subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | The sides of a cube are in the ratio 1:2 the ratio of their volume is? | [
"1:9",
"1:7",
"1:8",
"1:6",
"1:4"
] | 1:8
Answer: C
The answer is: C | C |
mathematics | P is four times as fast as Q and working together, they can complete a work in 5 days. In how many days can Q alone complete the work? | [
"5 3/4 days",
"6 1/4 days",
"16 days",
"25 days",
"18 days"
] | P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 5 days, which means Q can do the work in 25 days.
Hence, P can do the work in 6 1/4 days.
ANSWER:B
The answer is: B | B |
mathematics | A sock drawer contains seven socks, each one a different solid color. The colors of the socks are orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether... | [
"12",
"15",
"21",
"36",
"30"
] | It's a question of permutation since order matters here ....
It can be deduced to-
6P2 = 6!/4! = 6*5 = 30 .........Answer is - E
The answer is: E | E |
mathematics | In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school? | [
"72",
"80",
"120",
"150",
"100"
] | Answer: Option E
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% OF X= 48+2/3 OF 48
80/100 X=80
X=100
The answer is: E | E |
mathematics | In a mixture of milk and water, the proportion of milk by weight was 70%. If, in a 150-gram mixture, 50 grams of pure milk is added, what would be the percentage of milk in the resulting mixture? | [
"75.5%",
"76.5%",
"77.5%",
"78.5%",
"79.5%"
] | The amount of milk is 0.7(150) + 50 = 155 grams.
The proportion is 155/200 = 0.775 which is 77.5%
The answer is C.
The answer is: C | C |
mathematics | John has 4 friends who want to ride in his new car that can accommodate only 3 people at a time (John plus 2 passengers). How many different combinations of 2 passengers can be formed from John's 4 friends? | [
"6",
"8",
"10",
"15",
"18"
] | 4C2 = 6
The answer is A.
The answer is: A | A |
mathematics | A coin is tossed live times. What is the probability that there is at the least one tail? | [
"31/32",
"31/38",
"31/34",
"31/31",
"31/36"
] | Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: A
The answer is: A | A |
mathematics | If a/b = 5/4, Then (4a + 3b) / (4a - 3b) = ? | [
"7",
"6",
"3",
"5",
"4"
] | Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (4a + 3b) / (4a - 3b) = (4a/b + 3) / (4a/b - 3)
Since a/b = 5/4
this implies that
=[(4*5)/4 +3]/[(4*5)/4 -3)]
= (5+ 3) / (5 - 3)
= 4
Option: E
The answer is: E | E |
mathematics | Find the area of trapezium whose parallel sides are 18 cm and 12 cm long, and the distance between them is 14 cm? | [
"288 cm2",
"277 cm2",
"224 cm2",
"226 cm2",
"227 cm2"
] | Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (18 + 12) * (14)
= 224 cm2
Answer: C
The answer is: C | C |
mathematics | Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 9 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her? | [
"8 mph",
"5.25 mph",
"3.5 mph",
"5 mph",
"0.5 mph"
] | (1 mph +9 mph)/2 = 5 mph
Correct option is: D
The answer is: D | D |
mathematics | 3,6,9,12,15.... | [
"58",
"60",
"18",
"62",
"63"
] | 1*3=3
2*3=6
3*3=9
4*3=12
5*3=15
6*3=18
ANSWER:C
The answer is: C | C |
mathematics | Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings? | [
"15400",
"14300",
"13200",
"12800",
"None of these"
] | Let the monthly salary of Aamir be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
ANSWER:D
The answer is: D | D |
mathematics | How many factors of 880 are odd numbers greater than 1? | [
"3",
"4",
"5",
"6",
"7"
] | When factorized, 880 has 6 prime factors. Of these prime factors 2 are odd and 4 are even. Hence total number of odd factors is 2*2(4), which includes 4. The total number of odd factors greater than 1 are 3.(option A)
The answer is: A | A |
mathematics | The length of a side of a hexagon is 5 inches. What is the perimeter? | [
"116",
"25",
"30",
"24",
"15"
] | Hexagon. It means 6 equal sides.
p = 5 + 5 + 5 + 5 + 5 + 5 = 10+ 10 + 10 = 30 inches
Answer C
The answer is: C | C |
mathematics | For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 105 units raises the average to 55 units per day, what is the value of n? | [
"8",
"10",
"12",
"14",
"16"
] | The daily production was raised by 5 units for n days, which has a weighting of 5n.
5n = 105-55 = 50
n = 10
The answer is B.
The answer is: B | B |
mathematics | Two employees X and Y are paid a total of Rs. 330 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? | [
"s.150",
"s.200",
"s.250",
"s.350",
"s.400"
] | Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 330
But x = 120% of y = 120y/100 = 12y/10
Γ’ΛΒ΄12y/10 + y = 330
Γ’β‘β y[12/10 + 1] = 330
Γ’β‘β 22y/10 = 330
Γ’β‘β 22y = 3300
Γ’β‘β y = 3300/22 = 300/2 = Rs.150
A)
The answer is: A | A |
mathematics | It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010? | [
"Tuesday",
"Saturday",
"Monday",
"Friday",
"Sunday"
] | On 31st December, 2005 it was Saturday.
Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday
Answer is D.
The answer is: D | D |
mathematics | If the sides of a triangle are 26 cm, 24 cm and 12 cm, what is its area? | [
"144",
"772",
"288",
"266",
"2848"
] | The triangle with sides 26 cm, 24 cm and 12 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 12 = 144 cm2
Answer: A
The answer is: A | A |
mathematics | An bus covers a certain distance at a speed of 260 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? | [
"600 km/hr",
"720 km/hr",
"730 km/hr",
"750 km/hr",
"780 km/hr"
] | Distance = (260 x 5) = 1300 km.
Speed = Distance/Time
Speed = 1300/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1300 x 3 km/hr = 780 km/hr.
E
The answer is: E | E |
mathematics | A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480? | [
"170Rs",
"108Rs",
"100Rs",
"160Rs",
"103Rs"
] | 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x =100Rs.
Answer:C
The answer is: C | C |
mathematics | The number of girls in a class is 5 times the number of boys. Which one of the following numbers cannot represent the total number of children in the class. | [
"36",
"41",
"48",
"72",
"11"
] | Answer:A
The answer is: A | A |
mathematics | The combined age of husband and wife on their 20th wedding anniversary was twice than it was at the time of wedding. If the husband is 3 years older than his wife. How old was he at the time of his marriage? | [
"21.5 years",
"21.9 years",
"31.5 years",
"21.7 years",
"61.5 years"
] | Explanation:
Let the ages of husband and wife at the time of their 20th wedding anniversary be X years and Y years respectively and X > Y.
Their combined age = (X + Y) years.
The ages of both husband and wife at the time of wedding will be (X β 20) years and (Y β 20) years respectively.
Their combined age = (X β 20) + ... | A |
mathematics | Which of the following is a prime number ? | [
"72",
"86",
"88",
"97",
"98"
] | Clearly, 97 is a prime number.
Option D
The answer is: D | D |
mathematics | If the height of an equilateral triangle TBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΞTBC is how many times as long as a leg of the right triangle DEF? | [
"(β2)/(β3)",
"(β3)/(β2)",
"β2",
"(2β2)/(β3)",
"2/(β3)"
] | Side of the equilateral triangle TBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle TBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
The answer is: D | D |
mathematics | John and David can finish a job together in 6 hours. If John can do the job by himself in 8 hours, what percent of the job does David do? | [
"35%",
"45%",
"25%",
"30%",
"20%"
] | You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 24 donuts which is the job ( I picked this as a SMART number).
John on his own works 24/8 = 3 donuts per hour.
John and David work 24/6 = 4 donuts per hour so David works 1 donuts/hour
To find out the percentage, David works 1 don... | C |
mathematics | Find the L.C.M of 32,84,126 | [
"2000",
"2018",
"5032",
"1008",
"2016"
] | 32=2^5 84=2^2*3*7 126=2*3^2*7
L.C.M=2^5*3^2*7=2016
Answer=(E)
The answer is: E | E |
mathematics | Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 57.2 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period? | [
"1.3",
"1.0",
"1.1",
"10.5",
"41.8"
] | Change in production of motor vehicles = 57.2 - 3.9 = 53.3 million in 41 years (1987 - 1946)
average increase per year = 53.3/41 = 1.3 million (apporx.)
Answer (A)
The answer is: A | A |
mathematics | 10 2 = 0.3010, the value of log10 80 is: | [
"1.602",
"1.903",
"2.903",
"3.903",
"4.903"
] | log10 80 = log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
Answer: Option B
The answer is: B | B |
mathematics | If a, b, y are integers, 33 = aby, and a < b < y, what is the smallest possible value of a? | [
"-33",
"-3",
"1",
"3",
"11"
] | Given : a * b * y = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. ... | A |
mathematics | Find out the square of a number which when doubled exceeds its quarter by 7 ? | [
"16",
"25",
"19",
"26",
"17"
] | A
Let the number be p, then the square will be p^2
According to question:
2p = (p/4) + 7
=> 8p = p + 28
=> p = 4
p^2 = 4^2 = 16.
The answer is: A | A |
mathematics | In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.? | [
"22 years",
"17 years",
"97 years",
"16 years",
"14 years"
] | T = (100 * 16500)/(15 * 5000)
= 22 years
Answer: A
The answer is: A | A |
mathematics | Find out the wrong term in the series 2, 5, 10, 50, 500, 5000 | [
"5000",
"3877",
"6777",
"2892",
"2881"
] | Explanation:
Each term of the series is the product of the preceding two terms
So, 5000 is wrong and it must be replaced by (500*50) = 25000
Answer: A) 5000
The answer is: A | A |
mathematics | 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) = | [
"2^24(2^(21)-1)",
"2^24(2^(20)-1)",
"2^24(2^(23)-1)",
"2^21(2^(20)-1)",
"2^21(2^(21)-1)"
] | 2^(24) + 2^(25) + 2^(26) + ... + 2^(43) + 2^(44) =
2^(24)*(1+2+4+...+2^(20)) =
2^(24)*(2^(21) - 1)
The answer is A.
The answer is: A | A |
mathematics | An elementary school houses primarily kindergartners, first graders, second graders, and third graders. If an assembly included 30 kindergartners, 20 first graders, and 80 other children, and the ratio of first graders to third graders is tripled, what is the ratio of the first graders to the rest of the children? | [
"40: 20",
"42: 21",
"50: 100",
"15: 25",
"It cannot be determined by the information given."
] | While you can figure out most of this question, there is not enough information to completely tell. the answer is E.
The answer is: E | E |
mathematics | With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity W of the pool? | [
"9000 cubic meters",
"10500 cubic meters",
"11750 cubic meters",
"12000 cubic meters",
"12500 cubic meters"
] | D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).... | D |
mathematics | A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is? | [
"288",
"150",
"277",
"269",
"261"
] | Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
The answer is: B | B |
mathematics | P, Q, R, S and T are five speakers who have to speak on a particular day, not necessarily in the same order. R is neither the first nor the last speaker. There are three speakers after S and three speakers ahead of T. If P speaks after Q, then who is the last speaker to speak? | [
"S",
"T",
"P",
"Q",
"Cannot be determined."
] | Explanation:
There are three speakers after S. So, S is the 2nd speaker.
There are three speakers before T. So, T is the 4th speaker.
R is neither the 1st nor the 5th. So, R is the 3rd speaker.
P speaks after Q, So P is the 5th and Q is the 1st speaker. So, P is the last speaker.
ANSWER IS C
The answer is: C | C |
mathematics | M = {-6, -5, -4, -3, -2}
T = {-2, -1, 1, 2, 3, 4}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? | [
"0",
"1/3",
"2/5",
"1/2",
"4/5"
] | Answer E.
Total # of outcomes: 5*6= 30
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 24
Probability: 24/30 = 4/5
The answer is: E | E |
mathematics | Dylan is on a road trip. He planned on arriving at his destination, 2150 miles away, in 6 days. In the first day, he traveled 310 miles. In the next three days, he travels 1140 miles. How many miles, on average, does Dylan need to travel in the next two days to reach his destination? | [
"330",
"340",
"350",
"360",
"370"
] | He still has to travel 2150 - 300 - 1130 = 720 miles
720 miles / 2 days = 360 miles per day.
Correct answer D
The answer is: D | D |
mathematics | if the price of a book is first decreased by 20% and then increased by 10%, then the net change in the price will be : | [
"10",
"12",
"37",
"29",
"22"
] | Explanation:
Let the original price be Rs. 100.
Decreased by 20% = 80
Then increased 10% on Rs 80 = 80 + 8 = 88
Net change in price = 100 - 88 = 12
Answer : B
The answer is: B | B |
mathematics | Siva Reddy walked 2 km west of his house and then turned south covering 4 km. Finally, He moved 3 km towards east and then again 1 km west. How far is he from his initial position? | [
"10 km",
"9 km",
"2 km",
"4 km",
"8 km"
] | 4 km
ANSWER D
The answer is: D | D |
mathematics | 12.1212+17.0005 - 9.1104 = ? | [
"20.0015",
"20.0105",
"20.0113",
"20.1015",
"None"
] | Solution
Given expression
=(12.1212+17.0005)-9.1104
= (29.1217 - 9.1104)
=20.0113.
Answer C
The answer is: C | C |
mathematics | Two trains 100 meters and 120 meters long are running in the same direction with speeds of 100 km/hr, 82 km/hr. In how much time will the first train cross the second | [
"37 sec",
"35 sec",
"48 sec",
"44 sec",
"36 sec"
] | Explanation:
Relative speed of the trains = (100 - 82) km/hr = 18 km/hr
= (18Γβ 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.
Answer: Option D
The answer is: D | D |
mathematics | There are 14 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? | [
"91",
"30",
"45",
"60",
"90"
] | 10 players are there.
two players play one game with one another.
so 14C2=14*13/2
=91
SO OPTION A is correct
The answer is: A | A |
mathematics | A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? | [
"20%",
"30%",
"40%",
"50%",
"55%"
] | Let the side of the square(ABCD) be x metres.
Then, AB + BC = 2x metres.
AC = 2x = (1.41x) m.
Saving on 2x metres = (0.59x) m.
Saving % = (0.59x)/2x x 100 % = 30% (approx.)
B)
The answer is: B | B |
mathematics | Each child has 3 crayons and 12 apples. If there are 6 children, how many crayons are there in total? | [
"22",
"65",
"18",
"36",
"10"
] | 3*6=18.Answer is C.
The answer is: C | C |
mathematics | The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result. | [
"66",
"55",
"44",
"77",
"88"
] | 6th result = (58*6+63*6-60*11)
=66
Answer is A.
The answer is: A | A |
mathematics | Dacid obtained 86, 85, 92, 87 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | [
"67",
"26",
"89",
"26",
"75"
] | Average
= (86+ 85+ 92+ 87+95)/5
= 445/5 = 89.
Answer: C
The answer is: C | C |
mathematics | When a number is added to another number the total becomes 33 1β3 per cent of the second number. What is the ratio between the first and the second number? | [
"3 : 7",
"7 : 4",
"7 : 3",
"Data inadequate",
"None of these"
] | Let the first and second numbers be x and y respectively.
Then, x + y = 10β3y
or, x = 7β3y
β΄ x : y = 7 : 3
Answer C
The answer is: C | C |
mathematics | How many combinations of three letters taken from letters (a, a, b, b, c, c, d) are possible? | [
"12",
"13",
"35",
"36",
"56"
] | Combinations only... total 13
So 4C3 for abcd - 4 choices
3 more for aa(b,c or d)
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 13
(Answer B)
The answer is: B | B |
mathematics | If the two-digit integers F and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of F and N? | [
"181",
"165",
"121",
"99",
"44"
] | Since the question asks for the answer that CANNOT be the sum of F and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that F and N are two-digit positive integers and have the SAME DIGITS... | A |
mathematics | A man is 24 years older than his son. In three years, his age will be twice the age of his son. The present age of the son is | [
"14 years",
"18 years",
"20 years",
"21 years",
"None"
] | Solution
Let the son's present age be x years .Then, man's present age = (x+24)years.
Then Γ’β¬ΒΉ=Γ’β¬ΒΊ(x+24)+3= 2(x+3)
Γ’β¬ΒΉ=Γ’β¬ΒΊx+27=2x+6
x= 21.
Answer D
The answer is: D | D |
mathematics | Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 200 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters? | [
"250",
"300",
"350",
"400",
"500"
] | Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 200 meters, thus the circumf... | D |
mathematics | The tax on a commodity is diminished by 14% and its consumption increased by 15%. The effect on revenue is? | [
"2.1%",
"8.1%",
"5.1%",
"6.1%",
"1.1%"
] | 100 * 100 = 10000
86 * 115 = 9890
-----------
10000-----------110
100-----------? => 1.1% decrease
Answer: E
The answer is: E | E |
mathematics | 60, 67, 63, 15, 61, 10, 15
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list? | [
"25",
"36",
"53",
"60",
"62"
] | Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 10, 15 ,15, 60, 61, 63, 67
Median is very easy to tell - its 60. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 60
DE are already out.
Now, we have 25, 36 and 53 and we wan... | C |
mathematics | Two sides of a triangle have lengths x and e and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to e ? | [
"a) 2 : 3",
"b) 3 : 4",
"c) 4 : 3",
"d) 3 : 2",
"e) 2 : 1"
] | Ahhhh....my bad. Thank you, you're correct. 8x = 6e --> x/e = 3/4.
Actually B is the right answer.
The answer is: B | B |
mathematics | Which is a better investment 9% stock at 580 or 6 2/5 stock at 312? | [
"9% stock at 580",
"Both are equally good",
"6 2/5 stock at 312",
"None",
"Cannot be compared, as the total amount of investment is not given"
] | Let investment in each case be Rs. (580 x 312).
Income in 1st case = Rs. 9 x 580 x 312/580= Rs. 2808.
Income in 2nd case = Rs.32 x 580 x 312/(5*312)= Rs. 3712
Clearly, 6 2/5 stock at 312 is better.
ANSWER:C
The answer is: C | C |
mathematics | 50 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor? | [
"14.4",
"180/7",
"50.4",
"64.8",
"90"
] | 50% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/50)*100 = 64.8 square feet
Answer: Option D
The answer is: D | D |
mathematics | Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is ... | [
"5",
"8",
"11",
"15",
"17"
] | Explanation :
Let a, b, c be the Englishmen and d, e, f be the Frenchmen.
Let a be the Englishman who knows French. 'a' calls 'b & c' and now knows the secret of both of them. So now 'a' knows 'abc' secrets. 'd' calls 'e & f' and now knows the secret of both of them. So now 'd' knows 'def' secrets. 'a' now calls 'd', a... | B |
mathematics | If 8^x = 2^9, what is x? | [
"2",
"3",
"4",
"5",
"6"
] | 2^3x= 2^9
3x=9, therefore x=3
Answer B
The answer is: B | B |
mathematics | Find the value of x from the equation:
x^2β7x+10=0 | [
"5 or 2",
"4 or 1",
"4 or 2",
"6 or 1",
"7 or 4"
] | Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x
2
β
7
x
+
10
=
(
x
β
5
)
(
x
β
2
)
x2β7x+10=(xβ5)(xβ2)
x
2
β
7
x
+
10
=
0
β
(
x
β
5
)
(
x
β
2
)
=
0
x2β7x+10=0β(xβ5)(xβ2)=0
Step 3: Equate each factor to 0 and solve the equations
(
x
β
5
)
(
x
β
... | A |
mathematics | A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty? | [
"2/3",
"2/5",
"4/9",
"5/7",
"4/11"
] | 2/3 ---- 12
? ----- 8 ==> 4/9
C
The answer is: C | C |
mathematics | If the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there? | [
"2",
"3",
"4",
"5",
"6"
] | If the tens digit of positive integers m, y are 6, how many values of the tens digit of 2(m+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If m=y=60, 2(m+y)=240 is derived. If m=y=69, 2(m+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
The answer is: C | C |
mathematics | What is the difference between the C.I. on Rs. 6000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? | [
"s.2.04",
"s.2.08",
"s.2.02",
"s.2.83",
"s.2.45"
] | C.I. when interest is compounded yearly
= [6000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 6000 * 26/25 * 51/50 = Rs. 6364.8
C.I. when interest is compounded half-yearly
= [6000 * (1 + 2/100)2]
= (6000 * 51/50 * 51/50 * 51/50)
= Rs. 6367.25 Difference
= (6367.25 - 6364.8)
= Rs.2.45.
Answer: E
The answer is: E | E |
mathematics | An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets? | [
"4:5",
"9:10",
"14:15",
"19:20",
"24:25"
] | Let the length and width of one carpet be 3x and 2x.
Let the length and width of the other carpet be y and y.
2(3x + 2x) = 2(y + y)
5x = 2y
(5/2) * x = y
The ratio of the areas of the carpet in both cases:
= 3x * 2x : y * y
= 6x^2 : y^2
= 6x^2 : (25/4) * x^2
= 24 : 25
The answer is E.
The answer is: E | E |
mathematics | A certain manufacturer of cake, muffin, and bread mixes has 140 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake ... | [
"a. 1/10",
"b. 3/10",
"c. 1/2",
"d. 7/10",
"e. 3/14"
] | C+M+B-CM-MB-CB-2CMB = 140
C - cake buyers, M - muffin an0d B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 140
B-CB-MB-2CMB = 30
hence the probability = 30/140 = 3/14.
E
The answer ... | E |
mathematics | A 2-year certificate of deposit is purchased for K dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years? | [
"k(1.06)^2",
"k(1.06)^8",
"k(1.015)^2",
"k(1.015)^8",
"k(1.03)^4"
] | term (n) = 2
value of k at the end of 2 yrs, if compounded annually=k(1+r)^n=k(1+0.06)^2
quarterly int. rate (r) = 1.5%
term (n) = 2x4 = 8
value of k at the end of 2 yrs, if compounded qtrly =k(1+r)^n=k(1+0.015)^8
ANSWER:D
The answer is: D | D |
mathematics | The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers? | [
"14",
"17",
"18",
"19",
"20"
] | let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18
ANSWER:C
The answer is: C | C |
mathematics | If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is? | [
"8118",
"8127",
"8618",
"8436",
"8128"
] | A = 7500(26/25)3
= 8436
Answer: D
The answer is: D | D |
mathematics | If the set S is composed of the following numbers {99, 100, 100, 105, 106, 115, 124}, which of the following is largest? | [
"The average (arithmetic mean) of set S",
"The median of set S",
"The mode of set S",
"The range of set S",
"The standard deviation of set S"
] | A) 99, 100, 100, 105, 106, 115, 124 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 124 -99 = 25.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n => < 100
IMO ... | A |
mathematics | Two letters from the word JARKHANT are selected at random. What is the probability that at least one of the selected letters is a consonant? | [
"40/28",
"30/28",
"50/28",
"26/28",
"27/28"
] | There are 6 consonants and 2 vowels in JARKHANT .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : E
The answer is: E | E |
mathematics | The cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is: | [
"7 m",
"7.5 m",
"8 m",
"8.5 m",
"None of these"
] | Length of the carpet = TotalCost/Rate/m
= (8100β45)m = 180 m.
Area of the room = Area of the carpet
= (180 Γ 75β100) m2 = 135 m2
β΄ Breadth of the room = AreaLength=135/18m
= 7.5 m
Answer B
The answer is: B | B |
mathematics | How many consonants are present between the first and third vowel in the sequence of English alphabet ? | [
"12",
"13",
"6",
"10",
"None of these"
] | Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and third vowels are A and I respectively. There are 7 letters between A and I; out of which 'E' is a vowel. Thus, there are 6 consonants between A and I.
ANSWER C
The answer is: C | C |
mathematics | A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.25,000 earned at the end of 2years from the startingof the business? | [
"Rs. 5,000",
"Rs. 5,500",
"Rs. 5,700",
"Rs. 6,500",
"Rs. 7,500"
] | A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 25000 x 3/10 = Rs. 7,500.
E
The answer is: E | E |
mathematics | On a counter of a donuts store, there are only 16 identical donuts, 11 filled with chocolate and 5 filled with jelly, but the seller tells me that the donuts are randomly placed on the counter. If would want to buy two, what is the probability that I choose one donuts of each flavor? | [
"2/16",
"1/32",
"11/12",
"11/48",
"11/24"
] | We are told that we have 16 donuts, 11 of chocolate and 5 of jelly. The donuts are picked simultaneous and randomly, D1 and D2, in different flavors. There are two acceptable outcomes: 1) D1 is chocolate and D2 is jelly; 2) D1 is jelly and D2 is chocolate. Let's go: 1) D1 = (11/16)(5/15)= 11/48 chance of this happening... | E |
mathematics | Each truck from Jones Removal Company can haul 500 pounds of trash at a time.
On Wednesday the company has jobs to remove 1,500 pounds of trash from one
site, 500 from another site, and 2,500 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
J... | [
"5500 lbs.-2 Trips",
"4500 lbs.-9 Trips",
"2500 lbs.-3 Trips",
"3500 lbs.-7 Trips",
"6500 lbs.-8 Trips"
] | Add: 1500 4,500 Γ· 500 = 9
2500
+ 500
4500
Answer 1: 4500 lbs. (Total) Answer 2: 9 Trips
correct answer B
The answer is: B | B |
mathematics | The distance from City A to City B is 60 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob? | [
"45",
"48",
"50",
"52",
"60"
] | The time it takes Bob to drive to City B is 60 / 40 = 1.5 hours.
Alice needs to take less than 1 hour for the trip.
Alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour.
The answer is E.
The answer is: E | E |
mathematics | Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 60% problems right. How many more questions he would have to answer more to get
passed | [
"5",
"6",
"7",
"8",
"9"
] | Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer: Option A
The answer is: A | A |
mathematics | Zada has to distribute 15 choclates among 5 of her children Sana,ada,jaya,amir and farhan. She has to make sure that sana gets at least 3 and ada at most 6 choclates. In how many ways can this be done? | [
"495",
"77",
"417",
"435",
"455"
] | (3,1,11)=165
(4,1,10)=120
(5,1,9)=84
(6,1,8)=56
ANSWER:A
The answer is: A | A |
mathematics | How much interest can a person get on Rs. 6280 at 15.5% p.a. simple interest for a period of five years and six months? | [
"5353.72",
"5353.71",
"5353.7",
"5353.73",
"5353.74"
] | I = (6280 * 5.5 * 15.5)/100
= (6280 * 11 * 31)/(100 * 2 * 2)
= Rs. 5353.7
Answer: C
The answer is: C | C |
mathematics | A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 6 minutes less than they can row it in still water. How long would they take to row down with the stream | [
"45 or 23 minutes",
"63 or 12 minutes",
"78 minutes",
"19 minutes",
"25 minutes"
] | A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-6))
giving t = 78
C.
The answer is: C | C |
mathematics | If n is a positive integer, which of the following is a possible value of |71 - 5n| ? | [
"7",
"5",
"19",
"15",
"20"
] | When 71>5n, then |71- 5n| = 71- 5n = (70-5n) + 1 = {multiple of 5} + 1
When 71<=5n, then |71 - 5n| = -(71- 5n) = (5n-70) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.
Answer: C
The answer is: C | C |
mathematics | A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is : | [
"120 m",
"140 m",
"240 m",
"300 m",
"None"
] | Sol.
Speed = [12/10 * 60] km/hr = [72 * 5/18] m/sec = 20 m/sec.
Length of the train = (speed * Time) = (20 * 6) m = 120 m.
Answer A
The answer is: A | A |
mathematics | Machine A produces pencils at a constant rate of 9000 pencils per hour, and machine B produces pencils at a constant rate of 7000 pencils per hour. If the two machines to gather must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S, in hours, that machine B... | [
"4",
"4 2/3",
"5 1/3",
"6",
"6 1/4"
] | Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time S , in hours, that machine... | A |
mathematics | The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money? | [
"7 months",
"10 months",
"9 months",
"11 months",
"8 months"
] | 7*5: 5*x = 7:10
x = 10
ANSWER:B
The answer is: B | B |
mathematics | David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their ... | [
"19",
"28",
"30",
"37",
"None"
] | EXPLANATION
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 β 63x <=> 120x = 40
x= 1/3
Number of floors covered by david in (1/3) min = (1/3 x 57) = 19
So, their paths cross at (11 +19) i.e., 30th floor.
Answer C
The answer is: C | C |
mathematics | A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn? | [
"2/27",
"1/9",
"1/3",
"4/27",
"2/9"
] | P=2β3/9β2/9=4/27
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
The answer is: D | D |
mathematics | Total number of people attending a party is 600. 70% of the men are wearing black shirt and rest are wearing red. If 60% of the total people are women then how many men are wearing red shirts? | [
"168",
"72",
"56",
"170",
"60"
] | Number of woman in the party = 0.60*600 = 360
number of men in the party = 600-360 = 240
% of men wearing red shirts = 100-70 = 30%
number of men wearing red shirt = 0.30*240 = 72. B is the correct answer
The answer is: B | B |
mathematics | An insect leaps 48 centimeters in 1.2 seconds. What is its speed? | [
"0.4 meters per second",
"4 meters per second",
"40 meters per second",
"4 centimeters per second",
"0.4 centimeters per second"
] | 48 / 1.2 = 40 cm/s = 0.4 m/s
The answer is A.
The answer is: A | A |
mathematics | A train running at the speed of 180 km/hr crosses a pole in 8 seconds. Find the length of the train. | [
"150",
"88",
"480",
"288",
"400"
] | Speed = 180*(5/18) m/sec = 50 m/sec
Length of Train (Distance) = Speed * Time
50 *8 = 400 meter
Answer: E
The answer is: E | E |
mathematics | Rs.1560 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? | [
"s.528",
"s.542",
"s.528",
"s.720",
"s.549"
] | A+B+C = 1560
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1560 = Rs.720
Answer: D
The answer is: D | D |
mathematics | In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 82% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? | [
"63.",
"73.",
"81",
"91",
"108"
] | Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
82%of 250 = 205 are boys who play soccer.
Girls who play soccer = 45.
Total girls who do not play soccer = 108 - 45 = 63.
Correct option: A
The answer is: A | A |
mathematics | A boat can move upstream at 20 kmph and downstream at 35 kmph, then the speed of the current is? | [
"5",
"6",
"7.5",
"8",
"9"
] | US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer: C
The answer is: C | C |
mathematics | What will be the difference between simple interest and compound interest @10% per annum on a sum of Rs. 1000 after 4 years? | [
"Rs. 31",
"Rs. 32.10",
"Rs. 40.40",
"Rs. 64.10",
"None"
] | Solution
S.I. =Rs(1000x10x4 / 100)
= Rs.400.
C.I. =Rs.[1000x(1x10/100)4-1000]
= Rs. 464.10
β΄ Difference = Rs.(464.10 - 400)
= Rs. 64.10
Answer D
The answer is: D | D |
mathematics | Stella buys an advertising agency for rs.16,000,000 and sells it for rs.20,000,000. Find her gain %. | [
"9%",
"20%",
"14%",
"87%",
"25%"
] | sol. cp=rs16,000,000, sp=rs 20,000,000
gain=rs(20,000,000 β16,000,000)=rs4,000,000
so gain%={(4,000,000/16,000,000)*100}=25%
Answer is E.
The answer is: E | E |
mathematics | A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order P? (1 cubic meter = 1,000 liters) | [
"92",
"90",
"82",
"78",
"75"
] | I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
P=12.5*6 = 75.E
The answer is: E | E |
mathematics | A salesman travels a distance of 100 km in 5hours. How much faster in kilometer per hour, on an average, must he travel to make such trip in 1 hour less time? | [
"2km/hr",
"3km/hr",
"5km/hr",
"7km/hr",
"10km/hr"
] | Time required = 5 hrs- 1hr = 4hr
Required speed = 100/4 = 25km/hr
Original speed = 100/5 = 20 km/hr
Difference = 25-20 = 5 km/hr
Answer is C
The answer is: C | C |
mathematics | In Cliffβs impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 4/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 40 shiny igneous rocks, how many total rocks does Cliff have? | [
"30",
"150",
"60",
"90",
"135"
] | We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 40. These are (4/5) of total igneous rocks.
(4/5)*Total igneous rocks = 40
Total igneous rocks = 40 * (5/4) = 50
Total sedimentary rocks = 2*Total igneous rocks = 2*50 = 100
Total number of rocks = 50 + 100 = 150
Answer (B)
... | B |
mathematics | Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 65 percent of the total number of employees work in research, how many male employees do NOT work in research? | [
"520",
"480",
"392",
"208",
"38"
] | total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =65% =650
Total male employees =48%=480
male employees working in research =650-208=442
male employees not working in research =480-442=38
Answer E
The answer is: E | E |
mathematics | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? | [
"289",
"278",
"211",
"450",
"476"
] | 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 β 1050
= 450
Answer:D
The answer is: D | D |
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