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mathematics
In how many ways can 16 different gifts be divided among four children such that each child receives exactly three gifts?
[ "16^4", "(4!)^4", "16!/(3!)^4", "16!/4!", "4^16" ]
Total 16 different Gifts, and 4 children. Thus any one child gets 16C3 gifts, then the other child gets 13C3 gifts(16 total - 3 already given), then the third one gets 10C3 gifts, and the last child gets 7C3 gifts. Since order in which each child gets the gift is not imp, thus, ans : 16C3 * 13C3 * 10C3 * 7C3 = 16! / (3!)^4 Ans : C. The answer is: C
C
mathematics
What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, x
[ "29", "31", "23", "43", "53" ]
(D) The pattern is + 3, + 5, + 3, + 5, ………… So the missing term is = 38 + 5 = 43. The answer is: D
D
mathematics
If |b| β‰₯ 1 and x= -| a| b, then which one of the following is necessarily true?
[ "a -xb < 0", "a -xb β‰₯ 0", "a -xb > 0", "a -xb ≀ 0", "None of these" ]
Explanation : x = –|a| b Now a – xb = a – (– |a| b) b = a + |a| b2 ∴ a – xb = a + ab2 … a 0 β‰₯ OR a – xb = a - ab2 …a < 0 = a(1 + b2) = a(1 – b2). Consider first case: As a β‰₯ 0 and |b| β‰₯ 1, therefore (1 + b2) is positive. ∴ a (1 + b2) β‰₯ 0 ∴ a – xb β‰₯ 0 Consider second case. As a < 0 and |b| β‰₯ 1, therefore (1 – b2) ≀ 0 ∴ a (1 – b2) β‰₯ 0 (Since –ve Γ— -ve = +ve and 1 – b2 can be zero also), i.e. a – xb β‰₯ 0 Therefore, in both cases a – xb β‰₯ 0. Answer : B The answer is: B
B
mathematics
The cost of 6 pens is 10 more than 5 marker's cost. The 12 pens is Rs.240.
[ "Rs.11", "Rs.42", "Rs.24", "Rs.110", "Rs.22" ]
Let the cost of each pen and marker be 'p' and 'q' respectively. 6p - 5q = 10 --- (1) 12p= 240 . P=20 6p - 5q = 10 --- (2) 120-5q =10 =>5q = 110 => q=22 ANSWER:E The answer is: E
E
mathematics
Find the sum of the number of combinations possible by using 1,2,3,4 such that no number is repeated(ex:- 1223,4322 are invalid 1234,4321 are valid)more than once.
[ "66660", "66760", "66860", "66960", "67660" ]
total no. formed = 4!=4*3*2*1=24 each digit will be used at each positions, 6 times sum of digits at unit place = 6*1+6*2+6*3+6*4 = 6*(1+2+3+4)= 60 this sum will be same for hundred, tens & unit places sum of all 4 digit numbers formed using digits 1,2,3,4 = 1000*60+100*60+10*60+60 =60*(1000+100+10+1) =60*1111 =66660 ANSWER:A The answer is: A
A
mathematics
Club X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
[ "1", "2", "3", "4", "5" ]
The number of members is 4j+3 = 5k+3. Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3. 31, 35, 39, 43 = 5(8) + 3 The club has 43 members. 43/6 = 6(7) + 1 The answer is A. The answer is: A
A
mathematics
If a/x = 1/3 and a/y =1/ 6, then (x + y) =
[ "A)2a", "B)a/2", "C)6a", "D)7a", "E)9a" ]
Ratio 1: 3a = x Ratio 2: 6a = y x+y = 9a Answer is E The answer is: E
E
mathematics
Compound interest earned on a sum for the second and the third years are Rs.2400 and Rs.2640 respectively. Find the rate of interest?
[ "10% p.a.", "20% p.a.", "15% p.a.", "12% p.a.", "None of these." ]
Rs.2640 - 2400 = Rs.240 is the interest on Rs.2400 for one year. Rate of interest = (240/2400) * 100 = 10% p.a ANSWER:A The answer is: A
A
mathematics
During a certain two-week period, 60 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
[ "5 A", "6 A", "8 A", "14 A", "20 A" ]
Movies: 60 % comedies. 40 % remaining genre. Now in this 40 %, there are only 2 categories. Action movies and Drama Movies. If Action = x; Drama movies = 3x. Total 4x. 4x = 40; x = 10 Action movies: 10 % Drama movies: 30 % we can say that out of 100z,: comedies: 60z action: 10z drama: 30 z Now action movies wereA This means: A = 10z. z = (A/10) Comedies: 60z = 60 * (A/10) 6 A B is the answer. The answer is: B
B
mathematics
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
[ "35 years", "40 years", "50 years", "55 years", "None" ]
Solution Sum of the present ages of husband, wife and child = (27x3+3x3) years = 90 years. Sum of the present ages of wife and child = (20x2+5x2) years = 50 years. ∴ Husband's present age = (90 - 50) years = 40 years. Answer B The answer is: B
B
mathematics
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
[ "5000", "2889", "2779", "6257", "5362" ]
Income = Rs. 100 Expenditure = Rs. 80 Savings = Rs. 20 Present Expenditure 80*(20/100) = Rs. 96 Present Savings = 100 – 96 =Rs. 4 100 ------ 4 ? --------- 200 => 5000 Answer: A The answer is: A
A
mathematics
The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
[ "876 m", "157 m", "235 m", "156 m", "167 m" ]
Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m. Answer: C The answer is: C
C
mathematics
A salesman's income consists of a commission and a base salary of $400 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
[ "$150", "$245", "$365", "$315", "$730" ]
Total weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070 For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500 Now, $3500-$2070=$1430 From this, we subtract base salary for 2 weeks i.e $350*2=$700 Therefore, commission=$1430-$800=$630 for 2 weeks Avg weekly commission=$315 Answer D The answer is: D
D
mathematics
Express a speed of 56 kmph in meters per second?
[ "10.2 mps", "05 mps", "09.1 mps", "12 mps", "15.5 mps" ]
E 15.5 mps 56 * 5/18 = 15.5 mps The answer is: E
E
mathematics
The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 9!?
[ "3(5!)", "4(5!)", "6(5!)", "5(5!)", "7(5!)" ]
GCF is the product of common factors of the numbers involved. GCF = 5! a = 9! = 9*8*7*6*5! b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF) Looking at the answers only 5 (5!) and 9! will have GCF as 5! Ans D The answer is: D
D
mathematics
(17)4.25 x (17)? = 178
[ "2.29", "2.75", "4.25", "3.75", "None of these" ]
Solution let (17)4.25 * (17)x = 178. then, (17)4.25 + x = (17)8. ∴ 4.25 + x = 8 ⇔ x = (8 - 4.25) ⇔ x = 3.75 Answer D The answer is: D
D
mathematics
Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ?
[ "1660", "2500", "3250", "4150", "5250" ]
Let the numbers be x and y. Then , 7.5 % of x =12.5% of y X = 125*y/75 = 5*y/3. Now, x-y =1660 5*y/3 –y =1660 2*y/3= 1660 y =[ (1660*3)/2] =2490. One number = 2490, Second number =5*y/3 =4150. Answer Option D) 4150. The answer is: D
D
mathematics
The average of 25 results is 8. The average of first 12 of them is 14 and that of last 12 is 17. Find the 13 result?
[ "52", "68", "78", "92", "65" ]
13th result = sum of 25results - sum of 24 results 18*25-14*12+17*12 = 78 Answer is D The answer is: D
D
mathematics
If 4/(a + 5) = 7/(a - 4), then a = ?
[ "-15", "-19", "-17", "-18", "-13" ]
Multiply all terms of the given equation by (a + 5)(a - 4), simplify and solve (a + 5)(a - 4)[ 4/(a + 5) ] = (a + 5)(a - 4) [ 7/(a - 4) ] 4 (a - 4) =7 (a + 5) a = -17 correct answer C The answer is: C
C
mathematics
Seats for Maths, Physics and Biology are in the ratio of 6 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
[ "12 : 15 : 20", "6 : 7 : 8", "6 : 8 : 9", "Cannot be determined", "None of these" ]
Reqd ratio 6 Γƒβ€” 140Γ’Ββ€ž100 : 7 Γƒβ€” 150Γ’Ββ€ž100 : 8 Γƒβ€” 175Γ’Ββ€ž100 = 6 Γƒβ€” 140 : 7 Γƒβ€” 150 : 8 Γƒβ€” 175 = 12 : 15 : 20 Answer A The answer is: A
A
mathematics
In Town X, 64 percent of the population are employed, and 44 percent of the population are employed males. What percent of the employed people in Town X are females?
[ "16%", "55%", "29%", "40%", "52%" ]
answer b male-employed - 64% female-employed-20% Total employed 64% means total unemployed = 36% therefore d and e are not correct because female unemployed has to be less than 36% female-unemployed = 32% male unemployed = 4% 48% + 4% = 52% 16% + 32% = 48% plug in a and b in place of 32% and the sum is not 100% 20/64 =29 C The answer is: C
C
mathematics
Abbey's income is 30 percent more than Abigail's income, and Abigail's income is 35 percent less than Jenny's income. What percent of Jenny's income is Abbey's income?
[ "84.5%", "81.5%", "82.5%", "83.5%", "86.5%" ]
Jenny's income = 100 (assume); Abigail's income = 65 (40 percent less than Jenny's income); Abbey's income = 84.5 (30 percent more than Abigail's income). Thus, Abbey's income (84.5) is 84.5% of Juan's income (100). Answer: A The answer is: A
A
mathematics
In a division, divident is 690, divisior is 36 and quotient is 19. Find the remainder.
[ "A)4", "B)3", "C)2", "D)5", "E)6" ]
Explanation: 690 = 36 x 19 + r 690 = 684 + r r = 690 - 684 = 6 Answer: Option E The answer is: E
E
mathematics
If x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9?
[ "-2.4", "0.268", "1.166 repeating", "4.555 repeating", "8.125" ]
x is an integer, which of the following is a possible value of Q=(x^2 +2x – 7)/9? Used process of elimination A. -2.4 when this is multiplied by 9, x is not an integer B. 0.268 when this is multiplied by 9, x is not an integer C. 1.166 repeating when this is multiplied by 9, x is not an integer D. 4.555 repeating E. 8.125 when this is multiplied by 9, x is not an integer Answer choice D seems to fit.D The answer is: D
D
mathematics
Of the teams competing in the world archery championships, Forty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
[ "13/20", "15/20", "13/15", "17/20", "7/17" ]
Assume 100 total people. 40% of 100 = 40 --->Europeans 1/2 of 40 ---> 20 Americans 1/20 of 100 ---> 5 Africans Now you would add them all up, and minus it by the total (100). 100 - 65= 35. So, 35 people out of 100 are not EU, US or Africans. 35/100 is also equal to 7/20. So therefore, the answer is E. The answer is: E
E
mathematics
In the formula A = 22/7*b^2, if b is halved, then A is multiplied by
[ "4", "1/8", "1/4", "8", "1/2" ]
Say b=2 => A1 = 88/7 when r=1; A2 = 22/7 A2 = 1/4*A1. Answer : C The answer is: C
C
mathematics
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.6 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
[ "1/4", "1/2", "5/8", "5/6", "15/16" ]
X - fraction of products Jane inspected (1 - X) - fraction of products John inspected 0.6(X) + 0.5(1-X) = 0.75 0.1X = 0.75 - 0.5 X = 0.25/0.1 X = 1/4 Therefore the answer is A: 1/4. The answer is: A
A
mathematics
Complete the sequence: D F J P ?
[ "M", "D", "S", "F", "X" ]
D+2=F F+4=J J+6=P P+8=X E The answer is: E
E
mathematics
in a soccer bet,we play 4 teams.first team odd 1.26,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros. how much money we expect to win?
[ "219.5", "225.5", "235.01", "266.74", "669.0" ]
in the case we won the bet,we have: 1.26* 5.23* 3.25* 2.0*5.00=219.50 we will win 219.50 so correct answer is A)219.50 The answer is: A
A
mathematics
The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
[ "6", "8", "10", "12", "14" ]
For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 5 guards. To choose 2 out of 5, we will have 5C2 = 10 different pairs. The answer is C. The answer is: C
C
mathematics
There are 12 cans in the refrigerator. 8 of them are red and 4 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
[ "460", "490", "493", "455", "424" ]
Ways to pick 4 cans so that at least one red and at least one blue cans to remain the refrigerator = total ways to pick 4 can out of 12 - ways to pick 4 red out of 8 red - ways to pick 4 blue out of 4 blue 12C4Òˆ’8C4Òˆ’4C4=495Òˆ’70Òˆ’1=424 ANSWER:E The answer is: E
E
mathematics
Chandigarh express of 100 m runs at a speed of 60 km/hr. What will be the time taken to cross a platform of 150 meters long?
[ "11.00 sec", "12.50 sec", "15.00 sec", "15.23 sec", "5.23 sec" ]
EXPLANATION: Given: Length of train = 100 m, speed of train = 60 km/hr, length of platform = 150 m 1) Always remember first step is the conversion of units. Convert 60 km/hr into m/s by multiplying it with (5/18) Speed of the train = 60 x 5/18=16.66 m/s 2) Distance covered by the train in passing the platform = (Length of train + Length of platform) = (100 + 150) = 250 m Therefore, The time taken = Distance/Speed = 250/16.66 = 15 sec ANSWER IS C The answer is: C
C
mathematics
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
[ "18", "74", "15", "44", "63" ]
Explanation: Let the capacity of the can be T litres. Quantity of milk in the mixture before adding milk = 4/9 (T - 8) After adding milk, quantity of milk in the mixture = 6/11 T. 6T/11 - 8 = 4/9(T - 8) 10T = 792 - 352 => T = 44. Correct Option : D The answer is: D
D
mathematics
You collect pens. Suppose you start out with 5. Mike gives you another 20 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 10 pens. How many pens do you have at the end?
[ "39", "40", "41", "42", "43" ]
Solution Start with 5 pens. Mike gives you 20 pens: 5 + 20 = 25 pens. Cindy doubles the number of pens you have: 25 Γƒβ€” 2 = 50 pens. Sharon takes 10 pens from you: 50 - 10 = 40 pens. So you have 40 at the end. Correct answer: B The answer is: B
B
mathematics
Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?
[ "2 : 3", "3 : 2", "1 : 3", "2 : 1", "None of these" ]
? Required ratio = 6?4 = 3 : 2 Answer B The answer is: B
B
mathematics
A certain galaxy is known to comprise approximately 4 x 10^10 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
[ "800", "1,250", "8,000", "12,000", "80,000" ]
Total no. of stars on galaxy = 4 * 10^10 Of every 50 million stars, 1 is larger than sun. 1 million = 10^6 therofore, 50 million = 50 * 10^6 total no. of stars larger than sun = 4 * 10^10 / 50 * 10^6 =40 * 10^2 /5 = 800 therefore answer is A The answer is: A
A
mathematics
Jack and Christina are standing 150 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 7 feet per second and Christina walks in a straight line toward Jack at a constant speed of 8 feet per second. Lindy runs at a constant speed of 10 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
[ "40", "60", "80", "100", "120" ]
The relative speed of Jack and Christina is 7 + 8 = 15 feet per second. The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 150/15 = 10 seconds. For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 10*10 = 100 feet. Answer: D. The answer is: D
D
mathematics
Can you deduce the pattern and find the next number in the series? 7, 15, 27, 99, __?
[ "276", "277", "278", "279", "None of these" ]
Solution: 277 Explanation: 7 = (1^1 + 2^1 + 3^1) +1 15 = (1^2 + 2^2 + 3^2) +1 37 = (1^3 + 2^3 + 3^3) +1 99 = (1^4 + 2^4 + 3^4) +1 Thus the next number will be (1^5 + 2^5 + 3^5) +1 = 277 Answer B The answer is: B
B
mathematics
RAJA complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
[ "200 km", "250 km", "224 km", "255 km", "260 km" ]
consider x -- > (1/2)x/21 + (1/2)x/24 = 10 ==> x/21+x/24 = 20 15x = 168 * 20 ==> 224km ANSWER C The answer is: C
C
mathematics
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
[ "2 : 3", "3 : 2", "3 : 4", "4 : 3", "4:6" ]
Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120/x + 480/y = 8 --> 1/x + 4/y = 1/15 ------ (i) Also, 200/x + 400/y = 25/3 --> 1/x + 2/y = 1/24 ----(ii) Solving (i) and (ii), we get: x = 60 and y = 80. Ratio of speeds = 60 : 80 = 3 : 4. Answer : C. The answer is: C
C
mathematics
7 members have to be selected from 12 men and 3 women ,Such that no two women can come together .In how many ways we can select them ?
[ "12c6*3c1 + 12c7", "12c6*3c1 + 2c7", "1c6*3c1 + 12c7", "11c6*3c1 + 12c7", "12c6*3c1 + 11c7" ]
since no two women can come together,therfore women can be selected in 3c1 ways ...and men will be chosen in 12c6 so to complete the 7 group members... =12c6*3c1 and only selection of men also possible = 12c7 so final ans : 12c6*3c1 + 12c7 ANSWER:A The answer is: A
A
mathematics
A man is trying to climb over a frozen mountain that is sixty feet high. Every minute, he can climb 3 feet, but due to the slippery ice, he slips back 2 feet. How long will it take him to reach the top of the mountain?
[ "57 minutes", "58 minutes", "59 minutes", "53 minutes", "54 minutes" ]
Solution: It will take the man 58 minutes to reach the top. Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute. Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back. 58 minutes Answer B The answer is: B
B
mathematics
A card is drawn from a pack of 52 cards. The probability of geΖ«ng a queen of club or a king of heart is
[ "1/13", "2/13", "1/26", "1/52", "None of these" ]
Explanation: Total number of cases = 52 Favourable cases = 2 Probability = 2/56 = 1/26 Answer: C The answer is: C
C
mathematics
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle? I. 4 II. 12 III. 24
[ "I, II, and III", "I and II only", "II and III only", "I and III only", "II only" ]
Answer = A. I, II, and III With dimensions of only 2 sides given (for a triangle), this becomes an open ended question Any area is possible out of the three The answer is: A
A
mathematics
A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
[ "150 m", "200 m", "170 m", "100 m", "350 m" ]
Relative speed of the thief and policeman = 11 - 10 = 1 km/hr. Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m. Distance between the thief and policeman = 450 - 100 = 350 m E The answer is: E
E
mathematics
Suresh borrowed some money at the rate of 4% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
[ "s.8500", "s.6000", "s.8500", "s.9000", "s.7000" ]
using the formula S.I=P*T*R/100 (x*4*3/100)+(x*9*5/100)+(x*13*3/100)=8160 x=8500 i.e money borrowed is Rs.8500 ANSWER:C The answer is: C
C
mathematics
A school having four classes only have student strength of 10, 40, 30 and 20 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
[ "56%", "76%", "52%", "66%", "46%" ]
20% of 10+30% of 40+60% of 30+100% of 20 =2+12+18+20 = now 52 of 100 = 52% ANSWER:C The answer is: C
C
mathematics
The value of x + x(x^x) when x = 10 is
[ "100000000010", "10000000010", "10000000000", "1200000000", "12000000010" ]
Solution: x + x(x^x) Put the value of x = 10 in the above expression we get, 10 + 10(10^10) = 10 + 10(10 Γƒβ€” 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10) = 10 + 10(10000000000) = 10 + 100000000000 = 100000000010 Answer: (a) The answer is: A
A
mathematics
Three number are in the ratio 5:6:7. The sum of its largest and smallest numbers equals the sum of the third number and 48. Find the third number?
[ "87", "57", "48", "26", "28" ]
Let the numbers be 5x, 6x and 7x. Largest number = 7x Smallest number = 5x Third number = 6x 7x + 5x = 6x + 48 6x = 48 Third number is: 48. Answer: C The answer is: C
C
mathematics
A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
[ "15", "66", "77", "88", "11" ]
One days's work of A, B and C = 1/90 + 1/30 + 1/45 = (1 + 3 + 2)/90 = 1/15 A, B and C together can do the work in 15 days. Answer:A The answer is: A
A
mathematics
A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?
[ "28%", "25%", "55%", "17.6%", "55%" ]
850 --- 150 100 --- ? => 17.6% Answer: D The answer is: D
D
mathematics
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 15 km/hr. For how many minutes does the bus stop per hour?
[ "22", "88", "77", "20", "45" ]
In 1hr, the bus covers 60 km without stoppages and 15 km with stoppages. Stoppage time = time take to travel (60 - 15) km i.e 45 km at 60 km/hr. stoppage time = 45/60 hrs = 45 min. Answer: E The answer is: E
E
mathematics
Find the value for m? 21(m + n) + 21 = 21(-m + n) + 21
[ "0", "-1", "1", "2", "3" ]
21m + 21n - 21 = -21m + 21n + 21 42m= 42 => m = 1 C The answer is: C
C
mathematics
In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is :
[ "5", "6", "7", "10", "12" ]
Let no of cows be x, no of hens be y. So heads=x+y Legs=4x+2y Now, 4x+2y = 2(x+y)+ 14 2x = 14 x = 7. ANSWER:C The answer is: C
C
mathematics
A cubical tank is filled with water to a level of 1 foot. If the water in the tank occupies 16 cubic feet, to what fraction of its capacity is the tank filled with water?
[ "1/2", "1/3", "1/4", "1/5", "1/6" ]
The volume of water in the tank is H*L*B = 16 cubic feet. Since H = 1, then L*B = 16 and L = B = 4. Since the tank is cubical, the capacity of the tank is 4*4*4 = 64. The ratio of the water in the tank to the capacity is 16/64 = 1/4 The answer is C. The answer is: C
C
mathematics
A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
[ "288 m", "256 m", "500 m", "278 m", "287 m" ]
Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (800 + x)/60 = 65/3 x = 500 m. Answer:C The answer is: C
C
mathematics
How long does a train 110 m long running at the speed of 90 km/hr takes to cross a bridge 132 m length?
[ "82.1 sec", "9.68 sec", "16.1 sec", "13.1 sec", "12.15sec" ]
Speed = 90 * 5/18 = 25 m/sec Total distance covered = 110 + 132 = 242 m. Required time = 242/25 = 9.68 sec. Answer:B The answer is: B
B
mathematics
Express the following as a fraction 56%
[ "13/50", "17/30", "11/25", "14/25", "14/19" ]
56% = 56/100 = 14/25 Answer is D. The answer is: D
D
mathematics
A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1660 are infected, how manyworkersinhabit the colony?
[ "1500", "2500", "2750", "3000", "3250" ]
From two question we get wo equations: (1) 0,3s + 0,14w = 1660 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1660 0,16s=680 68000:16= 4250 =s In (2) 4250 + w = 7000 w= 2750 C The answer is: C
C
mathematics
The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament?
[ "6", "7", "8", "9", "10" ]
To get 45 points as end of season we need another 35 points or more from remaining 15 matches: Option A= 6*3+9*1=27 Option B=7*3 + 8*1=29 Option C=8*3+7*1=31 Option D=9*3+6*1=33 Option E=10*3+5*1=35 hence option E-10 The answer is: E
E
mathematics
Lorna invests $8000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
[ "$160", "$1,700", "$2,200", "$4,400", "$5,840" ]
We have that 'x' invested at 6% We also have that '8000-x' invested at 11% Now then 580/8000 is approx 10% Therefore, -4x+8000-x=0 5x=8000 x=1600 approximately. Probably higher Only B matches The answer is: B
B
mathematics
The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 1 year is
[ "s.9621", "s.6921", "s.8400", "s.6261", "s.6361" ]
c.i=p(1+r/100)^n =8000(1+5/100) =Rs8400 ANSWER:C The answer is: C
C
mathematics
Find the value for m? 19(m + n) + 17 = 19(-m + n) - 173
[ "0", "-1", "-5", "2", "3" ]
19m + 19n + 17 = -19m + 19n - 173 38m= -190 => m = -5 A The answer is: A
A
mathematics
Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share thrice, no apples were left.How many apples were there?
[ "500", "510", "511", "501", "504" ]
Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 9 times. So answer is (2^9)-1=511. ANSWER:C The answer is: C
C
mathematics
A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change. Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill. Later that day he tries to figure out how much money he lost. What did he lose?
[ "$5", "$10", "$12", "$15", "$20" ]
He lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut. The answer is: A
A
mathematics
A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
[ "7 km/hr", "7.2 km/hr", "8 km/hr", "8.2 km/hr", "8.3 km/hr" ]
Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B The answer is: B
B
mathematics
If (A-B-C+D = 18) and (A+B-C-D = 4), what is the value of (B-D)^2?
[ "49.", "8.", "12.", "16.", "64." ]
EQ1: A - B - C + D = 18 EQ2: A + B - C - D = 4 (1) Subtract EQ1 from EQ2 A - B - C + D = 18 - A +B - C - D = 4 ------------------------ -2B + 2D = 14 (2) Simplify -B + D = 7 B - D = -7 (B-D)^2 = (-7)^2 = 49 My answer: A The answer is: A
A
mathematics
If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 1480 will be:
[ "Rs. 300", "Rs. 200", "Rs. 240", "Rs. 400", "None of these" ]
Z share = Z, Y = 1.2Z X = 1.25Γƒβ€”1.2Z, X+Y+Z =1480 (1.25Γƒβ€” 1.2+1.2+1)Z=1480 3.7Z=1480, Z=400 Answer: . D The answer is: D
D
mathematics
Two horses begin running on an oval course at the same time. One runs each lap in 4 minutes; the other takes 16 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
[ "36", "12", "16/3", "4", "3" ]
The rate of the faster horse is 1/4 lap/minute; The rate of the slower horse is 1/16 lap/minute; Their relative rate is 1/4-1/16=3/16 lap/minute; The faster horse to gain one full lap will need time=distance/rate=1/(3/16)=16/3 minutes. Answer: C The answer is: C
C
mathematics
In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.1, 9.0, 6.0, and 8.5, what was the point value of the dive?
[ "68.8", "73.6", "75.2", "77.12", "81.6" ]
Degree of difficulty of dive = 3.2 Scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0 We can drop 6.0 and 9.0 Sum of the remaining scores = (7.5+8.1+8.5)= 24 Point of value of the dive = 24.1*3.2 =77.12 Answer D The answer is: D
D
mathematics
What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
[ "354665677", "436557678", "457676788", "725117481", "567768788" ]
Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted Answer: Option D The answer is: D
D
mathematics
The average (arithmetic mean) of 20, 40, and 60 is 8 more than the average of 10, 70, and what number?
[ "16", "25", "35", "45", "55" ]
a1 = 120/3 = 40 a2 = a1 -8 = 32 sum of second list = 32*3 = 96 therefore the number = 96 -80 = 16 ANSWER:A The answer is: A
A
mathematics
Working simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 8 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 3x units of product P in 4 days?
[ "30", "18", "16", "12", "8" ]
5 machines do x units in 8 days we have x/8 => rate of the 5 machines we know that we need to have 3x units in 4 days therefore, we need to get to 3x/4 rate of the machines. rate of one machine is x/8*1/5 = x/40. now, we need to know how many machines need to work simultaneously, to get 3x done in 4 days. 3x/4 work needs to be done by machines that work at x/40 rate. let's assign a constant Y for the number of machines: (x/40)*y = 3x/4 y = 3x/4 * 40/x cancel 4 with 40, and x with x and get -> 30. Answer choice A The answer is: A
A
mathematics
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
[ "3", "4", "9", "11", "None of these" ]
Answer: Option B Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (10y + x) = 36 9(x - y) = 36 x - y = 4. The answer is: B
B
mathematics
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
[ "54", "63", "75", "86", "98" ]
(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c) Therefore, the product should have factors with a difference of 2. 63 = 7*9, so this is a possible value for the original expression. The answer is B. The answer is: B
B
mathematics
In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
[ "200", "120", "245", "320", "147" ]
(3 men out 6) and (2 ladies out of 5) are to be chosen. Required number of ways = (6c3x5c2) = [6x5x4/3x2x1] x [5x4/2x1] = 200. Ans: A The answer is: A
A
mathematics
Find the greatest number which on dividing 1255 and 1490, leaves a reminder of 8 and 11 respectively
[ "27", "29", "33", "39", "41" ]
Explanation: In this type of question, its obvious we need to calculate the HCF, trick is HCF of (1255 - 8) and (1490 -11) = HCF (1247, 1479) = 29 Option B The answer is: B
B
mathematics
Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
[ "8", "10", "12", "11", "15" ]
Speed = 120/10 = 12 m/sec speed of the second train = 120/5 = 8 m/sec relative speed = 12+8 = 20 m/sec Req time = 120+120/20 = 12 sec ANSWER C The answer is: C
C
mathematics
A and B started a business investing Rs. 92,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
[ "9:2", "3:2", "23:5", "18:4", "17:4" ]
A: B = 92000 : 20000 = 92 : 20 = 46 : 10 = 23 : 5 ANSWER:C The answer is: C
C
mathematics
When 1/20% of 6,000 is subtracted from 1/10 of 6,000, the difference is
[ "50", "200", "380", "598", "400" ]
1/20 % of 6000 = 3 1/10 of 6000 = 600 600-3 = 598 Ans:D The answer is: D
D
mathematics
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
[ "120 m", "240 m", "300 m", "400 m", "None of these" ]
Speed = 54 * 5/18 = 15 m/sec. Length of the train = 15 * 20 = 300 m. Let the length of the platform be x m . Then, (x + 300)/36 = 15 => x = 240 m. ANSWER:B The answer is: B
B
mathematics
The ratio of the two natural numbers is 6 : 5. If a certain number is subtracted to both the numbers, the ratio becomes 5 : 4. If the larger number exceeds the smaller number by 5, find the number subtracted?
[ "8", "5", "15", "22", "6" ]
Let the two numbers be 6x and 5x. Let the numbers subtracted to both so that their ratio becomes 5 : 4 be k. (6x - k) / (5x - k) = 5/4 => 24x - 4k = 25x - 5k => k = x. 6x - 5x = 5 => x = 5 k = x = 5. Answer:B The answer is: B
B
mathematics
The average of first five prime numbers greater than 20 is?
[ "32.2", "32.98", "32.3", "32.8", "32.4" ]
23 + 29 + 31 + 37 + 41 = 161/5 = 32.2 Answer: A The answer is: A
A
mathematics
|x+3| – |4-x| = |9+x| How many solutions will this equation have?
[ "0", "1", "2", "3", "4" ]
You have |x+3| - |4-x| = |8+x| First, look at the three values independently of their absolute value sign, in other words: |x+3| - |4-x| = |8+x| (x+3) - (4-x) = (8+x) Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand. when x=-10 I.) (x+3) (-10+3) (-7) II.) (4-x) (4-[-10]) (double negative, so it becomes positive) (4+10) (14) III.) (8+x) (8+-10) (-2) In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change. Here is how I do it step by step. I.) |x+3| - |4-x| = |8+x| II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows: (x+3) x=-3 (-3+3) = 0 (4-x) x=4 (4-4) = 0 (8+x) x=-8 (8+-8) = 1 B The answer is: B
B
mathematics
Two negative numbers are multiplied to give a product of 48. If the lesser number is 10 less than thrice the greater number, what is the greater number?
[ "-6", "-8", "-5", "-9", "-10" ]
Test the options. The options give you the greater number. (A) - 6 Triple of -6 is -18 and 10 less is -8. -8 * -6 =48 (Correct) Correct Answer (A) The answer is: A
A
mathematics
A store sells a certain product at a fixed price per unit. At the product's current price, w units cost a total of exactly $300. If the price were lowered by $5 from its current value, then w + 2n units would cost exactly $300; if the price were raised by $5, then w – n units would cost exactly $300. What is the value of w?
[ "10", "15", "20", "25", "30" ]
It got too complicated when I used algebra. Using plugging in, it was quite fast. Price Quantity total value p w pw = 300 p-5 w+2n (p-5)(w+2n) = 300 p+5 w-n (p+5)(w-n) = 300 Solving three equations for three unknowns. Tough!! Plugging in, I always start with C. C was the answer here, so saved calculation! Putting values in above equations: Price Quantity total value 15 20 300 10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5 20 15 300 So w = 20 satisfies all equations!! The answer is: C
C
mathematics
The 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
[ "4", "6", "8", "9", "10" ]
The formula is Total = A+B+C - sum of exactly two + 2*all three + neither 21+18+19-x-2*5=44 solving for x you get 4 Answer A The answer is: A
A
mathematics
A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
[ "24 days", "65 days", "86 days", "45 days", "17 days" ]
10/40 + 10/30 + 10/x = 1 x = 24 days Answer:A The answer is: A
A
mathematics
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
[ "7500", "4366", "2877", "2768", "26871" ]
A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 25000 * 3/10 = Rs. 7500. Answer: A The answer is: A
A
mathematics
Calculate the ratio between x and y if 25% of x equal to 40% of y?
[ "5 : 8", "5 : 9", "5 : 7", "5 : 6", "5 : 4" ]
Explanation: 25 x = 40 y x: y = 25 : 40 = 5 : 8 Answer:A The answer is: A
A
mathematics
A cube of edge 6 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to:
[ "1:25", "1:36", "1:52", "1:522", "None" ]
Sol. Required ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1/36 = 1:36. Answer B The answer is: B
B
mathematics
85% of a number is added to 24, the result is the same number. Find the number?
[ "257", "267", "187", "one hundred sixty (160)", "122" ]
(85/100) * X + 24 = X 3X = 480 X = 160 Answer:D The answer is: D
D
mathematics
Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
[ "$24 million", "$120 million", "$144 million", "$240 million", "$888 million" ]
Convert units to millions as answer is in millions 1996 Imports = $1.44 bill = $1440 mill i.e. 1440/12 = $120 mill/month 1997 Imports = $388 mill/2 month i.e. $194 mill/month Difference/month = 194-120 = 74 Difference/year = $74 mill * 12 = $988 mill ANSWER: E The answer is: E
E
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", "9927", "267", "1268", "181" ]
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
A credit card number has 6 digits (between 1 to 9 inclusive). The first two digits are 12 in that order, the third digit is bigger than 6, the fourth digit is divisible by 2, and the fifth digit is 4 times the sixth. How many different credit card numbers are possible?
[ "12", "18", "24", "36", "48" ]
The first two digits are fixed. The third digit can be 7, 8, or 9 so there are 3 choices. The fourth digit can be 2, 4, 6, or 8 so there are 4 choices. The fifth digit depends entirely on the sixth digit. The sixth digit can be 1 or 2 so there are 2 choices. The number of possibilities is 3*4*2 = 24 The answer is C. The answer is: C
C
mathematics
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
[ "$ 280,000", "$ 320,000", "$ 360,000", "$ 480,000", "$ 540,000" ]
The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later? The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times. So the amount invested will get doubled thrice. So, 60000 *2^3 = 480000 Hence, the answer is D. The answer is: D
D
mathematics
Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
[ "40", "48", "43", "45", "41" ]
Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. Ele = 3*Lyn Usually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3). Then age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele. Answer (D) The answer is: D
D
mathematics
A lady bought five books namely A,B,C,D,E to distribute her 6 children. How many ways she can distribute books?
[ "6^3", "5^6", "6^5", "6^6", "3^6" ]
6*6*6*6*6 6^5 ANSWER:C The answer is: C
C
mathematics
Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip?
[ "P=26.7", "P=30.0", "P=40.0", "P=53.3", "P=60.0" ]
VERITAS PREPOFFICIAL SOLUTION Correct Answer : C Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour. Answer choice C is correct. The answer is: C
C
mathematics
A train 140 m long is running with a speed of 50 km/hr. In what time will it pass a man who is running at 4 km/hr in the direction opposite to that in which the train is going?
[ "8.1", "7.0", "9.33", "8", "9" ]
Speed of train relative to man = 50 +4 = 54 km/hr. = 54 * 5/18 = 15 m/sec. Time taken to pass the men = 140 * 1/15 = 9.33 sec. Answer: Option C The answer is: C
C