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The Wordsmiths 3

mathematics

Townville has 100 residents, and 20 of them are females. If half of Townville’s male residents are smokers, and 1/2 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?

Number of people =100 Females = 20 men = 100-20=80 Half of the men are smoker80/2=40, that means the remaining men 80-40=40 are non smokers. 1/2 females are smoker. i.e 1/2*20 = 10 20-10=10 females are non smokers So, total number of non smokers in the town are 40+10 =50 Answer : C The answer is: C

C

mathematics

If a and b are digits, and the number a,11b is evenly divisible by 88, what are the values of a and b?

a,11b, divisible by 88. Factors of 88 = (8)(11) Divisible by 8: if the last 3 digits of the number are divisible by 8. 11b/8 => 112/8 = 14 => b = 2 Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11. a11-2 => a09 => 209/11 = 19. So a = 2. Answer: D The answer is: D

D

mathematics

A person is traveling at 25km/hr and reached his destiny in 6hr find the distance?

speed = 25km/hr time = 6hr distance = 25*6 = 150km Answer is D The answer is: D

D

mathematics

What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x

46080 /12 = 3840 3840 /10 = 384 384 /8 = 48 48 /6 = 8 8/4 = 2 2 /2 = 1 A The answer is: A

A

mathematics

A baseball card decreased in value 60% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?

Let the initial value of baseball card = 100 After first year , value of baseball card = (1- 60/100)* 100 = 40 After second year , value of baseball card =(1 - 10/100)* 40 = 36 total percent decrease of the card's value over the two years = (100-36)/100 *100% =64% Answer E The answer is: E

E

mathematics

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?

2:3 2x + 10 : 3x + 10 = 5 : 7 7[2x + 10] = 5[3x + 10] 14x + 70 = 15x + 50 15x - 14x = 70 - 50 x = 20 Then the first number is = 2 2x = 40 D The answer is: D

D

mathematics

If (-4)^(6x) = 4^(30 + x) and x is an integer, what is the value of x ?

Since x is an integer, (-4)^(6x) is always positive. So, 4^6x = 4^(30 + x) 6x = 30 + x 5x = 30 x = 6 Answer: E The answer is: E

E

mathematics

After decreasing 50% in the price of an article costs Rs.620. Find the actual cost of an article?

CP* (50/100) = 620 CP= 12.4 * 100 => CP = 1240 ANSWER:B The answer is: B

B

mathematics

A man rows his boat 80 km downstream and 38 km upstream, taking 3 hours each time. Find the speed of the stream?

Speed downstream = d/t = 80/(3) = 27 kmph Speed upstream = d/t = 38/(3) = 9 kmph The speed of the stream = (27 - 9)/2 = 9 kmph Answer:B The answer is: B

B

mathematics

A chocolate has 12 equal piece. Monju gave 1/4th of it to Anju, 1/3rd of it to Sujata and 1/6th of it to Fiza. The number of piece of chocolate left with Manju is?

Answer The number of pieces of chocolate left with Manju = 1- [(1/4) + (1/3) + (1/6) = 1 - (3 + 4 + 2)/12 = 1 - 9/12 = (12 - 9) / 12 = 3/12 Option: C The answer is: C

C

mathematics

A 16% stock yielding 10% is quoted at :

Solution To earn Rs. 10, money invested = Rs. 100. To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160. ∴ Market value of Rs. 100 stock =Rs. 160 Answer E The answer is: E

E

mathematics

180 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?

180 = 2^2*3^3*5 There are factors in each range except for 65~75 The answer is D. The answer is: D

D

mathematics

The average age of 20 men in the class is 14.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?

Total age of 20 men = 14.6 x 20 = 292 Now, total age of 25 men = 389. Total age of five men added later = 389 - 292 = 97. Hence, the total average of five men = 97/5 = 19.4 ANSWER:B The answer is: B

B

mathematics

Pakistan, India and Srilanka are engaged in a missile war, such that they fire one after the other, in a sequence, the sequence selected by draw of lots. The rules of war are such that the 3 countries keep on shooting at each other until they hit with the missile. This goes on until there is one last country left unhit, and then the war ends. The chances that Pakistan hits its target is 100%, Srilanka hits the target is 80% and India hits the target is 50%. Who has the highest chance of winning the war?

Solution: India has the highest chances of winning the war (47/90) Missile Firing order: Chances of Remaining Unhit - Pakistan: Chances of Remaining Unhit - Srilanka: Chances of Remaining Unhit - India Pakistan - Srilanka - India 1/2 0 1/2 Pakistan - India - Srilanka 1/2 0 1/2 India - Pakistan - Srilanka 1/10 16/45 49/90 Srilanka- Pakistan - India 1/2 0 1/2 Srilanka - India - Pakistan 1/10 16/45 49/90 India - Srilanka - Pakistan 1/10 16/45 49/90 Total chances of being unhit (sum of the probabilities divided by 6): 27/90 16/90 47/90 Answer D The answer is: D

D

mathematics

On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 8 more tea cups than hot chocolate cups, then how many rainy days were there last week?

T= the number of cups of tea C= the number of cups of hot chocolate T+C = 22 T-C=8 -> T= 15. C=7. Mo drinks 5 cups of tea a day then number of days that are not rainy = 15/5 = 3 So number of rainy days = 7-3 = 4 B is the answer. The answer is: B

B

mathematics

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?

Speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5/18 = 5 m/s Hence time taken to cover 60 m = 60/5 = 12 seconds. Answer:C The answer is: C

C

mathematics

A fair price shopkeeper takes 10% profit on his goods. He lost 70% goods during theft. His loss percent is:

Explanation: Suppose he has 100 items. Let C.P. of each item be Re. 1. Total cost = Rs. 100. Number of items left after theft = 30. S.P. of each item = Rs. 1.10 Total sale = 1.10 * 30 = Rs. 33 Hence, loss % = 67/100 * 100 = 67% Answer:D The answer is: D

D

mathematics

Find the ones digit of 73^356

The units digit of 73^356 will be the same as the units digit of 3^356. 3^1=3 --> the units digit is 3; 3^2=9 --> the units digit is 9; 3^3=27 --> the units digit is 7; 3^4=81 --> the units digit is 1; 3^5=243 --> the units digit is 3 AGAIN; ... So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 356=356+0=(multiple of 4)+0, then the units digit of 3^356 will be thus 1. Answer: A. The answer is: A

A

mathematics

The average of 11 results is 46, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?

1 to 11 = 11 * 46 = 506 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6th = 294 + 312 – 506 = 100 Answer:C The answer is: C

C

mathematics

If x^2=x-2, then x^3=?

Given X^2 = X-2 X^3 = X*X^2 = x*(X-2)-- Substituted from above. = X^2 - 2X = X-2-2X = -X-2. Hence D. The answer is: D

D

mathematics

What percent of a day is 5 hours?

Total hours in a day = 24 Required percent =5/24×100=20.83 % answer :E The answer is: E

E

mathematics

Point (g,h) is on the circle represented by g^2+h^2=10, and g, h are integers. How many such points are possible?

g^2+h^2=10 and g, h are integers means that 10 is the sum of two perfect squares. 10 is the sum of only one pair of perfect squares 1 and 9. So, there can be 8 such points, 4 in each quadrant: (1, 3); (1, -3); (-1, 3); (-1, -3); (3, 1); (3, -1); (-3, 1); (-3, -1). Answer: E. The answer is: E

E

mathematics

If it would take one machine 15 minutes to fill a large production order and another machine 20 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?

Since , Machine 1-M1 take 15 mins to fill the order The work done by M1 in a min = 1/15 Machine 2- M2 take 20 mins to fill the same order and work done by M2 in a min = 1/20 Total work done by M1 and M2 in a min = 1/15 + 1/20 = 7/60 Time needed for M1 and M2 to complete the order = 60/7 = 8 4/11 Answer E The answer is: E

E

mathematics

Murali travelled from city A to city B at a speed of 70 kmph and from city B to city C at 30 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?

Let the distances between city A to B and B to C be 2x km and 3x km respectively. Total time taken to cover from A to C = (2x)/70 + (3x)/30 = (6x + 21x)/210 = 27x/210 = x/10 Average speed = (2x + 3x)/(27x/210) = 38.9 kmph. Answer: B The answer is: B

B

mathematics

The unit digit in the product (784 x 618 x 917 x 463) is:

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2 Answer B) 2. The answer is: B

B

mathematics

Calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length, if the speed of the train is 40 km/hour ?

Speed = 40 Km/hr = 40*(5/18) m/sec = 11.1111 m/sec Total distance = 120+160 = 280 meter Time = Distance/speed = 280 * (1/11.1111) = 25.2 seconds Answer: B The answer is: B

B

mathematics

What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

LCM of 5, 6, 7 and 8 = 840 Hence the number can be written in the form (840k + 3) which is divisible by 9. If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9. If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9. Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. Answer: Option B The answer is: B

B

mathematics

Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?

4/12 + x/15 = 1 x = 10.Answer: B The answer is: B

B

mathematics

What is the units' digit of the following expression (10)^5*(12)^5*(18)^5?

We do not have to do any calculations or find units digit of remaining numbers... all three terms - 10,12,18 - are EVEN and since the PRODUCT contains 0, the units digit of the product will remain 0 A The answer is: A

A

mathematics

A 6% stock yields 8%. The market value of the stock is

For an income of Rs. 8, investment = Rs. 100. For an income of Rs. 6, investment = Rs. 100 x 6 = Rs. 75. 8 Market value of Rs. 100 stock = Rs. 75. Answer: B The answer is: B

B

mathematics

In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 160 vote’s majority. What is the total number of votes polled?

Explanation: Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %) 40 % = 70 % - 30 % 40% -----> 160 (40*4 = 160) 100% -----> 400 (100*4 = 400) Answer: Option B The answer is: B

B

mathematics

A certain candy manufacturer reduced the weight of Candy Bar M by 5 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?

assume 1oz candy cost $1 before. now price remain same $1 but weight of candy reduces to 0.95 oz new price of candy = 1/0.95 =1.052 price increase 5.2 % D The answer is: D

D

mathematics

A test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232?

A test has a mean of 220 and a standard deviation of 10, find the corresponding z score for: a) a test score of 232, z(232) = (232-220)/10 = 12/10 = 1.2 Option A The answer is: A

A

mathematics

A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 80 kmph. When and at what distance from Mumbai do the two trains meet?

When the second train leaves Mumbai the first train covers 40 * 1 = 40 km So, the distance between first train and second train is 40 km at 10.00am Time taken by the trains to meet = Distance / relative speed = 40 / (80 -40) = 1 hours So, the two trains meet at 11 a.m. The two trains meet 1 * 80 = 80 km away from Mumbai. Answer:C The answer is: C

C

mathematics

Calculate the different number of ways 7 boys and 2 girls can sit on a bench?

npn = n! 9p9 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880 B The answer is: B

B

mathematics

If the value of a piece of house decreases by 10% while the new tax rate on the house represent 110% of the original tax rate, what is the effect on the taxes?

Cansider the value of house = 100, Original tax rate 10%, hence tax value = 100*10% = 10. Decreased value of house = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9 10-9.9 = decrease by 1%. Answer D. The answer is: D

D

mathematics

Positive Integer A gives the remainder of 12 when divided by another positive Integer B. If A/B = 47.24, what is the value of B?

.24 of B = Remainder .24 of B = 12 B = (12 *100) / 24 = 50. E The answer is: E

E

mathematics

In a company of 16 employees, 8 employees earn $38,000, 4 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 16 employees is $44,000, what is the annual salary for each of the highest-paid employees?

8*38,000+4*42,000+4x=16*44,000 4x=704,000-304,000-168,000 4x=232,000 x=58,000 The answer is E. The answer is: E

E

mathematics

The positive value of x that satisfies the equation (1 + 2x)^5 = (1 + 3x)^6 is between Bunuel, can you please explain this one?

Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase). Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1. Answer: E. The answer is: E

E

mathematics

The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?

Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 276 - (A + D) = 276 - 132 = 144. B + B -28 = 144 B = (144 + 28)/2 = 86 Answer: B The answer is: B

B

mathematics

The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount.The rate percent is

Solution Let T.D be Rs 1.Then, B.D =Rs.11 / 10 = Rs.1.10. Sum =Rs.(1.10 x 1/ 1.10-1) = Rs.(110 / 10) = Rs. 11. S.I on Rs.11 for 2 years is Rs.1.10. Rate =(100 x 1.10 / 11 x 2)% = 5% Answer C The answer is: C

C

mathematics

A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?

Perimeter of the plot = 2(90+50) = 280m no of poles =280/5 =56m Answer: D The answer is: D

D

mathematics

o mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33×13%33×13%, and finished the work 1 day earlier than it was planned. A) What is the area of the grass field? B) How many days did it take to mow the whole field? C) How many days were scheduled initially for this job?

Hint: See problem 20 and solve by yourself. Answer: A) 120 hectares; B) 7 days; C) 8 days. Answer:D The answer is: D

D

mathematics

In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount Q in 1996 as they paid in 1995?

water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio Q=150-> 100 means 1/3 rd= 33(1/3) %=A The answer is: A

A

mathematics

John purchased some shirts and trousers for $1100. He paid $550 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?

Given that the total purchase of two items cost 1100. So the average purchase of one item will cost 1100/2 = 550. Its given as total shirt cost 100$ less. Hence Total Shirt cost = 550 - 275 and Total trouser cost = 300 + 275 5 shirts = 275$ ==> One shirt = 55$ One trouser = 55 + 20 = 75$ Total trousers = 825 / 75 = 11. E The answer is: E

E

mathematics

Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 3 times before stopping?

The probability that Molly will roll the die less than 4 times before stopping is the sum of the following: The probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll); The probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1); P = 1/6 + 5/6*1/6 = 11/216. Answer: D. The answer is: D

D

mathematics

At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?

150 = (750*5*R)/100 R = 4%.Answer: C The answer is: C

C

mathematics

find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.

when unit digit 1,2,3,5,6 then no. formed will be divisible by the digit at the unit place. => 5*5p5 numbers when unit place is 4, tenth place should be 2 or 6 => 2*4p4 numbers total = 5*5p5 + 2*4p4 = 5*5! + 2*4! = 648 ANSWER:A The answer is: A

A

mathematics

A boy wants to go abroad by boat and return by flight. He has a choice of 2 different boat to go and 8 flight to return. In how many ways, can the boy perform his journey?

Ans.(B) Sol. Number of choices to go by ship = 2 Number of choices to return by airline = 8 From, fundamental principle, total number of ways of performing the journey = 2 x 8 = 16 ways The answer is: B

B

mathematics

If x is 50 percent greater than 88, then x =

x=88*1.5=132 So the answer is B. The answer is: B

B

mathematics

If x is an integer, then x(x - 1)(x - b) must be evenly divisible by three when b is any of the following values EXCEPT

here's another approach x(x - 1)(x - b) all three are consecutive, so the product MUST be a multiple of 3 we don't know the value of b just yet ... so let's extend the series ... the extension itself reveals the answers ..(x-5)..(x-2)(x-1)x(x+1)..(x+4).. we can see the possible values of b too from the series b = 2 OR 2+3n [25] b = -1 OR -1+3n [-1-4] B i.e. -2 does not fit in any value of b so B it is The answer is: B

B

mathematics

The present ratio of students to teachers at a certain school is 70 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

We are given that the ratio of students to teacher is 70 to 1. We can rewrite this using variable multipliers. students : teachers = 70x : x We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation: Students/Teachers  25/1 = (70x + 50)/(x + 5) If we cross multiply we have: 25(x + 5) =70x + 50 25x + 125 = 70x + 50 1.667 = x x~2 Since x is the present number of teachers, currently there are 2 teachers. Answer A. The answer is: A

A

mathematics

How many days will there be from 29th January,1996 to 15th May,1996(both days included)?

Explanation: Number of days from 29-Jan-1996 to 15-May-1996 (both days included) = 3(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 108 Answer: Option E The answer is: E

E

mathematics

A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?

Length of the train be ‘X’ X + 150/15 = X + 250/20 4X + 600 = 3X + 750 X = 150m Answer: A The answer is: A

A

mathematics

The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?

Explanation: The temperature for first 4 days = 4 * 36 = 144 The temperature for last 4 days = 4 * 38 = 152 The difference between the temperatures is (152 – 144) = 8 The ratio of temperature between first and fifth day is 4 : 5 The temperature on fifth day is 5*8 = 40 ANSWER D The answer is: D

D

mathematics

Read the following three equations: 5 ~ 4 ~ 3 ~ 9 = 4215 6 ~ 9 ~ 2 ~ 6 = 3816 4 ~ 7 ~ 3 ~ 3 = 1122 Now based on the rule that has been used, solve the following equation: 6 ~ 2 ~ 7 ~ 4 = ____

A 2414 2414 The rule that is being followed here is P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)] Using the same rule in the incomplete equation, 6 ~ 2 ~ 7 ~ 4 = [first digit of (6 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (6 * 4)] = 2414 Thus 2414 is the missing number. The answer is: A

A

mathematics

On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 4 cups of tea. Last week Mo drank a total of 42 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?

T= the number of cups of tea C= the number of cups of hot chocolate T+C = 42 T-C=14 -> T= 28. C=14. Mo drinks 4 cups of tea a day then number of days that are not rainy = 28/4= 7 So number of rainy days = 7-7 = 0 A is the answer. The answer is: A

A

mathematics

If y is 40 percent greater than x, then x is what percent less than y?

y = 1.4x x = y/1.4 = 10y/14 = y - (2/7)*y 2/7 is about 29%. The answer is D. The answer is: D

D

mathematics

A sum of money place at compound interest doubles itself in 6 years. In how many years will it amount to eight times itself?

100 ---- 200 ---- 6 400 ---- 6 800 ---- 6 ------ 18 years Answer: D The answer is: D

D

mathematics

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 18 hrs and a machine of type S does the same job in 9 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

Rate of machine R =1/18 Rate of machine S =1/9 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/18 +x/9 =1/2 3x/18=1/2 x=18/6=3 So no of machine R is 3 Answer A The answer is: A

A

mathematics

How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime no.s (2,3,5,7)

we know prime no. are 2 ,3 , 5, 7 mulply by 1 is prime no 2 = 21(2*1)=73(7*3) 2 = 21 (2*1)=37(3*7) 2= 12(1*2)=43(4*3)or34(3*4) or26(2*6)or62(6*2) . . .similarly for all prime no then u will got it.... 12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75 ans is 18 ANSWER:C The answer is: C

C

mathematics

On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.

Explanation: Difference between C.I and S.I for 2 years = 36.30 S.I. for one year = 330. S.I. on Rs 330 for one year = 36.30 So R% = \frac{100*36.30}{330*1} = 11% Option D The answer is: D

D

mathematics

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 5m3 , then the rise in the water level in the tank will be:

Explanation: Total volume of water displaced =(5 x 50) m3 = 250 m3 Rise in water level = 250/40×20= 0.3125m = 31.25cm Answer: A The answer is: A

A

mathematics

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9* 60)/54min = 10 min. Answer:B The answer is: B

B

mathematics

The sale price sarees listed for Rs.175 after successive discount is 20% and 5% is?

175*(80/100)*(95/100) = 133 Answer:B The answer is: B

B

mathematics

If an item that originally sold for A dollars was marked up by x percent and then discounted by M percent, which of the following expressions represents the final price of the item?

value of item =A ..marked up by x% = Ax/100 total value = A +ax/100 .discounted by L% on Total M/100 * ( A+Ax/100) Final price =(A+ Ax/100) - M/100 ( A +Ax/100) D The answer is: D

D

mathematics

Jane makes toy bears. When she works with an assistant, she makes 100 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?

We can use fractional equivalents here to solve the problem 80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears 10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours Now we come to productivity Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour Hence the productivity is double with the assistant i.e. the increase in productivity is 200% E The answer is: E

E

mathematics

A train 420 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 60 m long?

total length= 420+60=480 speed=48km/h=(48*5)/18= 40/3 m/s time=(480*3)/40=36 sec. ANSWER:B The answer is: B

B

mathematics

Hockey Stick and ball cost $50. If the Stick cost $49 more than the ball. what is the cost of each ?

D Hockey Stick $49.50 & ball $0.50 The answer is: D

D

mathematics

Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 6 km each. Then they turned left and ran for another 4.5 km. What is the distance (in kilometers) between the the two twins when they stop?

The distance between them is the hypotenuse of a right angle triangle with sides 9 km and 12 km. hypotenuse = sqrt(9^2 + 12^2) = 15 The answer is B. The answer is: B

B

mathematics

Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 16,100, Deepak's share is:?

Ratio of their shares = 22500 : 35000 = 9:14 Deepak's share = 16100 * 14/23 = Rs.9800. Answer:D The answer is: D

D

mathematics

The ages of X and Y are in the proportion of 6:5 and total of their ages is 44 years. The proportion of their ages after 8 years will be

Explanation: Let current ages of X and Y correspondingly, is 6A & 5A Given: 6A + 5A = 44 => A = 4 Proportion of ages after 0.8 decades will be 6A + 8 : 5A + 8 32:28 (or) 8:7 . Answer: C The answer is: C

C

mathematics

When Rahul was born, his father was 35 years older than his brother and his mother was 25 years older than his sister. If Rahul's brother is 5 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?

When Rahul was born, his brother's age = 5 years; his father's age = (5 + 35) years = 40 years, his mother's age = (40 - 3) years = 37 years; his sister's age = (37 - 25) years = 12 years. Answer: Option C The answer is: C

C

mathematics

Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?

P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year Amount = [15000 * (1 + 5/100)2] = (15000 * 21/20 * 21/20) = Rs. 16537.50 Answer:C The answer is: C

C

mathematics

Evaluate the expression m - (m - n) : (-2) ⋅ (-5) when m = -4, n = -6

Solution: m - (m - n) : (-2) ⋅ (-5) = (-4) - [-4 - (-6)] : (-2) ⋅ (-5) = -4 - 2 : (-2) ⋅ (-5) = -4 - (-1) ⋅ (-5) = -4 - (+5) = -9 Answer B The answer is: B

B

mathematics

20-3*4^2+53 = ?

20-3*4^2+53= 20-3*16+53=20-48+53=25.. A The answer is: A

A

mathematics

A tradesman by means of his false balance defrauds to the extent of 14%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?

g% = 14 + 14 + (14*14)/100 = 29.96% Answer: B The answer is: B

B

mathematics

The positive two-digit integers s and t have the same digits, but in reverse order. Which of the following must be a factor of s + t?

Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9 and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187 44 is multiple of 11 Answer : C The answer is: C

C

mathematics

What value of K gives the equation,3k-2=2k-1?

3k-2=2k-1 If k=1 3(1)-2=2(1)-1 3-2=2-1 1=1 Option A is answer The answer is: A

A

mathematics

Ajay pays Rs 8.0 per litre of spirit. He adds water and sells the mixture at Rs 9 per litre, thereby making 40 % profit. The proportion of water to spirit received by the customers is

Suppose the quantity of spirit purchased = X lites Suppose quantity of water mixed = Y litres Required ratio of the water and the spirit in the mixture = Y:X C.P. of x litres of spirit = Rs 8.0X S.P of x litres of spirit = 9(X + Y) Thus,C.P = S.P x 100/(100 + gain% ) => 64 = (9X+9Y) x 100/100 + 40 => 1120X =900X +900Y => 220X= 900Y => Y/X = 220/900 = 11/45 ANSWER:B The answer is: B

B

mathematics

Ramesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh. If they work together how many days will they need to finish the same amount of work?

Ramesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh. So Rohan can finish a piece of work in 11 days. days needed to finish the same amount of work = 1/(1/11+1/22)=22/3 days ANSWER:A The answer is: A

A

mathematics

If a and b are the two values of t that satisfy the equation t^2 – 12t + 20 = 0, with a > b, what is the value of a – b?

Factor the left side of the equation: t^2 – 12t + 20 = 0 (t – 2)(t – 10) = 0 t = 2, t = 10 Thus, a = 10 and b = 2. So a – b = 10 – 2 = 8. The answer is D. The answer is: D

D

mathematics

A car travels at a speed of 65 miles per hour. How far will it travel in 4 hours?

During each hour, the car travels 65 miles. For 4 hours it will travel 65 + 65 + 65 + 65 = 4 × 65 = 260 miles correct answer is C) 260 miles The answer is: C

C

mathematics

An investor receives a total combined return of 7% on his two different investments. On his $20,000 investment he receives a return of 6%. What is the return on his $20,000 investment?

0.06 * 20000 + 20000x = 0.07(40000) solving for x give x = 8% option C The answer is: C

C

mathematics

In a Express Train passengers traveling in A.C. Sleeper Class, First Class and Sleeper Class are in the ratio 1:2:3, and fare to each class in the ratio 5:4:2. If the income from this train is Rs. 57000, the income of A.C. Sleeper Class is

Income is divided in the ratio 1×5:2×4:3×2= 5:8:6. Now 5x + 8x + 6x = 19x = 57000. ∴ x =3000. Therefore income from A.C. Sleeper Class = 30005=15000. Answer:C. The answer is: C

C

mathematics

On a certain day, Tim invested $500 at 10 percent annual interest, compounded annually, and Lana invested 1,000 at 5 percent annual interest, compounded annually.The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?

Compounded annually means that the interest is applied once per year. One can have 10% annual interest compounded monthly - in this case 10%/12 would be applied each month, or 10% annual interest compounded daily etc. With respect to the problem at hand, at the end of two years, Tim would have 500(1.10)^2 = 500(1.21) = 605 and Lana would have 1,000(1.05)^2 = 1,000(1.1025) =1102.5 Thus, Tim earned 105 dollars, while Lana earned 102.5 dollars The difference is $2.5 and the answer is A. The answer is: A

A

mathematics

In covering a distance of 60 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:

Let A's speed be X km/hr. Then, 60/x - 60/2x = 3 30/x = 3 x = 10 km/hr. Answer : C The answer is: C

C

mathematics

The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1000 per sq.metre.

Solution Area of the floor = (5.5 x 3.75)m² = 20.635m ² Cost of paying = Rs. (1000 x 20.625) = Rs.20625. Answer D The answer is: D

D

mathematics

How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 14?

200/13 = 15 (plus remainder) so there are 15 multiples of 13 200/14 = 14 (plus remainder) so there are 14 multiples of 14 We need to subtract 1 because 13*14 is a multiple of both so it was counted twice. The total is 15+14-1 = 28 The answer is D. The answer is: D

D

mathematics

In your classes you counted 126 hands. How many students were at the class?

Total number of hands = 126 We have 2 hands. To find how many students were at the class, divide the total number of hands by the number of hands we have. We get, divide 126 by 2 126 ÷ 2 = 63 Therefore, there were 63 students at the class. ANSWER IS A The answer is: A

A

mathematics

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?

Explanation : Let the number of candidates applied for the examination = x Given that 5% of the applicants were found ineligible. It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%) Hence total eligible candidates = 95x/100 Given that 85% of the eligible candidates belonged to the general category It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%) Hence Total eligible candidates belonged to other categories = total eligible candidates × (15/100) = (95x/100) × (15/100) = (95x × 15)/(100 × 100) Given that Total eligible candidates belonged to other categories = 4275 ⇒ (95x × 15)/(100 × 100) = 4275 ⇒ (19x × 15)/(100 × 100) = 855 ⇒ (19x × 3)/(100 × 100) = 171 ⇒ (x × 3)/(100 × 100) = 9 ⇒ x/(100 × 100) = 3 ⇒ x = 3 × 100 × 100 = 30000 Answer : Option B The answer is: B

B

mathematics

How many meters are there in 660 centimeters?

Solution: 1 meter = 100 centimeters Just divide 660 by 100 660 ÷ 100 = 6.6, so there are 6.6 meters in 660 centimeters Option A The answer is: A

A

mathematics

If k = 2n - 1, where n is an integer, what is the remainder of k^2/8?

Let us assume that k = 4(n)(n-1) This is divisible by 8. So k+1 when divided by 8 will give reminder 1. For example, consider n = 2 We have 4*2*1 + 1 = 9 When we divide this by 8 we get reminder 1. ANSWER:A The answer is: A

A

mathematics

A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 15m/h. what is the speedof the person while he was going to his office?

u = k , v= 3k \inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=15 \inline \Rightarrow 1.5k = 15 \inline \Rightarrow k=10km/h B The answer is: B

B

mathematics

A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6 Total profit = Rs. 52000 Share of B = 6/13 (52000) = Rs. 24000 Answer:B The answer is: B

B

mathematics

The value of 5 in the number 357.21 is

Ans: C The number 357.21 consists of: 3 hundreds, 5 tens, 7 ones, 2 tenths and 1 hundredth =>the value of 5 in 357.21 is 5 tens The answer is: C

C

mathematics

Twenty people at a meeting were born during the month of September, which has 30 days. The probability that at least two of the people in the room share the same birthday is closest to which of the following?

The probability that at least two people sharing the same birthday = 1 - the probability that none of them sharing the same birthday A = The number of ways of none of them sharing the same birthday = 30P20 = 30!/(30-20)! = 30!/10! = 11*12*...*29*30 B = The total number of possible ways of 20 people born in September = 20*20*....*20*20 = 20^30 ( each day has 20 options) A/B = the probability that none of them sharing the same birthday since B is much greater than A, A/B may equal 1% --> The probability that at least two people sharing the same birthday = 1 - 1% = 99% Answer E The answer is: E

E

mathematics

Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?

N * 50 = (325000 - 300000) = 25000 N = 25000 / 50 = 500 C The answer is: C

C

mathematics

What is the difference between the place value and the face value of 8 in the numeral 296487?

Explanation: Place value of 8 = 80 Face value of 8 = 8 Difference = 80 - 8 = 72 Answer: E The answer is: E

E

mathematics

Solve below question 4x + 1 = 37

1. Subtract 1 from both sides: 4x + 1 - 1 = 37 - 1 2. Simplify both sides: 4x = 36 3. Divide both sides by 4: 4. Simplify both sides: x = 9 D The answer is: D

D