subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 55km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is | [
"8.95km/hr",
"26.7km/hr",
"27.8km/hr",
"29.3km/hr",
"8.45km/hr"
] | average speed = (2*55*20)/55+20 km/hr
=29.3 km/hr
Answer (D)
The answer is: D | D |
mathematics | Two trains travelling in the same direction at 72 and 36 kmph completely pass off another in 1 minute. If the length of the first train is 250 m, what is the length of the second train? | [
"228",
"350",
"175",
"99",
"171"
] | RS = 72 – 36 = 36 * 5/18 = 10 mps
T = 60 sec
D = 10 * 60 = 600 m
250
--------
350 m
Answer: B
The answer is: B | B |
mathematics | When simplified, the product (1 – 1/2) (1 – 1/3) (1 – 1/4)…… (1 – 1/n) gives: | [
"1/n",
"2/n",
"2(n – 1)/n",
"2/n(n + 1)",
"3/n(n + 1)"
] | 1/2 x 2/3 x 3/4 x …..x (n – 1)/n
= 1/n
ANSWER:A
The answer is: A | A |
mathematics | Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? | [
"12, 9",
"12,7",
"7, 14",
"13,12",
"12,8"
] | x – y = 5
4x – 6y = 6
x = 12 y = 7
Answer B
The answer is: B | B |
mathematics | Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 3/5 of the students are female, what is ratio of male to female students on honor roll? | [
"5/9",
"8/15",
"23/30",
"43/60",
"53/90"
] | let the total students be 30
given 3/5 of the students are females = 18
then males = 2/5 = 12
5/6 of the females are on honor roll = 15
males on the honor roll = 2/3= 8
ratio of M:F students on honor roll = 8/15
B
The answer is: B | B |
mathematics | A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/4. What is the sum of the numerator and denominator of the original fraction? | [
"49",
"35",
"56",
"26",
"21"
] | x/y = 2/5 -> 1
(x+4)/2y = 1/4 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 8/5
=> 5x = 4x + 16
=> x = 16
=> y = 5/2 *16 = 40
so x + y = 56
The answer is C
The answer is: C | C |
mathematics | In order to obtain an income of Rs. 500 from 30% stock at Rs. 90, one must make an investment of | [
"Rs.1550",
"Rs.1430",
"Rs.1450",
"Rs.1400",
"Rs.1500"
] | Explanation :
Market Value = Rs. 90
Required Income = Rs. 500.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.30 (ie,30% of the face value 100), investment = Rs.90
To obtain Rs.15000, investment = 90/30×500=Rs.1500
Answer : Option E
The answer is: E | E |
mathematics | At what rate percent on simple interest will a sum of money double itself in 30 years? | [
"3 1/3%",
"8 1/3%",
"3 5/3%",
"5 1/3%",
"3 1/7%"
] | P = (P*30*R)/100
R = 3 1/3%
Answer: A
The answer is: A | A |
mathematics | A question paper has 2 parts, A & B, each containing 5 questions. If a student has to choose 3 from part A & 4 from part B, in how many ways can he choose the questions? | [
"50",
"100",
"152",
"150",
"55"
] | There 3 questions in part A out of which 4 question can be chosen as = 5C3.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 5C4.
Hence, total number of ways,
=5C3*5C4
=[5!/(2!3!)]*[5!/(4!*1)]
= {10}*{5*4!/(4!)}
= 10*5=50.
A
The answer is: A | A |
mathematics | A taxi company with a fleet of 50 taxis, plans to replace all their taxis with electric cars. Every year it retires 10 of their old taxis and buys 12 electric cars to replace them. How many years will it take to reduce their old taxi fleet to below 50% of their entire fleet if they started in 2003. | [
"3",
"4",
"1",
"2",
"10"
] | Total fleet--50
End of year 2003 -- (retires 10 and buys 12) total fleet--52(40 old 12 new).
End of year 2004 -- (retires 10 and buys 12) total fleet--54(30 old 24 new).
End of year 2005 -- (retires 10 and buys 12) total fleet--56(20 old 36 new).
Answer is A--after 3 years the company has a total of 56 taxis (20 old 36... | A |
mathematics | How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?
Options: | [
"ONE",
"TWO",
"THREE",
"FOUR",
"FIVE"
] | Numbers giving remainder 3 when divided by 10 = 13,23, 33,43, 53,63, 73,83, 93
Numbers giving remainder 3 when divided by 4 = Alternate numbers (coloured in red) = 4
Correct Option: D
The answer is: D | D |
mathematics | A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0019)? | [
"25",
"20",
"21",
"18.81",
"22"
] | You get 10^2 (100-1) (.0019)
we know 19/10000 = .0019
10^2 (99) * (19/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(19/100).
0.99*19 = 18.81
Answer : D
The answer is: D | D |
mathematics | How many pairs (n, n+1) have one or more prime factors common, where n is an integer and 2 ≤ n ≤9 ? | [
"0",
"1",
"2",
"3",
"4"
] | n and n+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
The answer is: A | A |
mathematics | There are 7 dozen mangoes in a box. If there are 29
such boxes, how many mangoes are there in all the
boxes together? | [
"516",
"2436",
"6192",
"628",
"None"
] | Number of mangoes = 7 dozens
= 7 × 12 = 84
∴ Number of mangoes in 29 boxes
= 29 × 84 = 2436
Answer B
The answer is: B | B |
mathematics | Calculate the average of first 14 even numbers is? | [
"11",
"15",
"16",
"14",
"12"
] | Explanation:
Sum of 14 even numbers = 14 * 15 = 210
Average = 210/14 = 15
Answer: Option B
The answer is: B | B |
mathematics | If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are | [
"rational",
"irrational",
"non real",
"real",
"none of these."
] | Sol.(a) The sum of coefficients
= (b + c - a) + (c + a - b) + (a + b - c) = a + b + c = 0 (given)
∴ x = 1 is a root of the equation
∴ The other root is a+b−cb+c−aa+b−cb+c−a , which is rational as a,b, c, are rational
Hence, both the roots are rational.
ALTERNATIVE :
D = (c + a - b)2 - 4(b + c - a)(a + b - c)
= (-2b)2 -... | A |
mathematics | What is the sum of the integers from -190 to 191 inclusive? | [
"0",
"191",
"375",
"875",
"965"
] | sum/n= average.
sum=(average)(n)
average=a+b/2=190+191/2=0.5
number of items(n)=B-A+1=191-(-190)+1=195+191=382.
sum=average*n=0.5*382=191.
answer is B
The answer is: B | B |
mathematics | Ashok secured average of 77 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? | [
"38",
"27",
"92",
"17",
"80"
] | Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 77
Therefore total marks in 6 subjects = 77 * 6 = 462
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 462 – 370 = 92
ANSWER: C
The answer is: C | C |
mathematics | (1/32)+(1/33)+……+(1/62)+(1/63) is including in which of the following ranges? | [
"2",
"1",
"1/2~1",
"1/2",
"3"
] | Number of terms in the given series = 32.
The lowest term is 1/63 , the largest being 1/32.
Thus, the sum of the given series will be more than
1/63 + 1/63.....1/63 (32 times)
---> 32*(1/63) = 32/63
less than 1/32 + 1/32...... 1/32 (32 times)
---> 32*(1/32) = 32/32 = 1 (approx)
C is thus the correct answer.
The answer ... | C |
mathematics | When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters? | [
"√10/2",
"√10",
"4",
"5",
"10"
] | V = pi(R^2)(H)
We have the Volume (22 cubic meters) and the Height (0.7 meters)...
22 = pi(R^2)(0.7)
pi = about 3.14
.7(pi) = about 2.2
22 = 2.2(R^2)
10 = R^2
\sqrt{10} = R
Final Answer:
B
The answer is: B | B |
mathematics | There are n cities. What is the number of airlines that connected 7 different cities (airline from city A to city B is different with airline from city B to city A)? | [
"n(n-1)",
"n(n+1)",
"n(n-1)/2",
"n(n-6)",
"n2"
] | First of all, the possible number of airlines is n. Then, the possible number of airlines departing from one city to another becomes (n-6). Hence, the answer is n(n-6), which makes A an answer choice.
D
The answer is: D | D |
mathematics | What is the least number of square tiles required to pave the floor of a room 50 m 00 cm long and 11m 25 cm broad? | [
"724",
"804",
"814",
"9000",
"None"
] | Solution
Length of largest tile = H.C.F. of 5000cm & 1125cm = 25cm.
Area of each tile = (25 x 25)cm2
∴ Required number of tiles = [5000x1125/25x25]
= 9000.
Answer D
The answer is: D | D |
mathematics | A worm is at the bottom of a forty foot hole. It can crawl upwards at the rate of four feet in one day, but at night, it slips back three feet. At this rate, how long will it take the worm to crawl out of the hole? | [
"33",
"87",
"37",
"28",
"921"
] | Explanation:
For each day worm climb only 4 - 3 = 1feet.
After 36 days worm reach the 36 foot.
Exactly the 37th day worm reach 40 foot and won't slips back.
Answer: C
The answer is: C | C |
mathematics | When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is | [
"0.005",
"0.002",
"0.001",
"0.0003",
"0.0002"
] | It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=0.3 then x=0.3/1000=0.0003.
The answer is D
The answer is: D | D |
mathematics | The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? | [
"297 m",
"178 m",
"245 m",
"278 m",
"297 m"
] | Speed = (45 * 5/18) m/sec
= (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2
==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
The answer is: C | C |
mathematics | The final exam of a particular class makes up 40% of the final grade, and Moe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam. What grade does Moe need on his final exam in order to receive the passing grade average of 60% for the class? | [
"75%",
"82.5%",
"85%",
"90%",
"92.5%"
] | Lets Assume that total marks are 100.
Final exam weightage : 40
Rest of the exams : 60
Percentage scored by Moe out of 60 = 45%
Hence, Total marks obtained out of 60 = 45% of 60 = 27
Marks required in the final exam to get 60% in end = 60(marks) - 27 = 33 marks
i.e. 33 marks required out of 40 = 82.5 marks required out... | B |
mathematics | Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary? | [
"Rs.5000",
"Rs. 38,000",
"Rs.6300",
"Rs.9000",
"Rs.12000"
] | Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x+4000/3x+4000=40/57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Answer:B
The answer is: B | B |
mathematics | The famous church in the city of Kumbakonnam has a big clock tower and is said to be over 300 years old. Every Monday 10.00 A M the clock is set by Antony, doing service in the church. The Clock loses 6 mins every hour. What will be the actual time when the faulty clock shows 3 P.M on Friday? | [
"2.19",
"2.12",
"2.13",
"2.11",
"2.1"
] | Total time passed in the faulty clock = Monday 10 am to Friday 3 pm = 24 x 4 + 5 hours = 96 and 5 hours = 101 hrs
54 min in the faulty clock = 60 minutes of the correct clock
101 hrs in the faulcty clock = ?
10154×6010154×60 = 112.2 Hrs.
96 Hrs + 16.2 Hrs
Friday 10 am + 16 hrs = Saturday 2am
0.2 x 60 min = 12 min
So Sa... | B |
mathematics | Two bottles A and B contain diluted ammonium nitric acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture Should be taken from each bottle in order to prepare 5 litres of diluted sulphuric acid containing equal amount of acid... | [
"1, 4",
"Required ratio= 3, 2",
"2, 3",
"4, 1",
"1,5"
] | A B
Acid water Acid water
1 : 2 3 : 1
Acid=1/3 Acid=3/4
Mixture=Acid:Water=1:1 Required acid=1/2
Now,Required ratio=(1/4): (1/6)=3:2
So the required quantity is 3 and 2 litres respectively.
ANSWER:B
The answer is: B | B |
mathematics | How many terms are there in 2, 4, 8, 16,..., 256? | [
"14",
"11",
"12",
"10",
"8"
] | 2, 4, 8, 16, ..., 256 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 256
or 2^n-1 =128 = 2^7
Thus n - 1 =7
n= 8
ANSWER:E
The answer is: E | E |
mathematics | A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 3 days. B can do the work alone in? | [
"18",
"12",
"11",
"19",
"114"
] | Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/3
6/x = 1/3 => x = 18
So, B takes 9 hours to finish the work.
Answer: A
The answer is: A | A |
mathematics | John spends $320 buying his favorite dolls. If he buys only small Monkey dolls, which are $4 cheaper than the large Monkey dolls, he could buy 40 more dolls than if he were to buy only large Monkey dolls. How much does a large Monkey doll cost? | [
"$7.2",
"$7.5",
"$8",
"$9",
"$10"
] | A and B is not an integer. So we start with C
If large doll costs $8, then he can buy 320/8 = 40 large dolls and 320/4 =80 small dolls.
Difference is 40, which is we wanted.
Answer C.
The answer is: C | C |
mathematics | 325325 is a six digit number.It is divisible by | [
"7 only",
"11 only",
"13 only",
"all 7,11,and 13",
"none"
] | Solution
Clearly,325325 is divisible by all 7,11,and 13.
Answer D
The answer is: D | D |
mathematics | A person travelled from his house to office at 36km/hr and office to house at 12km/hr. Then find the average speed? | [
"15km/hr",
"20km/hr",
"32km/hr",
"24km/hr",
"18km/hr"
] | Average speed = (2*36*12)/(36+12)
= 18km/hr
Answer is E
The answer is: E | E |
mathematics | A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes? | [
"100",
"377",
"399",
"277",
"271"
] | Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes = {\color{Blue} \left ( \frac{1}{60}\times 6 \right )} km = {\color{Blue} \frac{1}{10}} km = 100 m
{\color{Blue} \therefore } Distance between the thief and policeman = (200 – 100) m = 100 m.
Answer: A) 100 ... | A |
mathematics | If 4 men and 1 boy working together, can do two times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? | [
"3:2",
"2:1",
"3:3",
"1:2",
"6:1"
] | 4M + 1B =2(1M + 1B)
4M + 1B = 2M + 2B
2M = 1B
The required ratio of work done by a man and a boy = 1:2
D
The answer is: D | D |
mathematics | The value of log5(1/ 125) is | [
"3",
"-3",
"1/3",
"-1/3",
"None"
] | Solution
Let log5(1/125) = n.
Then, 5n= 1/125
‹=›5n =5-3
n= -3.
Answer B
The answer is: B | B |
mathematics | At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 12 months? | [
"2^3",
"3^2",
"2(3^10)",
"3(2^12)",
"3(10^2)"
] | 3*2^n where n is the #of month --> 3*2^12 Answer (D)
The answer is: D | D |
mathematics | Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly? | [
"2888",
"2690",
"2668",
"9261",
"2312"
] | A = 8000(21/20)3 = 9261.Answer:D
The answer is: D | D |
mathematics | What will come in place of (a) in the following expression?
a - 896.21 + 498.05 = 215.50 – 425.01 | [
"188.65",
"88.6",
"188.67",
"83.65",
"88.61"
] | Explanation:
a - 896.21 + 498.05 = 215.50 - 425.01
a = 188.65
ANSWER: A
The answer is: A | A |
mathematics | Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 60 percent on clothing, 10 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of th... | [
"2.8%",
"3.6%",
"4.4%",
"5.2%",
"4.8%"
] | Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2.4
Tax on others=2.4
Percentage= 4.8/100 =4.8%
Answer: E
The answer is: E | E |
mathematics | If x is a positive number and 2 the square root of x is equal to x/2, then x = | [
"1/16",
"4",
"1",
"2",
"8"
] | 2 of sqrt(x) = x/2, which means that sqrt(x) = x
or x = x^2 -> divide by x
1= x
x=1
C.
The answer is: C | C |
mathematics | How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 25%? | [
"100 ml",
"60 ml",
"125 ml",
"130 ml",
"150 ml"
] | we can also go by answer choices
Tke 100 ml for eg
400 (old)+100 (new concentr)ml
500*25/100 = 125 ml (25ml is de old concentration +100 ml (newly added)
Answer C
The answer is: C | C |
mathematics | A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 40% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? | [
"45%",
"40%",
"25%",
"28%",
"33.33%"
] | I year
Best is to give a number to his income, say 100..
and let saving be x..
so expenditure = 100-x
next year-
Income = 140
savings = 2x
expenditure = 140-2x..
Now 140-2x+100-x = 2(100-x)...
240-3x = 200-2x ................x = 40...
saving % = 40/100 * 100 = 40%
ANSWER:B
The answer is: B | B |
mathematics | If m is a positive integer greater than 1, what is the sum of the multiples of m from m to m^2, inclusive? | [
"m(m + 1)(m-1)",
"m^2(m + 1)/2",
"m^2(m-1)",
"(x^3 + 2x)/2",
"x(x-1)^2"
] | Ans :- B=m^2(m + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
The answer is: B | B |
mathematics | Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every five people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets thre... | [
"8/27",
"117/125",
"49/81",
"98/125",
"125/144"
] | Probability that she guesses the height correctly P(h)=3/4
Probability that she guesses the weight correctlyP(w)=4/5
Probability that she guesses both weight and height correctly(P(h)*P(w))=3/4 * 4/5= 12/20
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability o... | B |
mathematics | A bag contains 3 white balls, 3 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? | [
"0.25",
"0.15",
"0.35",
"0.45",
"0.4"
] | Each ball has an equal probability of being the third ball drawn.
P(3rd ball is red) = 4/10 = 0.4
The answer is E.
The answer is: E | E |
mathematics | When positive integer x is divided by positive integer y, the remainder is 3. If x/y = 96.15, what is the value of y? | [
"96",
"75",
"48",
"25",
"20"
] | by the definition of a remainder, the remainder here is equal to 3/y. the remainder in decimal form is given as .15
therefore, 3/y = .15
solve for y and get 20.
E
The answer is: E | E |
mathematics | A corporation double its annual bonus to 100 of its employees. What percent of the employees’ new bonus is the increase? | [
"50%",
"12%",
"8%",
"6%",
"5%"
] | Let the annual bonus be X.
A corporation double its annual bonus.
So new bonus = 2X.
Increase = 2X-X =X
The increase is what percent of the employees’ new bonus
= (X/2X)*100
= 50%
Hence A.
The answer is: A | A |
mathematics | What is the area inscribed by the lines y =4, x = 2, y = 6-2x on an xy-coordinate plane? | [
"a) 1",
"b) 2",
"c) 4",
"d) 6",
"e) 8"
] | First, let's graph the lines y = 4 and x = 2
At this point, we need to find the points where the line y = 6-2x INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = 6-2x to get y = 6-2(2) = 2
Perfect, when x = 2, y = 2, so one point of intersection is (2,2)... | A |
mathematics | A meal cost $ 35.50 adn there was no tax. If the tip was more than 5 pc but less than 8pc of the price, then the total amount paid should be: | [
"40-42",
"39-41",
"38-40",
"37-38",
"36-37"
] | 5%(35.5) = 1.775
8%(35.5) = 2.84
total amount could have been 35.5+1.775 and 35.5+2.84
=> could have been between 37.275 and 38.34
=> approximately between 37 and 38
Answer is B.D
The answer is: D | D |
mathematics | If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (3 Ø 1) Ø 2 = ? | [
"2",
"4",
"8",
"16",
"32"
] | 3 Ø 1 = 2^3/2^1 = 4
4 Ø 2 = 2^4/2^2 = 4
The answer is B.
The answer is: B | B |
mathematics | At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four used a bowl of meat between them. There were altogether 65 dishes. How many guests were present at the party ? | [
"60",
"65",
"90",
"95",
"None of these"
] | no. of rice bowl=x
no. of dal bowl=y
no. of meat bowl=z
then, x+y+z=65(eq 1)
also, 2x=3y=4z
substituting value of y&z in terms of x in eq 1, x=30.
as 1 rice bowl is shared between 2 guests, therefore there are 60 guests...
ANSWER:A
The answer is: A | A |
mathematics | The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 60 kg is replaced by a new man. What is the weight of the new man? | [
"80 kg",
"83 kg",
"70 kg",
"75 kg",
"85 kg"
] | Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 60+10x1.5
60+15=75 Kg
Ans: 'D'
The answer is: D | D |
mathematics | Find the amount on Rs.5000 in 2 years, the rate of interest being 5% per first year and 6% for the second year? | [
"3377",
"2678",
"5565",
"1976",
"1671"
] | 5000 * 105/100 * 106/100 => 5565
Answer: C
The answer is: C | C |
mathematics | A man & his wife appear in an interview for 2vacancies in the same post. The probability of husband's selection is 1/7 & the probability of wife's selection is 1/5. What is the probability that only 1 of them is selected ? | [
"1/3",
"2/3",
"2/7",
"3/11",
"4/5"
] | Let A = Event that the husband is selected and
B = Event that the wife is selected.
Then, P (A) = 1/7
and P(B) = 1/5
∴P(A¯) = (1 - 17/5) = 6/7
and
= (1 - 1/5) = 4/5
Required probability = P [(A and not B) or (B and not A)]
= P[(A and B¯) or (B and A¯)]
= P(A and B¯) + P(B and A¯)
= P(A).P(B¯) + P(B).P(A¯)
= (1/7* 4/5) ... | C |
mathematics | Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 65 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped? | [
"15",
"20",
"40",
"47",
"49"
] | Car Y began travelling after 72 minutes or 1.2 hours.
Let t be the time for which car Y travelled before it stopped.
Both cars stop when they have travelled the same distance.
So,
35(t+1.2) = 65t
t=1.4
Distance traveled by car X from the time car Y began traveling until both cars stopped is
35 x 1.4
= 49 miles
Answer:-... | E |
mathematics | Rectangular Floors X and Y have equal area. If Floor X is 16 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet? | [
"13 1/2",
"18",
"18 3/4",
"21",
"32"
] | The area of a rectangle is: Area = length x width
We are given that floor X is 16 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 16
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(16)(... | E |
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 tha... | [
"18/79",
"1/200",
"1/25",
"1/50",
"1/900"
] | So there are 900 cars that they have to search.. Each takes 40mins, total of 36000 mins.. Have to find in 180 mins.. Prob180/36000 = 1/200 (ANSWER B)
The answer is: B | B |
mathematics | At a certain college 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport? | [
"1) 3/4",
"2)1/5",
"3)2/5",
"4)1/2",
"5)4/5"
] | This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band
If a randomly selected student is a member of th... | E |
mathematics | Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ? | [
"Rs.86",
"Rs.87.48",
"Rs.89",
"Rs.90",
"None"
] | Explanation:
C.P of 120 reams = Rs.(120×80+280+72+120×0.40)= Rs.10000.
C.P. of 1 ream = 10000/120= Rs.250/3
S.P. of 1 ream = Rs.108/100×250/3=Rs.90
Correct Option : D
The answer is: D | D |
mathematics | Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after? | [
"7",
"9",
"11",
"13",
"15"
] | Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x 2 + 1 + (30 - x). 2 = 1
75 45 75
11x + (60 -2x) = 1
225 75
11x + 180 - 6x = 225.
x = 9.
B)
The answer is: B | B |
mathematics | A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn? | [
"188",
"258",
"376",
"470",
"517"
] | consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn Y= 4 * 94 = 376
correct option - C
The answer is: C | C |
mathematics | I. a2 - 2a - 8 = 0,
II. b2 = 9 to solve both the equations to find the values of a and b? | [
"If a < b",
"If a ≤ b",
"If the relationship between a and b cannot be established",
"If a > b",
"If a ≥ b"
] | Explanation:
I. (a - 4)(a + 2) = 0
=> a = 4, -2
II. b2 = 9
=> b = ± 3
-2 < 3, -2 > -3, 4 > 3, 4 > -3,
No relation can be established between a and b.
C)
The answer is: C | C |
mathematics | If 1*548 is divisible by 3, which of the following digits can replace *? | [
"0",
"1",
"2",
"3",
"4"
] | Solution
1 + x + 5 + 4 + 8 = (18 + x).
Clearly, when x=0, then sum of digits divisible by 3.
Answer D
The answer is: D | D |
mathematics | It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym? | [
"70",
"72",
"74",
"76",
"78"
] | Jim can wash (1/3) of the gym per hour.
Julia can wash (1/2) gym per hour.
Together they can wash 1/3+1/2=5/6 of the gym per hour.
1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes.
The answer is B.
The answer is: B | B |
mathematics | A boat can move upstream at 22 kmph and downstream at 42 kmph, then the speed of the current is? | [
"15",
"16",
"18",
"10",
"12"
] | US = 22
DS = 42
M = (42 - 22)/2 = 10 Answer:D
The answer is: D | D |
mathematics | Which of the following is equal to 3^k*7^(k-1)? | [
"3*21^(k-1)",
"7*21^(k-1)",
"21^k",
"3*21^k )",
"21^(2k-1)"
] | 3^k*7^(k-1) = 3*3^(k-1)*7^(k-1) = 3*21^(k-1)
The answer is A.
The answer is: A | A |
mathematics | If N = 2^0.25 and N^b = 8, b must equal | [
"3/80",
"3/5",
"12",
"5/3",
"80/3"
] | 25/100 = 1/4
N = 2 ^ 1/4
N^b = 2^3
(2^1/4)^b = 2^3
b =12
Answer: C
The answer is: C | C |
mathematics | The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that y > x or x < 0? | [
"5/8",
"4/5",
"3/8",
"1/2",
"3/4"
] | The line y=x divides the circle into two equal areas.
All the points above the line y=x satisfy the condition that y > x.
All the points to the left of the y-axis satisfy the condition that x < 0.
The union of these two areas is 5/8 of the circle.
The answer is A.
The answer is: A | A |
mathematics | There are 900 jelly beans divided between two jars, Jar X and Jar Y. If there are 500 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X? | [
"510",
"520",
"530",
"540",
"550"
] | X+Y=900 so Y=900-X
X=3Y-500
X=3(900-X)-500
4X=2200
X=550
The answer is E.
The answer is: E | E |
mathematics | How many common two-digit whole numbers are there which gives a remainder of 2 when divided by 9 and gives a remainder of 5 when divided by 8? | [
"Five",
"Three",
"One",
"Two",
"Four"
] | Answer = C) One
Two digit numbers giving remainder 2 when divided by 9 = 11, 20, 29, 38, 47, 56, 65, 74, 83, 92
Two digit numbers giving remainder 5 when divided by 8 = 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93
Common Numbers = 29 = 1
The answer is: C | C |
mathematics | Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n? | [
"50 years",
"25 years",
"12 years 6 months",
"37 years 6 months",
"40 years"
] | Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $400.
Therefore, the Simple Interest earned = 400 - 100 = $300.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 300 = (100 * ... | D |
mathematics | If a particular player is always chosen, in how many ways cana cricket-be chosen out of 15 players? | [
"1223",
"1376",
"1245",
"1456",
"1365"
] | A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
The answer is: E | E |
mathematics | A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest? | [
"28%",
"12%",
"72%",
"82%",
"13%"
] | Let the interest for one year be x.
As amount = Principal + Interest, we have
P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)
Solving the equations (1) and (2), we can get
P = Rs. 14000 and x = Rs. 1680
Interest for one year on Rs. 14000 is Rs. 1680
So, R = (100 * 1680)/(14000 * 1) = 12% p.a.
Answer:B
The answer is: B | B |
mathematics | P can do a work in 36 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days. | [
"7",
"8",
"9",
"10",
"15"
] | Work done by P in 1 day = 1/36
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/36) = 15
Option E
The ans... | E |
mathematics | If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ? | [
"0",
"1",
"2",
"3",
"5"
] | There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.
n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.
Answer: B
The answer i... | B |
mathematics | A van takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | [
"50 Kmph",
"60 Kmph",
"70 Kmph",
"80 Kmph",
"90 Kmph"
] | Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B
The answer is: B | B |
mathematics | Two dice are tossed. The probability that the total score is a prime number is | [
"1/6",
"5/12",
"1/2",
"7/9",
"3/8"
] | n(S)=36
E= {(1,1),(1,2), (1,4),….(6,5)}
n(E)=15
P(E)=15/36
=5/12
Option B
The answer is: B | B |
mathematics | The average of 26,29,n,35 and 43 lies between 25 and 35. If n is always an integer and greater than the average of the given integers then the value of n is : | [
"36",
"29",
"33",
"28",
"21"
] | Explanation:
Average of 26,29,35 and 43 is 33.25 . Also the average of 26 , 29, n, 35 and 43 lies between 25 and 35 i.e,
Rightarrow 125 < 26+29+n+35+43 < 175
Rightarrow 125 < 133 + n < 175
Rightarrow n < 42
Since the value of n is an integer and greater than 33.25 then 33 < n < 42 for every integer n.
Answer: C
The ans... | C |
mathematics | A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle? | [
"13π",
"26π",
"262√π",
"52π",
"4π"
] | The distance between the two points is sqrt(8)
radius = sqrt(8)/2
Area= pi*(sqrt(8)/2)^2
E.4π
The answer is: E | E |
mathematics | How long will it take a sum of money invested at 20% p.a. S.I. to increase double the value? | [
"12 years.",
"8 years.",
"15 years.",
"13 years.",
"10 years."
] | Sol.
Let the sum be x. Then, S.I. = 200% of x = 2x; Rate =20%.
∴ Time = [100 * 2x/5 * 1/x*5] = 10 years.
Answer E
The answer is: E | E |
mathematics | City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 5:00 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet? | [
"5:00",
"5:30",
"6:00",
"6:30",
"7:00"
] | Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
5:00pm + 2 hrs = 7:00pm
Answer:
E. 7:00
The answer is: E | E |
mathematics | In a company ones salary increases 6/5 times in every year. After 4 year of joining average salary is 1342. Then what's the starting salary of the company? | [
"900",
"1000",
"1100",
"1200",
"1300"
] | Let x be initial salary.
After one year it becomes 6/5*x
4 months salary is
x+6/5x +6/5*6/5x+ 6/5*6/5*6/5x + 6/5*6/5*6/5*6/5x =1342*4
By solving we get x =1000
ANSWER:B
The answer is: B | B |
mathematics | 286, 462, 362, 527, 671, 253 | [
"286",
"462",
"352",
"537",
"671"
] | In each number except 537, the middle digit is the sum of other two.
Answer: Option D
The answer is: D | D |
mathematics | A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16? | [
"16 = 1.02^(x/4)",
"2 = 1.02^x",
"16 = 1.08^(4x)",
"2 = 1.02^(x/4)",
"1/16 = 1.02^(4x)"
] | Now we can take the fourth root of both sides of the equation. (i.e.the equivalent of taking the square root twice) We will only consider the positive root because a negative 2 doesn't make sense here.
161/4 = [(1.02)^(4x)]^(1/4)
2 = (1.02)^x
The correct answer is B."
The answer is: B | B |
mathematics | (a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? | [
"8/2",
"2/4",
"1/8",
"2/4",
"4/6"
] | (a/2)/(b/c)
= (a*c)/2b
The expression will have the largest value when numerator (a*c) is the largest.
= (2*4)/2*1
=8/2
Answer A
The answer is: A | A |
mathematics | Two trains travelling in the same direction at 50.8 and 14.8 kmph completely pass off another in 45 sec.. If the length of the first train is 112 m, what is the length of the second train? | [
"338 m",
"287 m",
"450 m",
"383 m",
"833 m"
] | RS = 50.8 – 14.8= 36* 5/18 =10 mps
T = 45 sec
D = 10* 45= 450 m
112
--------
338 m
Answer: A
The answer is: A | A |
mathematics | Entry fee in an exhibition is $1. Later this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is? | [
"20%",
"40%",
"50%",
"60%",
"100%"
] | Let the total original sale be $100
Then original number of visitors = 100
New number of visitors = 120/0.75 = 160
Increase % = 60%
Answer is D
The answer is: D | D |
mathematics | A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? | [
"230",
"288",
"267",
"256",
"298"
] | Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
The answer is: A | A |
mathematics | Quentin's income is 60% less than Rex's income, and Ram's income is 25% less than Quentin's income. If Rex gave 60% of his income to Ram and 40% of his income to Quentin, Quentin's new income would be what fraction of Ram's new income? | [
"8/9",
"11/12",
"8/13",
"11/13",
"12/13"
] | We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Quentin's income) = 40%R = 40
S (Ram's income) = 75% Q = (3/4)*40 = 30
Now, if Rex gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Ram --> S = 30+60 = 90
The ratio is : Q/S = 80/90 = 8/9=A
The answer is: A | A |
mathematics | Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 46 years. What will be the age of the B ten years hence? | [
"39",
"92",
"28",
"96",
"26"
] | Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 46 => b + c = 92 --- (2)
Answer: B
The answer is: B | B |
mathematics | The average (arithmetic mean) of six numbers is 5. If 3 is subtracted from each of four of the numbers, what is the new average? | [
"1.5",
"2",
"3",
"4",
"4.5"
] | Sum of 6 numbers = 6*5 =30
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 30 - 12 = 18
New average = 18/6 = 3
Answer C
The answer is: C | C |
mathematics | Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? | [
"A)7",
"B)6",
"C)8",
"D)9",
"E)4.74"
] | 1/5 + 1/15 - 1/x = 1/18
x = 4.74
Answer:E
The answer is: E | E |
mathematics | Cost price of 12 mangoes is equal to the selling price of 9 mangoes and the discount on 10 mangoes is equal to the profit on 5 mangoes. What is the percentage point difference between the profit percentage and discount percentage? | [
"1.5 %",
"1.75 %",
"1.85 %",
"2 %",
"None of these"
] | Cost price of 12 mangoes is equal to the selling price of 9 mangoes,
Let the C.P. of one mango = Re. 1
C.P. of 9 mangoes = Rs. 9
S.P. of 9 mangoes = Rs. 12
Profit % of 9 mangoes = 3/9 x 100 = 33.33 %
Profit % of 1 mango = 33.33/9 = 3.703 %
Profit % of 5 mangoes = 3.703 x 5 = 18.51 %
Given, the discount on 10 mangoes is... | C |
mathematics | X does 80% of a work in 20 days. He then calls in Y and they together finish the remaining work in 3 days. How long Y alone would take to do the whole work? | [
"37 1/2",
"35",
"36",
"25",
"34"
] | Whole work is done by X in ( 20 x 5/4) = 25 days.
Now, ( 1 - 4 /5) i.e., 1/5 work is done by X and Y in 3 days.
Whole work will be done by X and Y in (3 x 5) = 15 days.
A's 1 day's work = 1 , (X + Y)'s 1 day's work = 1 .
25 15
Therefore Y's 1 day's work = ( 1/15 - 1 /25 ) = 4/150 = 2/75
So, Y alone would do the work in... | A |
mathematics | If p and q are two different prime numbers, which of the following cannot be true? | [
"pq is odd.",
"p + q is even.",
"p + q is odd.",
"pq is even.",
"p/q is an integer"
] | A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q).
Answer: E.
All other options are possible:
A. pq is odd --> p=3 and q=5;
B. p ... | E |
mathematics | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 37. In the company, what is the maximum number of non-managers in a department that has 9 managers? | [
"44",
"45",
"46",
"47",
"48"
] | 9/7 * 37 = 47.6
The answer is D.
The answer is: D | D |
mathematics | A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 84 km/h. At what time will the second train catch the first train? | [
"4:30",
"5:00",
"5:30",
"6:00",
"6:30"
] | In one hour and thirty minutes the first train travels 105 km.
The second train catches the first train at a rate of 84 km/h - 70 km/h = 14 km/h.
The second train will catch the first train in 105/14 = 7.5 hours, so at 6:00 pm.
The answer is D.
The answer is: D | D |
mathematics | Tom wants to buy items costing $25.35, $50.69, and $85.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour. | [
"8 hours",
"48 hours",
"38 hours",
"18 hours",
"28 hours"
] | $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $50.69 + $85.96 = $162 total needed
$162 ÷ $5.85 = 27.69... rounds to 28 hours
correct answer E
The answer is: E | E |
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