subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | If 6 men and 2 boys working together, can do four 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",
"2:2",
"3:4",
"1:2",
"6:1"
] | B
2:2
6M + 2B = 4(1M + 1B)
6M + 2B = 4M + 4B
2M = 2B
The required ratio of work done by a man and a boy = 2:2
The answer is: B | B |
mathematics | ? x 240 = 173 x 240 | [
"173",
"685",
"865",
"495",
"534"
] | Let y x 240 = 173 x 240
Then y = (173 x 240) / 240
=173
ANSWER :A
The answer is: A | A |
mathematics | A train 260 m long passed a pole in 26 sec. How long will it take to pass a platform 650 m long? | [
"91 sec",
"89 sec",
"54 sec",
"27 sec",
"22 sec"
] | Speed = 260/26 = 10 m/sec.
Required time = (260 + 650)/10
= 91 sec.
Answer: A
The answer is: A | A |
mathematics | What is the sum of natural numbers between 90 and 100 | [
"1045",
"4860",
"5000",
"5500",
"5550"
] | a = first number
l = last number
Sn = n/2[a + l]
between 90 and 100 numbers = 11 => 100 - 90 = 10 + 1 = 11
Sn = 11/2 × 190 = 11 × 95 = 1045
Answer : A
The answer is: A | A |
mathematics | 4 dice are thrown simultaneously on the board. Find the probability show the same face. | [
"1/113",
"1/115",
"1/216",
"2/113",
"3/111"
] | The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5... | C |
mathematics | A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 1540 in all from both of them as interest. The rate of interest per annum is? | [
"7%",
"12%",
"74%",
"10%",
"45%"
] | Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 1540
100 R + 120 R = 1540
R = 7%
Answer:A
The answer is: A | A |
mathematics | A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either red or green? | [
"53/105",
"43/105",
"42/105",
"32/105",
"46/105"
] | given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are red = 4Câ‚‚/¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 3/21
Probability that both are green = 6Câ‚‚/¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one red and other is green = (4Câ‚ * 6Câ... | B |
mathematics | Having scored 99 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings? | [
"28",
"27",
"26",
"22",
"24"
] | Explanation :
Let the average score of the first 18 innings be n
18n + 99 = 19(n+4)=> n = 23
So, Average score after 19th innings = x+4 =27.
Answer : B
The answer is: B | B |
mathematics | Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 152. If the ratio of his marks in English and Maths is 1:5, find his marks in Science? | [
"8",
"77",
"66",
"55",
"31"
] | S:E = 1:3
E:M = 1:5
------------
S:E:M = 1:3:15
1/19 * 152 = 8
Answer: A
The answer is: A | A |
mathematics | One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 50 students are not between 3 years old and 4 years old, how many children are in the nursery school? | [
"150",
"300",
"450",
"490",
"620"
] | x/10 students are > 4 yrs
20 students are < 3 yrs
x/10+ 20 = 50
x/10 = 30
x = 300
Answer: B
The answer is: B | B |
mathematics | Simplify (3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y) | [
"15^y+1",
"12^y+1",
"16^y + 9^y",
"12^y",
"4^y * 12^y"
] | A
(3^y + 3^y + 3^y + 3^y + 3^y) (5^y + 5^y + 5^y)
(5*3^y)(3*5^y)
15*15^y=15^(y+1)..
The answer is: A | A |
mathematics | 155 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4? | [
"12 liters",
"62 liters",
"41 liters",
"50 liters",
"34 liters"
] | Milk = 3/5 * 155 = 93 liters
Water = 62 liters
93 : (62+P) = 3:4
186 + 3P = 372 => P = 62
62 liters of water are to be added for the ratio become 3:4.
Answer:B
The answer is: B | B |
mathematics | If x/y = 9/8, Then (8x + 7y) / (8x – 7y) = ? | [
"8",
"7",
"10",
"9",
"6"
] | Answer
Dividing numerator as well as denominator by y, we get
Given Exp. = (8x + 7y) / (8x – 7y) = (8x/y + 7) / (8x/y – 7)
Since x/y = 9/8
this implies that
=[(8*9)/8 +7]/[(8*9)/8 -7)]
= (9+ 7) / (9 - 7)
= 8
Option: A
The answer is: A | A |
mathematics | If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = -y | [
"I only",
"II only",
"III only",
"I and III only",
"I, II, and III"
] | Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer B
The answer is: B | B |
mathematics | The average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class. | [
"48.68077",
"42.25983",
"50",
"51.25388",
"52.25"
] | Explanation:
Average weight of 18 boys = 50.25
Total weight of 18 boys = 50.25 × 18
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 18)+ (45.15 × 8)
Total boys = 18 + 8 = 26
Average weight of all the boys = (50.25×18)+(45.15×8)/26
... | A |
mathematics | How many different arrangements of letters are possible if three letters are chosen from the letters A through J and the letters E and A must be among the letters selected? | [
"36",
"39",
"42",
"45",
"48"
] | Besides A and E, there are 8 letters and we can choose one of them.
8C1 = 8
Three letters can be arranged in 3! ways.
The number of arrangements is 8*3! = 48
The answer is E.
The answer is: E | E |
mathematics | The letters B,G,I,N and R are rearranged to form the word 'Bring'. Find its probability. | [
"1/120",
"1/235",
"1/24",
"1/76",
"1/53"
] | Explanation :
There are total 5 letters. The probability that B gets the first position is 1/5.
The probability that G is in the second position is 1/4.
Likewise, probability for I,N and G are 1/3, 1/2 and 1/1.
Hence, the required probability is:-
=> (1/5) x (1/4) x (1/3) x (1/2) x 1.
=> 1/120.
Answer : A
The answer is... | A |
mathematics | The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined? | [
"13√7",
"13√2",
"13√8",
"13√9",
"12√2"
] | 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
The answer is: B | B |
mathematics | A hall is 24 meters long and 12 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)? | [
"1896",
"1912",
"2108",
"2304",
"2524"
] | 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 2304
The answer is D.
The answer is: D | D |
mathematics | The average marks of a class of 28 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? | [
"52.2",
"59.5",
"52.8",
"52.5",
"52.1"
] | Sum of the marks for the class of 28 students = 28 * 40 = 1120
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 78 students =
1120 + 3000 = 4120
Average marks of all the students = 4120/78
= 52.8
Answer:C
The answer is: C | C |
mathematics | A family has two children. find the probability that both the children are girls given that at least
one of them is a girl? | [
"1/2",
"1by3",
"3/5",
"3/7",
"3/11"
] | Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E... | B |
mathematics | How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? | [
"482",
"442",
"552",
"662",
"526"
] | 20000(11/10)4 - 20000(6/5)2 = 482
Answer: A
The answer is: A | A |
mathematics | In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen? | [
"85",
"140",
"60",
"80",
"75"
] | The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 10
r = 3
So, total teams is 10C3 = 10!/(3!(10 - 3)!) = 120, and
n = 10 - 3 = 7
r = 3
for teams without a pediatrician is 7C3 = 7!/(3!(7 - 3)!) = 35,
so, teams with a... | A |
mathematics | A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.) | [
"81",
"84",
"85",
"88",
"90"
] | LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8 = 84
B
The answer is: B | B |
mathematics | Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $850 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ? | [
"670",
"664",
"698",
"744",
"710"
] | Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 850 - 815 = 35
Interest ... | E |
mathematics | Antonio works in a bakery. He made cookies that cost $3 and made $300. How many customer did he have? | [
"100 customers",
"185 customers",
"250 customers",
"200customers",
"270 customers"
] | A cookie costs $3 adding another one is $6. 300 divided by 6 is 50x 2 is 100. He had 100 customers.
The correct answer is A.
The answer is: A | A |
mathematics | Aravamudhan, Balakrishnan and Chinnan work in a developing software company in starting level positions. However their salaries are different. Aravamudhan's salary to Balakrishnan's salary and Balakrishnan's salary to Chinnan's salary are in the ratio 4:3. If the total salary of all the three employees is Rs.29230, wha... | [
"Rs.12640",
"Rs.9480",
"Rs.7110",
"Rs.8660",
"Rs.9660"
] | making them in equal proportion of Aravind:Bala:Cinnana=16:12:9
and given total salary 37*x=29230
x=790
Chinnana salary is 9*790=7110
ANSWER:C
The answer is: C | C |
mathematics | Goldenrod and No Hope are in a horse race with 7 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? | [
"5040",
"2520",
"1200",
"240",
"210"
] | All 7 horses can finish the race in 7! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 7!/2=2520 different arrangements of fini... | B |
mathematics | A man invests Rs. 6,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum? | [
"Rs. 1200",
"Rs. 1300",
"Rs. 1500",
"Rs. 3000",
"None of these"
] | Explanation :
Interest on Rs.6000 at 5% per annum = ( 6000 × 5 × 1) / 100 = Rs. 300
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (6000 + x) × 6 × 1/100.
=> 300 + 2x/25 = (6000 + x) × 6 × 1/100.
=> 30000 + 8x = (600... | D |
mathematics | A can do a piece of work in 4hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? | [
"8 hours",
"10 hours",
"12 hours",
"24 hours",
"30 hours"
] | A's 1 hour work= 1/4
(B+C)'s 1 hour work= 1/3
(A+C)'s 1 hour work= 1/2
(A+B+C)'s 1 hour work= (1/4+1/3)=7/12
B's 1hour's work= (7/12-1/2)= 1/12
B alone will take 12 hours to do the work.
correct option is C
The answer is: C | C |
mathematics | A girl swims downstream 48 km and upstream 16 km taking 8 hours each time; what is the speed of the current? | [
"2.0",
"2.1",
"2.2",
"2.3",
"2.4"
] | 48 --- 8 DS = 6
? ---- 1
16 ---- 8 US = 2
? ---- 1 S = ?
S = (6 - 2)/2 = 2
Answer:A
The answer is: A | A |
mathematics | The ratio of radius of a circle and the side of a square is 2 : 9. Find the ratio of their areas: | [
"2 : 1",
"4 : 7",
"8 : 77",
"4 : 81",
"None"
] | radius/side = 2/9
⇒ area of circle/area of square= 4/81
Answer: D
The answer is: D | D |
mathematics | Each shelf of a bookcase contained 11 books. If the librarian took out 30 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 5 books, how many shelves does the bookcase have? | [
"5",
"6",
"7",
"8",
"9"
] | Let x be the number of shelves.
11x - 30 = 7(x-1) + 5
4x = 28
x = 7
The answer is C.
The answer is: C | C |
mathematics | A dog takes 5 leaps for every 7 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is : | [
"16 : 7",
"15 : 7",
"20 : 7",
"7 :15",
"14 : 7"
] | Explanation:
Dog : Hare = (5*3) leaps of hare : 7 leaps of hare = 15 : 7
Answer: B
The answer is: B | B |
mathematics | 3/x + 3x = 3(x-9) | [
"-9",
"-1/6",
"-1/9",
"1/9",
"9"
] | We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(3/X) + 3x = 3(x-9)
(3/x) + 3x = 3x - 18
3 + 3x^2 = 3x^2 - 18x
3 = -18x
-1/6 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
B
The an... | B |
mathematics | A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? | [
"9",
"7",
"5",
"4",
"6"
] | Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec.
Answer: E
The answer is: E | E |
mathematics | What is the sum of the numbers between 1 and 10, inclusive? | [
"85",
"95",
"100",
"105",
"55"
] | Sol. add all the numbers between 1 and 10.
Final Answer =E, 55.
The answer is: E | E |
mathematics | From a group of 4 boys and 4 girls, 2 children are to be randomly selected. What is the probability that 1 boy and 1 girl will be selected? | [
"1/2",
"2/3",
"3/5",
"4/7",
"5/9"
] | The total number of ways to choose 2 children from 8 is 8C2 = 28
The number of ways to choose 1 boy and 1 girl is 4*4 = 16
P(1 boy and 1 girl) = 16/28 = 4/7
The answer is D.
The answer is: D | D |
mathematics | A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? | [
"30",
"35",
"36",
"37",
"38"
] | Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: Option C
The answer is: C | C |
mathematics | A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m? | [
"22377",
"27782",
"27891",
"24000",
"18771"
] | 24 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
24 = 1/100 * x => x = 24000
Answer: D
The answer is: D | D |
mathematics | A,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days? | [
"2",
"4/5",
"7/9",
"36/11",
"24/7"
] | A+B+C 1day work = 1/18 + 1/6 + 1/12 = 11/36
A,B,C together will complete the job in 36/11 days
Answer is D
The answer is: D | D |
mathematics | A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color? | [
"224/8855",
"225/8855",
"245/8855",
"285/8855",
"244/8855"
] | Explanation:
Total marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles
4 marbles are drawn from 23 marbles at random. Therefore,
n(S) = 23C4 = 8855 ways
Let A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 5C4 + 10C4 + 8C4 = 5 +210 ... | D |
mathematics | What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 857.48 = 743.095 + ? | [
"870",
"790",
"580",
"770",
"890"
] | ? = 285 + 1895 – 855 – 745 or, ? = 580
Answer C
The answer is: C | C |
mathematics | A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at: | [
"5.30 a.m",
"6.42 a.m",
"7.55 a.m",
"7.42 a.m",
"None"
] | Sol.
Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two
Relative speed of A and B = (6-1) = 5 rounds per hour.
Time taken to complete one round at this speed = 1/5 hr = 12 min.
Answer D
The answer is: D | D |
mathematics | In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y = | [
"6",
"7",
"5",
"8",
"3"
] | Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x.
Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6.
Answer: 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 kmph",
"7.5 kmph",
"8 kmph",
"9 kmph",
"4 kmph"
] | US = 20
DS = 35
M = (35 - 20)/2 = 7.5
Answer:B
The answer is: B | B |
mathematics | If 35 percent of 400 is 20 percent of x, then what is 70 percent of x? | [
"200",
"490",
"700",
"900",
"1,400"
] | 35/100(400) = 2/10(x)
X = 700..
70 percent of x =70/100(700) =490
Option B.
The answer is: B | B |
mathematics | Cost is expressed by the formula tb^4. If b is doubled, the new cost E is what percent of the original cost? | [
"E=200",
"E=600",
"E=800",
"E=1600",
"50"
] | Original Cost E, C1=t1*b1^4
New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
The answer is: D | D |
mathematics | Two trains of equal length 120 metres move in the same direction. The faster train completely
overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over
taking would take in 10 seconds. At what speeds are the 2 trains moving ? | [
"24,22",
"32,16",
"30,18",
"28,14",
"None of these"
] | Explanation :
The total distance covered for over taking = length of the two trains = 120 +120 = 240
Speed of faster train be x m/s and slower train be y m/s
In the first case Relative speed = x-y
Relative Speed = Distance / Time taken = x-y = 240/15 = 16 m/s(1)
In the second case, the slower train moves at half its sp... | B |
mathematics | If x is a positive integer, then the least value of x for which x! is divisible by 10,000 is?
Can someone please explain intuitively what the question is asking? | [
"5",
"9",
"12",
"15",
"20"
] | In order x! to be divisible by 1,000, it should have at least 3 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 3.
5! = 120 has 1 trailing zeros.
10! will have 2 trailing zeros.
15! will have 3 trailing zeros.
20! will have 5 ... | E |
mathematics | Two pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank? | [
"450",
"540",
"542",
"829",
"279"
] | 1/10 + 1/15 - 1/x = 1/15
x = 10
10 * 45 = 450
Answer: A
The answer is: A | A |
mathematics | A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 60% total profit if he has already sold one of the four cars at Rs. 1.2 lakh? | [
"1.8 lakh",
"1.2 lakh",
"1.9 lakh",
"8.1 lakh",
"6.1 lakh"
] | Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.6 = 4.8 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 4.8 - 1.2 = 3.6 lakh
Average SP of all the 3 cars = 1.2 lakh
Answer: B)
The answer is: B | B |
mathematics | The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability S that Tommy CA... | [
"11/32",
"13/32",
"15/32",
"17/32",
"19/32"
] | In order to form a triangle, the sum of two sides must be greater than the third side.
So we can choose the combination of numbers which will NOT result in a triangle.
Favorable outcomes:
1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or
1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (... | C |
mathematics | A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? | [
"89.2 km/hr",
"79.9 km/hr",
"99.2 km/hr",
"79.2 km/hr",
"72.2 km/hr"
] | Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer: D
The answer is: D | D |
mathematics | A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent? | [
"6%",
"8%",
"5%",
"2%",
"4%"
] | Let CP of an article = RS. 100
MP= Rs. 120
Discount = 20%
SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96
Clearly, the trader gets 4% loss.
Answer: E
The answer is: E | E |
mathematics | There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number? | [
"25",
"81",
"86",
"16",
"27"
] | Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 15
3x = 15 => x = 5
=> Smaller number = 5x = 25.
Answer: A
The answer is: A | A |
mathematics | There are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red? | [
"312/16808",
"312/16807",
"312/16805",
"312/16838",
"312/16111"
] | At least 3 reds means we get either : 3 red or 4 red or 5 red. And this is a case of replacement.
case 1 : 3 red balls : 6/21 x 6/21 x 6/21 x 15/21 x 15/21
case 2 : 4 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 15/21
case 3 : 5 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 6/21
Total probability = = (6/21 x 6/21 x 6/21 x 15/21 x... | B |
mathematics | John is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare? | [
"$1010",
"$1100",
"$1110",
"$1101",
"$1200"
] | Answer= B
The total cost of the trip ($12100.00) divided by 11 equals $1100.00.
The answer is: B | B |
mathematics | A man's speed with the current is 20 kmph and speed of the current is 5 kmph. The Man's speed
against the current will be | [
"11 kmph",
"10 kmph",
"14 kmph",
"17 kmph",
"None of these"
] | Explanation:
Speed with current is 20,
speed of the man + It is speed of the current
Speed in sƟll water = 20 - 5 = 15
Now speed against the current will be
speed of the man - speed of the current
= 15 - 5 = 10 kmph
Answer: B
The answer is: B | B |
mathematics | Convert the following units:
(a) 60 cm² in mm² | [
"600 mm²",
"1600 mm²",
"6000 mm²",
"600 mm²",
"6600 mm²"
] | 60 cm² in mm²
1 cm = 10 mm
1 cm² = 100 mm²
Therefore, 60 cm² = 60 × 100 mm²
= 6000 mm²
ANSWER : OPTION C
The answer is: C | C |
mathematics | The average weight of 25 boys sitting in a class had some value. A new boy added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the boys decreased by 5 kg. Find the average weight of first 25 boys? | [
"150",
"152",
"176",
"180",
"182"
] | 25x + 46 = 26(x – 5)
x = 176
C
The answer is: C | C |
mathematics | A motorcyclist goes from Bombay to Pune, a distance of 288 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car? | [
"1:2",
"1:5",
"1:4",
"2:3",
"1:8"
] | T = 288/32 = 9 h
T = 9 - 3 = 6
Time Ratio = 9:6 = 3:2
Speed Ratio = 2:3
Answer: D
The answer is: D | D |
mathematics | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. | [
"2/1",
"4/1",
"2/3",
"3/4",
"3/1"
] | Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+3) = 36/12 = 3/1.
Answer: E.
The answer is: E | E |
mathematics | A tourist purchased a total of $1,550 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks tha... | [
"$1,430",
"$1,320",
"$1,290",
"$1,270",
"$1,150"
] | since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value o... | B |
mathematics | Two numbers x and y are such that the sum of 3% of x and 4% of y is one-third of the sum of 2% of of x and 8% of y. Find the ratio of x : y. | [
"3:8",
"6:7",
"4:7",
"2:5",
"None of these"
] | Explanation :
Solution: 3% of x+ 4% of y=1/3(2% of x+8% of y)
3x/100 + 4y/100 = 2x/300 + 8y/300
(3x+4y)3 = 2x+8y
7x = 4y
x/y = 4/7
Answer : C
The answer is: C | C |
mathematics | A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400? | [
"2998",
"1900",
"2788",
"2662",
"1122"
] | 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74
=> 1900
Answer:B
The answer is: B | B |
mathematics | 2,345
2,354
2,435
.....
....
+5,432
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 2,3,4,5 exactly once in each integer. What is the sum of these 24 integers? | [
"81,218",
"85,546",
"89,928",
"93,324",
"97,716"
] | In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(2222)+6(3333)+6(4444)+6(5555) = 93,324
The answer is D.
The answer is: D | D |
mathematics | A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | [
"500",
"289",
"350",
"882",
"281"
] | Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: A
The answer is: A | A |
mathematics | On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 25 inch from the base of the mountain. How many km is he from the base of the mountain? | [
"10.89",
"14.81",
"14.8",
"14.82",
"14.12"
] | Explanation:
Since 312 inch = 136 km
So 1 inch = 136/312 km
So 25 inch = (136 × 25)/ 312 = 10.89 km
Answer: A
The answer is: A | A |
mathematics | For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually? | [
"26m",
"32m",
"24m",
"28m",
"None of these"
] | Explanation:
This is a simple speed time problem. Given conditions:
=>Speed of P= 224/28 = 8m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 4 seconds
Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres
ANSWER: B
The answer is: B | B |
mathematics | By selling 100 pens, a trader gains the cost of 40 pens. Find his gain percentage? | [
"40%",
"50%",
"60%",
"70%",
"30%"
] | Let the CP of each pen be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 40 pens
= Rs. 40
Profit% = 40/100* 100
= 40%
Answer: A
The answer is: A | A |
mathematics | The average age of a group of n people is 14 years old. One more person aged 32 joins the group and the new average is 15 years old. What is the value of n? | [
"13",
"14",
"15",
"16",
"17"
] | 14n + 32 = 15(n+1)
n = 17
The answer is E.
The answer is: E | E |
mathematics | If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 85, what is the value of K? | [
"11",
"15 3/4",
"31",
"23",
"25 3/10"
] | K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 85
11K = 85 * 4 +1 = 340 +1 = 341
K = 253 / 11 = 31.
Answer C.
The answer is: C | C |
mathematics | It rained on exactly 7 of the days during Jane's summer holiday trip. On
each day that it rained, it rained either in the morning or the afternoon
but not both. There were exactly 5 afternoons when it did not rain and
exactly 6 mornings when it did not rain. How many days did the trip
last? | [
"7",
"8",
"9",
"10",
"11"
] | Let M be the number of days it rained in the morning; A - the number of
days it rained in the afternoon; and let N be the number of days when it did not rain.
We have M + A = 7 (days when it rained); M + N = 5 (afternoons when it did not
rain); and A + N = 6 (mornings when it did not rain). Adding the equations we get
... | C |
mathematics | The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? | [
"18/35",
"18/35",
"18/39",
"18/31",
"18/32"
] | If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: A
The answer is: A | A |
mathematics | How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits F equal to 28? | [
"14",
"24",
"28",
"48",
"96"
] | First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise ... | D |
mathematics | When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%? | [
"25300",
"22000",
"21000",
"23560",
"24540"
] | sell at 18700 he got a loss of 15% means, This 18700 is 85% not 100%.
To get 1% : 18700/85=220; Then 220 is 1%.
To get 100% : 220*100=22000.
To get 115% : 220*115=25300.
ANSWER :A
The answer is: A | A |
mathematics | The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 3 shirts each of them then average number of shirt each of them now has | [
"66",
"63",
"62",
"64",
"61"
] | Required average
= Old average + New average
= 60 + 3 = 63
answer :B
The answer is: B | B |
mathematics | Evaluate: 19 + sqrt(- 2 + 12×6÷9) =? | [
"51",
"53",
"55",
"57",
"59"
] | According to order of operations, inner brackets first where 12x6÷9 is first calculated since it has a multiplication and a division.
12x6÷9 = 72÷9 = 8
Hence
19 + sqrt(- 2 + 12×6÷9) = 19+ sqrt(- 2 + 8)
= 19 + sqrt(6) = 19 + 36 = 55
correct answer C)55
The answer is: C | C |
mathematics | Find the numbers which are in the ratio 3:2:4 such that the sum of the first and the second added to the difference of the third and the second is 21. | [
"9, 6, 16",
"9, 6, 19",
"9, 6, 16",
"9, 6, 12",
"9, 6, 11"
] | Let the numbers be a, b and c.
a:b:c = 3:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 21
=> 3x + 4x = 21 => x = 3
a, b, c are 3x, 2x, 4x
a, b, c are 9, 6, 12.
Answer: D
The answer is: D | D |
mathematics | If T = 5/9 * (K - 32), and if T = 75, then what is the value of K? | [
"158",
"161",
"164",
"167",
"170"
] | K-32=9T/5
K=9T/5 + 32
K=9(75)/5 + 32 = 167
The answer is D.
The answer is: D | D |
mathematics | Find the area of circle whose radius is 7m? | [
"124 sq m",
"154 sq m",
"145 sq m",
"167 sq m",
"180 sq m"
] | r = 7
Area of Circle =∏r2
= (22/7)(7)(7)
= 154 sq m.Answer: B
The answer is: B | B |
mathematics | How much time will take for an amount of Rs. 400 to yield Rs. 81 as interest at 4.5% per annum of simple interest? | [
"4 1/2 years",
"6 1/2years",
"7 1/2years",
"12 1/2years",
"15 1/2years"
] | Time = (100 * 81) / (400 * 4.5) = 4 1/2years
ANSWER:A
The answer is: A | A |
mathematics | Evaluate: 50 - 12÷4×2 = | [
"44",
"54",
"16",
"27",
"30"
] | According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
50 - 12÷4×2 = 50 - 6 = 44
correct answer A)44
The answer is: A | A |
mathematics | It takes Joey the postman 1 hours to run a 2 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 6 mile/hour, what is the speed with which Joey returns? | [
"9",
"12",
"13",
"14",
"15"
] | let his speed for one half of the journey be 3 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*2*x/3+x=6
4x=6x+18=>2x=18
x=9
A
The answer is: A | A |
mathematics | The speed of the boat in still water in 12 kmph. It can travel downstream through 42 kms in 3 hrs. In what time would it cover the same distance upstream? | [
"8 hours",
"6 hours",
"4.2 hours",
"5 hours",
"6 hours"
] | Still Water=12km/hr
Downstream=42/3=14km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+14/2 = 10km/hr
So time taken in upstream = 42/10 =4.2hrs
ANSWER:C
The answer is: C | C |
mathematics | At a dinner party, 8 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group? | [
"5",
"10",
"24",
"32",
"5040"
] | Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position i... | E |
mathematics | A number, x is chosen at random from the set of positive integers less than 20. What is the probability that (18/x) > x? | [
"1/5",
"2/9",
"3/19",
"4/19",
"7/9"
] | Number x has to be chosen from numbers 1-19
(18/x) > x
=> 18 > x^2
=>x^2 - 18 < 0
x can have 2 values only 1 , 2 , 3 , 4
Therefore , probability = 4 / 19
Answer D
The answer is: D | D |
mathematics | In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students? | [
"80%",
"20%",
"40%",
"50%",
"None of these"
] | Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D
The answer is: D | D |
mathematics | A cricketer scored 152 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. | [
"46.2%",
"54.54 %",
"60.52%",
"70%",
"None of these"
] | Explanation :
Number of runs made by running = 152 - (12 x 4 + 2 x 6)
= 152 - (60)
= 92
Now, we need to calculate 92 is what percent of 152.
=> 92/152 * 100 = 60.52 %
Answer : C
The answer is: C | C |
mathematics | In a mayoral election, Candidate X received 1/5 more votes than candidate Y, and Candidate Y received 1/2 fewer votes than Z. If Z received 20,000 votes how many votes did candidate X received? | [
"12000",
"22000",
"24000",
"26000",
"32000"
] | Z=20 --> Y received 1/2 fewer votes than Z --> Y=Z-1/2*Z=10;
X received 1/5 more votes than Y --> X=Y+1/5*Y=12.
Answer: A.
The answer is: A | A |
mathematics | A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? | [
"229",
"277",
"600",
"275",
"221"
] | D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km.,Answer: C
The answer is: C | C |
mathematics | If k is an integer and 0.0010101 x 10^k is greater than 10, what is the least possible value of k? | [
"2",
"3",
"4",
"5",
"6"
] | 0.0010101 * 10^k > 10
We need to move the decimal point to the right 4 places to get 10.101
This is equivalent to multiplying by 10^4.
The answer is C.
The answer is: C | C |
mathematics | In a group of 150 readers who read science fiction or literacy works or both, 120 read science fiction and 90 read literacy works. How many read both science fiction and literacy works? | [
"70",
"60",
"90",
"100",
"110"
] | Consider total number of reader n(S U L) = 150
People who read science fiction n(S) = 120
People who read literacy works n(L) = 90
both science fiction and literacy n(S ∩ L) = ?
n(S U L) = n(S)+ n(L) - n(S ∩ L)
150 = 120 + 90- n(S ∩ L)
n(S ∩ L) = 210 -150
n(S ∩ L) = 60
SO People read both science fiction and ... | B |
mathematics | How many words can be formed by using all letters of the word ‘ILLINOIS’ ? | [
"40230",
"40320",
"30420",
"20340",
"40240"
] | Solution
The word ILLINOIS contains 8 different letters.
Required number of words = 8P8 = 8 ! = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 40320
Answer B
The answer is: B | B |
mathematics | Siddharth wants to borrow Rs.7000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction? | [
"s.21.60",
"s.21.68",
"s.25.2",
"s.21.98",
"s.21.29"
] | Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.7,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 7,000{ [1 + 6/100]2 - 1 - 12/100}
= 7,000 {(1.06)2- 1 - 0.12} = 7,000(1.1236 - 1 - 0.... | C |
mathematics | A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? | [
"Rs.3630",
"Rs.2840",
"Rs.3200",
"Rs.5600",
"Rs.5700"
] | 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
ANSWER:A
The answer is: A | A |
mathematics | 12 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? | [
"190",
"132",
"210",
"220",
"225"
] | Though 2*(12C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 11, so he'll play 22 matches.
Similarly, second guy has to play with the rest of 10 as his 2 games with the first guy are ... | B |
mathematics | A company has 17 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter? | [
"2380",
"2400",
"2420",
"2440",
"2460"
] | 17C4=2380
The answer is A.
The answer is: A | A |
mathematics | A can do a piece of work in 80 days. He works at it for 10 days & then B alone
finishes the remaining work in 42 days. In how much time will A and B, working
together, finish the work? | [
"122days",
"41days",
"80days",
"42days",
"30days"
] | Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
answer E 30days
Th... | E |
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