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mathematics

Which of the following is equal to 1(1/7)%?

This notation may be confusing for some, since it looks like we're multiplying 1 and 1/7 How about adding a space:Which of the following is equal to (1 1/7)% (1 1/7)% = 1.14% = 1.14/100 Answer: C The answer is: C

C

mathematics

A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?

Explanation: Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random. Therefore, n(S) = 18C2 = 153 ways Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49 Therefore, by definition of probability of event A, P(A) = n(A)/n(S) = 49/153 ANSWER:A The answer is: A

A

mathematics

If each term in the sum a1+ a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40). To illustrate consider adding: *7 *7 ... 77 77 ---- =350 So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40). Answer: C. The answer is: C

C

mathematics

Peter must choose a lab partner by picking a name out of a bag. If the bag has 9 male names and F female names, what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?

Male Names in the bag = 9 Female Names in the bag = F Probability of selecting a male name is = P = 9/(9+F) The question asked is "what is the least number of female names in the bag if the probability of choosing a male lab partner is less than 3 out of 7?" so, we need to find out the minimum value of F for which P<3/7 9/(9+F) < 3/7 Solving for F gives the equation; F>12 Since the question asked is the minimum value F should be 13 ( F should be an integer). ANSWER:C The answer is: C

C

mathematics

By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 7 p.c?

Option B Explanation: CP + CP/8 = 45000 CP = 40000 SP = 40000*(93/100) = 37200 Option D The answer is: D

D

mathematics

The sum of two numbers is twice their difference. If one of the numbers is 10, the other number is

Explanation: Let the other number be a. Given that, 10+a=2(a−10)⇒a=30 or if the other number is less than 10, 10+a=2(10−a)⇒a=10/3=3 1/3 Correct Option: D The answer is: D

D

mathematics

How many such letter-pairs are there in the word SMUGGLER having same no.of letters left between them as they have in the series?

S,U And E,G ANSWER:A The answer is: A

A

mathematics

The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

Let the length of the bridge:L The equation now is L+160/12.5m/s(45km/hr or12.5m/s)=30 Solving, L =215m ANSWER:B The answer is: B

B

mathematics

The area of a square is subtracted from one of its sides, and the perimeter is then added to this total, the result is 4. What is the length of one side?

The equation is; side - Area + Perimeter = s - A + P = s - s^2 + 4s = s(1 - s + 4). By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer. Answer: A The answer is: A

A

mathematics

A sum of Rs.1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs.300. The ratio of the money lent at 5% to that lent at 8% is :

let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then, Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300 Required ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15 Answer: C) 16:15 The answer is: C

C

mathematics

Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 5 days?

Explanation: If six computers require 15 days to process the data, thats a total of 90 computer-days the product of 6 and 15. If you change the number of computers or the number of days, 90 will have to remain the product, whether that means 90 days of one computer or one day with 90 computers. In 5 days, the number of computers is: 5c = 90 c = 18 18 computers is 12 more than the 6 that it took to do the job in 15 days, so the correct choice is (E). The answer is: E

E

mathematics

Divide Rs. 3364 between A and B, so that A's Share at the end of 5 years may equal to B's share at the end of 7 years, compound interest being at 5 percent.

Explanation: A's share after 5 years = B's share after 7 years (A's present share)(1+5100)5 = (B's present share)(1+5100)7 =>(A's present share)/(B's present share) = (1+5/100)7/(1+5/100)5 = (1+5/100)(7−5) = (1+5/100)2 =(21/20)2 =441/400 i.e, A's present share : B's present share = 441 : 400 Since the total present amount is Rs.3364, A's share = 3364 × 441/(441 + 400) = (3364 × 441)/841 = 4 × 441 = Rs. 1764 B's present share = 3364 - 1764 = Rs.1600 Answer: Option A The answer is: A

A

mathematics

If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 9 m of the same rod?

Explanation : Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion) => 11.25 : 9 :: 42.75 : x => 11.25 x x = 9 x 42.75 => x = (9 x 42.75) / 11.25 => x = 34.2 Answer : B The answer is: B

B

mathematics

On a Monday in a certain restaurant, 30 percent of the 180 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?

30% of 180= 54 10% of 120=12 Total =66 percent for 2 days combined =66/300=0.22. so it should be less than 0.22 so it is 22% Answer:D The answer is: D

D

mathematics

What is the value of n if the sum of the consecutive odd intergers W from 1 to n equals 169?

Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules. Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value. a=1 (first term) d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2 *On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence. But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2. Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value. It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is. The answer is: B

B

mathematics

The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?

Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1) Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2) Subtracting (1) From (2), we get : Temp, on 5th day - Temp on 1st day = 8 degrees. Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively. Then, 8x - 7x = 8 or x = 8. Temperature on the 5th day = 8x = 64 degrees. Answer: B The answer is: B

B

mathematics

A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?

100 --- 10 DS = 10 ? ---- 1 75 ---- 15 US = 5 ? ----- 1 S = (10 - 5)/2 = 2 2 ½ kmph Answer: D The answer is: D

D

mathematics

The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $2.00 in 1970 was 150 percent of its price in 1960, what was its price in 1980?

The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980). Therefore the price in 1980 = $2.0*1.5 = $3.00. Answer: E. The answer is: E

E

mathematics

A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?

Explanation: Length of the train = distance covered in crossing the post = speed × time = speed × 18 Speed of the train = 300/18 m/s = 50/3 m/s Time taken to cross the platform = 39 s (300+x)/(50/3) = 39 s where x is the length of the platform 300+x = (39 × 50) / 3 = 650 meter x = 650-300 = 350 meter Answer: Option B The answer is: B

B

mathematics

In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?

Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. ANSWER:A The answer is: A

A

mathematics

Find the greatest number of four digits which is perfectly divisible by 3 and when divided by 5, 7 and 9 leaves a remainder 3 in each case.

LCM of 3, 5, 7, 9 = 315. Greatest number of four digits which is divisible by 315 is 9765. The required number = 9765 + 3 = 9768. Ask doubt with Question Id: 1658 13) Find greatest number of four digits which when increased by 3568 is exactly divisible by 6, 8, 12, 20. a) 9992 b) 9785 c) 9840 d) None Explanation: Greatest number of 4 digits = 9999. 9999 + 3568 = 13567. LCM of 6, 8, 12 and 20 is 120. ∴ Required number of 4 digits = 9999 – 7 = 9992 i.e. 9992 is the number to which if 3568 is added, then it is exactly divisible by 6, 8, 12, 20. Ask doubt with Question Id: 1659 Answer:B The answer is: B

B

mathematics

The circulation for magazine P in 1971 was 4 times the average (arithmetic mean) yearly circulation for magazine P for the years 1972-1980. What is the ratio of the circulation in 1971 to the total circulation during 1971-1980 for magazine P ?

There are 9 years from 1972-1980, inclusive. Let's say the average circulation every year between 1972-1980 inclusive is x. So the total circulation is 9x from 1972-1980, inclusive. In 1971, the circulation is 4x. So total circulation for 1971-1980 is 4x + 9x = 13x. Ratio of circulation in 1971 to total circulation during 1971-1980 is 4x to 14x or 4/14=2/7 Answer : D The answer is: D

D

mathematics

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 6 km in stationary water?

speed (upstream) =2/1 = 2 kmhr speed (downstream)=1/(10/60)= 6 kmhr speed in still water = 1/2 (2+6) = 4 kmhr time taken in stationary = 6/4 = 1 hrs 30 min ANSWER:D The answer is: D

D

mathematics

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.18 per cubic meter?

22/7 * 14 * 3/2 * 3/2 = 99 m2 99 * 18 = 1782 Answer:C The answer is: C

C

mathematics

The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?

Explanation: 1 to 11 = 11 * 10.9 = 119.9 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.4 = 68.4 63 + 68.4 = 131.4 – 119.9 = 11.5 6th number = 11.5 Option D The answer is: D

D

mathematics

The average mark of a class of twenty five students is 66. If five students whose marks are 32,28, 30, 26 and 34 are removed , then find the average mark of the remaining students of the class.

Exp. Total mark of 25 students = 66*25 = 1650, Total mark after the removal of 5 students = 1650 –(32 +28+30+26+34 ) = 1650 – 150 = 1500 Average mark = 1500/(25-5) = 1500/ 20 = 75 Answer: A The answer is: A

A

mathematics

35 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 4:3. How many liters of Liquid Q must be added to make the ratio 5:7?

Let x be the amount of liquid Q to be added. (3/7)*35 + x = (7/12)*(35+x) 1260 + 84x = 1715 + 49x 35x = 455 x = 13 The answer is D. The answer is: D

D

mathematics

A cylinder of radius R and height H is reshaped. Which of the following changes results in the cylinder of greatest volume?

Volume of a cylinder = Pi. R^2.H Check for options as per given Q. A. (1.5)^2 * (0.8) = 2.25 * 0.8 = 1.8 (Since 20% decrease in H and a 50% increase in R.) B. (0.5)^2 * (6) = 0.25 * 6 = 1.5 (Since 500% increase in H and a 50% decrease in R) C. (0.7)^2 * (4) = 0.49 * 4 = 1.96 (Since 300% increase in H and a 30% decrease in R ) D. (2)^2 * (0.3) = 4 * 0.3 = 1.2 (Since 70% decrease in H and a 100% increase in R. ) E. (0.9)^2 * (2) = 0.81 * 2 = 1.62 (Since 100% increase in H and a 10% decrease in R. ) Maximum value is 1.96 Option C The answer is: C

C

mathematics

A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?

Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively. Given x + y = 18 --- (1) and x - y = 10 --- (2) From (1) & (2) 2x = 28 => x = 14, y = 4. Answer: D The answer is: D

D

mathematics

From the word 'ASTOUNDER', how many independent words can be made with-out changing the order of the letters and using each letter only once ?

Explanation: The words formed are AT and UNDER, AS and UNDER (or) AT and SOUND Answer: D) 2 The answer is: D

D

mathematics

Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 20 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 25 meters. What distance is she from the starting point and in which direction?

The net distance is 20 + 25 = 45 meters to the east. The answer is E. The answer is: E

E

mathematics

What is the greatest integer that will always evenly divide the sum of three consecutive integers?

Let the three consecutive integers be x , x + 1 , x + 2 Sum = x + x + 1 + x + 2 = 3x+3 = 3(x+1) Therefore , 3 will always be a factor . Answer B The answer is: B

B

mathematics

How many positive three-digit integers are divisible by both 3 and 5?

A number to be divisible by both 3 and 5 should be divisible by the least common multiple of 3 and 5 so by 15. Multiples of 15 between 100 and 999, inclusive is (last-first)/multiple+1=(990-105)/15+1=59+1=60 Answer: B. The answer is: B

B

mathematics

You buy a piece of land with an area of √900, how long is one side of the land plot?

Try filling the numbers into the answer y x y = Find the closest to 900. Answer C The answer is: C

C

mathematics

A man can row downstream at the rate of 16 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?

Explanation: Rate of still water = 1/2 (16 + 6) = 11 Km/hr Rate of current = 1/2 (16-6) = 5 Km/hr Answer: Option B The answer is: B

B

mathematics

The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations Q of soloists can appear in the liner notes?

Total Soloists to choose from = 10 Soloist Required = 5 Question : How many different combinations Q of soloists can appear in the liner notes? The language of the question clearly mentions that only the combinations need to be calculated i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question) Method-1: Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!) Method-2: No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6 Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter, Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!) Answer: Option B The answer is: B

B

mathematics

A man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?

Speed in still water = 6 kmph Speed of the current = 2 kmph Speed downstream = (6+2) = 8 kmph Speed upstream = (6-2) = 4 kmph Let the required distance be x km Total time taken = 2 hour x/8 +x/4 =2 x+2x/8 =2 3x/8=2 3x=16 x=5.33 km ANSWER:A The answer is: A

A

mathematics

If 60 percent of 600 is 50 percent of x, then x=?

0.6 * 600 = 0.5 * x x = 6/5 * 600 = 720 The answer is: B

B

mathematics

5 x 1.6 - 2 x 1.4/1.3 = ?

Given Expression = (8 - 2.8)/1.3 = 5.2/1.3 = 52/1.3 = 4. Answer is D. The answer is: D

D

mathematics

An oil cylinder was 3/4th full. When ONE bottles of oil is poured into it, it is 4/5th full. How many bottles of oil can the full cylinder hold?

(4/5 -3/4) cylinder is filled by 1 bottles 0.8 -0.75 = 0.05 cylinder is filled by 1 bottles 1 cylinder is filled by 1/0.05 = 20 bottles ANSWER:A The answer is: A

A

mathematics

How many minutes does it take John to type u words if he types at the rate of x words per minute?

time*rate=job --> time*x=u --> time=u/x. Answer: B. The answer is: B

B

mathematics

A student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student? .

1) preferred one as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five choose 2 in first 5 and all 5 from later half.. ways = 5C2 = 10.. total ways = 10C3 = 120 ans = 120-10 = 110 ANSWER:C The answer is: C

C

mathematics

A completes a work in 6 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be?

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days Therefore, here, the required number of days = 6 × 12/ 18 = 4 days. Option 'A' The answer is: A

A

mathematics

A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂ = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7 = 46/70 = 23/35 Answer:A The answer is: A

A

mathematics

A vessel of capacity 2 litre has 35% of alcohol and another vessel of capacity 6 litre had 50% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?

35% of 2 litres = 0.7 litres 50% of 6 litres = 3 litres Therefore, total quantity of alcohol is 3.7 litres. This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 37% E The answer is: E

E

mathematics

Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 2 minutes after that how many times will exactly two lamps flash?

lamp A flashes every 6 secs, b flashes every 8 secs, c flashes every 10 secs. At certain time three flashes simultaneously. after that calculate when the three lamps flashes simultaneously in 2 minutes. take a L.C.M of three 6,8,10 sec then it is 120 secs. so exactly after 2 minutes it flashes simultaneoulsy. question stem asks exactly two lamps falshes . take lcm of a and b .6 and 8 is 24 secs. so two lamp flashes 5times in 2minutes. lcm of b and c . 8 and 10 secs is 40 secs. so both flashes 3times in 2minutes. lcm of c and a ,6 and 10 secs is 30 secs . pair flashes 4times.. all three pairs flashes simultaenoulsy at 2 minutes. we have to minus one from all three pairs. then 12-3=9. so option C is correct The answer is: C

C

mathematics

Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?

Let the amount lent at 7% be Rs. x Amount lent at 10% is Rs. (6000 - x) Total interest for one year on the two sums lent = 7/100 x + 10/100 (6000 - x) = 600 - 3x/100 => 600 - 3/100 x = 450 => x = 5000 Amount lent at 10% = 1000 Required ratio = 5000 : 1000 = 5:1 Answer:A The answer is: A

A

mathematics

The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

Explanation: Let the sides of the rectangle be l and b respectively. From the given data, (√l2 + b2) = (1 + 108 1/3 %)lb => l2 + b2 = (1 + 325/3 * 1/100)lb = (1 + 13/12)lb = 25/12 lb => (l2 + b2)/lb = 25/12 12(l2 + b2) = 25lb Adding 24lb on both sides 12l2 + 12b2 + 24lb = 49lb 12(l2 + b2 + 2lb) = 49lb but 2(l + b) = 28 => l + b = 14 12(l + b)2 = 49lb => 12(14)2 = 49lb => lb = 48 Since l + b = 14, l = 8 and b = 6 l - b = 8 - 6 = 2m. Answer: Option D The answer is: D

D

mathematics

HCF and LCM two numbers are 20 and 396 respectively. If one of the numbers is 36, then the other number is?

20 * 396 = 36 * x x = 220 ANSWER:E The answer is: E

E

mathematics

In a rectangular axis system, what is the area of a parallelogram with the coordinates: (2,2), (8,2), (3,5), (9,5) ?

Delta x will give us the dimension of one side of the parallelogram = 8-2= 6 unit Delta y will give us the dimension of the other side of parallelogram = 5-2=3 unit Area of parallelogram = 6*3 = 18 ANSWER IS A The answer is: A

A

mathematics

According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?

This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base? E The answer is: E

E

mathematics

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S? I. 1/10 II. 1/9 III. 1/8

Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10. On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91. We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer. The answer is: B

B

mathematics

A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 35 instead of 99 then find the correct average marks up to two decimal places.

Total marks = 35 x 72 =2520 Corrected total marks = 2520 - 35 + 99 =2584 Correct Average = 2584/35 = 73.82 Answer : E The answer is: E

E

mathematics

If (2x + 2)(x + 3) = 2x^2 + x, what is a possible value of x?

Rearranging the given expression: (2x + 2)(x + 3) = 2x^2 + x i.e. 2x^2 + 8x + 6 = 2x^2 + x i.e. 7x = -6 i.e. x = -6/7 Answer: Option A Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible. The answer is: A

A

mathematics

Find the one which does not belong to that group ?

Explanation: 16, 36, 64 and 4 are perfect squares but not 28. ANSWER IS C The answer is: C

C

mathematics

The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Explanation: Let the average age of the whole team by x years. 11x – (24 + 27) = 9(x -1) 11x – 9x = 42 2x = 42 x = 21. So, average age of the team is 21 years. Answer B The answer is: B

B

mathematics

Albert borrowed a total of $ 6000 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1400 as total interest. What is the interest paid to Brian at the end of three years?

Let x be the amount borrowed form Brian. So amount borrowed form Charlie = 6000-x. 1400 = 21/100x + 27/100(6000-x) =>x = 22000/6. Interest paid = 3*7/100*22000/6 = 770. E The answer is: E

E

mathematics

A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders W when the order of the divisors is reversed.

My approach would be Three Divisors : 3, 5, 8 Three Remain: 1, 4, 7 Start from the bottom of the last column i.e. from the third remainder: Go up diagonally and multiply by the second divisor: 5*7 = 35 Go down and add the second remainder: 35 + 4 = 39 Go up diagonally and multiply by the first divisor: 39* 3 = 117 Go down and add the first remainder: 117 + 1 = 118 Divide 118 by 8, 5, 3 118/8 gives quotient = 14 and remainder = 6 14/5 gives quotient = 2 and remainder = 4 2/3 gives quotient = 0 and remainder = 2 Ans is D i.e. 6,4,2 The answer is: D

D

mathematics

What inequality represents the condition 1<x<11?

1<x<11 represents segment with length: 11-1 = 10 center: (11+1)/2 = 6 For any |x-a|<b a is a center and b is a half of length. So, |x-6|<10/2 represents our inequality (answer B) The answer is: B

B

mathematics

A train travelled from station P to Q in 8 hours and came back from station Q to P is 6 hours. What would be the ratio of the speed of the train while traveling from station P to Q to that from station Q to P?

Since S # 1/t S1 : S2 = 1/t1 : 1/t2 = 1/8 : 1/6 = 3 : 4 Answer:D The answer is: D

D

mathematics

A hiker walked for 3 days. She walked 18 miles on the first day, walking 6 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?

She walked 18 miles on the first day, walking 6 miles per hour i.e. total time of walk on Day-1 = 18/6 = 3 Hours Second day time of walk = 3-1 = 2 hours and Speed = 6+1=7 miles per hour i.e. Distance walked on second day = 2*7 = 14 miles Third day time of walk = 3 hours and Speed = 7 miles per hour i.e. Distance walked on second day = 3*7 = 21 miles Total Distance travelled on three days = 18+14+21 = 53 Answer: Option C The answer is: C

C

mathematics

How many positive even integers less than 100 contain digits 5 or 9?

Two digit numbers: 5 at tens place: 50,52,54,56,58 9 at tens place: 90,92,94,96,98 If 5 and 9 is at units place, the number cant be even Total:5+5= 10 Answer B The answer is: B

B

mathematics

How many times thekeys of a writter have to bepressed in order to write first 400 counting no's?

1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 400 = 301 * 3 = 903 ----------- 1092 D The answer is: D

D

mathematics

A meeting has to be conducted with 5 managers. Find the number of ways in which the managers may be selected from among 7 managers, if there are 2 managers who refuse to attend the meeting together.

The total number of ways to choose 5 managers is 7C5 = 21 We need to subtract the number of groups which include the two managers, which is 5C3 = 10. 21 - 10 = 11 The answer is D. The answer is: D

D

mathematics

In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $843,000 invested in preferred stocks, what is the total amount of money invested in the fund?

Portion invested in preferred stock = 3/5 * 1/3 = 1/5 1/5 of fund = 843--- Fund = 5 * 843--- Here, we can avoid the math and simply look at 5 * 3 -> 15. Only option E has 15 in it. Answer (E). The answer is: E

E

mathematics

A began business with 12500 and is joined afterwards by B with 50000. When did B join, if the profits at the end of the year are divided equally?

Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months. ∴ Profit ratio is 12 × 12500 : (12 – x) × 50000 or 12 : 4(12 – x) Since profit is equally divided so 12 = 4(12 – x) or x = 3. Thus B joined after 8 months. Answer A The answer is: A

A

mathematics

The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?

Answer: Option D Explanation: Let the present ages of Anil and his son be 7x and 3x years respectively. Let the present age of the son's mother be m years. (m + 6) / (3x + 6) = 2/1 m + 6 = 6x + 12 => m = 6x + 6 Ratio of the present ages of Anil and the son's mother = 7x / (6x + 6). This cannot be found uniquely. Answer:D The answer is: D

D

mathematics

A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 20-sided polygon have?

There's a direct formula for this. Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon. Here, n = 20. Plugging it in, we get 170 diagonals! Answer (B). The answer is: B

B

mathematics

Given two sets A = {1,1,4,4,5,5} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number

One way to look at it: The number from set A can be ANYTHING. The number selected from set B will determine whether the sum is odd or even. For example, if a 4 is selected from set A, we need a 0 from set B to get an even sum. If a 5 is selected from set A, we need a 1 from set B to get an even sum. And so on. So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even) = P(select ANY number from set A)xP(select the number from set B that makes the sum even) = 1x1/2 = 1/2 = D The answer is: D

D

mathematics

A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 600. Find the sum?

Let the sum be Rs. x. (x * 18 * 2)/100 - (x * 12 * 2)/100 = 600 => 36x/100 - 24x/100 =600 => 12x/100 = 600 => x = 5000.Answer:E The answer is: E

E

mathematics

How many numbers with 2 different digits can be formed using only the odd digits?

Odd digits are 1, 3, 5, 7, 9. We want 3 different digits. First digit can be chosen in 5 ways. Second digit can be chosen in 4 ways. Total ways = 5*4 = 20 Hence option (B). The answer is: B

B

mathematics

A math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.

a square is a special kind of rhombus (sides are perpendicular) a square is a special kind of rectangles (sides with same length) Among the 27 cards with have: 15 rectangles 10 rhombus 8 squares Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square. Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square. We have 8 squares. So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17 Which means that the maximum number of circles that you could have is 27 - 17 = 10 Answer (B) The answer is: B

B

mathematics

By selling 175 apples, a shopkeeper gains the price of 25 apples. His gain per cent is

Suppose S.P of 175 apples = Rs 175 Therefore, Gain = Rs 25 => C.P = Rs 150 Gain % = 25/150 x 100 = 16.66% Gain = 16.66% ANSWER:C The answer is: C

C

mathematics

Which number need to add to 172835 to get a number exactly divisible by 136?

172835 / 136 = 1270 and reminder = 115. 136-115 = 21 So, the next number divisible by 115 is 21 places in front of 172835 Which means 21 + 172835 =172856 21 should be added to 172835 D The answer is: D

D

mathematics

A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?

Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 => y = x/15 (x + 100)/25 = x/15 => x = 150 m. Answer:B The answer is: B

B

mathematics

A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?

Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x. This must be equal to 360. 3x=360 x=360/3 x=120 Therefore, the salesman sold 120 kg in the morning and 2*120=240 kg in the afternoon. Answer is C. The answer is: C

C

mathematics

In the manufacture of a certain product, 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?

Percent of defective produced = 4% Percent of the defective units that are shipped for sale = 4% Percent of units produced are defective units that are shipped for sale = (4/100)*(4/100)*100% = (16/10000)*100% = (16/100)% = .16 % Answer C The answer is: C

C

mathematics

If p and r are integers, and p^2 = 20r, then r must be divisible by which of the following?

Ans: D Solution: for p to be an int 20 r must be whole square of a number. 20r= 5*2*2*r to make it whole square we need 5 so r can must be divisible by 5y where y is itself a whole square. so C is the ans The answer is: C

C

mathematics

The average age of 30 boys of a class is equal to 14 yrs. When the age of the class teacher is included the average becomes 15 yrs. Find the age of the class teacher.

The average age of 30 boys of a class is equal to 14 yrs: i.e Sum of all boys:30*14 include class teacher:31 candidates in a class & avg age is:15 yr i.e. sum of all:31*15(include class teacher)=465 so,the age of the class teacher:465-420=45yr answer will be 45 yrs ANSWER:C The answer is: C

C

mathematics

Calculate 85184 ÷ ? = 352

Answer Let 85184 ÷ X = 242 Then X = 85184/242 = 352. Option: B The answer is: B

B

mathematics

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 750 m long?

Speed = 240/24 = 10 m/sec. Required time = (240 + 750)/10 = 99 sec. Answer:D The answer is: D

D

mathematics

Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?

2*8=16.Answer is A. The answer is: A

A

mathematics

Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?

Total distance = 8 Km Total time = 50 Km Time taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours Remaining distance = 8 - 3 = 5 Km Required speed = 5/1/3 = 15 Kmph A) The answer is: A

A

mathematics

If 18 is 15 percent of 20 percent of a certain number, what is the number?

Let the certain number be x. => (15/100)*(20/100)*x = 18; 300x=18*10000; 3x = 1800; x=1800/3 => x=600; Ans is (D). The answer is: D

D

mathematics

A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 7600 a year. What is his average monthly income?

Total expenditure for the first 3 months = 3 × 1600 = 4800 Total expenditure for 4 months = 4 × 1550 = 6200 Total expenditure for 5 months = 5 × 1800 = 9000 Total expenditure and saving (which is income for one year) = 4800 + 6200 + 9000 + 7600 = Rs. 27600 So, Average monthly income = 27600/12 = Rs. 2300 E The answer is: E

E

mathematics

a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers R was deleted?

a+b+c+d+e => 1+2+3+4+5=15 20%*15= 3 =>C The answer is: C

C

mathematics

A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?

A : B (6000*4)+(3000*8) : (12000*6)+(9000*6) 48000 : 126000 8 : 21 Answer:B The answer is: B

B

mathematics

Convert 30miles into yards?

1 mile = 1760 yards 30 miles = 30*1760 = 52800 yards Answer is C The answer is: C

C

mathematics

For integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?

At least one of U and V is odd A The answer is: A

A

mathematics

If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?

A:B = 1/2:1/3 = 3:2 B:C = 1/2:1/3 = 3:2 -------------------- A:B:C = 9:6:4 Answer:D: The answer is: D

D

mathematics

A car covers a distance of 624 km in 4 hours. Find its speed?

624/4 = 156 kmph Answer:C The answer is: C

C

mathematics

A train covers a certain distance at a speed of 150kmph in 4 hours. To cover the same distance in 2 hours, it must travel at a speed of

Explanation: Distance = 150×4 = 600km Required speed = (600/2) = 300km/hr Answer: Option E The answer is: E

E

mathematics

The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?

Let the side of the square be a cm. Parameter of the rectangle = 2(18 + 10) = 56 cm Parameter of the square = 56 cm i.e. 4a = 56 a = 14 Diameter of the semicircle = 15 cm Circimference of the semicircle = 1/2(∏)(14) = 1/2(22/7)(14) = 308/14 = 22 cm to two decimal places Answer: B The answer is: B

B

mathematics

An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers. How many coins did the old man have?

Let the number of coins one son got be x and the number of coins another got be y. Total = x + y. x^2 - y^2 = 25(x - y) --> x + y = 25. Answer: D. The answer is: D

D

mathematics

In the first 10 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

Required run rate = 282 - (4.6x 10) = 236 236/40= 5.9 B) The answer is: B

B

mathematics

Sum of 24 odd numbers is?

sum of 1st n odd no.s = 1+3+5+7+... = n^2 so, Sum of 1st 24 odd numbers = 24^2 = 576 ANSWER:E The answer is: E

E

mathematics

Kanul spent $80000 in buying raw materials, $30000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?

Let the total amount be x then, (100-20)% of x = 80000+30000 80% of x = 110000 80x/100 = 110000 x = $1100000/8 x = $137500 Answer is B The answer is: B

B

mathematics

There is one highland where planes get fuel. A plan can cover the half of the world with full tank. A plane can transfer fuel from one plane to the other in the air. How many planes are required to make one plane cover the entire world once. Starting point of the travel is the Highland and coming back to the same Highland. All the other planes giving fuels to this Plane should also come back to the same highland and they don't have to cover the entire world.

Divide the world as 6 parts. To cover 1/6 th of the distance 1/3 rd of fuel is required. 1 plane, B, can start in same direction of target flight say A. It can travel 1/6 th of the distance and give 1/3rd of fuel to A and return home with 1/3rd fuel. Now A can cover 4/6th world with that full tank. Let C and D start from home at opposite direction. Let C cover 1/6th dist and give 1/3rd fuel to D. Now D travels 1/3 rd more distance and meets A and gives 1/3rd fuel. Both are now 1/6th distance away from home. Let E take fuel and bring one plane home and F take fuel and bring home A. Now excluding A.. 5 supporting planes are required. ANSWER:D The answer is: D

D

mathematics

a printer number the page of a book starting with 1 and uses 3189 digits in all How many pages dose the book have ?

Solution No of digits in 1-digit page nos. = 1 * 9 = 9 . No of digits in 2-digit page nos. = 2 * 90 = 180. No of digits in 3-digit page nos. = 3 * 900 = 2700 . No of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300. ∴ N0. of pages with 4-digit page nos. = (300/4) =75 Hence, total number of pages = (999 + 75) = 1074 . Answer B The answer is: B

B

mathematics

How many numbers from 10 to 10000 are exactly divisible by 9?

10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110 Answer : C The answer is: C

C