subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | The moon revolves around the earth at a speed of approximately 1.05 kilometers per second. This approximate speed is how many kilometers per hour? | [
"60",
"61.2",
"62.5",
"3,780",
"3,672"
] | moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 1.05*3600=3780kilometers per hour.
Option D is correct
The answer is: D | D |
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 | [
"15",
"20",
"25",
"30",
"35"
] | Explanation:
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: Option D
The answer is: D | D |
mathematics | 80 is what percent of 40?
. | [
"0.2%",
"2%",
"200%",
"20%",
"500%"
] | 80= x*40/100
x = 200%
Ans; 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. 250 per month. What is his monthly salary? | [
"5000",
"2999",
"2878",
"6250",
"2771"
] | Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 250 => 6250
Answer: D
The answer is: D | D |
mathematics | A semicircle has a radius of 9. What is the approximate perimeter of the semicircle? | [
"16",
"25",
"33",
"46",
"58"
] | 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*9 + 2*9 which is about 46.
The answer is D.
The answer is: D | D |
mathematics | Two trains of equal length, running with the speeds of 60 and 40 kmph, take 36 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? | [
"10 sec",
"16 sec",
"19 sec",
"7.2 sec",
"13 sec"
] | RS = 60 -40 = 20 * 5/18 = 100/18
T = 36
D = 36 * 100/18 = 200
RS = 60 + 40 = 100 * 5/18
T = 200 * 18/500 = 7.2 sec
Answer: D
The answer is: D | D |
mathematics | A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? | [
"24",
"21",
"20",
"22",
"25"
] | 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer: B
The answer is: B | B |
mathematics | The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher | [
"49 Years",
"51 Years",
"53 Years",
"54 Years",
"55 Years"
] | Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
A
The answer is: A | A |
mathematics | January 1, 2004 was a Thursday, what day of the week lies on January 1 2005. | [
"Saturday",
"Monday",
"Saturday",
"Tuesday",
"Wednesday"
] | Explanation:
Given that January 1, 2004 was Thursday.
Odd days in 2004 = 2 (because 2004 is a leap year)
(Also note that we have taken the complete year 2004 because we need to find out the odd days from 01-Jan-2004 to 31-Dec-2004, that is the whole year 2004)
Hence January 1, 2005 = (Thursday + 2 odd days) = Saturday
... | C |
mathematics | In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of | [
"3100",
"6220",
"6210",
"6240",
"6670"
] | Market Value = Rs. 96.
Required Income = Rs. 650.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96
To obtain Rs.650, investment = 96/10×650=6240
Answer is D.
The answer is: D | D |
mathematics | A boy has 9 trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? | [
"100",
"140",
"104",
"135",
"125"
] | The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 15 = 135 ways.
D
The answer is: D | D |
mathematics | For dinner at a restaurant, there are x + 1 choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal? | [
"x + y + z + 1",
"xyz + xz",
"xyz+xz+yz+z",
"xyz + 1",
"xyz + 1/2"
] | x +1 appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = (x+1)C1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = (x+1)(y+1)z = (yz+z)(x+1)=xyz+xz+yz+z
Correct Option: C
The answer is: C | C |
mathematics | A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability K that the sum of the three numbers on the balls selected from the box will be odd? | [
"1/4",
"3/8",
"1/2",
"5/8",
"3/4"
] | The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered ... | C |
mathematics | Find the third proportional to 3 and 9? | [
"10",
"12",
"27",
"19",
"20"
] | Formula = Third proportional = (b × b)/a
A = 3 and B = 9
(9 x 9)/ 3 = 81/3 = 27
C
The answer is: C | C |
mathematics | On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade w... | [
"$015",
"$0.20",
"$0.30",
"$0.32",
"$0.45"
] | On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to... | D |
mathematics | In order to obtain an income of Rs. 900 from 20% stock at Rs. 102, one must make an investment of | [
"Rs.6000",
"Rs.4590",
"Rs.4560",
"Rs.4500",
"Rs.4570"
] | Explanation :
Market Value = Rs. 102.
Required Income = Rs. 900.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.20(ie,20% of the face value 100), investment = Rs.102
To obtain Rs.900, investment = 102/20×900=Rs.4590
Answer : Option B
The answer is: B | B |
mathematics | If p and q are prime numbers, how many divisors does the product p^3 * q^6 have? | [
"9",
"12",
"18",
"28",
"36"
] | Lets take an example: find the number of factors of 100
try to represent 100 in least possible prime numbers
100= 2^2 * 5^2=p^a*q^b
no of factors is given by the formula (a+1)* (b+1)=(2+1)(2+1)=9
similarly find the number of factors of p^3 * q^6--->a=3,b=6
(3+1)(6+1)=28 Ans D.
The answer is: D | D |
mathematics | A man divides $6800 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive? | [
"A)$200",
"B)$1000",
"C)$800",
"D)$1200",
"E)$400"
] | Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=6800
16X+16X+2X=8600
34X=6800, X=200.
Daughter receives four times of nephew so 4 * 200 = 800.
So Each Daughter receives $800. answer is option C) $800.
The answer is: C | C |
mathematics | 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim? | [
"93",
"77",
"68",
"90",
"62"
] | Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (60 + 120)/2 = 90.... | D |
mathematics | Andrew has a certain number of coins in his pocket. He has three times as many dimes as quarters and six times as many nickels as dimes. A nickel is worth $0.05, a dime is worth $0.10 and a quarter is worth $0.25. If he has a total of $10.15, then which of the following represents the number of dimes in Nickles’s pocke... | [
"9",
"10",
"18",
"112",
"116"
] | E.
Let number of quarters be q. Therefore , dimes are 3q and nickels are 18q.
Total value = 18q(.05) + 3q(0.1) + .25q =1.45q
Given total value = 10.15
therefore, 1.45q=10.15 or q=7
Number of dimes = 18q or 116
Answer : E
The answer is: E | E |
mathematics | Line Q has the equation 5y – 3x = 30. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.) | [
"22",
"33",
"36",
"41",
"58"
] | 5y - 3x = 30 and so y = 3x/5 + 6
When x = 0, then y = 6.
When y = 0, then x = -10
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-10, 0), 0 = -5(-10)/3 + c
The y-intercept is c = -50/3 < -16.
Thus the perpendicular line S can have y-intercepts from -16 up to 5.
The number of possible lines is 16 +... | A |
mathematics | In a cricket match, five batsmen A, B, C, D and E scored an average of 36 runs. D Scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored 107 between them. How many runs did E score ? | [
"62",
"45",
"28",
"20",
"25"
] | Explanation:
Total runs scored = (36 x 5) = 180.
Let the runs scored by E be x.
Then, runs scored by D = x + 5; runs scored by A = x + 8;
runs scored by B = x + x + 5 = 2x + 5;
runs scored by C = (107 - B) = 107 - (2x + 5) = 102 - 2x.
So, total runs = (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 3x + 120.
Therefore ... | D |
mathematics | A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ? | [
"3 hrs",
"7 hrs",
"9 hrs",
"2 hrs",
"6 hrs"
] | Explanation:
Speed in downstream = 96/8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12 – 4 = 8 kmph
Speed in upstream = 8 – 4 = 4 kmph
Time taken to cover 8 km upstream = 8/4 = 2 hours.
Answer: D
The answer is: D | D |
mathematics | If two students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then three rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated? | [
"0",
"3",
"4",
"5",
"9"
] | Let there be a rows.
Then 2a + 6 = 6(a-3) [equating the number of students]
=> a= 6
and total number of students = 18
Therefore 3 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (B)
The answer is: B | B |
mathematics | Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L | [
"1/3.",
"1/2.",
"2.",
"3.",
"6."
] | Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 21 and L be 7, 21- 7= (21 + 7 )/2
D
The answer is: D | D |
mathematics | If b is an integer greater than 6, which of the following must be divisible by 3? | [
"b (b+3) (b-5)",
"b (b+2) (b-1)",
"b (b+1) (b-4)",
"b (b+4) (b-2)",
"b (b+5) (b-6)"
] | anything in the form of (b-1) (b) (b+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
b (b+1) (b-4) = b (b+1) ((b-1)-3) is equivalant to (b-1) (b) (b+1)
b (b+2) (b-1) is equivalant to (b+1) missing.
b (b+3) (b-5) is equivalant to (b-1) missing and b repeating.
b (b+4) (b-2... | C |
mathematics | If a and b are positive integers of Y such that a/b=2.86, which of the following must be a divisor of a? | [
"10",
"B.13",
"18",
"26",
"50"
] | The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we ha... | B |
mathematics | Two trains of length 90 m and 100 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 71 kmph and 89 kmph. After how much time will the trains meet? | [
"47/10",
"46/10",
"45/10",
"42/10",
"43/10"
] | They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (71 + 89)*5/18 = 44.4mps.
The time required = d/s = 200/44.4= 45/10 sec.
Answer:C
The answer is: C | C |
mathematics | if f(f(X))=81. then. value of x=?
when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0 | [
"2",
"3",
"4",
"5",
"6"
] | f(X=0) = 0
f(X=1) = 2*1-1+f(1-1)
= 2-1+0
= 1
f(X=2) = 2*2-1+f(2-1)
= 4-1+1
= 4
f(X=3) = 2*3-1+f(3-1)
= 6-1+4
= 9
===>f(X=n) = n^2
f(f(X)) = 81
X = sqrt(sqrt(81)) = 3
ANSWER:B
The answer is: B | B |
mathematics | 50% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim? | [
"70",
"97",
"84",
"90",
"76"
] | Given, 50% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 50% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/50 =48
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (48 + 120)/2 = 84.
... | C |
mathematics | The positive number a is q percent greater than the positive number b, which is l percent less than a itself. If a is increased by l percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a | [
"I only",
"II only",
"III only",
"I and II only",
"II and III only"
] | Let q = 10% then l = 100/11 %
let b = 100 then a = 110
after increasing a by l and decreasing b yq we get c= 108
therefore c<a
C it is answer
The answer is: C | C |
mathematics | If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day? | [
"100",
"102",
"104",
"106",
"108"
] | Using the chain rule,
M1 x T1 = M2 x T2
Thus, (34 x 8 x 9) / 2/5 = (M2 x 6 x 9) / 3/5
M2 = 68.
Therefore, required number of men = (68 + 34) = 102
ANSWER:B
The answer is: B | B |
mathematics | 20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability. | [
"1/19",
"2/29",
"3/29",
"4/29",
"5/29"
] | 20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person
(s1 p s2) be 1 set
then 20-3 persons => 17 persons + 1 set= 18
18 can be arranged in 17! ways bcz it is circular permutuation
the 2 sis can be arranged in 2! ways
and the p place can be filled in 18 ways
and the t... | B |
mathematics | If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x? | [
"9,827",
"10,816",
"11,433",
"12,908",
"13,482"
] | The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is B.
The answer is: B | B |
mathematics | When running a mile during a recent track meet, Nuria was initially credited with a final time of 4 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise cor... | [
"4 minutes, 17.6 seconds",
"4 minutes, 21.8 seconds",
"4 minutes, 43.56 seconds",
"5 minutes, 10.4 seconds",
"4 minutes, 44.44 seconds"
] | One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 4 minutes, 44 seconds. The only number is 5 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 4 minutes, 44 seconds, it means it passes 5 minute.
Answer: D
The answer... | D |
mathematics | The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 6. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A? | [
"8",
"9",
"10",
"11",
"12"
] | Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.
so ans can either be 8 0r 12.
With 8 as answer - no of girls = 8
With 12 as answer - no of girls = 12
Now Class A has one more boy and two more girls than class B and als... | D |
mathematics | A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 7 brown mice in the experiment, how many mice in total are in the experiment? | [
"39",
"33",
"26",
"21",
"10"
] | Let total number of mice = M
Number of white mice = 2/3 M
Number of brown mice = 1/3 M = 7
=> M = 21
Answer D
The answer is: D | D |
mathematics | A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start? | [
"2",
"5",
"7",
"5",
"8"
] | Explanation:
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: Option A
The answer is: A | A |
mathematics | The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is | [
"45",
"50",
"55",
"60",
"65"
] | Option A
The answer is: A | A |
mathematics | A carton contains 25 bulbs, 8 of which are defective. What is the probability that if a sample of 4 bulbs is chosen, exactly 2 of them will be defective ? | [
"(8/25) x (7/24) x (17/23) x (16/22)",
"(4C2) x (8/25) x (7/24) x (17/23) x (16/22)",
"(8/26) x (8/24) x (17/33) x (16/22)",
"None of these",
"Cannot be determined"
] | Explanation :
The probability that exactly two bulbs are defective and exactly two are not defective will be given by
(4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Answer : B
The answer is: B | B |
mathematics | A and B are two circles. The radius of A is four times as large as the diameter of B. What is the ratio between the areas of the circles? | [
"1:8.",
"1:2.",
"1:24.",
"1:64.",
"1:6."
] | Given : The radius of A is 4 times as large as the diameter of B. => R(a) = 4*D(b) = 4*2*R(b) = 8R(b). The radius are in ratio of 1:8 thus the area will be in the ratio of square of radius. 1:64. Hence D.
The answer is: D | D |
mathematics | If 4 men can colour 48 m long cloth in 2 days, then 8 men can colour 36 m long cloth in | [
"0.75 day",
"2 days",
"1.2 days",
"4 days",
"5 days"
] | The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 8 = 0.75 day.
A
The answer is: A | A |
mathematics | A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? | [
"8:8",
"9:8",
"9:9",
"9:5",
"9:1"
] | (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
The answer is: B | B |
mathematics | A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000? | [
"1687",
"1478",
"1480",
"14000",
"1500"
] | 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
The answer is: D | D |
mathematics | A number of 47 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes? | [
"10",
"12",
"15",
"16",
"17"
] | To maximize # of boxes we should minimize marbles per box: 14*3+1*5=47 --> 14+1=15.
Answer: C.
The answer is: C | C |
mathematics | A man has some hens and cows. If the number of heads be 46 and the number of feet equals 140, then the number of hens will be: | [
"22",
"23",
"24",
"26",
"28"
] | let hens be x and cows be y
now,
feet: x*2+y*4=140
heads: x*1+y*1=46
implies, 2x+4y=140 and x+y=46
solving these two equations, we get x=22 and y=24
Therefore, hens are 22.
ANSWER:A
The answer is: A | A |
mathematics | What is the 28th digit to the right of the decimal point in the decimal form of 4/11? | [
"3",
"4",
"5",
"6",
"7"
] | 4/11 = 0.363636...
The even numbered positions in the decimal expansion are all 6.
The answer is D.
The answer is: D | D |
mathematics | 60 boys can complete a work in 40 days.how many men need to complete twice the work in 20 days | [
"160",
"170",
"180",
"190",
"240"
] | one man can complete the work in 40*60=2400 days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*2400
M=240 workers
ANSWER:E
The answer is: E | E |
mathematics | It takes one machine to paint 1000 sq.m. surface in 24 minutes.Another machine does the same job in 40 seconds.How much time will it take if both machines are put on the same work? | [
"10.0 seconds",
"20.0 seconds",
"38.9 seconds",
"40.0 seconds",
"52.0 seconds"
] | By guess it is clear that the time taken will be less than 40 seconds and very near to it. Therefore, answer 38.9 seconds will be correct. Answer-C
The answer is: C | C |
mathematics | Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year 6 members of the club traveled to both England and France, no members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club ... | [
"52",
"71",
"67",
"73",
"79"
] | n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 26 + 26 + 32 - 6 - 11 - 0 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Ita... | C |
mathematics | Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent? | [
"25%",
"11 1/8%",
"11 9/9%",
"11 5/9%",
"11 1/5%"
] | 800 --- 200
100 --- ? => 25%
Answer:A
The answer is: A | A |
mathematics | How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320 | [
"4",
"5",
"6",
"7",
"8"
] | Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 6 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: C
The answer is: C | C |
mathematics | A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker? | [
"$50",
"$60",
"$70",
"$80",
"$90"
] | Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
correct answer is C)$70
The answer is: C | C |
mathematics | If the radius of a circle is decreased 30%, what happens to the area? | [
"51% decrease",
"20% decrease",
"36% decrease",
"40% decrease",
"50% decrease"
] | Area of Square = Pi* radius^2
New Radius = 0.7 * old radius
so new area = (0.7)^2 old area => 0.49 of old area => 49% old area
Ans : A
The answer is: A | A |
mathematics | If two sides of a triangle have lengths 1 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19 | [
"None",
"I only",
"II only",
"II and III only",
"I, II, and III"
] | The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(5-1) < {third side} < (5+1).
4 < {third side} < 6.
Perimeter = {third side} + 1 + 5 = {third side} + 6.
10 < {perimeter} < 12.
answer A
The answer is: A | A |
mathematics | If m=9^(x−1), then in terms of m, 3^(4x−2) must be which of the following? | [
"m/3",
"9m",
"9m^2",
"m^2/3",
"m^2/9"
] | 3(4x−2)=3^2(2x−1)=9(2x−1)=9∗9(2x−2)=9∗(9(x−1))2=9m
Answer: C.
The answer is: C | C |
mathematics | It takes 40 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers? | [
"16",
"18",
"20",
"21",
"24"
] | 40 printing presses can do 1/15 of the job each hour.
30 printing presses can do 3/4*1/15 = 1/20 of the job each hour.
The answer is C.
The answer is: C | C |
mathematics | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 12% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportion... | [
"43°",
"10°",
"18°",
"36°",
"52°"
] | Here all percentage when summed we need to get 100% . As per data 12+24+15+29+8 = 88%.
So remaining 12% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 12% will be 43 degrees..
IMO option A.
The answer is: A | A |
mathematics | Two out of ten employees are capable of doing a certain task. Sixty percent of the five employees, including the two who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable? | [
"43.33%",
"66.66%",
"13.33%",
"38.33%",
"23.33%"
] | Given 60% of 10 employees including 2 who are capable of doing task.
60% of 10 employeees
= 60/100 * 10
= 6 employees
===> 2 employees who are capable of doing the task and four employee who is not capable.
percentage of employees assigned who are not capable
= 4/6 * 100
= 66.66%
ANSWER:B
The answer is: B | B |
mathematics | A man ran 20 miles in 2 hours 2 minutes. What was the average speed of the man in miles per hour? | [
"9.72 miles / hour",
"9.73 miles / hour",
"9.75 miles / hour",
"9.78 miles / hour",
"9.79 miles / hour"
] | We first convert the time of 2 hours 2 minutes in minutes
2 hours 2 minutes = 2* 60 + 2 = 122 minutes
Average speed S is given by distance / time. Hence
S = 20 miles / 122 minutes = 0.163mile / minute
= 9.78 miles / hour
correct answer D
The answer is: D | D |
mathematics | which of the following could be the greatest common factor of positive integers 10 and 15 ? I) 5 II) 4 III) 2 | [
"II only",
"I only",
"III only",
"I,II only",
"I,III only"
] | 10=2*5
15=3*5
GCF =5
Answer : B
The answer is: B | B |
mathematics | A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | [
"10",
"20",
"30",
"40",
"50"
] | 1: 2/5 = 5: 2
2/7 * 70 = 20
ANSWER B
The answer is: B | B |
mathematics | In a room are five chairs to accommodate 3 people, one person to a chair. How many seating arrangements are possible? | [
"45",
"60",
"72",
"90",
"120"
] | I actually solved this problem by the following thoughts (derived from factorials):
First Person: 5 Chairs to choose
Second Person: 4 Chairs to choose
Third Person: 3 Chairs to choose
Then I simply multiplied this values and got the answer. Basically it’s 5! – 2!.=60
Answer: B.
The answer is: B | B |
mathematics | if the price of a book is first decreased by 30% and then increased by 20%, then the net change in the price will be : | [
"10",
"16",
"37",
"29",
"22"
] | Explanation:
Let the original price be Rs. 100.
Decreased by 30% = 70
Then increased 20% on Rs 70 = 70 + 14 = 84
Net change in price = 100 - 84 = 16
Answer : B
The answer is: B | B |
mathematics | In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of... | [
"6",
"8",
"9",
"10",
"12"
] | The question has a catch.. It would seem on the face of it it would be 3 x 3 x3 = 27 arrangements, but what it is asking is how many arrangements the family leaves with.. so that is going to be
Pick all 3 = 1 way
Pick all of a kind = 3 x 1 = 3 ways
Pick 2 of a kind = 3 x 1 x 2 = 6 ways
Total of 10
ANS:D
The answer is: ... | D |
mathematics | Find the percentage gain if a shop owner sells 39 mtr of fabric and gains Cost Price of 12 meters? | [
"20.5%",
"23.5%",
"21.5%",
"13.5%",
"32.5%"
] | Let cost of each metre be Rs. 100.
Therefore, cost price of 12m cloth = 12*100 =1200
cost price of 39m cloth = 39*100 = 3900
Since the trader made the CP of 12m from the sale of 39m therefore
Profit on sale of 39m = cost price of 12 m cloth = 1200
Selling price of 39m = 3900+1200 = 5100
Profit % = 23.5%
B
The answer is... | B |
mathematics | Stalin and Heather are 20 miles apart and walk towards each other along the same route. Stalin walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 20 minutes after Stalin, how far from the original destination has Heather walked when the two ... | [
"4 miles",
"6 miles",
"9 miles",
"10 miles",
"12 mile"
] | Original distance between S and H = 20 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+20/60 = t+2/6 hours.
Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/6)+5*t=20 ---> t= 8/11 hours. Thus H has traveled for 8/11 hours giving you a tota... | A |
mathematics | In business, A and C invested amounts in the ratio 4:2, whereas the ratio between amounts invested by A and B was 4:1, If Rs 20,000 was their profit, how much amount did A receive. | [
"13333",
"26758",
"45896",
"14639",
"89576"
] | Explanation:
A:B = 4:1 = 4:1
=> A:C = 4:2 = 4:2
=> A:B:C = 4:1:2
A share = (4/6)*20000
= 13333
Option A
The answer is: A | A |
mathematics | A goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds.What is the length of the goods train? | [
"230 m",
"250 m",
"260 m",
"270 m",
"240 m"
] | s=270+x/t
72*5/18=270+x/26
x=250
ANSWER:B
The answer is: B | B |
mathematics | The present ratio between the ages of Paul and Ben is 5:2. In 4 years time Paul will be 28. What is the present age of Ben? | [
"13",
"12",
"11",
"15",
"10"
] | Let the present ages of Paul and Ben be 5x years and 2x years respectively
4x+4 = 28
4x = 24
x = 6
Ben's age = 2x = 12 years
Answer is B
The answer is: B | B |
mathematics | A collection of books went on sale, and 2/3 of them were sold for $3.25 each. If none of the 20 remaining books were sold, what was the total amount received for the books that were sold? | [
"$130",
"$185",
"$175",
"$165",
"$155"
] | If 20 books constitute 1/3rd of the total, then 2/3rd of the total = 40 books
Amount received for sold books = 40 * 3.25 = $130
Answer :A
The answer is: A | A |
mathematics | How many such three letter passwords can exist? | [
"216",
"26C6 *3",
"(26C6)^3",
"((26C6)^3) *63",
"215"
] | 1st ring: 6 out of 26 alphabets can be selected in 26C6 ways.
And is for 2nd and 3rd ring.
Also, these 3 set of 6 letters can be arranged amongst themselves in 63 ways.
Hence, total number of 3 letter passwords = 26C6 * 26C6 *26C6 *63 ways.
ANSWER:D
The answer is: D | D |
mathematics | The workforce of Company X is 50% female. The company hired 20 additional male workers, and as a result, the percent of female workers dropped to 50%.How many employees did the company have after hiring the additional male workers? | [
"225",
"220",
"230",
"235",
"240"
] | let x be the total worker then 0.5x =female worker and 0.5x is male worker then 20 male worker added
05x/(0.5x +20) = 50/100 or 50x = 50*( 0.5x+100) = 25x+ 5000 or 25x = 5000 , x = 5000/25=200
total worker = 200 +20= 220
B
The answer is: B | B |
mathematics | In a class, 30 students pass in English and 20 students in Math, while some students among these pass in both. How many more students do only English as compared to those doing only Maths? | [
"10",
"15",
"20",
"25",
"Indeterminate"
] | Let us consider tht x student are tohse who passed in both English and Maths...
So first we remove x student from both of them
Therefore,
English = 30-x
Maths = 20-x
Now, Number of Students more in English = (30-x)-(20-x)
= 30-x-20+x
= 10
ANSWER:A
The answer is: A | A |
mathematics | What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/3 | [
"2/5",
"3/5",
"1/6",
"1",
"None of these"
] | Explanation:
2/3 = .66, 3/4 = .75, 4/5 = .8 and 5/3 = 1.66
So biggest is 5/3 and smallest is 2/3
Their difference is 5/3 - 2/3 = 3/3 = 1
Option D
The answer is: D | D |
mathematics | A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is? | [
"28",
"21",
"29",
"27",
"13"
] | 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer:B
The answer is: B | B |
mathematics | If 10 gallons of grape juice are added to 50 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice? | [
"14%",
"25%",
"28%",
"34%",
"50%"
] | OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
50 × 0.10 = 5 gallons of grape juice.
50 × 0.90 = 45 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 15 gallons of grape juice and 45 gallons of other components, and we will have a t... | B |
mathematics | A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds ... | [
"23:41",
"Either ;35:1",
"41:54",
"35:43",
"12:31"
] | Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
The answer is: B | B |
mathematics | In one hour, a boat goes 4 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is: | [
"3 km/hr",
"4 km/hr",
"5 km/hr",
"6 km/hr",
"8 km/hr"
] | Upstream relative speed is u + v=4km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =4+2
2u=6
Finally, u=3.
ANSWER : A
The answer is: A | A |
mathematics | A company, Chauncy Co., has an annual travel budget of $50,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-relate... | [
"Expenses will not go over the budget.",
"$500",
"$4,225",
"$5,725",
"$10,725"
] | annual travel budget of $50,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 50000-60725 = 1... | E |
mathematics | The average of first five multiples of 3 is | [
"3",
"6",
"9",
"12",
"15"
] | Solution
Average = 3(1+2+3+4+5) / 5
= 45 / 5.
= 9.
Answer C
The answer is: C | C |
mathematics | The present age of the father is 4years more than 4 times the age of his son. 4 years hence, father's age will be 20 years more than twice the age of the son. Find the present age of the father? | [
"25",
"56",
"45",
"36",
"44"
] | Let the son's present age be x years
father's present age = (4x+4)
4x+4+4 = 2(x+4)+10
4x+8 = 2x+18
x = 5
father's present age = 4x+4 = 4*10+4 = 44 years
Answer is E
The answer is: E | E |
mathematics | Bill’s compact disc player randomly plays a song, so that no song is repeated before the entire album is played. If Bill plays a disc with 17 songs, what are the chances that the third song he hears will be his favorite? | [
"1/17",
"1/12",
"1/11",
"3/14",
"1/3"
] | The player plays the songs on the album at random, so there are 17 songs that can be the third one played. Only 1 of these ways will result in Bill's favorite song being the third one played.
Total outcomes ==> 17
Total positive outcomes ==> 1
Correct answer is A) 1/17
The answer is: A | A |
mathematics | The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %? | [
"18%",
"19%",
"28%",
"38%",
"58%"
] | 1500 ---- 270
100 ---- ? => 18%
Answer: A
The answer is: A | A |
mathematics | Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share? | [
"Rs.130",
"Rs.145",
"Rs.154",
"Rs.160",
"Rs.164"
] | Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B
The answer is: B | B |
mathematics | The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, what is x? | [
"18",
"20",
"22",
"24",
"26"
] | Let the cost price = y
The cost price of 30 articles = 30y
The selling price of x articles = 1.25y*x
1.25y*x = 30y
x = 30 / 1.25 = 24
The answer is D.
The answer is: D | D |
mathematics | Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively. | [
"127",
"157",
"147",
"137",
"None of them"
] | Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032
_______
1651 ) 2032 ( 1 1651
1651_______
381 ) 1651 ( 4
1524_________
127 ) 381 ( 3
381
0
Required number = 127.
Answer is A.
The answer is: A | A |
mathematics | In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 28 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? | [
"70",
"245",
"150",
"200",
"350"
] | Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 28, so 0.14*{tota... | D |
mathematics | In a factory, there are 90% technicians and 10% non-technicians. If the 90% of the technicians and 10% of non-technicians are permanent employees, then the percentage of workers who are temporary is? | [
"62%",
"57%",
"52%",
"82%",
"42%"
] | Total = 100
T= 90 NT= 10
90*(10/100)=910*(90/100)=9
9 + 9 = 18=> 100 - 18 = 82%
Answer:D
The answer is: D | D |
mathematics | The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is ? | [
"6 years",
"7 years",
"8 years",
"9 years",
"None"
] | Answer
Let the age of youngest child be y.
so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12
⇒ 4y + 24= 48
∴ y = 6 years
Correct Option: A
The answer is: A | A |
mathematics | Priya covers journey from kavali to nellore by car at average speed of 80 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey? | [
"50Km/hr",
"53.33Km/hr",
"60Km/hr",
"66Km/hr",
"72km/hr"
] | Explanation:
Average speed = 2 xy/x+y
= 2*80*40/120
= 53.33 Km/hr
Answer: Option B
The answer is: B | B |
mathematics | A bat is bought for Rs.400 and sold at a gain of 20% find its selling price | [
"Rs.480/-",
"Rs.500/-",
"Rs.520/-",
"Rs.540/-",
"Rs.560/-"
] | 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A
The answer is: A | A |
mathematics | Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? | [
"5",
"9",
"11",
"13",
"15"
] | Explanation:
x + y = 15
2x – 3y = 5
x = 10 y = 5
A)
The answer is: A | A |
mathematics | Amit and Ananthu can do a work in 15 days and 25 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed? | [
"28 days",
"20 days",
"23 days",
"25 days",
"27 days"
] | Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/25
Ananthu can do work in = 4/5 *25 = 20/1 days
So total days = 25+3 = 28 days
ANSWER:A
The answer is: A | A |
mathematics | In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way ti... | [
"24",
"52",
"96",
"144",
"648"
] | Gold can be awarded in 4 ways, then silver can be awarded in 3 ways and Bronze in 2 ways.
therefore the total number of ways are : 4*3*2=24ways of awarding the medals and the same number of ways of forming the circle.
This is when there is no tie. And if there is tie, for example all three receive the GOLD or the Silve... | C |
mathematics | A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? | [
"10 days",
"20 days",
"5 days",
"25 days",
"15 days"
] | 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
ANSWER A
The answer is: A | A |
mathematics | A club with a total membership of 30 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees? | [
"5",
"7",
"8",
"10",
"12"
] | {total} = {M} + {S} + {R} - {Both} + {Neither}
We want to maximize Neither, so Both has to be as large as possible. The max of {Both} is 5 because {R} = 5.
30 = 8 + 12 + 5 - 5 + Neither
Neither = 10
ANSWER:D
The answer is: D | D |
mathematics | Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 130 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical coul... | [
"30 to 70",
"70 to 100",
"110 to 130",
"130 to 150",
"150 to 170"
] | lower point = Sum in each - total possible = 150+130- (200-30) = 280-170 =110...
higher point = entire 130 majoring in electrical major in mechanical too , so = 130..
range = 110 to 130
ANSWER:C
The answer is: C | C |
mathematics | A bus travel 5/7 of its speed covers 42 km in 1 hr 40 min48 sec. What is theactual speed of the bus ? | [
"20 km/hr",
"35 km/hr",
"40 km/hr",
"53 km/hr",
"55 km/hr"
] | Time = 1 hr 40 min 48 sec = 1hr +4060hr+483600hr=1+23+175=12675hrdistance = 42 kmspeed=distancetime=42(12675)=42×75126⇒57 of the actual speed = 42×75126⇒actual speed = 42×75126×75=42×1518=7×153=7×5=35 km/hr
B
The answer is: B | B |
mathematics | The average height of 35 boys in a class was calculated as 183cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).? | [
"178.27 cm",
"181.29 cm",
"978.29 cm",
"178.89 cm",
"176.29 cm"
] | Calculated average height of 35 boys = 183 cm.
Wrong total height of 35 boys = 183 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm - 106 cm)/35
= 183 cm - 60 /35 cm
= 183 cm - 1.71 cm = 181.29 cm.
Answer: B
The answer is: B | B |
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