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mathematics
A is a working partner and B is a sleeping partner in a business. A puts in 50,000 and B 60,000. A gets 12.5% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 8800.
[ "3500", "4600", "5400", "4800", "None of these" ]
The amount A gets for managing = 12.5% of Rs. 8800 = 1100 Remaining profit = 8800 – 1100 = 7700 This is to be divided in the ratio 5 : 6. Share of A = 5/11 of 7700 = 3500 β‡’ Total share of A = 3500 + 1100 = 4600. Answer B The answer is: B
B
mathematics
Which is the least number, which, when divided by 12 and 16, leave the same remainder, but is exactly divisible by 11?
[ "55", "27", "29", "12", "01" ]
Explanation: No explanation is available for this question! ANSWER: A The answer is: A
A
mathematics
A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of Y square inches. Which of the following equations must be true?
[ "2W^2 + PW + 2Y = 0", "W^2 βˆ’ PW + 2Y = 0", "2W^2 βˆ’ PW βˆ’ 2Y = 0", "W^2 + PW + Y = 0", "2W^2 βˆ’ PW + 2Y = 0" ]
P = 2(L+W)-----------------1) Y= LW------------------------2) option A is not possible why ?? because all the terms are positive. lets try option B , put value of P and A from 1 and 2 we have, 2W^2-2(L+W)W + 2(LW) 2W^2 - 2LW - 2W^2 + 2LW=0. hence answer is B. The answer is: B
B
mathematics
In a room there are 7 people. Each person shook hands with every other person. How many hand shakes were there?
[ "19", "20", "21", "22", "23" ]
7C2 = 21 The answer is C. The answer is: C
C
mathematics
Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
[ "4/7", "5/3", "4/5", "5/8", "7/18" ]
Clearly n(S)=6*6=36 Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2), (6,6)} n(E)=14. Hence p(e)=n(e)/n(s)=14/36=7/18 ANS: E The answer is: E
E
mathematics
On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
[ "Rs.5000", "Rs.20000", "Rs.25000", "Rs.30000", "Rs.50000" ]
Explanation: P(1+10/100)^2Γ—(1+1/2Γ—10/100))=31762.5 P(11/10)^2Γ—(21/20)=31762.5 P=31762.5Γ—20Γ—10Γ—10/21Γ—11Γ—11=1512.5Γ—20Γ—10Γ—10/11Γ—11 =137.5Γ—20Γ—10Γ—10/11 =12.5Γ—20Γ—10Γ—10=Rs. 25000 Answer : Option C The answer is: C
C
mathematics
9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?
[ "19 days", "18 days", "12 days", "27 days", "26 days" ]
9M + 12B ----- 12 days 12M + 12B ------- 10 days 10M + 10B -------? 108M + 144B = 120M +120B 24B = 12M => 1M = 2B 18B + 12B = 30B ---- 12 days 20B + 10B = 30B -----? => 12 days Answer: C The answer is: C
C
mathematics
If takes 25.5 minutes to download a file using Modem A. Modem B work at 17% of the speed of Modem A. How long does it take to download a file using a Modem B?
[ "130 minutes", "140 minutes", "150 minutes", "160 minutes", "170 minutes" ]
Let Speed of modem A be k So Speed of modem B is 17/100*k Time taken by modem A = 25.5 minutes Let time taken by modem B = x k*25.5 = 17/100*k*x 0.17*x = 25.5 x = 25.5/0.17 = 150 minutes ANSWER:C The answer is: C
C
mathematics
A train 140 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
[ "30.5 kmph", "31.5 kmph", "32.5 kmph", "33.5 kmph", "21.5 kmph" ]
S = 140/16 * 18/5 = 31.5 kmph ANSWER:B The answer is: B
B
mathematics
A bowl was filled with 10 ounces of water, and 0.014 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
[ "0.004%", "0.04%", "0.40%", "7%", "40%" ]
Total amount of water evaporated each day during a 50-day period = .014 * 50 =.014 * 100/2 = 1.4/2 = .7 percent of the original amount of water evaporated during this period = (.7/10) * 100% = 7 % Answer D The answer is: D
D
mathematics
Find the one which does not belong to that group ?
[ "3", "4", "5", "8", "6" ]
Explanation: 3, 5, 9 and 7 are odd numbers, but not 4. Answer: B The answer is: B
B
mathematics
Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
[ "12", "99", "20", "88", "21" ]
1/x + 1/(x + 10) = 1/12 x = 20 Answer: C The answer is: C
C
mathematics
A toy train produces 10 different sounds when it moves around a circular toy track of radius 5 m at 10 m per min. However, the toy train is defective and it now produces only 2 different tunes at random. What are the odds that the train produces for consecutive music tones of the same type?
[ "1 in 16", "1 in 4", "1 in 8", "1 in 32", "1 in 3" ]
1/(2^2)=1in4 ANSWER:B The answer is: B
B
mathematics
A train 250 m long, running with a speed of 50 km/hr will pass a tree in?
[ "18sec", "20sec", "25sec", "30sec", "1min" ]
Speed = 50 * 5/18 = 125/9 m/sec Time taken = 250 *9/125 = 18 sec Answer:A The answer is: A
A
mathematics
Exactly 15% of the reporters for a certain wire service cover local politics in Country X. If 25% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
[ "20%", "42%", "44%", "66%", "84%" ]
You are correct. People who cover local politics are a subset of people who cover politics. 25% of reporters who cover politics do not cover local politics so 75% DO cover local politics. Reporters covering local politics= 75% of reporters covering politics= 25% of all reporters Reporters covering politics/All Reporters = 25/75 = 1/3 Reporters not covering politics/All Reporters = 2/3 = 66%=D The answer is: D
D
mathematics
Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?
[ "1:2", "3:4", "3:8", "3:1", "3:2" ]
The ratio of the investments made by A and B = 100000: 50000=> 2:1.Answer: A The answer is: A
A
mathematics
25 children are going to a picnic. What is the smallest number of cakes that must be brought to the picnic so that each child receives the same number of cakes?
[ "35", "40", "15", "75", "9" ]
The number of children going to the picnic are 25 The answer will be D because only 75 is divisible by 25 The answer is: D
D
mathematics
A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
[ "33", "66", "24", "88", "99" ]
B = 1/8 – 1/2 = 1/24 => 24 days Answer:C The answer is: C
C
mathematics
Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
[ "81000", "81027", "81089", "81027", "28939" ]
64000* 9/8 * 9/8 = 81000 Answer: A The answer is: A
A
mathematics
Rahul went to a shop and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
[ "15", "12.1", "19.7", "16.0", "20.0" ]
Total cost of item he pirchased = 25 tot tax = 30 paise = 30/100 tax free = x given tax rate = 6% 25-30/100 - x6/100 = 30/100 6(25-0.3-x) = 30 x=19.7 ANSWER C The answer is: C
C
mathematics
The expression 10^14βˆ’110 is divisible by all of the following integers EXCEPT
[ "2", "3", "4", "7", "11" ]
Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (D) is correct. The answer is: D
D
mathematics
Yesterday's closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday?
[ "960", "726", "1,100", "1,320", "1,694" ]
Lets consider the below - The number of stocks that closed at a higher price = H The number of stocks that closed at a lower price = L We understand from first statement -> H+L = 1760 ----(1) We understand from second statement -> H = (120/100)L => H = 1.2L ----(2) Solve eq (1)(2) to get H = 960. A is my answer. The answer is: A
A
mathematics
Which of the following is equal to 2^k*3^(k-1)?
[ "2*6^(k-1)", "3*6^(k-1)", "6^k", "2*6^k", "6^(2k-1)" ]
2^k*3^(k-1) = 2*2^(k-1)*3^(k-1) = 2*6^(k-1) The answer is A. The answer is: A
A
mathematics
what is the smallest integer that is multiple of 5,7 and 20
[ "141", "180", "130", "122", "140" ]
Correct Answer :E It is the lcm of 5,7 and 20 which is 140 The answer is: E
E
mathematics
In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/6 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
[ "50", "70", "10", "105", "140" ]
Rented = 4/7*490 = 280. Rented two-bedroom = 6/7*280 = 240; Rented one-bedroom = 1/7*280 = 40 (or 280-240=40). Rented one-bedroom units are 1/5 of all one-bedroom: 1/6*{All one bedroom} = 40 --> {All one-bedroom} = 240. {All two-bedroom} = 490 - 240 = 250. Two-bedroom not rented = 250 - 240 = 10. Answer: C. The answer is: C
C
mathematics
The average runs of ten batsmen is 25. If three players whose marks are 3,8 and 4 are removed , then find the approximate average runs of the remaining players.
[ "28", "34", "55", "29", "52" ]
Exp. Total runs of 10 players = 25*10 = 250, Total runs after the removal of 3 players = 250 –(3 + 8 + 4) = 250 – 15 = 235 Approximate average runs = 235/(10-3) = 235/ 7 = 34 Answer: B The answer is: B
B
mathematics
A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?
[ "2", "3", "4", "5", "6" ]
Let n=3q+1 and let q= 2p+1. Then, n= 3(2p+1)+1= 6p+4 Therefore, the number when divided by 6, we get remainder= 4 ANSWER:C The answer is: C
C
mathematics
A certain sum of money at simple interest amounted Rs.1448 in 9 years at 4% per annum, find the sum?
[ "1064", "1080", "1980", "646", "168" ]
840 = P [1 + (9*4)/100] P = 1064 Answer:A The answer is: A
A
mathematics
A room contains 180 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
[ "25", "35", "45", "55", "65" ]
Say group of x people left the room. # of women in the room was 0.15*180=27; # of women in the group that left 0.3x; # of women in the room after the group left it is 0.1(180-x); So, 27-0.3x= 0.1(180-x) --> x=45. Answer: C. The answer is: C
C
mathematics
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 450 bolts?
[ "36", "72", "120", "144", "108" ]
Old Machine 100 bolts in 60 mins so, 5/3 bolts in 1 min New Machine 150 bolts in 60 mins so, 5/2 bolts in 1 min together, 5/3 + 5/2 = 25/6 bolts in 1 min so, for 450 bolts 450 * 6 / 25 = 108 mins Ans E The answer is: E
E
mathematics
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 1 year?
[ "12300", "12350", "12000", "12500", "12600" ]
Formula : ( After =100 denominator Ago = 100 numerator) 10000 Γƒβ€” 120/100 = 12000 C The answer is: C
C
mathematics
A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?
[ "$70 under budget", "$30 under budget", "$30 over budget", "$70 over budget", "$180 over budget" ]
The budget for 3 months is (3/12)*$1320 = $330 The company is $70 over budget. The answer is D. The answer is: D
D
mathematics
When f is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when f + y is divided by 5?
[ "0", "1", "2", "3", "4" ]
In my view the answer should be C f/5 has Remainder=3 -> f = 5 x Q + 3 Y/5 has a Remainder=4 -> Y = 5 x Q + 3 Combining both ((5 x Q1 + 3) + (5 x Q2 + 3))/5 = 5(Q1+Q2)/5 + 7/5 = Q1+Q2 + 7/5 7/5 = 1+ 2/5 => Remainder 2 Answer C The answer is: C
C
mathematics
Rs.2080 is divided so that 3 times the first share, thrice the 2nd share and four times the third share amount to the same. What is the value of the second share?
[ "s802", "s208", "s960", "s690", "s906" ]
A+B+C = 2080 3A = 2B = 4C = x A:B:C = 1/3:1/2:1/4 = 4:6:3 6/13 * 2080 =Rs960 Answer:C The answer is: C
C
mathematics
What number continues the sequence? 25, 50, 27, 46, 31, 38, 39, ?
[ "21", "22", "23", "24", "25" ]
B 22 There are two alternate sequences, the first increases by 2, 4, 8 etc and the second decreases by 4, 8, 16 etc. The answer is: B
B
mathematics
The average of 65 numbers is 40. If two numbers, 79 and 60 are discarded, then the average of the remaining numbers is nearly
[ "28.32", "39", "38.78", "39.06", "30" ]
Explanation : Total sum of 63 numbers = (65*40) - (79 +60) = 2600 - 139 = 2461 Average = 2457/63 = 39.06 Answer : D The answer is: D
D
mathematics
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements are possible?
[ "30", "60", "90", "180", "540" ]
Ways of selecting group = 6C2 * 4C2 * 2C2 / 3! = 15 Three groups can select three subjects in 6 ways Therefore total combinations = 15*6 = 90 ANSWER:C The answer is: C
C
mathematics
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 12 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
[ "18/79", "16/900", "1/25", "1/50", "1/900" ]
Everything is correct except that you assumed the letters can't be repeated. It can be repeated. AA BB CC AB, AC, BC, BA, CA, CB. Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900 Vehicles inspected within 3 hours = 60*3/12 = 16 P = 16/900 Ans:B The answer is: B
B
mathematics
10 friends are living in 10 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 10 parking spots. In how many ways can they park their cars so that exactly 8 people park their cars in the spots allotted to them?
[ "35", "40", "45", "50", "55" ]
10C8 = 45 The remaining 2 people in each case will be parked in each other's parking spots. The answer is C. The answer is: C
C
mathematics
In Kaya's teacher's desk there are 24 pink highlighters, 28 yellow highlighters, and 25 blue highlighters. How many highlighters are there in all?
[ "11", "22", "77", "33", "88" ]
Add the numbers of highlighters. 24 + 28 + 25 =77. Answer is C. The answer is: C
C
mathematics
A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 15 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
[ "1650", "2750", "3850", "4950", "6050" ]
The distance the sound traveled to the man is 15*330 = 4950 meters The answer is D. The answer is: D
D
mathematics
Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 6 inches from his current location, Gardensquare. Pete arrives in Madison 2.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?
[ "1/25", "1/30", "1/10", "2", "30" ]
Pete covered 2.5*60=150 miles which correspond to 6 inches on the map --> scale in inches per mile is 6/150=1/25. Answer: A. The answer is: A
A
mathematics
The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
[ "12", "25", "28", "245", "21" ]
39x = 5 + 12 + 15 + 19 + (x – 4)44 x = 25 Answer: B The answer is: B
B
mathematics
Solve This 6 + 7 = 12 8 + 9 = 16 5 + 6 = 10 7 + 8 = 14 Then, 9 + 9 = ??
[ "11", "12", "17", "14", "18" ]
17 ANSWER:C The answer is: C
C
mathematics
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 300 as interest at the end of the loan period, what was the rate of interest?
[ "3.6", "6", "5", "24", "None of these" ]
Let rate = R% and time = R years. Then, (1200 x R x R)/100 = 300 12R2 = 300 R2 = 25 R = 5. Answer: Option C The answer is: C
C
mathematics
The total of company C's assets in 1994 was 700% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
[ "7N", "18N", "29N", "32N", "40N" ]
Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets. In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992: $100 + 4x$100 = $100 + $400 = $500 In 1994, the total assets were 700% GREATER than they were in 1993, which means 1993 PLUS 700% of 1993: $500 + 7x$500 = $500 + $3500 = $4000 This is 40 times the 1992 number, so the correct answer is 40N. The answer is: E
E
mathematics
The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?
[ "5 hours 5 minutes", "8 hours 5 minutes", "7 hours 5 minutes", "6 hours 5 minutes", "3 hours 5 minutes" ]
If L and W be the original length and width of the rectangle and its area is given by L * W After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) * (3 W) and is known. Hence (2 L) * (3 W) = 1800 Solve the above equation to find L* W 6 L * W = 1800 L * W = 1800 / 6 = 300 square meters , area of original rectangle Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute). Solution In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill 1/5 + 1/8 = 13 / 40 of a tank Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving (13/40) t = 1 t = 40 / 13 = 39/13 + 1/13 hours = 3 hours and (1/13)*60 minutes = 3 hours 5 minutes (rounded to the nearest minute) correct answer E The answer is: E
E
mathematics
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
[ "1/3", "2/3", "2/5", "3/5", "4/5" ]
Explanation: By the rule of alligation, we have: So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2 Required quantity replaced =2/3. ANSWER IS B The answer is: B
B
mathematics
When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the reminder when A is divided by B?
[ "11", "14", "15", "24", "19" ]
the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44 0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44. Only option A-11 satisfies this for remainder 11, Ans - A The answer is: A
A
mathematics
In how many ways can a four-letter password be chosen, using the letters A, B, C, D, and/or E, such that at least one letter is repeated within the password?
[ "505", "864", "900", "936", "1,296" ]
Total number of four letter passwords = 5*5*5*5= 625 ------(1) Total number of passwords in which no letter repeats = 5C4*4!= 5*24=120------(2) therefore required value = (1)-(2)= 625-120=505 A The answer is: A
A
mathematics
For what value of Ò€œkÒ€ will the equation (2kx2 + 5kx +1)=0 have equal roots?
[ "2/7", "9/4", "8/25", "7/1", "7/2" ]
for a 2nd degree equation ax2+bx_c=0 has equal roots the condition is b2-4ac =0 in the given equation (5k)^2-4*2k*1=0 by solving this equation we get k=0, k=8/25 ANSWER:C The answer is: C
C
mathematics
if the ratio of two number is 2:3 and LCM of the number is 120 then what is the number.
[ "15", "20", "25", "30", "35" ]
product of two no = lcm *hcf 2x*3x=120*x x=20 ANSWER:B The answer is: B
B
mathematics
A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
[ "110", "130", "126", "135", "156" ]
There are 8 students and the maximum capacity of the cars together is 9. We may divide the 8 students as follows Case I: 5 students in the first car and 3 in the second Or Case II: 4 students in the first car and 4 in the second Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways. Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways. Therefore, the total number of ways in which 8 students can travel is: \inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126 C The answer is: C
C
mathematics
Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 36 meter head start. If Cristina runs at a pace of 4 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
[ "15 seconds", "18 seconds", "25 seconds", "36 seconds", "45 seconds" ]
used pluging in method say t is the time for cristina to catch up with Nicky, the equation will be as under: for Nicky=N=3*t+36 for Cristina=C=5*t @t=36, N=144 C=144 right answer ans:D The answer is: D
D
mathematics
In a party attended by 14 persons, each clinch their glass with every other. How many glass clinches?
[ "91", "92", "93", "94", "95" ]
Total no. of person = 11 Total no. of glass clinches = n(n-1)/2 =14*13/2 =91 ANSWER:A The answer is: A
A
mathematics
Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 30 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
[ "10%", "12%", "15%", "17%", "28%" ]
Lets assume that candidate got 30% votes and total votes is 100. Candidate won = 30 Remaining = 70 To get 50%, candidate requires 20 votes from 100 which is 20% and 20 votes from 70. 20/70 = 28.57% Which is approx 28%. Hence the answer is E The answer is: E
E
mathematics
Square M is inscribed in circle N. If the perimeter of M is 20, what is the circumference of N?
[ "33√ 2Ο€", "2√ 2Ο€", "6√ 2Ο€", "7√ 2Ο€", "5√ 2Ο€" ]
square forms two right angled triangles. Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter. hypotenuse here = diagonal of the square = 5 sqrt(2) = diameter => radius = 2.5 sqrt(2) Circumference of the circle = 2pi r = 5 pi sqrt(2) Answer is E. The answer is: E
E
mathematics
sue has 3 apples. Billy has 5 apples. If billy steals all of sues apples and eats 2 how many does he have left?
[ "2", "5", "6", "4", "8" ]
6 C The answer is: C
C
mathematics
Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 28 have long fur, 17 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
[ "26", "19", "11", "8", "6" ]
No of dogs=45 Long fur=28 Brown=17 Neither long fur nor brown=8 Therefore, either long fur or brown=45-8=37 37=28+17-Both Both=8 Answer D The answer is: D
D
mathematics
In a game of billiards, A can give B 30 points in 50 and he can give C 40 points in 50. How many points can B give C in a game of 100?
[ "18", "27", "50", "21", "17" ]
A scores 50 while B score 20 and C scores 10. The number of points that C scores when B scores 100 = (100 * 10)/20 = 50. In a game of 100 points, B gives (100 - 50) = 50 points to C. Answer: C The answer is: C
C
mathematics
1/(3-2√2)=?
[ "9+4√5", "9-4√5", "3+2√2", "9-2√5", "4+9√5" ]
This question requires us to rationalize (fix) the denominator. For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044 Given: 1/(3-2√2) Multiply top and bottom by the CONJUGATE of 3-2√2, which is 3+2√2 So, 1/(3-2√2) = (1)(3+2√2)/(3-2√2)(3+2√2) = (3+2√2)/(1) = 3+2√2 = C The answer is: C
C
mathematics
In a class, the average age of 35 boys is 10 years and the average of 25 girls is 15 years. what is the average age of the whole class?
[ "11 Years", "12.1 Years", "13 Years", "13.5 Years", "14 Years" ]
Total age of 60 students (35X 10+25 X 15) = 725 Average = 725/60 = 12.1 Years B) The answer is: B
B
mathematics
The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 72 metres, what is its area?
[ "315 sq.metres", "260 sq.metres", "280 sq.metres", "380 sq.metres", "None of these" ]
Let the length and breadth be 7x and 5x respectively. Then, P = 2(7x + 5x) = 72 Ò‑’ x = 3 Area = 7 Γƒβ€” 3 Γƒβ€” 5 Γƒβ€” 3 = 315 sq.m. Answer A The answer is: A
A
mathematics
10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.
[ "1/10", "9/10", "1/5", "3/10", "1/2" ]
Explanation: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2! Required probability = 1/5 ANSWER IS C The answer is: C
C
mathematics
If x and y are positive integers, and 4x^2=3y, then which of the following must be a multiple of 8? I. x^2 II. y^2 III. xy
[ "I only", "II only", "III only", "I and II only", "I, II and III" ]
4x^2 = 3y since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2 -> x^2 and y is divisible by 9 -> y^2 is divisible by 9 (1),(2), and (3) must be true Answer is C The answer is: C
C
mathematics
John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 65 miles per hour, what is v in miles per hour?
[ "30", "40", "50", "55", "70" ]
HiBunuel THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55. The question is correct. Here's the explanation: Let distance be D. We can find the total timeequate it, which comes as: 0.8D / 80 + 0.2D / v = D / 65 => v = 55 (Option D). The answer is: D
D
mathematics
If points A and B are (8-3) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB
[ "I only", "II only", "III only", "I and II only", "I and III only" ]
I. The area of a square region with side AB --> side=AB=(8-3) or 5 --> the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). Answer: A. The answer is: A
A
mathematics
Two boats are heading towards each other at constant speeds of 5 miles/hr and 21 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
[ "1/12", "5/12", "1/6", "13/30", "1/5" ]
The question asks: how far apart will they be 1 minute=1/60 hours before they collide? Since the combined rate of the boats is 5+21=26 mph then 1/60 hours before they collide they'll be rate*time=distance --> 26*1/60=13/30 miles apart. Answer: D. The answer is: D
D
mathematics
A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $50, how many pounds of premium chocolates are in the box?
[ "[A] 1", "[B] 2", "[C] 3", "[D] 4", "[E] 5" ]
This question is a bit of Special equations with a single set of unique values. the Equation stands : 5X + 4Y =50 Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4 31 - 5 = 26 -> Not divisible by 4 31 - 10 = 21 -> Not divisible by 4 31 - 15 =16 -> Divisible by 4 31 - 20 =11 -> Not divisible by 4 31 - 25 =6 -> Not divisible by 4 31 - 30 =1 -> Not divisible by 4 Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible Thus Amount spent on regular chocolate= $16 Amount spent on Premium chocolate= $15 Price per premium chocolate = $5 No. Of boxes of premium chocolate bought = 25 / 5 = 5 Correct Option : E The answer is: E
E
mathematics
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
[ "31 5/7years", "31", "30", "33", "35" ]
Required average = (67 x 2 + 35 x 2 + 6 x 3 )/(2 + 2 + 3) = (134 + 70 + 18)/7 = 222/7 = 31 5/7years. Answer is A The answer is: A
A
mathematics
In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?
[ "360", "720", "480", "5040", "None of these" ]
Treat B and T as a single letter. Then the remaining letters (5 + 1 = 6) can be arranged in 6! ways. Since, O is repeated twice, we have to divide by 2 and the B and T letters can be arranged in 2! ways. Total no. of ways = 6!Γ—2!/2=720 Answer B The answer is: B
B
mathematics
The volume of a cube is 1728 cc. Find its surface.
[ "864", "277", "299", "268", "191" ]
a3 = 1728 => a = 12 6a2 = 6 * 12 * 12 = 864 Answer: A The answer is: A
A
mathematics
The grade point average of the entire class is 84. If the average of one fourth of the class is 96, what is the average of the rest of the class?
[ "76", "77", "78", "79", "80" ]
Let x be the number of students in the class. Let P be the average of the rest of the class. 84x = (1/4)96x + (3/4)(P)x 336 = 96 + 3P 3P = 240 P = 80. The answer is E. The answer is: E
E
mathematics
A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?
[ "2 months", "4 months", "5 months", "7 months", "9 months" ]
Given their profits are equal per annum so 25000*12=30000*x x=10 months 12-10=2 months ANSWER:A The answer is: A
A
mathematics
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
[ "400 kg", "560 kg", "600 kg", "640 kg", "680 kg" ]
Profit on 1st part 8% Profit on 2nd part 18% Mean Profit 14% Ration of 1st and 2nd parts = 4 : 6 = 2 : 3 Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg. Answer:C The answer is: C
C
mathematics
The average age of a group of persons going for picnic is years. Fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
[ "5", "10", "15", "40", "50" ]
Solution Let the initial number of persons be x. Then 16x + 15 x 15 = 15.5(x+20) = 0.5x = 7.5 x = 15. Answer C The answer is: C
C
mathematics
The average of first 18 even numbers is?
[ "19", "18", "16", "11", "17" ]
Sum of 18 even numbers = 18 * 19 = 342 Average = 342/18 = 19 Answer:A The answer is: A
A
mathematics
If 4 men can colour 48 m long cloth in 2 days, then 5 men can colour 36 m long cloth in
[ "1.2 day", "2.0 days", "3 days", "4.2 days", "5 days" ]
The length of cloth painted by one man in one day = 48 / 4 Γ— 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 Γ— 5 = 1.2 day. A The answer is: A
A
mathematics
If the same letters represent the same digit and different letters represent different digits, what digit does the letter A represent?
[ "1", "2", "3", "4", "5" ]
Look at the digits in the ones place, there are 2 possible values for A + B + B: A + B + B = A or A + B + B = 10 + A. If A + B + B = A , B = 0. If A + B + B = 10 + A, B = 5. Since B is a leading digit of BA, B cannot be a 0. B has to be a 5. Look at the digits in the tens place, there are 2 possible values for 5 + A + A + 1: 5 + A + A + 1 = 10 + A or 5 + A + A + 1 = 20 + A If 5 + A + A + 1 = 10 + A, A = 4. If 5 + A + A + 1 = 20 + A, A = 14. Since A is a single digit number, A has to be 4. correct answer D The answer is: D
D
mathematics
The greatest number by which the product of three consecutive multiples of 7 is always
[ "54", "81", "162", "243", "None of these" ]
Explanation: 7*14*21 = 2058 Option E The answer is: E
E
mathematics
The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in sq. m)?
[ "153500", "153650", "153600", "153700", "153750" ]
Let length =3x km, breadth =2x km Distance travelled by the man at the speed of 12 km/hr in 8 minutes =2(3x+2x)=10x Therefore,12Γ—860=10xx=425 km=160 m Area =3xΓ—2x=6x2 =6Γ—1602=153600 m2 Answer is C. The answer is: C
C
mathematics
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 32150. What percentage of profit did he make?
[ "22", "44.5", "40", "26", "11" ]
The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 32150 Profit(%) = (32150 - 22250)/22250 * 100 = 44.5%.Answer:B The answer is: B
B
mathematics
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much Ɵme shall B take to do it
[ "40 days", "35 days", "30 days", "25 days", "None of these" ]
Explanation: Suppose B takes x days to do the work. As per question A will take 2 βˆ— 34 βˆ— x=3x2days (A+B)s 1 days work= 1/18 1/x + 2/3x = 1/18 or x = 30 days Answer: C The answer is: C
C
mathematics
A shop owners pays an average salary of $400 to his 10 employees and $100 to the 2 accountants. What is the average salary for the shop owner?
[ "$350", "$500", "$460", "$120", "$800" ]
Number of employees in the shop is 10 Their average salary is $400 Number of accountants in the shop is 2 Their average salary is $100 Total salary of the employees is 10*400=$4,000 Total salary of the accountants is 2*100=$200 Total salary for the shop owner is $4,200 Average salary for the shop owner is 4,200/12=$350 Answer is A The answer is: A
A
mathematics
Two pipes A and B can fill a tank in 15 min and 18 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
[ "14 min 19 sec", "13 min 36 sec", "14 min 20 sec", "14 min 40 sec", "14 min 10 sec" ]
: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15 Remaining part = 1 - 7/15 = 8/15 Part filled by B in 1 minute = 1/18 1/18 : 8/15 :: 1 ; x x = 8/15 * 1 * 18 = 9 3/5 min = 9 min 36 sec. The tank will be full in (4 min. + 9 min. 36 sec) = 13 min 36 sec.Answer: B The answer is: B
B
mathematics
Sudhir started a business with Rs.60,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
[ "3:1", "2:3", "4:3", "3:4", "3:5" ]
60000*12:60000*(12-8) =720000 :240000 =3:1 ANSWER:A The answer is: A
A
mathematics
What percent of 120 are 90?
[ "78%", "85%", "75%", "72%", "23%" ]
(?% /100) * 120 = 90 ? = 75% Answer:C The answer is: C
C
mathematics
Abhijit started a business investing 4000. Anuja joined him after six months with an amount of 8000 and Sunil joined them with 12,000 after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, two years after Abhijit started the business?
[ "2 : 4 : 3", "2 : 4 : 4", "2 : 5 : 5", "2 : 3 : 3", "2 : 5: 3" ]
Ratio of their investments = 4Γ— 24 : 8 Γ— 18 : 12 Γ— 12 = 2 : 3 : 3 Answer D The answer is: D
D
mathematics
In boring a well 50 m deep, the cost is Rs.4/– for the first meter. The cost of each successive meter increases by Rs.2/–. What is the cost of boring the entire well?
[ "1650", "2650", "3650", "4650", "2850" ]
For successive meters the cost of boring will be 4, 6, 8, 10, ......., which forms an arithmetic series with terms n=50, first term a=4 & difference d=2 So Sum=(n/2)[2a+(n-1)d]= Total cost of boring =(50/2)[2*4+(50-1)*2]=25(8+98) = 2650 ANSWER:B The answer is: B
B
mathematics
9, 16, 17, 25, 36,49
[ "9", "16", "17", "25", "36" ]
Each of the numbers except 17, is perfect square. Answer: Option C The answer is: C
C
mathematics
If (2^14)(25^S) = 5(10^m) what is the value of m ?
[ "7", "8", "15", "16", "14" ]
given 2^14 * 25^s = 5 * 10^2 => 2^14 * 5^(2s) = 2^m * 5^(m+1) Ans E on comparing the power of 2 => m=14 The answer is: E
E
mathematics
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.27000 after completion of one year. What will be Jose's share of profit?
[ "20000", "15000", "25000", "34000", "30000" ]
SoL = ~s- So Anju’s share = [5/9] x 27000 = 15000 B The answer is: B
B
mathematics
If x and y are positive numbers and z = xy^2, a 20 percent increase in x and a 10 percent decrease in y would result in which of the following changes in z?
[ "decrease of 2.8%", "decrease of 11.4%", "increase of 4.6%", "increase of 15.8%", "increase of 22.4%" ]
After the changes, z = 1.2x*(0.9y)^2 = (1.2*0.81)xy^2 = 0.972*z The answer is A. The answer is: A
A
mathematics
In a contest, a bowl contains 12 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
[ "1/11", "1/12", "1/6", "11/120", "2/11" ]
P(not winning) = 11/12*10/11 = 5/6 P(winning) = 1 - 5/6 = 1/6 The answer is C. The answer is: C
C
mathematics
Three integers are at random chosen between 0 and 9 inclusive. What is the probability W that each number is different ?
[ "A.18/25", "B.4/5", "C.81/100", "D.9/10", "E.1" ]
Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10 Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8 Probability W= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25 Answer: A The answer is: A
A
mathematics
In what time will a train 350 m long cross an electric pole, it its speed be 144 km/hr?
[ "2.5 sec", "2.95 sec", "1.3 sec", "8.75 sec", "1.85 sec" ]
Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 8.75 sec. Answer:D The answer is: D
D
mathematics
The side of a square is increased by 20% then how much % does its area increases?
[ "52.65", "56.25", "44", "42.75", "52.75" ]
a = 100 a2 = 10000 a = 120 a2 = 14400 ---------------- 10000 --------- 4400 100 -------? => 44 % ANSWER: C The answer is: C
C
mathematics
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
[ "6000", "5000", "5500", "4000", "3500" ]
Income = Rs. 100 Expenditure = Rs. 80 Savings = Rs. 20 Present Expenditure 80*(20/100) = Rs. 96 Present Savings = 100 Γ’β‚¬β€œ 96 =Rs. 4 100 ------ 4 ? --------- 200 => 5000 ANSWER B The answer is: B
B
mathematics
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-90 inclusive is the digital sum a multiple of 7?
[ "10", "8", "14", "16", "20" ]
is there other way than just listing? 25 34 43 52 59 61 68 70 77 86 10 ways.. A The answer is: A
A
mathematics
The value of 1 + 1/(4 x 3) + 1/(4 x 32) +1/(4 x 33) up to four places of decimals is ?
[ "1.1202", "1.1203", "1.1204", "None of these", "Cannot be determined" ]
Answer Given expression = (108 + 9 + 3 +1) / 108 = 121 / 108 = 1.1203 Correct Option: B The answer is: B
B