is Thursday after three days--->Sunday now, (sunday)after before day--->saturday then, (saturday)day after tomorrow--->monday ANSWER:B The answer is: B
B
mathematics
If a square mirror has a 20-inch diagonal, what is the approximate perimeter T of the mirror, in inches?
[ "40", "60", "80", "100", "120" ]
if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other. And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter T must be less than 80, so we can eliminate answer choice C, D and E. so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A. Now we are left with is B The answer is: B
B
mathematics
If in a certain code, If NEPOLEAN is written as OBFMPQFO, how can IMPOSING be written?
[ "HOJTPQNI", "HOJTPQNK", "HOJTPQNL", "HOJTPQNJ", "HOJTPQND" ]
NEPOLEAN - OBFMPQFO N+1 = O E+1 = F P+1 = Q O+1 = P L+1 = M E+1 = F A+1 = B N+1 = O Now write in reverse order... You ll get OBFMPQFO Similarly for IMPOSING I+1 = J M+1 = N P+1 = Q O+1 = P S+1 = T I+1 = J N+1 = O G+1 = H Now write in reverse order... HOJTPQNJ ANSWER:D The answer is: D
D
mathematics
A train 280 m long, running with a speed of 63 km/hr will pass a tree in
[ "15 sec.", "16 sec.", "18 sec.", "20 sec.", "None" ]
Solution Speed = (63 x 5/18) m/sec = 35/2 msec Time taken = (280 x 2 /35)m/sec = 16 sec. Answer B The answer is: B
B
mathematics
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
[ "378", "277", "389", "480", "881" ]
Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer:D The answer is: D
D
mathematics
A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length W of the fence including the fence posts on each end?
[ "mn", "m(n + x)", "W=m(n + x) + x", "m(n + x) + 2x", "2mn" ]
Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x. The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x. Answer: C. The answer is: C
C
mathematics
If |3x+20|=|5x-5|, which of the following could be a value of x?
[ "15/8", "12", "-25/8", "15/2", "25/2" ]
3x + 20 = 5x - 5 or 3x + 20 = -5x + 5 -2x = -25 or 8x = -15 x = 25/2 or x = -15/8 Answer: E The answer is: E
E
mathematics
A boat whose speed is 15 k/hr in still water goes 30 k/he downwards and come back in total 4 hr 30 min what is the speed of stream in k/hr ?
[ "1km/hr", "2km/hr", "3km/hr", "4km/hr", "5km/hr" ]
If the speed of stream=x Speed in downstream=15+x , Speed in Upstream=15-x, Total time=4 hr 30 min=9/2 hr [30/(15+x) + 30/(15-x)]=9/2,Solving x=5 x=5km/hr ANSWER:E The answer is: E
E
mathematics
If (10^4 * 3.456789)^14 is written as a single term, how many digits would be to the right of the decimal place?
[ "9", "14", "21", "28", "42" ]
3.456789^14 has 6*14 = 84 decimal places. 10^56 moves the decimal place to the right 56 places. (10^4 * 3.456789)^14 has 84-56 = 28 digits after the decimal point. The answer is D. The answer is: D
D
mathematics
There is a 4 digit no. in which 3rd digit is twice of first one. Second digit is the sum of first and third. Fourth digit is twice of third. What is the no?
[ "1224", "1324", "1444", "1524", "1354" ]
Let the 4-digit no. be "abcd" c = 2*a b=a+c d = 2*c => d=4a abcd => (a)(a+c)(2a)(4a) Possible values of a ll be 1 nd 2... Bcozzz a>2 implies d>10....Digits should ranges between 0 nd 9... If a=1, then c=2,d=4, b=3... The no. is 1324 If a=2, then c=4,d=8, b=6... The no. is 2648 Ans : 1324 (or) 2648 ANSWER:B The answer is: B
B
mathematics
A can complete the job in 4 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
[ "1/7", "3/10", "1/2", "5/6", "8/9" ]
A=1/7 The answer is: A
A
mathematics
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
[ "7", "6", "8", "2", "4" ]
Speed of train relative to man = 60 + 6 = 66 km/hr. = 66 * 5/18 = 55/3 m/sec. Time taken to pass the men = 110 * 3/55 = 6 sec. AnswerB The answer is: B
B
mathematics
At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 5 charts have been brought to the meeting, how many people are present?
[ "5", "7", "8", "9", "10" ]
Say there are 'A' associate professors. So we have 2A pencils and A charts. Say there are 'B' assistant professors. So we have B pencils and 2B charts. Total pencils are 10 so 2A + B = 10 Total charts are 11 so A + 2B = 5 Add both: 3A + 3B = 15 so A + B = 5 Total number of people = 5 A The answer is: A
A
mathematics
Mark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 6 feet longer than its width. If the total area of the driveway is 40 square feet, what is the length of the painted line (in feet)?
[ "Between 9 and 10", "Between 10 and 11", "Between 11 and 12", "Between 12 and 13", "Between 13 and 14" ]
To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have x(x + 6) = 40. By putting the equation in standard form, we get x^2+6x-40=0. By using the quadratic formula, we get roots of 4 and -10. We know that x is the width, and x+6 is the length, so by using the roots, we get 4 as the width (x), and 10 as the length (x+5). Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+10^2 =16+100 =116 The square root of 97 is more than 10, since 10^2 = 100. Going up a number, we can compute 11^2 = 121 >116. Therefore, the length of the diagonal must be between 10 and 11. The correct answer is B. The answer is: B
B