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mathematics
Two men can complete a piece of work in four days. Two women can complete the same work in eight days. Four boys can complete the same work in five days. If four men, eight women and 20 boys work together in how many days can the work be completed?
[ "1/2 day", "1/8 day", "1/3 day", "8/2 day", "1/7 day" ]
Two men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it. Similarly four women would take two days to complete it and 20 children would take one day to complete it. All the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day = 2 times the unit work in a day. They will take 1/2 a day to complete it working together. Answer: A The answer is: A
A
mathematics
What is the units digit of 18! + 2 ?
[ "1", "2", "3", "4", "5" ]
Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0. The units digit of 18! + 2 is 2. The answer is B. The answer is: B
B
mathematics
Find the odd man out 2, 7, 32, 157, 782, 3907, 17251
[ "7", "32", "157", "3907", "17251" ]
1*5-3 = 2 2*5-3 = 7 7*5-3 = 32 32*5-3 = 157 157*5-3 = 782 782*5-3 = 3907 3907*5-3= 19532 ANSWER:E The answer is: E
E
mathematics
If A : B = 4 : 7 and B : C = 5 : 8 then A : B : C is :
[ "20 : 35 : 56", "35 : 36 : 63", "30 : 35 : 65", "25 :34: 68", "None of these" ]
Expl : A : B = 4 : 7 B : C = 5 :8 = 5*7/5 : 8 *7/5 = 7 : 56/5 A : B : C = 4 : 7 : 56/5 = 20 : 35 : 56 Answer: A The answer is: A
A
mathematics
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/4rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
[ "1/3", "2/9", "9/49", "16/81", "1/6" ]
The first thing to notice is that A is faster than B and B is faster than C. Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work. If A works for 2 days, B works for 1 day and C works for only 2/3 of the day. Therefore total work done = (2*2) + (1*1) + (1/4*1/4) = 81/16 Proportion of work done by B = (1*1) / (81/16) = 16/81 Hence Answer D. The answer is: D
D
mathematics
Murphy and Cooper are having the same amount of petrol in the petrol tanks of their respective cars. Murphy can drive for four hours with that amount whole Cooper can drive for five hours. They both starts together and keep driving for a few hours. After some time, they find that the amount of petrol remaining in one car is four times that of the other car. Using all these facts, can you find out how long they drove their cars?
[ "2 3/4 hours.", "3 3/4 hours.", "4 3/4 hours.", "5 3/4 hours.", "6 3/4 hours." ]
Solution: 3 3/4 hours Explanation: Suppose that the amount of petrol in each of the cars in the beginning was M. Now, suppose that they drove for X hours. In that case, the amount of petrol used by one car in X hours will be = M*X /4 The amount of petrol used by the other car will be = M*X/5 Therefore, the petrol left in one car = M - M*X / 4 Petrol left in the other car = M - M*X / 5 Now, according to the question, M - M*X / 5 = 4 (M - M*X / 4) => X = 15 / 4 = 3 3/4 hours. Therefore Murphy and Cooper drove for 3 3/4 hours. Answer B The answer is: B
B
mathematics
A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
[ "32", "55", "6", "78", "81" ]
S = (100 + 300)/45 = 400/45 * 18/5 = 32 Answer: A The answer is: A
A
mathematics
In how many different number of ways 7 boys and 4 girls can sit on a shopa which can accommodate 3 persons?
[ "800", "900", "200", "990", "None" ]
Option 'D' 11p3 = 11x10x9 = 990 The answer is: D
D
mathematics
If 11 and 13 are prime numbers, which of the following CANNOT be the sum of a and b?
[ "24", "48", "72", "47", "96" ]
ans =D The answer is: D
D
mathematics
A person buys an article at $200. At what price should he sell the article so as to make a profit of 10%?
[ "240", "260", "220", "300", "360" ]
C 220 Cost price = $200 profit = 10% of 200 = $20 Selling price = Cost price + Profit = 200 + 20 = 220 The answer is: C
C
mathematics
The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1170. The perimeter of the plot is?
[ "126", "156", "180", "321", "260" ]
Sol. Let width = x, Length = (10+x) Perimeter = 2(x+(10+x)) = 2(2x=10) & 2(2x+10)*6.5 = 1170 X = 40 Required perimeter = 2(40+50) = 180 C The answer is: C
C
mathematics
John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
[ "6", "9", "36", "120", "720" ]
First place the maths book - since all are different books, they can be arranged in 3! ways - 6 ways... next we have 4 places for physics book, but leftmost is not a valid place as left is always maths.. _M_M_M_, but valid ways are M_M_M_ so 3 places for 3 books - again 3! ways... Total = 3!βˆ—3!=36 ANSWER:C The answer is: C
C
mathematics
What is the tens digit of 6^22?
[ "1", "3", "5", "7", "9" ]
The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}: The tens digit of 6^2=36 is 3. The tens digit of 6^3=216 is 1. The tens digit of 6^4=...96 is 9. The tens digit of 6^5=...76 is 7. The tens digit of 6^6=...56 is 5. The tens digit of 6^7=...36 is 3 again. etc... 22 has the form 5n+2, so the tens digit of 6^22 is 3. The answer is B. The answer is: B
B
mathematics
A part of Rs. 38800 is lent out at 6% per 6 months. The rest of the amount is lent out at 5% per annum after 1 year. The ratio of interest after 3 years from the time when first amount was lent out is 5:4. Find the second part that was lent out at 5%.
[ "28800", "27800", "29800", "26500", "55055" ]
Let the 1st part that is lent out be x at 6%. then 2nd part will be (38800-x) at 5%.then the S.I1 of 1st part is (p*r*t)/100 = (x*6*6)/100 [t=6 becoz we r calculating till 3yrs & der is six 6months in 3yrs] similarly S.I2 of 2nd part = {(38800-x)*5*2}/100 [t=2 since the 5% rate is to be calculated after the 1st year & per annum, so no. of years left is 2]therefore, S.I1/S.I2=5/4, by calculating it we get x=10000So, 2nd part is 38800-10000=28800 ANSWER:A The answer is: A
A
mathematics
If X = the product of six distinct prime numbers, how many factors does X have besides 1 and itself?
[ "50", "56", "62", "68", "74" ]
Since X has 6 distinct prime factors, X has a total of 2^6 = 64 factors. Besides 1 and itself, X has 62 factors. The answer is C. The answer is: C
C
mathematics
While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
[ "1/2", "17/36", "91/216", "11/36", "25/216" ]
Total outcomes possible: 36 Total outcomes possible with sum 7: 6 Probability to win when rolled once = 6/36 Probability not to win when rolled once = 30/36 = 5/6 Probability to win in three attempts= 1- Probability will not to win in all three attempts = 1- (5/6* 5/6*5/6) = 91/216 Answer is C. The answer is: C
C
mathematics
Complete the series 20, 19, 17, ...., 10, 5
[ "15", "16", "13", "14", "12" ]
Explanation : 20 - 1 = 19 19 - 2 = 17 17 - 3 = 14 14 - 4 = 10 10 - 5 = 5 Answer : Option D The answer is: D
D
mathematics
The probability of having a girl is identical to the probability of having a boy. In a family with seven children, what is the probability that all the children are of the same gender?
[ "1/64", "1/9", "1/16", "1/25", "1/2" ]
There are two cases. All boys and all girls case 1. all boys. 1/2*1/2*1/2*1/2*1/2*1/2*1/2= 1/128 case 2 .all girls. 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128 We will add the cases to get 1/64 The answer is: A
A
mathematics
There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
[ "120.", "132.", "141", "154.", "166." ]
Let the foam generators capacity be - A = 12 lit/hr B = 12 lit/hr C = 18 lit/hr Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate 42 + 21 => 63 litres... Now one of the first generators stops working ( Say A stops working ) , so we have - B = 12 lit/hr C = 18 lit/hr Total foam generation in 2 hour will be 60 litres {2 (12+18)} The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )... Foam generated by B will be 3/2 * 12 => 18 litres So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (C) The answer is: C
C
mathematics
A certain sum becomes three times itself at simple interest in five years. the sum become 1200 after 9 year.calculate the principal amount.
[ "250", "260.86", "288.6", "265.66", "280" ]
Let the sum be Rs. x, then it becomes Rs. 3x in five years Rs. 2x is the interest on x for five years. R = (100 * 2x)/(x * 5) = 40 % s.i=p*r*t/100=x*40*9/100=3.6x x+3.6x=1200=4.6x=1200,x=1200/4.6=260.86 ANSWER:B The answer is: B
B
mathematics
The list price of an article is Rs.69. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
[ "9.33%", "9.44%", "9.45%", "9.56%", "9.67%" ]
69*(90/100)*((100-x)/100) = 56.16 x = 9.56% ANSWER:D The answer is: D
D
mathematics
1397 x 1397 = ?
[ "1951609", "1951601", "1951602", "1951603", "1951604" ]
1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. Answer:A The answer is: A
A
mathematics
Seven unbiased coin are tossed. What is the probability of getting almost one head?
[ "1/2", "1/4", "127/128", "127/5", "127/6" ]
Here n(S)= 2^7 Let E=event of getting atmost one head = n(E)= 127 P(E)=n(E)/n(S)=127/128 Answer option C) The answer is: C
C
mathematics
30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.
[ "10", "11", "12", "13", "16" ]
Since average price of a pencil = 2 ∴ Price of 75 pencils = 150 ∴ Price of 30 pens = (630 – 150) = 480 ∴ Average price of a pen = 480⁄60 = 16 Answer E The answer is: E
E
mathematics
In a meeting of 3 representatives from each of 5 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?
[ "125", "120", "110", "90", "100" ]
In fact, all 15 people will shake hands with 12 others. So, it SEEMS like the TOTAL number of handshakes = (15)(12) HOWEVER, we need to keep in mind that we have counted each handshake TWICE. To account for this DUPLICATION, we must divide (15)(12) by 2. So, the TOTAL # of handshakes = (15)(12)/2 = 90 Answer : D The answer is: D
D
mathematics
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
[ "2010", "2011", "2012", "2013", "2014" ]
Suppose commodity X will cost 40 paise more than Y after z years. Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40 0.25z = 0.40 + 2.10 z = 2.50/0.25 z = 250/25 z =10 X will cost 40 paise more than Y 10 years after 2001 i.e., 2011. Answer = B The answer is: B
B
mathematics
what is the minimum value of f(x) where f(x)=(logax+logbx+logcx) and a>b>c>1..
[ "3", "2", "1", "4", "5" ]
here a,b,c are base for log..they aren't multiplied with x. so logax=logex/logea; f(x)= (logx/loga + logx/logb+ logx/logc); = logx * (1/loga + 1/logb + 1/logc); for minimum value of f(x) log values must me max 1 =1*3 = 3 ANSWER:A The answer is: A
A
mathematics
Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $78.2 after it went on sale for 15% off, what is the difference between the original price and the final price?
[ "$0.00", "$5.75", "$3.40", "$5.00", "$6.80" ]
0.85*{Original Price} = $78.2 --> {Original Price} = $92. {Final Price} = $78.2*1.25 = $97.75. The difference = $97.75 - $92 = $5.75 Answer: B. The answer is: B
B
mathematics
A retailer buys 60 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ?
[ "40", "65", "72", "78", "20" ]
let the market price of each pen be $1 then, Cost Price of 60 pens = $ 36 Selling Price of 60 pens =99% of $60=$ 59.40 profit %=((23.40*100)/36) %=65% Answer B The answer is: B
B
mathematics
If a sample of data has mean of 23 and SD of 3, which of the following values is more than 2.5 SDs from the mean?
[ "a. 16", "b. 13.5", "c. 17", "d. 23.5", "e. 26.5" ]
Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either <23-7.5=15.5 or >23+7.5=30.5. Answer: B. The answer is: B
B
mathematics
If v, w, x, y, and z are positive integers, which of the following could not become a terminating decimal?
[ "33/2^(4x)", "34/5^(2y)", "35/100^z", "36/4^w", "37/3^(5v)" ]
Knowledge of Decimal equivalent Fractions will work wonders here , no need to consider the Numerator part 1/ 2 = 0.50 ( Terminating ) 1/5 = 0.20 ( Terminating ) 1/100 = 0.01 ( Terminating ) 1/4 = 0.25 ( Terminating ) 1/3 = 0.33 ( Non Terminating ) Check the above rule with any higher powers the result will be same..... Among the given options only (E) has a non terminating denominator , so this will be our answer.. The answer is: E
E
mathematics
Find the odd man out 2880, 480, 90, 24, 8, 4, 4
[ "480", "90", "24", "8", "4" ]
from the right side 4*1=4, 4*2=8 8*3=24 24*4=96 but here given 90 so it's not. 96*5=480 480*6=2880 ANSWER:B The answer is: B
B
mathematics
One hour after Adrienne started walking the 60 miles from X to Y, John started walking from X to Y as well. Adrienne walks 3 miles per hour and John walks 1 mile per hour faster than Adrienne. How far from X will John be when he catches up to Adrienne?
[ "12 miles", "9 miles", "10 miles", "11 miles", "18 miles" ]
First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of John when he sets off. John walks at four miles/hour which means that every hour, John will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her. A slightly different way to solve... We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so, r*t (John ) = r*t (adrienne) r*(t) = r*(t+1) 4t = 3t+3 t=3 d=r*t d=4*3 d=12 A) 12 miles The answer is: A
A
mathematics
The H.C.F of two numbers is 15 and their L.C.M is 3300. If one of the numbers is 225, then the other is?
[ "200", "210", "220", "230", "240" ]
Other number = (15 * 3300)/225 = 220. Answer: C The answer is: C
C
mathematics
How many two-digit numbers are there whose remainder when divided by 15 is 1, and whose remainder when divided by 6 is 5?
[ "3", "4", "5", "6", "7" ]
2 digit numbers whose remainder when divided by 10 is 1 are 11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91 Out of above , numbers whose remainder when divided by 6 is 5 are 11 , 41 and 71 Answer E The answer is: E
E
mathematics
If (1 – 1.5)N = 1, then N =
[ "βˆ’400", "βˆ’140", "βˆ’2", "4", "400" ]
(1 – 1.5)N = 1 Simplify to get: -0.5N = 1 Rewrite as (-1/2)N = 1 Multiply both sides by -2 to get: N = -2 Answer: C The answer is: C
C
mathematics
If y is 80% greater than x, than x is what % less than y?
[ "20", "25", "33 1/3", "44 4/9", "80" ]
Let x = 100 So y = 180 We want percentage change. So, (100-180)/180 = -44.44% = 44 4/9% lesser than y. Hence option (D). The answer is: D
D
mathematics
In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein ?
[ "48", "37", "26", "98", "27" ]
Explanation: 3X + 4y = 240 by substitute through options 48 is correct Answer: A The answer is: A
A
mathematics
emblem is coded as 216; crude is coded as 125 Crickets will be ?
[ "243", "644", "512", "380", "464" ]
coding follows (no. of letters)^3 emblem = 216 = 6^3 crude = 125 = 5^3 Crickets = 8^3 =512 ANSWER:C The answer is: C
C
mathematics
Charlie, a painter, has 9 jars of paint: 4 are Red, 2 are yellow, and the rest are brown. Charlie will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no red paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of red paint 4) J2, if the paint contains exactly 1 jar of red paint What is the probability that the new colour will be a shade of J (J1 or J2)?
[ "21/37", "37/21", "37/42", "42/37", "74/42" ]
the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2 For C1-3C2(Brown)*2C1(Yellow)=3*2=6 For C2-3C3(all brown)=1 Total=9C3=84 1-7/84=77/84= 37/42 Answer : C The answer is: C
C
mathematics
Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?
[ "573", "608", "613", "616", "621" ]
The set S = {5, 13, 21, 29, ..................... } 1st Number = 8 * 0 + 5 = 5 2nd Number = 8 * 1 + 5 = 13 3rd Number = 8 * 2 + 5 = 21 72th Number = 8 * (72-1) + 5 = 573 Answer = A The answer is: A
A
mathematics
A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?
[ "200", "300", "400", "500", "None of them" ]
Let the share of each nephews be Rs.x. Then,share of each daughter=rs4x;share of each son=Rs.5x; So,5*5x+4*4x+2*x=8600 25x+16x+2x=8600 =43x=8600 x=200; Answer is A. The answer is: A
A
mathematics
If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?
[ "Equal to 3", "Less than 3", "More than 3", "Less than 1/3", "none of these" ]
Let number of boys = x Let number of girls = y Therefore x/y = B and y/x = G 5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5 ANSWER:E The answer is: E
E
mathematics
Find the least number of complete years in which a sum of money put out at 50% compound interest will be more than double of itself?
[ "2", "3", "4", "5", "6" ]
2 years Answer: A The answer is: A
A
mathematics
If x β‰  0 and x - (2+ x^2)/x = y/x, then y =
[ "-5", "-2", "-4", "-3", "-1" ]
x - (2+ x^2)/x = y/x x^2 -2 - x^2/x = y/x y= -2 Answer : B The answer is: B
B
mathematics
A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the total amount of money that the student earned for the 20 days? Amounts earned per day : $96 $84 $80 $70 $48 Number of days : 4 7 4 3 2
[ "(1) $120", "(2) $320", "(3) $378", "(4) $240", "(5) $296" ]
4+7+4+3+2 = 20 The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount. 1st to 2nd term = 48 (2 days) 3rd to 5th term = 70 (3 days) 6th to 9th term = 80 (4 days) 10th to 16th term = 84 (7 days) 17th to 20th term = 96 (4 days) total amount earned = 48+70+80+84+96 = 378 Pick C The answer is: C
C
mathematics
What is the remainder when 43^91 is divided by 5?
[ "0", "1", "2", "3", "4" ]
The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1} 91 has the form 4k+3 so the units digit of 43^91 is 7. The remainder when dividing by 5 is 2. The answer is C. The answer is: C
C
mathematics
If x-y=8, which of the following must be true? I. If x is negative, y must be negative II. Both x and y are positive III. If x is positive, y must be positive
[ "I only", "II only", "III only", "I and II", "II and III" ]
If x-y=8, which of the following must be true? I. Both x and y are positive II. If x is positive, y must be positive III. If x is negative, y must be negative 1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D 2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E A) I only B) II only C) III only D) I and II E) II and III Answer A The answer is: A
A
mathematics
587 x 999 = ?
[ "586413", "587523", "614823", "615173", "None of them" ]
=587 x 999 = 587 x (1000-1) =587 x 1000 - 587 - 1 =587000 - 587 =586413 Answer is A The answer is: A
A
mathematics
If the President and Vice President must sit next to each other in a row with 8 other members of the Board, how many different seating arrangements are possible?
[ "120510", "632010", "725760", "705262", "851032" ]
We need to take President and VP as one unit. Therefore we have 9 people to arrange=5! ways Also, we both President and VP can be arranged in 2 ! ways. Reqd no of ways=9!*2!= 725760 ways Answer C The answer is: C
C
mathematics
A man buys 58 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
[ "7.6 %", "7.7 %", "24.82 %", "13.6 %", "27.82 %" ]
Explanation: Let Marked price be Re. 1 each C.P. of 58 pens = Rs. 46 S.P. of 58 pens = 99% of Rs. 58 = Rs. 57.42 Profit % = (Profit /C.P.) x 100 Profit% = (11.42/46) x 100 = 24.82 % ANSWER: C The answer is: C
C
mathematics
A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 20 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
[ "36%", "40%", "44%", "48%", "52%" ]
Let x be the number of stamps in the original collection. The percentage of the collection given away is: 0.2x + 0.2(0.8x) = 0.2x + 0.16x = 0.36x = 36% The answer is A. The answer is: A
A
mathematics
Which one of the following is not a prime number?
[ "2", "3", "5", "9", "7" ]
9 is divisible by 3. So, it is not a prime number. Answer:D The answer is: D
D
mathematics
In a club with 310 peopl, 138 play tennis, 255 play baseball, and 94 people play both sports. How many people do not pla a sport?
[ "9", "8", "4", "10", "11" ]
Take 94 off the baseball players-->161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 Answer is E The answer is: E
E
mathematics
With an average speed of 40 km/hr a car reaches its destination on time. If it goes with an average speed of 35 km/h, it is late by 15 minutes. The total journey is?
[ "30 km", "40 km", "70 km", "80 km", "90 km" ]
Let the total journey be X km. X/35 - X/40 = 15/60 Solving for X, we get X = 70 Therefore, total journey = 70 km. ANSWER:C The answer is: C
C
mathematics
A box contains 4 black, 3 red and 6 green marbles. 3 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
[ "24/286", "25/709", "25/286", "24/268", "24/226" ]
Explanation: Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 3 marbles are drawn from 13 marbles at random. Therefore, n(S) = 13C3= 286 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 4C3 + 3C3+ 6C3 = 4 +1 + 20 = 25 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 25/286 ANSWER:C The answer is: C
C
mathematics
A boy was asked to find the arithmetic mean of the numbers 23, 17, 19, 25, 23, 18, 29, 27, 31 and P. He found the mean to be 24. What should be the number in place of P?
[ "3", "7", "33", "28", "38" ]
Explanation : Clearly, we have (23+17+19+25+23+18+29+27+31+P/10) =24 Number in place of P is => 212+P = 240 => P= 240 -212 => P = 28. Answer : D The answer is: D
D
mathematics
Six children β€” A, B, C, D, E and F β€” are going to sit in six chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
[ "240", "720", "1440", "4320", "4800" ]
for such questions , we can treat both as one then total person=5.. these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =5!*2=240 ans A The answer is: A
A
mathematics
The area of a square is equal to five times the area of a rectangle of dimensions 36 cm * 20 cm. What is the perimeter of the square?
[ "289 cm", "800 cm", "829 cm", "240 cm", "289 cm" ]
Area of the square = s * s = 5(36 * 20) => s = 60 = 60 cm Perimeter of the square = 4 * 60 = 240 cm. Answer: D The answer is: D
D
mathematics
If W is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, W, 0, 1, 3, K, 7}? I. -1.5 II. -2 III. 0
[ "I only", "II only", "III only", "I and III only", "None" ]
If W is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E The answer is: E
E
mathematics
A woman traveled 20 kilometer in 14 meter per second and another 20 kilometer in 18 miles per second. what is the average speed of the entire trip?
[ "12.25", "13.75", "15.75", "18.25", "19.75" ]
Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2) 2X14X18/32= 15.75. 'C' is the answer. The answer is: C
C
mathematics
How many times the keys of a writer have to be pressed in order to write first 500 counting no's?
[ "1372", "1382", "1392", "1362", "1352" ]
1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 500 = 401 * 3 = 1203 ----------- 1392 C The answer is: C
C
mathematics
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle
[ "18 cm", "16 cm", "40 cm", "20cm", "28 cm" ]
Explanation: Let breadth =x cm Then, length =2x cm Area =xΓ—2x=2x^2 sq.cm. New length =(2xβˆ’5) cm New breadth =(x+5) cm New area =(2xβˆ’5)(x+5) sq.cm. Given that, new area = initial area +75 sq.cm. β‡’(2xβˆ’5)(x+5)=2x^2+75 β‡’2x^2+10xβˆ’5xβˆ’25=2x^2+75 β‡’5xβˆ’25=75 β‡’5x=75+25=100 β‡’x=1005=20 cm Length =2x=2Γ—20=40 cm Answer: Option C The answer is: C
C
mathematics
Manish, Rahul and Bharti have some stones with each of them. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?
[ "113", "109", "93", "97", "66" ]
Explanation : Let the stones with Manish, rahul and Bharti be m,r and b respectively. Given, =>5r=7m and 5m=7b. =>25r=35m and 35m=49b. =>25r=35m=49b=k. =>r/49=m/35=b/25. The least possible integral values for r,m,b will be r=49, m=35 and b=25. =>Total=49+35+25=109. Answer : B The answer is: B
B
mathematics
Rs.1690 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
[ "s.528", "s.542", "s.780", "s.540", "s.549" ]
A+B+C = 1690 4A = 3B = 2C = x A:B:C = 1/4:1/3:1/2 = 3:4:6 6/13 * 1690 = Rs.780 Answer: C The answer is: C
C
mathematics
What is the dividend. divisor 14, the quotient is 9 and the remainder is 5?
[ "A)130", "B)131", "C)148", "D)158", "E)160" ]
D = d * Q + R D = 14 * 9 + 5 D = 126 + 5 D = 131 Answer B The answer is: B
B
mathematics
If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, WITHOUT N VALUE?
[ "1", "2", "3", "4", "5" ]
We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12 The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12? 12: 1,12 2,6 3,4 How many of these divisors are EVEN? 2, 4, 6, …..3 even divisors. ANSWER:C The answer is: C
C
mathematics
Sandy leaves her home and walks toward Ed's house. Two hours later, Ed leaves his home and walks toward Sandy's house. The distance between their homes is 52 kilometers, Sandy's walking speed is 6 km/h, and Ed's walking speed is 4 km/h. How many kilometers will Sandy walk before she meets Ed?
[ "33", "34", "35", "36", "37" ]
Sandy walks 12 km in the first two hours so there are 40 km remaining. When Ed starts walking, they complete a total of 10 km per hour. They will meet four hours after Ed starts walking. Since Sandy walks for 6 hours, she walks 36 km. The answer is D. The answer is: D
D
mathematics
Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long K would it have taken for him to walk both ways.
[ "8 h 45 min", "7 h 45 min", "6 h 45 min", "5 h 30 min", "None of these" ]
1.Walking to to a viewpoint+Driving back=6 hours 45 minutes 2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes. 3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes. 4.Walking to to a viewpoint+Walking back K=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes. Answer: A. The answer is: A
A
mathematics
In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73 students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and 16 students play all the sports. How many students are there in the class ?
[ "84", "164", "97", "94", "74" ]
total no. of students = n(B U T U C)= n(B)+n(T)+n(C)-n(B∩T)-n(B∩C)-n(C∩T)+n(B∩T∩C) = n(B U T U C)= 73+79+75-25-24-30+16 = n(B U T U C)= 164 ANSWER:B The answer is: B
B
mathematics
How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
[ "482", "725", "992", "837", "923" ]
20000(11/10)4 - 20000(6/5)2 = 482 Answer:A The answer is: A
A
mathematics
A group of medical interns at Bohemus Medical School want to go on dates. There are 6 girls and 6 guys. Assuming girls go on dates with guys, how many possible ways can these 12 medical interns date each other?
[ "A)320", "B)420", "C)520", "D)620", "E)720" ]
1st girl can go with 6 guys 2nd girl can go with remaining 5 3rd girl can go with remaining 4 and so on so the total ways are 6!= 720 E should be the answer The answer is: E
E
mathematics
On the coordinate plane , points M and Q are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) Ο€ , what are the coordinates of the center of the circle ?
[ "(1.5,1)", "(2,-5)", "(0,0)", "(1,1.5)", "(2,2)" ]
Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options. One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord). Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that MQ is the diameter of the circle. There can be a case when MQ is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle. If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D The answer is: D
D
mathematics
Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 11 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
[ "6 mph", "5.25 mph", "3.5 mph", "4 mph", "0.5 mph" ]
(1 mph +11 mph)/2 = 6 mph Correct option is: A The answer is: A
A
mathematics
The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
[ "79 kmph", "85 kmph", "34 kmph", "23 kmph", "14 kmph" ]
S = (90 + 60)/2 = 75 kmph Answer:B The answer is: B
B
mathematics
Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 7 hours. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
[ "8", "21", "24", "27", "30" ]
C = A + B D = 3C = 3(A+B) = 4B Then B = 3A and C = 4A The combined rate of the four machines is A + 3A + 4A + 12A = 20A Machine A can complete the work in 420 minutes, so its rate is 1/420 of the work per minute. The combined rate is 20/420 = 1/21 so the work will be completed in 21 minutes. The answer is B. The answer is: B
B
mathematics
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between
[ "0 and 3/20", "3/9 and 1/2", "1/5 and 1/4", "1/4 and 3/10", "3/10 and 1/2" ]
E. 3/9 and 1/2 Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation. Now you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it. B The answer is: B
B
mathematics
If you divide 7^84 by 5, which remainder do you get?
[ "0", "1", "2", "3", "4" ]
The units digit of 7^1 is 7. The units digit of 7^2 is 9. The units digit of 7^3 is 3. The units digit of 7^4 is 1. The units digit of 7^5 is 7. etc... The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1} The remainder of 84/4 is 0. So the units digit of 7^84 is 1. The remainder of 7^84 / 5 is 1. The answer is B. The answer is: B
B
mathematics
The average of 6 observations is 15. A new observation is included and the new average is decreased by 1. The seventh observation is?
[ "1", "8", "5", "6", "7" ]
Let seventh observation = X. Then, according to the question we have => (90 + X) / 7 = 14 => X = 8 Hence, the seventh observation is 8 ANSWER:B The answer is: B
B
mathematics
(2^2+4^2+6^2+.....+20^2)=?
[ "770", "1155", "1540", "385x385", "None of them" ]
=(1x2)^2+(2x2)^2,+(2x3)^3+......(2x10)^2 =2^2 x (1^2+2^2+3^2+.......+10^2) formula is =1/6 n(n+1)(2n+1) =(4x1/6x10x11x21) =(4x5x77)=1540 Answer is C The answer is: C
C
mathematics
A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane
[ "3 km", "4 km", "6 km", "9 km", "5 km" ]
Explanation: Let the distance be 3x km, then, x/3+x/4+x/5=47/60 47x /60= 47 /60 x=1 So total distance = 3*1 = 3 Km Option A The answer is: A
A
mathematics
What percent is 20% of 25%?
[ "20%", "30%", "50%", "60%", "80%" ]
Required percentage = 20%/25% * 100 = 20/25 * 100 = 80% Answer is E The answer is: E
E
mathematics
Find the SI on Rs 8000 for 4 yrs at 10% per annum rate of interest?
[ "Rs 3000", "Rs 3500", "Rs 4000", "Rs 4400", "Rs 4800" ]
Simple Interest = PTR 100 = 8000 X 5 X 10 100 = Rs 4000 C The answer is: C
C
mathematics
A class consists of 100 students, 20 of them are girls and 80 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
[ "2/125", "1/59", "1/56", "1/54", "1/53" ]
The probability of selecting girl is: 20/100 = 1/5 The probability of selecting rich is: 20/100 = 1/5 The probability of selecting fair complexioned is: 40/100 = 2/5 Three are independent;probability of rich and fair complexioned girl is: (1/5) Γƒβ€”(1/5) Γƒβ€” (2/5) = 2/125 Answer: A The answer is: A
A
mathematics
Simplify: 839478 x 625
[ "524673750", "546273750", "562473750", "564273750", "None of them" ]
839478 x 625 = 839478 x 5^4 = 8394780000/16 = 524673750. Answer is A The answer is: A
A
mathematics
Two pipes A and B can fill a tank in 2 and 6 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
[ "2.5 min", "1.8 min", "1.5 min", "3.5 min", "2 min" ]
Part filled by the first pipe in 1 minute = 1/2 Part filled by the second pipe in 1 minute = 1/6 Net part filled by pipe A and pipe B in 1 minute = (1/2)+(1/6)=2/3 i.e, pipe A and B together can fill the tank in 3/2 minutes = 1.5 minutes Answer is C The answer is: C
C
mathematics
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room?
[ "12", "14", "15", "24", "36" ]
the number of women doubled means that they have become 24 from 12.. and we have to tell the current strength so 24 is the answer.. let the number be 4x and 5x.. given 4x+2=14.. so x=3.. women number=5*3-3=12, then doubled=24.. ans D The answer is: D
D
mathematics
Which of the following is satisfied with |x-4|+|x-3|<6?
[ "1<x<5", "2<x<5", "0.5<x<6.5", "0.5<x<4", "3<x<4" ]
--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5 Therefore, the answer is C. The answer is: C
C
mathematics
A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number T of imported lamps stocked at the store?
[ "3", "10", "13", "20", "23" ]
We want to minimize not maximize the expression,. T=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23. But i'm guessing 123-5x/20 can be written as 123- x/4 if x has to be the greatest multiple of 4 less then 410, then it would be 408. Hence 123-408/4 --> 123-102 -->21 Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E The answer is: E
E
mathematics
Suppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 18 bananas in 18 minutes?
[ "9", "10", "11", "6", "13" ]
One monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18/3 =6 monkeys ANSWER:D The answer is: D
D
mathematics
If a man walks at a rate of 10kmph, he misses a train by 14minutes. However, if he walks at the rate of 12kmph, he reaches the station 10minutes before the arrival of the train. Find the distance covered by him to reach the station.
[ "6", "15", "12", "4", "8" ]
Let the required distance x km difference in the times taken at two speeds = 12min = 1/5 hr (x/10)-(x/12) = 1/10 x = 6 the required distance is 6 km Answer is A The answer is: A
A
mathematics
A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train?
[ "150 meter", "170 meter", "156 meter", "168 meter", "50 meter" ]
Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 3 = 50 meter Answer:E The answer is: E
E
mathematics
If p and q are integers and p divided by q is 16.15, then which of the following integers is a possible value for the remainder when p is divided by q? I. 15 II. 5 III. 3
[ "I only", "II only", "III only", "I,III only", "II,III only" ]
p=16.15q from which p = 16q + 15q/100 or p = 16q + 3q/20. Since p and q are integers, 3q/20 must also be an integer. 3 is not divisible by 20, then q must be divisible by 20, and therefore, q/20 is an integer and 3q/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3. Answer D The answer is: D
D
mathematics
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 18 hours and 8 hours respectively. The ratio of their speeds is
[ "4 : 9", "4 : 3", "4 : 12", "4 : 8", "4 : 5" ]
Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 18 = 4 : 9. Answer: A The answer is: A
A
mathematics
3 singers will pick a song among a list of 3 songs. What is the probability that exactly one singer will pick a different song?
[ "3!/3^3", "1/3^3", "3/3!", "3/3^3", "1/3!" ]
Each singer out of 3 has 3 options, hence total # of outcomes is 3^3; Favorable outcomes will be 3!, which is # of ways to assign 3 different song to 3 singers. P=favorable/total=3!/3^3 Answer: A. The answer is: A
A
mathematics
If we have 12 people in a meeting, in how many ways they can sit around a table?
[ "11*10!", "9*8!", "8*7!", "7*6!", "6*5!" ]
If there arenpeople sitting around a table, there are(n-1)!possible arrangements: Here, n=12 (n-1)!=11!=11*10! Ans:A The answer is: A
A
mathematics
What is the product of the prime numbers between 10 and 20
[ "10^1", "10^2", "10^3", "10^4", "10^5" ]
E) The answer is: E
E
mathematics
A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
[ "675", "680", "685", "690", "695" ]
Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec. Length of the train = 75 * 9 = 675 m. Answer: Option A The answer is: A
A
mathematics
If 15% of 40 is greater than 25% of a number by 2,then find the number is?
[ "20", "15", "16", "25", "30" ]
15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16 ANSWER C The answer is: C
C
mathematics
Ramu bought an old car for Rs. 48000. He spent Rs. 14000 on repairs and sold it for Rs. 72900. What is his profit percent?
[ "16%", "17.5%", "18.2%", "58.5%", "13%" ]
Total CP = Rs. 48000 + Rs. 14000 = Rs. 62000 and SP = Rs. 72900 Profit(%) = (72900 - 62000)/62000 * 100 = 17.5% Answer: B The answer is: B
B