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mathematics

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

Money collected = (59.29 x 100) paise = 5929 paise. Number of members = 5929 = 77. Answer: Option C The answer is: C

C

mathematics

If x > 5 and y < -5, then which of the following must be true ?

Pick x=3, y = -3 A) x/y > 1 - Incorrect as x/y = -1 B) x/y < -1 - Incorrect as x/y = -1 C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0 D) x + y > 0 - Incorrect. x + y = 0 E) xy > 0 - Incorrect. XY = -9 which is less than zero. A should be the answer. The answer is: A

A

mathematics

A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 30 percent of the drive from the center, what percent of the round-trip has the technician completed?

round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 30% of 50% i.e 15%. so he completed 50 +15 =65 % of total trip. B The answer is: B

B

mathematics

A man can row at 5 kmph in still water. If the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Explanation: Speed in still water = 5 kmph Speed of the current = 3 kmph Speed downstream = (5+3) = 8 kmph Speed upstream = (5-3) = 2 kmph Let the required distance be x km Total time taken = 1 hour ⇒ x/8+x/2=1 ⇒x+4x=8 ⇒5x=8 ⇒x=1.6 km Answer: Option E The answer is: E

E

mathematics

How many digits are required to write numbers between 1 to 100.

Explanation: Single digits are from 1 to 9 = 9 digits Doubt digits are from 10 to 99 = 90 x 2 = 180 digits 100 needs 3 digits. Total 192 digits Correct Option: C The answer is: C

C

mathematics

The respective ages of father and his son are 47 and 16 years. In how many years will the father be twice as old as his son ?

Suppose x years later the father will be twice as old as his son. x + 47 = 2 (x + 16) x = 47 - 32 = 15 years answer : D The answer is: D

D

mathematics

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?

6!/3!(6-3)! = 20 4!/1!(4-1)!=4 so number of different committees equals 20*4=80 ANS:D The answer is: D

D

mathematics

Two goods trains each 680 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?

Relative speed = 45 + 30 = 75 km/hr. 75 * 5/18 = 125/6 m/sec. Distance covered = 680 + 680 = 1360 m. Required time = 1360 * 6/125 = 65.28 sec. Answer:B The answer is: B

B

mathematics

Ajay and Sasi start walking towards each other at 6am at speed of 4kmph and 5kmph. They were initially 20km apart. At what time do they meet?

Time of meeting = distance / relative speed = 20/6+4 = 20/10 = 2 hrs after 6am = 8am Answer is B The answer is: B

B

mathematics

In a class,30 students pass in english and 20 students in maths,while some students among these pass in both.how many students do only english as compared to those doing only maths?

For doing Union or Intersection we would need three values. In this question the missing information in this question is Total no.of Students in the class. ANSWER:E The answer is: E

E

mathematics

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

Let the numbers be a, b and c. Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138+2x131= 400. (a + b + c) = square root of 400 = 20 answer :A The answer is: A

A

mathematics

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is ?

Let original length = x and original width = y Decrease in area will be =xy−(80x100×90y100)=(xy−1825xy)=725xyDecrease = (7xy25xy×100)%=28% Answer: D The answer is: D

D

mathematics

If R is between (4) and (-4), which of the following can be greatest?

7/(R+1) - can be as large as possible. for eg. if R = -1.000001 => 7/(R+1) = 7000000 Ans A The answer is: A

A

mathematics

If c is 25% of a and 10% of b, what percent of a is b?

c is 25% of a --> c=a/4; c is 10% of b --> c=b/10; Thus a/4=b/10 --> b=5/2*a=2.5a. Therefore, b is 250% of a. Answer: E The answer is: E

E

mathematics

What number comes next? 452, 693, 714, 526, 937, ?

C 145 The numbers 45269371 are being repeated in the same sequence. The answer is: C

C

mathematics

there are sixty markings on a clock, minutes hand was exactly on one of those markings. nine markings away from the minutes hand was hours hand. what could be the time.

given angle diff=9mins we know 1min=6 deg therefore 9mins=9*6=54 deg so the angle diff must be 54 deg better to go through the options let us consider A.5hrs 14mins find angle angle traced by hour hand=(5*30)+(14/2)=157 angle traced by minute hand=(14*6)=84 angle diff=157-84=73 similarly for option C. angle traced by hour hand=(7*30)+(48/2)=234 angle traced by minute hand=(48*6)=288 angle diff=(288-234)=54 ANSWER:C The answer is: C

C

mathematics

A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 10 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?

The correct answer is C. The answer is: C

C

mathematics

The cost of 14 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?

Explanation : Let the required cost be Rs. x. Then, More packets, More cost (Direct Proportion) More weight, More cost (Direct Proportion) Packets 14 : 27 Weight 900 : 1000 :: 28 : x (14 x 900 x x) = (27 x 1000 x 28) x = (27 x 1000 x 28) /14 x 900 =60 Answer D The answer is: D

D

mathematics

A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?

The complete round trip consists of driving to the service center and then back home again. So, once the technician drives to the service center he/she has already competed 50% of the entire trip. Since the technician completes a portion of the trip back home,the correct answer must be greater than 50% so 0.5+0.5*0.4=0.70 Answer: B The answer is: B

B

mathematics

A bicyclist's wheel has a circumference of 9 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?

The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour. To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/9*5=4 Answer (C) The answer is: C

C

mathematics

A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 450km less in time. Find his speed?

Let the speed be x km/hr 50x-50* 9/10 *x = 450 50x - 45x = 450 x = 90km/hr Answer is E The answer is: E

E

mathematics

A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent T should the number of hours worked be increased?

Correct Answer: C Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked T will be 25% greater than the original number. The answer is C. The answer is: C

C

mathematics

A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.

65 * 6 : 84 * 5 : 100 * 3 26:28:20 C share = 74000 * 95/100 = 7030 * 20/74 => 1900.Answer: B The answer is: B

B

mathematics

The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?

65*(90/100)*((100-x)/100) = 56.16 x = 4% Answer: B The answer is: B

B

mathematics

A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 30 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 6 hours . What was the average rate of speed of the train on the return trip to Albany?

30*T =120 THEREFORE T = 120/30 =4 ON RETURN SPEED * ( 6 -4) =120 THEREFORE T = 120/2 =60 C The answer is: C

C

mathematics

Which of the following CANNOT be a product of two distinct positive integers X and Y?

In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take X = 1 and Y = 2 and work with the options XY = 2 A) X take X =2, Y = 1 B) Y take X = 1 Y = 2 C) 3Y + 2X Seems tricky, lets see other options and then come back to it. D) Y - X take Y = 1 and X = 2 --> Y - X = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E) YX Always true You don't even have to worry what C is ! ans D The answer is: D

D

mathematics

Two girls started running simultaneously around a circular track of length 500 m from the same point at speeds of 30 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?

Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 500 / (30 + 20)5/18 = 500* 18 / 50 * 5 = 36 seconds. Answer:B The answer is: B

B

mathematics

In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?

Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps. The distance to be covered is equal to the length of the train. Required time t = d/s = 100/10 = 10 sec. Answer:D The answer is: D

D

mathematics

Two men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.

Let the distance be x km. Then, x/3 - x/4 = 1/2 (4x - 3x)/12 = 1/2 x = 6 km ANSWER:A The answer is: A

A

mathematics

When 242 is divided by a certain divisor the remainder obtained is 6. When 698 is divided by the same divisor the remainder obtained is 13. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?

let that divisor be x since remainder is 6 or 13 it means divisor is greater than 13. now 242-6=236 =kx (k is an integer and 234 is divisble by x) similarly 698-13=685 = lx (l is an integer and 689 is divisible by x) adding both 698 and 242 = (236+685)+6+13 =x(k+l) + 19 when we divide this number by x then remainder will be equal to remainder of (19 divided by x) = 5 hence x = 19-5 = 14 hence B The answer is: B

B

mathematics

If 15% of 30% of 50% of a number is 90, then what is the number?

Let the number be a Given, 15/100 * 30/100 * 50/100 * a = 90 => 3/20 * 3/10 * 1/2 * a = 90 => a = 10 * 20 * 10 * 2 = 4000. ANSWER:A The answer is: A

A

mathematics

A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.

Rate in still water=1/2(10+7)km/hr=8.5 km/hr. Rate of current=1/2(10-7)km/hr=1.5 km/hr. ANSWER A 1.5 km/hr The answer is: A

A

mathematics

Nine men went to a hotel. Eight of them spent Rs.1 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?

Average of 9 = x 9x = 8 * 1 + x * 2 x = 1.14 Total = 9 * 3.25 = 10.28 ANSWER:B The answer is: B

B

mathematics

One pipe can fill a pool three times faster than a second pipe. When both pipes are opened, they fill the pool in seven hours. How long would it take to fill the pool if only the slower pipe is used?

fast pipe + slow pipe = together One pipe fills the pool three times faster than the other pipe so, hourly fill rates: 1/x + 1/3x = 1/7 Let x = number of hours it would take the fast pipe to fill the pool thus, x=9.3 hours 9.3*3 = 28 hours Answer: E The answer is: E

E

mathematics

Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometers total did she hike east?

Set up two R x T =D cases. 1. 1/10 km/ min x T = 2.75 from which T= 27.5 mins. We know total journey time now is 45 +27.5 = 72.5 The rate is the same ie 1/10km/min. set up second R x T =D case. 1/10 km/min x 72.5 = 7.25 km Now the total journey would be halved as distance would be same in each direction. 7.25/2 =3.625. A. The answer is: A

A

mathematics

The average of temperatures at noontime from Monday to Friday is 30; the lowest one is 20, what is the possible maximum range of the temperatures?

Average=30, Sum of temperatures=30*5=150 As the min temperature is 20, max would be 150-4*20=30 --> The range=30(max)-20(min)=10 Answer: E The answer is: E

E

mathematics

P is able to do a piece of work in 5 days and Q can do the same work in 10 days. If they can work together for 3 days, what is the fraction of work completed?

Explanation : Amount of work P can do in 1 day = 1/5 Amount of work Q can do in 1 day = 1/10 Amount of work P and Q can do in 1 day = 1/5 + 1/10 = 3/10 Amount of work P and Q can together do in 3 days = 3 × (3/10) = 9/10 Answer : Option E The answer is: E

E

mathematics

A certain auto manufacturer sold 6% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?

Let's assume in 2006 the manufacturer sold X. In 2007 he sold X-6/100(X) If sales in 2006,X= 2.1 million find X-6/100(X) (2.1 x 10^6)-6/100(2.1 x 10^6) 2100000-126000=1,974,000-----> 1,980,000(approx) ANSWER:B The answer is: B

B

mathematics

If 250!/10^n is an integer, what is the largest possible value of n?

The question actually asks the highest power of 10 which divides 250! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator) 10 = 2 x 5 250 factorial will have 62 as - 250/5 = 50 50/5 = 10 10/5 =2 So answer will be (C) 62 The answer is: C

C

mathematics

In how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?

Explanation : Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years 150×6×n/100=800×9/2×2/100 150×6×n=800×9/2×2 150×6×n=800×9 3×6×n=16×9 6×n=16×3 2×n=16 n=8 years Answer : Option C The answer is: C

C

mathematics

A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?

A- B = 120 Miles B - C = 60 Miles Avg Speed = 25 Miles Time taken for A-B 3t and B-C be t avg speed = (120+60) / Total time 25 = 180/4t t = 108 B-C = 108mph Answer C The answer is: C

C

mathematics

In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons?

8p2 = 8 X 7 = 56 D) The answer is: D

D

mathematics

If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?

9 = (1*40*R)/100 R = 22 1/2 % Answer: D The answer is: D

D

mathematics

Four persons enter the lift of a six storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor

Each person out of 4 has 5 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 5*5*5*5=5^4=625. Answer: A. The answer is: A

A

mathematics

Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of 40 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?

M gains 50-40=10 pages per hour on R at 6pm R has read 60 pages and M is 60+5=65 pages behind him time=65/10=6.5 hours they are on the same page at 12:30 a.m. B The answer is: B

B

mathematics

x and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b?

Focus on the transition points and plug in the values. a> 6 so a could be 7, 8, 9, 10, 11 etc Look at a= 7 7 + b< 11 b< 4 b could be 3, 2, 1, 0, -1 etc When b is 3, we get a- b= 4 This must be the smallest value because as a increases, b reduces so a- b increases. Take another example. a= 11 so b< 0. a- b will give a value greater than 11. Answer (C). The answer is: C

C

mathematics

A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.

Given: After a% decrease the price of the article is reduced by $180 --> pa=180; After one more such change the price is further reduced by $153. After the first decrease the price became $(p−180), thus (p−180)a=153--> pa−180a=153a=15--->a=15 --> p∗0.15=180--> p=1,200 Answer: A. The answer is: A

A

mathematics

Find the sub-triplicate ratio of 27:125

The sub-triplicate ration of 27 : 125 = 3:5 Answer:A The answer is: A

A

mathematics

Gasoline varies in cost from $0.93 to $1.13 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?

Solution: We know that the per gallon cost of gasoline varies from $0.93 - $1.13. Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost. Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons. So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons). Case 1: for 30 gallons the cost is 30*0.93 to 30*1.13 which is $27.90 to $33.90 Case 2: for 20 gallons the cost is 20*0.93 to 20*1.13 which is $18.60 to $22.60 Thus, the maximum cost of the 480 mile trip is $33.90 and minimum is $18.60 so the difference is $33.90 - $18.60 = $15.30 Answer: B The answer is: B

B

mathematics

A certain company employs 8 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?

Number of ways to select 3 senior officers from 8 of them = 8C3 = 56 ways Next we can determine the number of ways to select 1 junior officer. number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways Thus the number of ways to select 3 senior officers and 1 junior officer is 56 x 4 = 224 ways. Answer: D The answer is: D

D

mathematics

9 - 3 ÷ 1/3 + 5 = ?

9 - 3 1/3 + 5 =9-3÷1/3+5 =9-(3X3) +5 =9-9+5 =5 CORRECT ANSWER : A The answer is: A

A

mathematics

Victor gets 92 % marks in examinations. If these are 184 marks, find the maximum marks.

Let the maximum marks be m Then 92 % of m = 184 ⇒ 92/100 × m = 184 ⇒ m = (184 × 100)/92 ⇒ m = 18400/92 ⇒ m = 200 Therefore, maximum marks in the examinations are 200. Answer: C The answer is: C

C

mathematics

A basket contains 5 apples of which one is rotten. If Henry is to select 2 apples from the basket simultaneously and at random what is the probability that the 2 apples selected will include the rotten apple?

Direct probability approach: P=15∗44+45∗14=25P=15∗44+45∗14=25: probability of {first apple rotten, second apple good} plus the probability of {first apple good, second apple rotten}. Reverse probability approach: Again 1- the probability of the opposite event --> P=1−45∗34=25P=1−45∗34=25. Answer: C The answer is: C

C

mathematics

A man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus. Let the speed of cyclist be c. Every 15 minutes a bus overtakes cyclist: \frac{d}{b-c}=15, d=15b-15c; Every 5 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c; d=15b-15c=5b+5c, --> b=2c, --> d=15b-15b/2=15b/2. Interval=\frac{d}{b}=\frac{15/2b}{b}=15/2 Answer: E (15/2 minutes). The answer is: E

E

mathematics

By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 5% on the marked price. His gain percent during the sale is?

Marked price = Rs. 300 C.P. = 100/120 * 300 = Rs. 250 Sale price = 95% of Rs. 300 = Rs. 285 Required gain % = 15/250 * 100 =6%. Answer: A The answer is: A

A

mathematics

18 times a positive integer is more than its square by 80, then the positive integer is

Explanation: Let the number be x. Then, 18x = x2 + 80 => x2 - 18x + 80 = 0 =>(x - 10)(x - 8) = 0 => x = 10 or 8 Answer: B The answer is: B

B

mathematics

The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?

262 – 102 = 242 d1 = 20 d2 = 48 1/2 * 20 * 48 = 480 Answer: D The answer is: D

D

mathematics

The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

Area of a triangle = r * s Where r is the inradius and s is the semi perimeter of the triangle. Area of triangle = 2.5 * 36/2 = 45 cm2 Answer:E The answer is: E

E

mathematics

A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Total number of balls = 2 + 3 + 2 = 7 Let S be the sample space. n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2 Let E = Event of drawing 2 balls , none of them is blue. n(E) = Number of ways of drawing 2 balls , none of them is blue = Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2 (∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5) P(E) = n(E)/n(S)=5C2/7C2=(5×4/2×1)/(7×6/2×1)=5×4/7×6=10/21 ANSWER:B The answer is: B

B

mathematics

The standard serial numbers for a bill are 2 letters followed by 5 digits. How many bills are possible if letters and digits can be repeated?

OFFICIAL SOLUTION: (A) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 options for the two letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of bills is 26 × 26 × 10 × 10 × 10 × 10 x 10 = 26 x 26 x 100 000. The correct answer is choice (A). The answer is: A

A

mathematics

George takes 30 days to do a piece of work and Mark takes 45 days for the same work. For the first 15 days only George works. Then Mark also joins him. Find the time taken to complete the entire work.

George 1 day work= 1/30 Mark 1 day work= 1/45 George 15 day work= 15*1/30 =1/2 Work remaining= 1-1/2 =1/2 George + Mark 1 day work= 1/30 + 1/45 =1/18 Number of day required to complete 1/2 work= (1/2)/(1/18)= 9 days So total days required to complete the work is 15+9= 24 days. ANSWER:A The answer is: A

A

mathematics

A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?

US = 25 DS = 35 M = (35 + 25)/2 = 30 Answer:C The answer is: C

C

mathematics

In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?

Explanation: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3 Answer: B) 1:3 The answer is: B

B

mathematics

A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.204 less than the sum lent. What was the sum lent?

P - 204 = (P*4*8)/100 P = 300 Answer: C The answer is: C

C

mathematics

Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/5 full and other jar 1/4 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?

Same amount of water made bigger jar 1/5 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/5+1/5=2/5 full. Answer: B. The answer is: B

B

mathematics

Of the 800 employees of Company P, 60 percent have been with the company for at least ten years. If q of theselong-termmembers were to retire and no other employee changes were to occur, what value of q would reduce the percent oflong-termemployees in the company to 50 percent ?

The # oflong-termemployees is 60%*800=480. After q of them retire new # oflong-termemployees would become 480-q. Total # of employees would become 800-q. We want 480-q to be 50% of 800-q --> 480-q=(800 -q)*50% --> q = 160. Answer: B. The answer is: B

B

mathematics

A Cuban cigar would cost 4 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?

The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each. From the given data we know French cigar < Cuban cigar < Arabic cigar and each is more expensive 1.5 times. Therefore eliminate options A,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer. Therefore C is the answer. The answer is: C

C

mathematics

The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?

28 * 2 = 56 21 * 3 = 63 ----------- 7 years.Answer: A The answer is: A

A

mathematics

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:

Let the actual distance travelled be x km. x/10 = (x+20)/14 14x = 10x + 200 4x = 200 x = 50 km. answer :A The answer is: A

A

mathematics

The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?

2(3x + x) = 96 l = 36 b = 12 lb = 36 * 12 = 432 Answer:A The answer is: A

A

mathematics

The original price of a certain TV set is discounted by g percent, and the reduced price is then discounted by 2g percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?

Youcansolve this problem with number plugging. Say the original price was $10 and g=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0. Now, since P is not zero, then the expression in the brackets must be zero for g=50. Only answer choice B works. Answer: B. On this problem - number pluggin is not giving me the answer.. I initially used g = 10, then g = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math. 100 (1-0.03(10) + 0.0002 (10)^2) 100 (1-0.3 + 0.0002 (100)) 100 (0.7 + 0.02) 100 (0.68) = 68???? double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B.. The answer is: B

B

mathematics

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior. What is the probability of choosing ANY sibling from junior class? 60/1000 (as there are 60 of them). What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be 1/800 (as there is only one sibling pair of chosen one). So the probability of that the 2 students selected will be a sibling pair is: 60/1000∗1/800=3/40000 Answer: A. The answer is: A

A

mathematics

The length of a rectangular field is 7/5 its width. If the perimeter of the field is 240 meters, what is the width of the field?

Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 240, 2(7/5)W + 2W = 240 Solve the above equation to find: W = 50 m and L = 70 m. correct answer A)50 The answer is: A

A

mathematics

A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?

90% 104% -------- 14% ---- 140 100% ---- ? => Rs.1000 Answer: A The answer is: A

A

mathematics

A room is 12 meters long, 10 meters wide 8 meters in height. The longest possible rod which can be placed in the room is

Square root of 12^2+10^2+8^2...(Diognal) which is square root of 308 that lies 17<√308<18. Hence the answer should be E The answer is: E

E

mathematics

The average of 30 numbers is 48. If three numbers namely 45, 55 and 43 are discarded, the average of remaining numbers is?

Explanation: Total of 30 numbers = 30 * 48 = 1440 Average o 27 numbers = 1440 - (45 + 55 + 43) / 27 = 48.03 Answer: Option C The answer is: C

C

mathematics

Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 40% and its breadth is decreased by 25%?

let L and B be 100 each 100 * 100 = 10000 L increase by 40% = 140 B decrease by 25% = 75 140 * 75 = 10500 5% increase ANSWER:A The answer is: A

A

mathematics

Given that a is the average (arithmetic mean) of the first six positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

The first nine positive multiples of six are {6, 12, 18, 24,30, 36} The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72} Both sets are evenly spaced, thus their median=mean: a=21 and b=(36+42)/2=39 --> a/b=21/39=7/13. Answer: E. The answer is: E

E

mathematics

If a boat goes 5km upstream in 25 minutes and the speed of the stream is 7 kmph, then the speed of the boat in still water is ?

Rate upsteram =(5/25*60)kmph=12kmph. speed of the stream =7kmph let speed in still water be xkm/hr. then speed upstream=(x-7)km/hr. x-7=12==>x=19km/hr Answer(B) The answer is: B

B

mathematics

In Town X, 120 percent of the population are employed, and 80 percent of the population are employed males. What percent of the employed people in Town X are females?

Total employed people 12%, out of which 80 are employed males, hence 40% are employed females. (employed females)/(total employed people)=40/120=1/3=33% Answer: C. The answer is: C

C

mathematics

The amount of water (in ml) that should be added to reduce 21 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?

10.5 10.5 30% 70% 30% ----- 10.5 70% ------? => 24.5 - 10.5 = 14.5 ml Answer:C The answer is: C

C

mathematics

A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 160. The dividend from the stock is :

Solution By investing Rs. 1552,income = Rs. 128. By investing Rs. 97, income = Rs. (160/1552x97)= Rs.10 ∴ Dividend =10%. Answer C The answer is: C

C

mathematics

A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid. The value of the 8th installment is:

Explanation : Let the first installment be 'a' and the common difference between any two consecutive installments be 'd' Using the formula for the sum of an A.P :- S=n/2[2a+(n−1)d]. We have, 3600=40/2[2a+(40-1)d]. 3600=20[2a+39d]. 180 =2a+39d. ----(i) Similarly, 2400=30/2[2a+(30-1)d]. 160=2a+29d. ----(ii) On solving both the equations we get: d=2 and a=51 Hence, the Value of 8th installment is :- =51+(8−1)2. =65. Answer : C The answer is: C

C

mathematics

Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?

T = 9/45 * 60 = 12 Answer:C The answer is: C

C

mathematics

A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?

100*(20/100) = 20 --- 10 ? --- 1 => Rs.2 100 --- 80 ? --- 2 => Rs.2.5 Answer:C The answer is: C

C

mathematics

Mike's age is 48 years. If he is 4 more than twice the age of his son, find the age of his son.

Let Mike's son age be x. 4 + 2 x = 48 x = 22 Hence Mike's son age is 22 years Answer : B The answer is: B

B

mathematics

A train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds. What is the length of the train?

Let the length of the train be x meters. The speed of the train is x / 15. Then, x + 110 = 25*(x / 15) 10x = 1650 x = 165 meters The answer is E. The answer is: E

E

mathematics

30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab?

Area of each slab =67.5/30m2=2.25m2 Length of each slab √2.25=1.5m=150cm The answer is: A

A

mathematics

120 is what percent of 80?

120= x*80/100 x = 150% Ans; D The answer is: D

D

mathematics

39! is divided by 41. Then what is the remainder?

Substituting p = 41 in the wilson's theorem, we get 40!+141=0 40×39!+141=0 −1×39!41=−1 Cancelling -1 on both sides, 39!41=1 A The answer is: A

A

mathematics

Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost?

Original Cost C1=t1*b1^4 New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1 C2=t2*(2b1)^4 =16(t1*b1^4) =16C1 16 times C1=>1600% of C1 Ans D=1600 The answer is: D

D

mathematics

A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability R that both will be juniors?

I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors. 2 seniors = P(Senior) * P(Senior) = 2/9 1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9 Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability R that it is two juniors is 1- (7/9) = 2/9.C The answer is: C

C

mathematics

A merchant sells an item at a 20% discount, but still makes a gross profit of 50 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

original SP = X Cost =C current selling price = .8x ( 20% discount) .8x = 1.5C (50% profit) x= 1.5/.8 *C x= 15/8 C Original selling price is 1.875C which is 87.5% profit Answer C The answer is: C

C

mathematics

2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?

1/x + 1/(x + 10) = 1/12 x = 20 B The answer is: B

B

mathematics

If the area of a circle is 36pi square feet, find its circumference.

The area is given by pi *r* r. Hence pi * r *r = 36 pi r * r = 36; hence r = 36 feet The circumference is given by 2 * pi * r = 2 * pi * 6 = 12 pi feet correct answer A The answer is: A

A

mathematics

If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability R that N is divisible by 3?

Prime digits are: 2, 3, 5, 7 Total number of 2 digit #s with both digits prime are: 4*4 = 16 out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above. => prob = 5/16. Ans D. Took me 3:20 mins. The answer is: D

D

mathematics

The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?

20 + 24 + 8 * 2 = 60/2 = 30 Answer: C The answer is: C

C

mathematics

The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?

First decrease in percent part / whole = (120 - 100) / 120 = 0.17 = 17% Second decrease in percent part / whole = (100 - 80) / 100 = 0.20 = 20% The second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease. Answer B The answer is: B

B

mathematics

A polygon has 44 diagonals, then the number of its sides are

Let the number of sides be n. The number of diagonals is given by nC2 - n Therefore, nC2 - n = 44, n>0 n(n - 1) / 2 - n = 44 n2 - 3n - 88 = 0 n2 -11n + 8n - 88 = 0 n(n - 11) + 8(n - 11) = 0 n = -8 or n = 11. ANSWER:A The answer is: A

A

mathematics

If 0 < x < 1 and x ≠ 0, which of the following inequalities must be true? I. x^3 < x II. x^2 < |x| III. x^4 – x^5 > x^3 – x^2

Answer is D. Let's look at the statements one by one Stmt I. x^3 < x if 0<x<1 then x^3< x but if -1<x<0 then x^3>x So this statement is not always true Stmt II. x^2 < |x| Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|. Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2 So Stmt II is always true Stmt III. x^4 – x^5 > x^3 – x^2 This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1). Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true. So Stmt III is always true B The answer is: B

B