subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.22? | [
"10 : 7",
"9 : 8",
"1 : 2",
"13 : 11",
"14 : 8"
] | Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 3 : 6 = 1 :2
The answer is: C | C |
mathematics | A fair coin is tossed repeatedly. If heads appears on first 5 tosses what is the probability that tail appears on the next two tosses? | [
"1/6",
"1/5",
"1/3",
"1/4",
"1/6"
] | Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
The answer is: D | D |
mathematics | Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 20 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | [
"A) 6.24",
"B) 8",
"C) 10",
"D) 19.1",
"E) 24"
] | Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9
New time in minutes to cross 10 miles stretch = 10*60/20 = 10*3 = 30
Time difference = 19.1
Ans:D
The answer is: D | D |
mathematics | Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 30 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister? | [
"3%",
"15%",
"8%",
"10%",
"12%"
] | Bob's time = 600 secs.
His sis' time = 510 secs.
Percent increase needed = (640-510/600) * 100 = 90/600 * 100 = 15%. Ans (B).
The answer is: B | B |
mathematics | What are the next two numbers in this sequence?
7, 14, 17, 21, 27, 28, 35, 37, ? | [
"40",
"41",
"42",
"43",
"44"
] | these are digits which are either multiples of 7 or containing the digit 7.
s0 next numbers are 42
ANSWER:C
The answer is: C | C |
mathematics | If the sides of a rectangle are increased by 35%, what is the percentage increase in the area? | [
"38.25%",
"40.25%",
"82.25%",
"50%",
"65%"
] | If sides are a and b, after increase sides would be 1.35a and 1.35 b.
Percentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25
Answer : C
The answer is: C | C |
mathematics | A sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is | [
"15%",
"12%",
"8%",
"7%",
"5%"
] | Explanation :
Simple Interest for 3 years = (Rs.12005 - Rs.9800) = Rs.2205
Simple Interest for 5 years = 22053×5=Rs.3675
Principal(P) = (Rs.9800 - Rs.3675) = Rs.6125
R = 100×SI/PT
=100×3675/6125×5
=12%
Answer : Option B
The answer is: B | B |
mathematics | Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114. | [
"2 or ½",
"2/3 or 3/2",
"¾ or 4/3",
"4 or ¼",
"5 or 1/5"
] | Let the terms be a/r, a , ar
a/r *a * ar = a 3 =216, a =6
(a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114
a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114
6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,
On solving, r = 2/3 or 3/2
ANSWER:B
The answer is: B | B |
mathematics | While playing a certain dice game, Chris wins if the sum of the two dice is 10, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win? | [
"1/2",
"17/36",
"190/827",
"11/36",
"25/216"
] | Probability of winning game = 1- Probability of losing game
Probability of losing game = (Probability of not getting sum 7 in any of the three attempts)
Ways of getting sum 10 = (4,6)(5,5)(6,4)= 3 ways
Total ways of getting outcome on two dice =6*6=36
Probability of getting sum as 10 in any attempt =3/36=1/12
Probabili... | C |
mathematics | A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were right handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of l... | [
"1/3",
"2/3",
"7/5",
"5/7",
"3/2"
] | Say the total number of players is 18, 9 right-handed and 9 left-handed.
On a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.
Of the players at practice that day, one-third were right-handed --> 6*1/3=2 were right-handed and 4 left-handed.
The number of right-handed players... | C |
mathematics | 12 year old Manick is three times as old as his brother Rahul. How old will Manick be when he is twice as old as Rahul ? | [
"16",
"27",
"21",
"10",
"11"
] | Manick's present age = 12 years, Rahul's present age = 4 years.
Let Manick be twice as old as Rahul after x years from now.
Then, 12 + x = 2 (4 + x) 12 + x = 8 + 2x x = 4.
Hence, Manick's required age = 12 + x = 16 years.
Answer: A
The answer is: A | A |
mathematics | A worker makes a toy in every 2h. If he works for 120h, then how many toys will he make ? | [
"40",
"60",
"45",
"39",
"None"
] | No. of toys = 120/2 = 60
Answer : B
The answer is: B | B |
mathematics | Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend? | [
"$6.80",
"$8.40",
"$7.70",
"$4.70",
"$3.90"
] | Linda spent
1.20 ? 3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80
correct answer A
The answer is: A | A |
mathematics | The faces of pyramid are to be painted by 4 different colors. In how many ways can be this be done? | [
"A.720",
"B.256",
"C.24",
"D.12",
"E.36"
] | If I have to paint 4 sides with 4 different colour...
First face can have 4c1 options,
2nd would have 3c1, and subsequent ones would have 2c1 and 1 options respectively.
Total options = 4c1 x 3c1 x 2c1 x 1 = 24 distinct ways
Correct answer - C
The answer is: C | C |
mathematics | Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is | [
"1/36",
"1/18",
"1/32",
"1/37",
"None of these"
] | Probability of getting yellow color = P(Y) = 3/6 = 1/2
Probability of getting red color = P(R) = 2/6 = 1/3
Probability of getting blue color = P(B) = 2/6=1/3
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/3 x 1/3 ... | B |
mathematics | A speaks the truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event? | [
"0.225",
"0.37",
"0.32",
"0.35",
"0.55"
] | Different possible cases of contradiction occurs when A speaks the truth and B does not speak the truth or A does not speak the truth and B speaks the truth.
(3/4 x 1/5) + (1/4 x 1/5) = 7/20 = 35%
= 0.35
ANSWER:D
The answer is: D | D |
mathematics | The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair? | [
"16",
"20.5",
"17.5",
"20",
"4.5"
] | Total entrance fee is (2*$5) + (1.20*5)= $16
Total rides fee is (0.50*3)*3= $4.50
Total money spent is $20.50
Answer is B
The answer is: B | B |
mathematics | What is the principal sum?
I. The sum amounts to Rs. 690 at S.I.
II. Total year is 8 years.
III. The rate of interest is 5% p.a. | [
"I and III only",
"II and III only",
"I and II only",
"Any two of the three",
"All I, II and III"
] | Explanation:
Clearly, all the three statements are needed to solve this question
Answer: E
The answer is: E | E |
mathematics | The side of a square has the length of 9. What is the area of the region shaded? | [
"48-8π",
"48-6 π",
"24+6π",
"16+8π",
"64-9π"
] | The area of a square whose side is 9 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is E.
The answer is: E | E |
mathematics | what is the compound interest on rs:80,000 for 4 months at the rate of 5% per annum | [
"1341.69",
"1342.69",
"1343.69",
"1344.69",
"1345.69"
] | it is monthly compound
rate=5/12% per month
80000*(1+5/1200)^4-80000=1341.69
ANSWER:A
The answer is: A | A |
mathematics | Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 450 players took part in that tournament.
How many matches were played? | [
"449 matches.",
"88 matches.",
"77 matches.",
"66 matches.",
"55 matches."
] | Solution:
449 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 449 matches were played.
Answer A
The answer is: A | A |
mathematics | What is the dividend. divisor 16, the quotient is 6 and the remainder is 2 | [
"86",
"87",
"88",
"89",
"90"
] | C = d * Q + R
C = 16 * 6 + 2
C = 86 + 2
C = 88
The answer is: C | C |
mathematics | John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/3:1/5 . What is the minimum no. of pencils that the person should have? | [
"41",
"65",
"70",
"77",
"98"
] | Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 3 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,3 and 5 is 30.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 30 ) = 15.
Rahul = ( 1 / 3 x 30 ) = 10.
Ranjan = ( 1 / 3 x 30 ) = 10.
Rohit = ( 1 / 5 x 30 ) = 6.
Step 3: Total numbe... | A |
mathematics | The Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women? | [
"14/33",
"7/33",
"2/7",
"13/73",
"12/27"
] | Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792.
To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6.
And, select 3 women from 8 = 8C3 = 56.
3 women and 2 men = (6)(56) = 336
Probability = (number outcomes favorable)/(to... | A |
mathematics | Truck X is 13 miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hour, how long will it take Truck Y to overtake and drive 5 miles ahead of Truck X? | [
"2 hours",
"2 hours 20 minutes",
"2 hours 30 minutes",
"2 hours 45 minutes",
"3 hours"
] | Relative speed = 53-47 = 6 miles per hour
Dist required = 13+5 = 18 miles
Time taken to overtake = 18/6 = 3 hours.
E is the answer.
The answer is: E | E |
mathematics | A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: | [
"110 m",
"120 m",
"190 m",
"150 m",
"180 m"
] | Answer: Option D
Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
The answer is: D | D |
mathematics | A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every three leaps of the hare, the jackal takes five leaps. Find the ratio of the speed of the hare to the speed of the jackal. | [
"6:7",
"4:5",
"5:8",
"25:64",
"3:5"
] | The hare takes 3 leaps and the jackal takes 5 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 3 leaps = 3*(4/3) = 4 jackal leaps.
The ratio of their speeds is 4:5.
The answer is B.
The answer is: B | B |
mathematics | A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 8 cm. What is the length of the wire? | [
"16 cm",
"24 cm",
"28 cm",
"36 cm",
"39 cm"
] | Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(8)^2 * h = (4/3)π (12)^3 => h
= 36 cm
Answer:D
The answer is: D | D |
mathematics | The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary? | [
"2000",
"3000",
"3600",
"4800",
"4000"
] | Manager's monthly salary
= Rs. (1600 * 21 - 1500 * 20) = Rs. 3600
ANSWER C
The answer is: C | C |
mathematics | The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is | [
"71.5",
"11.5",
"81.5",
"11.5",
"21.5"
] | Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.
Answer: B
The answer is: B | B |
mathematics | A right circular cylinder has a height of 22 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the... | [
"500(π – 3)",
"500(π – 2.5)",
"500(π – 2)",
"550(π – 1.5)",
"500(π – 1)"
] | [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the... | D |
mathematics | How many times are the hands of a clock at right angle in a day? | [
"22",
"44",
"41",
"21",
"40"
] | Correct Answer : B
In 12 hour hands of clock are at right angle 22 times
In 24 hour hands of clock are at right angle 44 times
The answer is: B | B |
mathematics | A train,130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge? | [
"210",
"225",
"235",
"245",
"260"
] | Speed =45 km/hr=45×5/18 m/s =12.5 m/s Distance travelled = (Speed x Time)
Distance travelled = 12.5×30=375 m
length of the bridge = 375-130 = 245 m
Answer: D
The answer is: D | D |
mathematics | A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 15 days, an eucalyptus plant (a green plant) creates 15,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per ... | [
"60,000",
"6,000",
"2,500",
"250",
"0"
] | Solution:
We know that 15,000 glucose molecules are created over a period of 15 days. Therefore 15,000/15 = 1,000 glucose molecules are created on average per day.
Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,0... | B |
mathematics | A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60 | [
"I & II",
"III",
"I & III",
"II & III",
"II"
] | 15 , 30 is not divisible by 60.But 60 is divisible by 3,5,15,30
So answer is III
Answer : B
The answer is: B | B |
mathematics | In a consumer survey, 88% of those surveyed liked at least one of three products: 1, 2, and 3. 55% of those asked liked product 1, 40% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three ... | [
"15",
"20",
"25",
"30",
"35"
] | 55 + 40 + 20 = 115
This number includes some people counted twice and some people counted three times.
115 - 88 = 27, and this number represents people counted twice or three times.
7% of the people are counted two extra times.
The percentage of people counted one extra time is 27 - 7(2) = 13.
The percentage of people ... | B |
mathematics | By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage? | [
"33 1/3%",
"68 1/3%",
"28 1/3%",
"18 1/3%",
"11 1/3%"
] | Explanation:
Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer: A
The answer is: A | A |
mathematics | If (c - a)/(c - b) = 3, then (5b - 5a)/(c - a) = | [
"0.5",
"1",
"1.5",
"3.33",
"2.5"
] | Let's say c=7, b=5, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 3.33
Answer D (hopefully )))
The answer is: D | D |
mathematics | If X = the product of five distinct prime numbers, how many factors does X have besides 1 and itself? | [
"24",
"30",
"36",
"42",
"48"
] | Since X has 5 distinct prime factors, X has a total of 2^5 = 32 factors.
Besides 1 and itself, X has 30 factors.
The answer is B.
The answer is: B | B |
mathematics | The variable x is inversely proportional to the square of the variable y. If y is divided by 6a, then x is multiplied by which of the following? | [
"1/36a",
"1/36a^2",
"1/6a",
"36a",
"36a^2"
] | initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/6a I got answer E)
The answer is: E | E |
mathematics | The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person | [
"11",
"66",
"28",
"30",
"99"
] | Let's take the present age of the elder person = x
and the present age of the younger person = x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30
Answer: D
The answer is: D | D |
mathematics | A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat? | [
"299m",
"287m",
"279m",
"100m",
"277m"
] | A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
The answer is: D | D |
mathematics | Given that 268x74= 19832, find the value of 2.68x.74. | [
"1.9832",
"1.0025",
"1.5693",
"1.0266",
"None"
] | Solution
Sum of decimals places =(2+2)
= 4.
Therefore, = 2.68×.74
= 1.9832
Answer A
The answer is: A | A |
mathematics | A local bank that has 11 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers ... | [
"3",
"11 ( 2 integers 4 codes)",
"5",
"6",
"7"
] | Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Total = 16 Codes. Enough. Answer: B
4 integers create 11 codes.
The answer is: B | B |
mathematics | 8^100 is divisible by 17. Find the remainder? | [
"10",
"12",
"16",
"21",
"26"
] | This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 =... | C |
mathematics | A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: | [
"45 km/hr",
"50 km/hr",
"77 km/hr",
"55 km/hr",
"56 km/hr"
] | Speed of the train relative to man = (200/10) m/sec = 20 m/sec. [20 * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72==> x = 77 km/hr.
ANSWER: C
The answer is: C | C |
mathematics | Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -. | [
"5/12",
"4/13",
"5/17",
"3/12",
"8/9"
] | Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
ANSWER A
The answer is: A | A |
mathematics | The area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the diameter of Circle O? | [
"4/π",
"4",
"8",
"10",
"6"
] | area+diameter-2*circumference=8
pi*r^2+2r=8+2*2pi*r
isolate r and get r(pi*r+2)=8+4pi*r
r=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)
r=4
Diameter = 2r = 8
C
The answer is: C | C |
mathematics | John and Lewis leave Chennai for Bangalore simultaneously at 6 P.M in the evening driving in two cars at speeds of 50 mph and 70 mph respectively. As soon as Lewis reaches Bangalore he returns back to Chennai along the same route and meets John on the way back. If the distance between the two cities is 140 miles, how f... | [
"110 miles",
"130 miles",
"100 miles",
"125 miles",
"25 mlies"
] | Time taken by Lewis to reach Bangalore = 140/70 = 2 hours
In 2 hours, John travels 50*2 = 100 miles
So distance at which they meet should be greater than 100 miles.
Only C satisfies.
Answer is C.
The answer is: C | C |
mathematics | in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 8 people all together .how many people can sit in a bus? | [
"52",
"49",
"95",
"88",
"89"
] | Right Side =15 seat
Left Side =15-3 (3 few seat in right side)= 12 seat
Total= 15+12= 27
People can seat in 27 seat= 27*3=81
People can seat in Last Seat = 8
Total People can seat= 81+8=89
ANSWER:E
The answer is: E | E |
mathematics | Solve below question 2x + 1 = -17 | [
"7",
"-9",
"10",
"-1",
"2"
] | 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
The answer is: B | B |
mathematics | 1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 ÷ 1)}] = ? | [
"5/3",
"4/3",
"2/3",
"1/3",
"1/5"
] | Explanation:
1 ÷ [1 + 1 ÷ {1 + 1 ÷ (1 ÷ 1)}]
= 1 ÷ [1 + 1 ÷ {1 + 1 ÷ 1}]
= 1 ÷ [1 + 1 ÷ {1 + 1}]
= 1 ÷ [1 + 1 ÷ 2]
= 1 ÷ [1 + (1/2)] = 1 ÷ 3/2 = 1 × 3/2 = 1 × 2/3 = 2/3
Answer: Option C
The answer is: C | C |
mathematics | A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 4 different offices? | [
"52",
"64",
"32",
"11",
"12"
] | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.
Answer: B.
The answer is: B | B |
mathematics | The average price of three items of furniture is Rs. 12000. If their prices are in the ratio 3:5:7, the price of the cheapest item is? | [
"2379",
"2889",
"9288",
"7200",
"28311"
] | Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (12000 * 3) or x = 2400.
Cost of cheapest item = 3x = Rs. 7200.
Answer: D
The answer is: D | D |
mathematics | A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? | [
"27",
"23",
"20",
"28",
"12"
] | M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
The answer is: C | C |
mathematics | If the difference between compound interest (interest compounded yearly) and simple interest on a certain sum at the rate 20% p.a. after 3 years is Rs.1280 then what is the principal? | [
"7900",
"8,000",
"10,000",
"8,300",
"9,300"
] | let p is the principal,so p([120/100]^3-1)-p*20/100*3=1280
p[728/1000-3/5]=1280
p=1280*5*1000/728*5-3000=10000
ANSWER:C
The answer is: C | C |
mathematics | What number has a 5:1 ratio to the number 10? | [
"42",
"50",
"55",
"62",
"65"
] | Explanation:
5:1 = x: 10
x = 50
ANSWER IS B
The answer is: B | B |
mathematics | If the average (arithmetic mean) of 5 positive temperatures is y degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be: | [
"6y",
"4y",
"5y/3",
"3y/2",
"3y/5"
] | The sum of three greatest should be more than sum of two lowest.
The total sum is; 5y
A. 6y; 6y is more than 5y. Not possible.
B. 4y; 5y-4y=y(Possible)
C. 5y/3; 10y/3; 10y/3 > 5y/3. Not possible
D. 3y/2; 7y/2; 7y/2 > 3y/2. Not possible
E. 3y/5; 22y/5; 22y/5 > 3y/5. Not possible.
Ans:B
The answer is: B | B |
mathematics | In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number? | [
"867",
"864",
"385",
"946",
"549"
] | B
864
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 18 => b = 6
So a = 8 and b = 4
Hence the three digit number is: 864
The answer is: B | B |
mathematics | The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table? | [
"2882",
"2277",
"2697",
"6725",
"2681"
] | CP = SP * (100/(100 + profit%))
= 8339(100/124)
= Rs. 6725.
Answer:D
The answer is: D | D |
mathematics | Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal | [
"8",
"9",
"10",
"11",
"12"
] | Since (ii) holds for every real number x, it will remain valid if we replace x with
-x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 14 = f(x)+f(1-x) = f(x)+3+f(-x)
so that f(x) + f(-x) = 14-3 = 11. (Observe that f(x) = 3x + 4 satisfies the conditions
in the problem.)
correct answer D
The answer is: D | D |
mathematics | For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation? | [
"(-3)^2",
"2",
"3",
"4",
"5"
] | Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4
Step 2, For each number: subtract the Mean and square the result =
(1-4)^2=(-3)^2
(2-4)^2=(-2)^2
(3-4)^2 =(-1)^2
(4-4)^2=(.0)^2
(5-4)^2=(1)^2
Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.
Hence A
The ... | A |
mathematics | Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 110kmph, find the rate at which the train B runs. | [
"40",
"165",
"120",
"80",
"100"
] | If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their spee... | B |
mathematics | If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 110 kilograms. What is the student's present weight in kilograms? | [
"71",
"72",
"73",
"74",
"75"
] | Let x be the weight of the sister.
Then the student's weight is 2x+5.
x + (2x+5) = 110
3x = 105
x = 35 kg
Then the student's weight is 75 kg.
The answer is E.
The answer is: E | E |
mathematics | In an election, candidate Douglas won 60 percent of the total vote in Counties X and Y. He won 72 percent of the vote in County X. If the ratio of people who voted in County X to County Y is 2: 1, what percent of the vote did candidate Douglas win in County Y? | [
"18%",
"30%",
"36%",
"48%",
"54%"
] | given voters in ratio 2:1
let X has 200 votersY has 100 voters
for X 72% voted means 72*200=144 votes
combined for XY has 300 voters and voted 60% so total votes =180
balance votes=180-144=36
As Y has 100 voters so 36 votes means 36% of votes required
Ans C
The answer is: C | C |
mathematics | A sum of Rs 1162.00 is divided among A, B and C such that 4 times A’s share is equal to 5 times B’s share and 7 times C’s share. What is the share of C? | [
"280",
"285",
"270",
"295",
"255"
] | given 4x=5y=7z
so x:y=5:4
y:z=7:5
x:y:z=35:28:20
c share=20*1162/(35+28+20) =280.
ANSWER:A
The answer is: A | A |
mathematics | In how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons? | [
"A)60",
"B)70",
"C)1",
"D)5",
"E)2"
] | 5p1 = 5
Option 'D'
The answer is: D | D |
mathematics | A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black? | [
"35/145",
"36/145",
"36/140",
"36/141",
"31/142"
] | The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
The answer is: B | B |
mathematics | A certain bag contains 100 balls — 50 white, 30 green, 10 yellow, 7 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? | [
"0.9",
"0.75",
"0.6",
"0.8",
"0.5"
] | According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 10)/100 = 90/100 = 0.9.
Answer is A
The answer is: A | A |
mathematics | A tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? | [
"56 hours",
"28 hours",
"55 hours",
"66 hours",
"47 hours"
] | 1/A + 1/B + 1/C = 1/16 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/16
=> (1 + 2 + 4)/2B = 1/16
=> 2B/7 = 16
=> B = 56 hours.
Answer: A
The answer is: A | A |
mathematics | Ravi and Kavi start a business by investing ₹ 3000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. | [
"2 : 24",
"5 : 24",
"7 : 24",
"1 : 24",
"3 : 24"
] | Ratio of profit = Ratio of investments
= 3000 : 72000 = 1 : 24
Answer : D
The answer is: D | D |
mathematics | Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, 63, 63, ? ... What number should fill the blank? | [
"51",
"39",
"75",
"15",
"None"
] | Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option C
The answer is: C | C |
mathematics | How many times the keys of a writer have to be pressed in order to write first 200 counting no's? | [
"452",
"462",
"472",
"482",
"492"
] | 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 200 = 101 * 3 = 303
-----------
492
E
The answer is: E | E |
mathematics | If a - b = 3 and a(power 2) + b(power 2) = 39, find the value of ab. | [
"15",
"8",
"4",
"10",
"3"
] | 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 39 - 9 = 30
ab = 15.
Answer is A.
The answer is: A | A |
mathematics | The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? | [
"None of these",
"11 years",
"10 years",
"8 years",
"4 years"
] | Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
Age of the youngest child = x = 4 years.
Answer: E
The answer is: E | E |
mathematics | In 1982 and 1983, Company B’s operating expenses were $11.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ? | [
"3%",
"16 2/3%",
"25%",
"4 1/3%",
"60%"
] | Profit in 1982 = 15.6 - 11 = 4.6 million $
Profit in 1983 = 18.8 - 14 = 4.8 million $
Percentage increase in profit = (4.8-4.6)/4.6 * 100 %
= 4 1/3%
Answer D
The answer is: D | D |
mathematics | A person took some amount with some interest for 3 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took? | [
"s.5500/-",
"s.6000/-",
"s.4000/-",
"s.7000/-",
"s.8000/-"
] | Explanation:
3 years = Rs.120/-
year = 120/3
Rate of Interest = 1%
100/1% × 120/3 = Rs.4000/-
P = Rs.4000/-
Answer: Option C
The answer is: C | C |
mathematics | When a 160 meters long rod is cut down into small pieces of length 3.2 meters each. Then how many pieces are available ? | [
"52",
"50",
"62",
"67",
"69"
] | Answer
No. of pieces = Total length / Length of each piece
= 160/3.2
= 50
Option: B
The answer is: B | B |
mathematics | One hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 1 miles per hour and Bobâs was 2 miles per hour, how many miles had Bob walked when they met? | [
"19",
"20",
"22",
"21",
"19.5"
] | Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked (t + 1) miles. These distances must sum to 31 miles, so 2t + (t + 1) = 31, which may be solved for t as follows
2t + (t + 1) = 31
2t + t + 1 = 31
3t = 30
T = 10 (hours)
Therefore, Bo... | B |
mathematics | For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[10] equivalent to? | [
"[25]",
"[135]",
"[30]",
"[90]",
"[45]"
] | [9]*[10] = 27*5 = 135 = 3*45 = [45]
The answer is E.
The answer is: E | E |
mathematics | A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 7 feet and a height of ... | [
"0.07",
"0.049",
"0.7",
"0.49",
"4.9"
] | The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.
pi*49*10 = pi*h*100*100 (h is distance that the oil level dropped)
h = 490/10,000 = 49/1000 = 0.049 ft
The answer is B.
The answer is: B | B |
mathematics | The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. | [
"22",
"27",
"25",
"99",
"21"
] | Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25.Answer: C
The answer is: C | C |
mathematics | What is the value of (P + Q)/(P - Q) if P/Q is 7? | [
"4/3",
"2/3",
"2/6",
"7/8",
"8/7"
] | (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (7 + 1)/(7 - 1)
= 8/6
= 4/3
ANSWER:A
The answer is: A | A |
mathematics | Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly? | [
"Rs.1652",
"Rs.2569",
"Rs.4587",
"Rs.479",
"Rs.2522"
] | Explanation:
A = 1600(21/20)3 = Rs.2522
Answer:E
The answer is: E | E |
mathematics | Ajay had purchased a second hand scooter for 18,000 and spent Rs.1800 for repairs. After one year he wanted to sell the scooter. At what price should he sell it to gain 100/9%, if 100/11% is to be deducted at the end of every year on account of deprecation? | [
"Rs.18000",
"Rs.19800",
"Rs.20000",
"Rs.22500",
"Rs.23500"
] | Cost Price =Rs.18000.
Cost on Reparing = Rs. 1800.
So, Total cost = 18000 +1800 = 19800.
Depreciation = 100/11% = 9.09%.
Gain = 100/9% = 11.11%.
After depreciation, the cost price would be = 19800 - 9.09% of 19800 = Rs. 18000
SP to gain 11.11% = 18000 + 11.11% of 18000 = 18000 + 1999.8 = Rs. 20,000.
ANSWER : C
The answ... | C |
mathematics | A boatman goes 3 km against the current of the stream in 3 hour and goes 1 km along the current in 30 minutes. How long will it take to go 3 km in stationary water? | [
"5 hours",
"4 hours",
"3 hours",
"2 hours",
"1 hours"
] | Explanation:
Speed upstream = 3/3 = 1 km/hr
Speed downstream = 1/(30/60)= 2 km/hr
Speed in still water = 1/2(2+1)= 3/2 km/hr
Time taken to travel 3 km in still water = 3/(3/2) = 6/3 = 2 hours
Answer: Option D
The answer is: D | D |
mathematics | circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2? | [
"44",
"55",
"66",
"78",
"49"
] | π (152 - 132) = 176
176 * 1/4 = Rs.44.Answer: A
The answer is: A | A |
mathematics | A certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 ½ years. Find the sum and rate of interests. | [
"13%",
"12%",
"25%",
"18%",
"52%"
] | S.I. for 1 ½ years = Rs.(1164-1008) = Rs.156.
S.l. for 2 years = Rs.(156*(2/3)*2)=Rs.208
Principal = Rs. (1008 - 208) = Rs. 800.
Now, P = 800, T = 2 and S.l. = 208.
Rate =(100* 208)/(800*2)% = 13%
Answer is A.
The answer is: A | A |
mathematics | In an xy-coordinate plane, a line is defined by y = kx + 1. If (3, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ? | [
"1/2",
"1",
"3/2",
"2/3",
"5/2"
] | b=3k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=3k+1
k=2/3
Answer : D
The answer is: D | D |
mathematics | there are five red shoe and 4 green. if one draw randomly a shoe then what is the probability of getting red | [
"1/9",
"2/9",
"3/9",
"4/9",
"5/9"
] | prob of getting red shoe = 5/9
ANSWER:E
The answer is: E | E |
mathematics | The difference between the length and breadth of a rectangle is 42 m. If its perimeter is 280 m, then its area is: | [
"1520 m2",
"4250 m2",
"4459 m2",
"4092 m2",
"None"
] | EXPLANATION
We have: (l – b) = 42 and 2(l + b) = 280 or (l + b) = 140.
Solving the two equations, we get: l = 91 and b = 49.
Area = (l x b) = (91x 49) m2 = 4459 m2.
Answer C
The answer is: C | C |
mathematics | A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls? | [
"22",
"60",
"77",
"26",
"23"
] | Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer: B
The answer is: B | B |
mathematics | A tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride? | [
"5.12%",
"6.12%",
"7.12%",
"8.12%",
"9.12%"
] | We start with 6,500 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 6,500 = 325 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,000 gallons of solution. From here we can determine what percent of the 4,000 gallon solution is sodium chlori... | D |
mathematics | In an interview , the probability of appointing Husband is 1/5 while that of wife is
¼.find probability that only one of them get selected in interview. | [
"3/20",
"4/20",
"5/20",
"6/20",
"7/20"
] | p(H)=1/5
p(w)=1/4
P(H bar)=1-1/5=4/5
p(w bar)=1-1/4=3/4
Required probability=p(H)*p(w bar)+p(w)*p(H bar)
1/5*3/4+1/4*4/5
7/20
ANSWER:E
The answer is: E | E |
mathematics | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? | [
"600",
"887",
"256",
"654",
"712"
] | Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer: A
The answer is: A | A |
mathematics | Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission? | [
"8",
"2",
"6",
"0",
"12"
] | If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : D
The answer is: D | D |
mathematics | A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is? | [
"25/42",
"25/49",
"25/46",
"25/48",
"35/49"
] | Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer:A
The answer is: A | A |
mathematics | A semicircle has a radius of 11. What is the approximate perimeter of the semicircle? | [
"45",
"51",
"57",
"63",
"69"
] | The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*11 + 2*11 which is about 57.
The answer is C.
The answer is: C | C |
mathematics | Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares Bobby had... | [
"a profit of 10",
"a profit of 8",
"a loss of 8",
"a loss of 10",
"neither a profit nor a loss"
] | Cost of the first stock: 96/1.2=80, so profit from it 96-80=16
Cost of the second stock: 96/0.8=120, so loss from it 96-120=-24
Overall loss 16-24=-8
Answer: C.
The answer is: C | C |
mathematics | The average of first five multiples of 3 is? | [
"2",
"9",
"8",
"6",
"3"
] | Average = 3(1 + 2 + 3 + 4 + 5)/5
= 45/5
= 9.
Answer:B
The answer is: B | B |
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