subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Find the cost of fencing around a circular field of diameter 30 m at the rate of Rs.5 a meter? | [
"288",
"132",
"772",
"592",
"471.25"
] | 2 * 22/7 * 15 = 94.25
94.25 * 5 = Rs.471.25
Answer: E
The answer is: E | E |
mathematics | Tom covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time? | [
"15 Kmph",
"29 Kmph",
"25 Kmph",
"30 Kmph",
"34 Kmph"
] | Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A
The answer is: A | A |
mathematics | A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.52 if each film contains 36 photos? | [
"4 films and 10 photos",
"5 films and 6 photos",
"5 films and 14 photos",
"6 films and 4 photos",
"6 films and 28 photos"
] | 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.52-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->4 full films and 1+11=12 photos
Answer: A
The answer is: A | A |
mathematics | The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red | [
"5.24%",
"5.35%",
"6.125%",
"7.45%",
"8%"
] | Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
The answer is: C | C |
mathematics | Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is? | [
"3/6",
"3/2",
"7/3",
"3/5",
"5/2"
] | Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 24 ==> 27 x + 17 y = 24 x + 24 y
==> 3 x = 7 y ==> x/y
= 7/3.
Answer:C
The answer is: C | C |
mathematics | A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? | [
"12/455",
"24/455",
"9/31",
"48/75",
"89/121"
] | Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (ΓΒ²CΓ’βΒ)(Γ’ΒΒ΄CΓ’ββ)/ΓΒΉΓ’ΒΒ΅CΓ’βΖ
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
ANSWER A
The answer is: A | A |
mathematics | Q is a set of four distinct prime numbers. If the sum of the integers in Q is odd and the number x is a member of Q, then what is the least value that x can be? | [
"2",
"3",
"4",
"5",
"7"
] | 2 + 3 + 5 + 7 = 17 ( sum is ODD)
Least number = 2
A
The answer is: A | A |
mathematics | A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 21, 34 and 55. Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box? | [
"7/72",
"1/6",
"1/7",
"15/36",
"21/36"
] | Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you wil... | C |
mathematics | A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train. | [
"200/3m",
"100m",
"50m",
"100/3",
"none of these"
] | A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
The man is moving forward at a speed of 5km/h while the train is moving forward at a speed of 25... | A |
mathematics | A can run 4 times as fast as B and gives B a start of 66 m. How long should the race course be so that A and B might reach in the same time? | [
"88 m",
"60 m",
"80 m",
"65 m",
"75 m"
] | Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 66m he gains 66*(4/3)
I.e 88m
ANSWER:A
The answer is: A | A |
mathematics | Let the polynomials be:
P1(x)=3x2β7x+5,
P2(x)=β5x2β4x+2,
P1(x)+P2(x)= | [
"2x2 + 11x - 7",
"-2x2 - 11x + 7",
"-2x2 - 11x + 6",
"2x2 - 9x + 7",
"None of these"
] | Solution:
P1(x)+P2(x)=(3x2β7x+5)+(β5x2β4x+2)=P1(x)+P2(x)=(3x2β7x+5)+(β5x2β4x+2)=
3x2β7x+5β5x2β4x+2=3x2β7x+5β5x2β4x+2=
β2x2β11x+7
Answer B
The answer is: B | B |
mathematics | A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe... | [
"6 hrs",
"10 hrs",
"15 hrs",
"30 hrs",
"25 hrs"
] | Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15
ANSWER:C
The answer is: C | C |
mathematics | If a(a - 9) = 10 and b(b -9) = 10, where a β b, then a + b = | [
"β48",
"β2",
"2",
"9",
"48"
] | i.e. if a = -1 then b = 10
or if a = 10 then b = -1
But in each case a+b = -1+10 = 9
Answer: option D
The answer is: D | D |
mathematics | Adding two non multiples of E always results in a multiple of E; which of the following must be the value of E ? | [
"[A] two",
"[B] three",
"[C] five",
"[D] ten",
"[E] hundred"
] | NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.
so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..
A
The answer is: A | A |
mathematics | Find the average of all the numbers between 6 and 34 which are divisible by 5? | [
"10",
"20",
"34",
"54",
"28"
] | Average = (10 + 15 + 20 + 25 + 30)/5
= 100/5 = 20.
Answer:B
The answer is: B | B |
mathematics | The radius of the two circular fields is in the ratio 3: 7 the area of the first field is what percent less than the area of the second? | [
"82.9%",
"84.2%",
"81.0%",
"80.6%",
"81.6%"
] | r = 3 Γβ¬r2 = 9
r = 7 Γβ¬r2 =49
49Γβ¬ Γ’β¬β 40 Γβ¬
100 ---- ? => 81.6%.Answer:E
The answer is: E | E |
mathematics | There are 30 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? | [
"6",
"12",
"15",
"24",
"27"
] | 30*2/3 *3/4= 15
Answer: C
The answer is: C | C |
mathematics | Morgan Goldman has 5 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of three managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Morgan Goldman possibly provide guidance for? | [
"16",
"36",
"110",
"154",
"210"
] | P(at least 1 S D) = P(Total) - P(0 Senior Director)
=10C3 - 5C3
= 110
The answer is: C | C |
mathematics | The area of a square garden is Q square feet and the perimeter is P feet. If Q=P+32, what is the perimeter of the garden in feet? | [
"32",
"36",
"40",
"44",
"48"
] | Let x be the length of one side of the square garden.
x^2 = 4x + 32
x^2 - 4x - 32 = 0
(x-8)(x+4) = 0
x = 8, -4
P = 4(8) = 32
The answer is A.
The answer is: A | A |
mathematics | A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | [
"320",
"600",
"700",
"350",
"500"
] | Speed = 300/18 m/sec = 50/3 m/sec
(x+300/39) = 50/3
x=350 m
ANSWER D
The answer is: D | D |
mathematics | John can row at 5 kmph and still water. He takes 5 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? | [
"28 km",
"12 km",
"16 km",
"30 km",
"20 km"
] | Let the distance between A and B be x km.
Total time = x/(5 + 1) + x/(5 - 1) = 5
=> x/6 + x/4 = 4 => (2x + 3x)/12 = 5 => x = 12 km.
ANSWER:B
The answer is: B | B |
mathematics | A bus 15 m long is running with a speed of 40 km/hr. In what time will it pass a man who is skateboarding at 8 km/hr in the direction opposite to that in which the car is going? | [
"1.125",
"1.5",
"1.75",
"1.25",
"1"
] | Speed of bus relative to man = 40 + 8 = 48 km/hr.
= 48 * 5/18 = 40/3 m/sec.
Time taken to pass the man = 5 * 3/40
= 1.125 sec.
Answer: A
The answer is: A | A |
mathematics | In a box of 7 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective? | [
"1/2",
"1/5",
"2/3",
"2/7",
"1/7"
] | First, there are 5C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 7C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 5C3/7C3=10/35 = 2/7
Answer is D
The answer is: D | D |
mathematics | When tossing two coins once, what is the probability of heads on both the coins? | [
"1/4",
"1/2",
"3/4",
"1/3",
"None of the above"
] | Total number of outcomes possible when a coin is tossed = 2 (Γ’ΛΒ΅ Head or Tail)
Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 Γβ 2 = 4
(Γ’ΛΒ΅ Here, S = {HH, HT, TH, TT})
E = event of getting heads on both the coins = {HH}
Hence, n(E) = 1
P(E) = n(E)/n(S)=1/4
Answer:A
The answer is: A | A |
mathematics | A conference is to have eight presentations over the course of one day, consisting of three long presentations, and five short presentations. If the conference organizer doesn't want consecutive long presentations, and the conference is to start with a short presentation, how many schedules of presentations are possibl... | [
"1200",
"7200",
"2880",
"5760",
"11520"
] | S*S*S*S*S*
5 short presentations can be arranged in 5!=120 ways.
As for 3 long presentations: each can be placed instead of any of the 5 star, so in C35=10C53=10 ways, and they also can be arranged in 3!=6 ways.
Total = 120*10*6 = 7,200
Ans:B
The answer is: B | B |
mathematics | A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price | [
"Rs.500/-",
"Rs.510/-",
"Rs.515/-",
"Rs.720/-",
"Rs.540/-"
] | Loss = 800*10/100 = 80
S.P = C.P - Loss
= 800- 80
=Rs.720/-
Answer :D
The answer is: D | D |
mathematics | In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples? | [
"5/21",
"5/22",
"5/20",
"5/18",
"5/19"
] | Number of ways of (selecting at least two couples among five people selected) = (β΅Cβ * βΆCβ)
As remaining person can be any one among three couples left.
Required probability = (β΅Cβ * βΆCβ)/ΒΉβ°Cβ
= (10 * 6)/252 = 5/21
Answer: A
The answer is: A | A |
mathematics | An empty pool being filled with water at a constant rate takes 6hours to fill to 3/5 of its capacity.how much more time will it take to finish filling the pool? | [
"5hr 30min",
"5hr 20min",
"4hr 48min",
"3 hr 12min",
"2hr 40 min"
] | As pool is filled to 3/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5... | D |
mathematics | What is the place value of 4 in the numeral 2436? | [
"400",
"500",
"700",
"800",
"840"
] | Option 'A'
4 * 100 = 400
The answer is: A | A |
mathematics | Mangala completes a piece of work in 15 days, Raju completes the same work in 30 days. If both of them work together, then the number of days required to complete the work is? | [
"10 days",
"12 days",
"14 days",
"16 days",
"18 days"
] | If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 15 Γ 30/45 = 10 days
A)
The answer is: A | A |
mathematics | If x and y are different prime numbers, each greater than 6, which of the following must be true? I. x+y is an even integer II. xy is an odd integer III. (x/y) is not an integer | [
"II only",
"II,III only",
"I,II and III",
"III only",
"I only"
] | Given: x and y are different prime numbers, both greater than 6
Statement I: x+y is an even integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore sum will be even.
Correct
Statement II: xy is an odd integer
Since x and y are prime numbers greater than 6, they will be odd
Therefore multiplic... | C |
mathematics | A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how mu... | [
"28%",
"25%",
"18.5%",
"16%",
"None of these"
] | Solution: Charge per call in February = 350/150 = 7/3 = 2.33
Charge per call in March = [350+(50*1.4)]/250 = 420/250 = 42/25 = 1.68
% Cheaper call rate in March = [(2.33-1.68)/2.33]*100 = 28%.
Answer: Option A
The answer is: A | A |
mathematics | A man can row 9 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? | [
"4.32",
"4.42",
"4.52",
"4.62",
"4.72"
] | M = 9
S = 1.2
DS = 9 + 1.2 = 10.2
US = 9 - 1.2 = 7.8
x/10.2 + x/7.8 = 1
x = 4.42.Answer: B
The answer is: B | B |
mathematics | Goldenrod and No Hope are in a horse race with 9 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? | [
"362880",
"181440",
"120000",
"24000",
"21000"
] | All 9 horses can finish the race in 9! 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 9!/2=181440 different arrangements of fi... | B |
mathematics | The length of rectangle is thrice its breadth and its perimeter is 104 m, find the area of the rectangle? | [
"507 sq m",
"356 sq m",
"452 sq m",
"428 sq m",
"525 sq m"
] | 2(3x + x) = 104
l = 39 b = 13
lb = 39 * 13 = 507
ANSWER:A
The answer is: A | A |
mathematics | Let the polynomials be:
P1(x)=3x2β7x+6,
P2(x)=β5x2β4x+2,
P1(x)+P2(x)= | [
"2x2 + 11x - 7",
"-2x2 - 11x + 8",
"-2x2 - 11x + 6",
"2x2 - 9x + 7",
"None of these"
] | Solution:
P1(x)+P2(x)=(3x2β7x+6)+(β5x2β4x+2)=P1(x)+P2(x)=(3x2β7x+6)+(β5x2β4x+2)=
3x2β7x+6β5x2β4x+2=3x2β7x+6β5x2β4x+2=
β2x2β11x+8
Answer B
The answer is: B | B |
mathematics | A train 1020 m long running at 102 kmph crosses a platform in 50 sec. What is the length of the platform? | [
"287",
"298",
"396",
"726",
"267"
] | D = 102 * 5/18 = 50
= 1416 Γ’β¬β 1020
= 396
Answer: C
The answer is: C | C |
mathematics | If it is 8:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.) | [
"8:22",
"8:24",
"8:27",
"8:31",
"8:30"
] | 8:27minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is E.
Answer: E.
The answer is: E | E |
mathematics | To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much
time A and C will take | [
"24 days",
"16 days",
"12 days",
"8 days",
"None of these"
] | Explanation:
A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6
We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)
So A 1 day work =
16β112=112
Similarly C 1 day work =
16β18=4β324=124
So A and C 1 day work =
112+124=324=18
So A and C can together do this work in 8 days
Answer: D
The answer is: D | D |
mathematics | To create paint with a certain shade of gray, one must combine 2.116 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray? | [
"165.4",
"176.4",
"347.1",
"694.4",
"705.6"
] | Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.116:1 Since the ratio is more than double, the amount of White Paint should be le... | A |
mathematics | A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? | [
"50 km/hr",
"24 km/hr",
"8 km/hr",
"5 km/hr",
"16 km/hr"
] | Explanation:
Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: A
The answer is: A | A |
mathematics | A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one... | [
"52.9%",
"55.4%",
"58.3%",
"61.7%",
"64.5%"
] | There are a total of 9*9*9 = 729 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 7*7*7 = 343 cubes.
The number of cubes with at least one side painted red is 729 - 343 = 386 cubes
The probability that a cube has at least one side painted red is 386/729 which is about 52.... | A |
mathematics | If a square mirror has a 20-inch diagonal, what is the approximate perimeter Q of the mirror, in inches? | [
"40",
"60",
"80",
"100",
"120"
] | if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter ... | B |
mathematics | A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? | [
"288",
"180",
"1288",
"1771",
"231"
] | Length of the train be βXβ
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
The answer is: B | B |
mathematics | In how many different number of ways 7 men and 3 women can sit on a shopa which can accommodate persons? | [
"200",
"230",
"240",
"250",
"5040"
] | 10p4 = 10 X 9 X 8 X 7 = 5040
E
The answer is: E | E |
mathematics | The product of all the prime numbers less than 15 is closest to which of the following powers of 10 ? | [
"10^9",
"10^8",
"10^7",
"10^6",
"10^4"
] | P = 2*3*5*7*11*13
= 21 * 11 * 13*10
~ 10^ 4
Answer : E
The answer is: E | E |
mathematics | Arun is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm? | [
"22",
"38",
"12",
"99",
"28"
] | Let the distance be x km
if travels at 10 kmph, Arun will reach point A at 2 pm
if travels at 15 kmph, Arun will reach point 12 noon
=> Time taken when traveling at 10 km = Time taken when traveling at 15 km + 2 hours
βx10=x15+2βx10βx15=2β3xβ2x=2Γ30βx=60βDistance = 60 km
Examine the any statement say, if travels at 10 ... | C |
mathematics | The sum of first eight prime numbers is? | [
"12",
"23",
"24",
"77",
"30"
] | Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) = 77.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
D
The answer is: D | D |
mathematics | Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour? | [
"A)12",
"B)18",
"C)24",
"D)30",
"E)36"
] | Explanation:
T = 24/60 * 60 = 24
Answer: Option C
The answer is: C | C |
mathematics | If x > 0.6, which of the following could be the value of x? | [
"β0.6",
"β0.007",
"β0.006",
"β0.008",
"β0.009"
] | Answer : A
The answer is: A | A |
mathematics | The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is: | [
"Rs. 72",
"Rs. 60",
"Rs. 75",
"Rs. 76",
"None"
] | Solution: Initial Cost = Rs. 75
After 20% increase in the cost, it becomes,
(75+ 20% of 75) = Rs. 90
Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90) = Rs. 72.
So, present cost is Rs. 72.
Mind Calculation Method: 75-----20%β--β90-----20%β-----β72.
Answer: Option A
The answer is: A | A |
mathematics | How many positive integers less than 50 are multiples of 6 but NOT multiples of 8? | [
"4",
"6",
"8",
"10",
"12"
] | The LCM of 6 and 8 is 24.
If x <50 and x is divisible by 6 not by 8 --> x is NOT divisible by 24.
From 1--> 50, we have 2 numbers which is divisible by 24: 24, 48.
From 1-->50, we have (48-6)/6 +1 =8 numbers divisible by 6.
Therefore, our answer is 8-2 = 6 numbers.
B
The answer is: B | B |
mathematics | Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? | [
"2887",
"444",
"877",
"278",
"178"
] | 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
The answer is: B | B |
mathematics | What was the day of the week on, 20th July, 1776? | [
"Tuesday",
"Wednesday",
"Monday",
"Saturday",
"SUNDAY"
] | 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 o... | D |
mathematics | The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second? | [
"24%",
"74%",
"69%",
"64%",
"54%"
] | r = 3 Οr2 = 9
r = 5 Οr2 = 25
25 Ο β 16 Ο
100 ---- ? => 64%
Answer: D
The answer is: D | D |
mathematics | In covering a distance of 120 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is: | [
"5 km/h",
"8 km/h",
"10 km/h",
"15 km/h",
"20 km/h"
] | Let A's speed be X km/hr.
Then, 120/x - 120/2x = 3
6x = 120
x = 20 km/hr.
Answer : E.
The answer is: E | E |
mathematics | let S is a set of all natural numbers less than 120 such that HCF of any element in S and 120 is 1. Find the sum of all elements in S? | [
"1584",
"7640",
"5640",
"7240",
"6780"
] | S is a set of all natural numbers less than 120 such that HCF of any element in S and 120 is 1.
Such numbers are,
S = {1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113}
Sum of S = 1584.
ANSWER:A
The answer is: A | A |
mathematics | sue has 3 apples. Billy has 6 apples. If billy steals all of sues apples and eats 4 how many does he have left? | [
"2",
"5",
"6",
"4",
"8"
] | 5 B
The answer is: B | B |
mathematics | A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 10:00, how many seconds elapse betwe... | [
"42",
"36",
"46",
"38",
"40"
] | at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 10 strikes, there would be 9 intervals.
According to the question, the time spent in the strike ... | D |
mathematics | How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 4? | [
"7",
"8",
"9",
"10",
"11"
] | Counting the different combinations possible is the easiest method as the options tell you that the correct number is a relatively small number.
The total cases possible are:
12
16
24
32
36
44 (not counted as we need distinct digits)
52
56
64
72
76
Edit: Total: 10
D is the correct answer.
The answer is: D | D |
mathematics | In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 24 standard orders? | [
"3",
"6",
"8",
"9",
"12"
] | the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*24/8 = 6
Ans B
The answer is: B | B |
mathematics | A train passes a station platform in 34 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? | [
"276 m",
"279 m",
"210 m",
"207 m",
"202 m"
] | Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 34 = 15
x + 300 = 510
x =210 m.
Answer: C
The answer is: C | C |
mathematics | Maggie has to buy 50 toys from a toy shop. She buys 13 hoola hoops, 15 beach balls, and 12 baseball bats. What percentage of Toys has she not bought ? | [
"26 %",
"34 %",
"30 %",
"20 %",
"38 %"
] | Explanation :
Toys not bought = 50 - 13 - 15 - 12 = 10
Toys not bought percentage (10/50 x 100) %
Answer : D
The answer is: D | D |
mathematics | 96% of the population of a village is 23040. The total population of the village is? | [
"29992",
"24000",
"26892",
"29991",
"29878"
] | X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: B
The answer is: B | B |
mathematics | If (x^2 + 1)y=7, which of the following is not a possible value for y? | [
"2",
"2/3",
"4/3",
"4",
"15/2"
] | Its simple
equation is (x^2 +1)y = 7 ===> x^2 = (7/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (7/y) - 1>= 0 ===> y =< 7. Now only option E has greater value of 'y' than 7.
Thus, correct ans is E
The answer is: E | E |
mathematics | A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 65000, then the share of B is? | [
"24008",
"24000",
"26000",
"26000",
"30000"
] | Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs.65000
Share of B = 6/13 (65000) = Rs. 30000
Answer: E
The answer is: E | E |
mathematics | A dealer purchased an book at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? | [
"79%",
"88%",
"100%",
"94%",
"103%"
] | C
100%
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
The answer is: C | C |
mathematics | What is the minimum percentage increase in the mean of set S {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes? | [
"25%",
"50%",
"75%",
"100%",
"200%"
] | Mean of S is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of S, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
The answer is: D | D |
mathematics | The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 8 months. At this time, the construction was behind schedule by how many projects? | [
"34",
"96",
"198",
"164",
"504"
] | Project/month : 612/18 = 34
Project in 6 month to be completed = 34*8 =272
Lag :272-108 = 164
D is the answer
The answer is: D | D |
mathematics | Tim went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | [
"17.13",
"18",
"19.7",
"21.3",
"21.5"
] | Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
β΄ (25β30/100βx)6/100 = 30/100
β 6(25 β0.3 βx) = 30
β (25 β 0.3 β x) = 5
β x = 25 β 0.3 β 5 = 19.7
C)
The answer... | C |
mathematics | X, Y and Z, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2350, what will be Z's share of the earnings? | [
"$525",
"$550.50",
"$1080.02",
"$522.3",
"$1020.2"
] | The dollars earned will be in the same ratio as amount of work done
1 day work of Z is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
Z's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2350 = $522.3
hence:D
The answer is: D | D |
mathematics | A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? | [
"299",
"240",
"277",
"255",
"143"
] | Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
The answer is: B | B |
mathematics | The speed of a train is 102 kmph. What is the distance covered by it in 30 minutes? | [
"50 kmph",
"51 kmph",
"41 kmph",
"61 kmph",
"21 kmph"
] | 102 * 30/60
=51 kmph
Answer: B
The answer is: B | B |
mathematics | JC has to visit at least 2 European cities on his vacation trip. If he can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can JC create? | [
"12",
"36",
"48",
"60",
"72"
] | The question asks the different itineraries, and we need to count the order. For example, visiting city A first and visiting city B later is different from visiting city B first and visiting city A later.
To visit 2 cities from 4 cities, there are 4Γβ3=124Γβ3=12 different itineraries
To visit 3 cities from 4 cities, th... | D |
mathematics | Johnny makes $8.25 per hour at his work. If he works 2 hours, how much money will he earn? | [
"$30.50",
"$16.50",
"$28.50",
"$12",
"$9.60"
] | 8.25*2=16.50. Answer is B.
The answer is: B | B |
mathematics | If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week? | [
"$374",
"$382",
"$385",
"$392",
"$399"
] | Soln:-
(406/116)110 =385
In this case long division does not take much time.
(406/116)=3.5
35*11=385(350+35)
ANSWER:C
The answer is: C | C |
mathematics | The value of ((x β y)Β³ + (y - z)Β³ + (z β x)Β³)/(18 (x β y) (y β z) (z β x))
is equal to : | [
"0",
"1/6",
"1",
"1/4",
"1/3"
] | Since (x β y) + (y β z) + (z β x) = 0,
so (x β y)Β³ + (y β z)Β³ + (z β x)Β³= 3 (x β y) (y β z) (z β x).
(3 (x β y) (y β z) (z β x))/(18(x β y) (y β z) (z β x)) = 1/6.
ANSWER:B
The answer is: B | B |
mathematics | If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+2) for all positive integers n, what is the third term of the sequence? | [
"3",
"4",
"6",
"8",
"9"
] | Tn = nth term
T1 = 1st term
T2 = 2nd term
and so on...
Sn = Sum of first n terms of the sequence
Sn = 1st term + 2nd term + 3rd term + ... + nth term
Sn = T1 + T2 + T3 + ....Tn
You are given here thatSn is the SUM of first n terms...So you have
Sn = T1 + T2 + T3 + ....Tn = n(n+1)
So S1 = T1
S2 = T1 + T2
S3 = T1 + T2 + ... | B |
mathematics | Ajay spends 25 per cent of his salary on house rent, 10 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is AjayΓ’β¬β’s income? | [
"Rs.67500",
"Rs.80500",
"Rs.60700",
"Rs.70500",
"None of these"
] | Explanation:
Savings = Income Γ’β¬β expenditure
100 Γ’β¬β (25+10+15+10) = 40%
40% of income = Rs.27000
:. Income = 27000 x 100/40 = Rs. 67500.
Answer: Option A
The answer is: A | A |
mathematics | A train 140m long is running at 60kmph. In how much time will it pass a platform 260m long? | [
"15 seconds",
"24 seconds",
"28 seconds",
"30 seconds",
"35 seconds"
] | Distance travelled = 140 + 260m = 400m
Speed = 60 * 5/8 = 50/3m
Time = 400 * 3/50 = 24 Second
Answer : B
The answer is: B | B |
mathematics | Ayeshaβs father was 38 years of age when she was born while her mother was 32 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? | [
"2 years",
"4 years",
"6 years",
"10 years",
"None"
] | EXPLANATION
Motherβs age when Ayeshaβs brother was born = 32 years.
Fatherβs age when Ayeshaβs brother was born = (38 + 4) years = 42 years.
Required difference = (42 β 32) years = 10 years.
Answer D
The answer is: D | D |
mathematics | The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is? | [
"61.4.",
"51.7",
"51.4",
"51.1",
"51.2"
] | Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 =51.4.
Answer:C
The answer is: C | C |
mathematics | The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number? | [
"34",
"28",
"12",
"17",
"15"
] | Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER:B
The answer is: B | B |
mathematics | An article is bought for Rs.675 and sold for Rs.900, find the gain percent? | [
"33 8/3%",
"33 1/7%",
"33 1/3%",
"33 7/3%",
"33 1/8%"
] | 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
The answer is: C | C |
mathematics | The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass? | [
"65 kg",
"35 kg",
"88 kg",
"66 kg",
"44 kg"
] | 7/20 * 100
= 35
Answer:B
The answer is: B | B |
mathematics | A began business with 6000 and is joined afterwards by B with 24000. When did B join, if the profits at the end of the year are divided equally? | [
"8 months",
"9 months",
"10 months",
"7 months",
"None of these"
] | Let B join after x months of the start of the business so that Bβs money is invested for (12 β x) months.
β΄ Profit ratio is 12 Γ 6000 : (12 β x) Γ 24000
or 12 : 4(12 β x)
Since profit is equally divided so
12 = 4(12 β x) or x = 9. Thus B joined after 9 months.
Answer B
The answer is: B | B |
mathematics | How many different subset of the set {I, II, III, IV, V, VI, VII, VIII, IX) do not contain V. | [
"273",
"282",
"285",
"283",
"281"
] | This is a combination solution
Since we have 8 different Roman Numerals other than the V we can take any Roman numeral from the set of 8 to make a subset.
8C1 +8C2 + 8C3 + 8C4 + 8C5 + 8C6 + 8C7 + 8 C8 = 282
Plus the one set that is null that is the Set having no element in it which is 8C0 =1
= 282 + 1 = 16
D = 283
The ... | D |
mathematics | The largest number amongst the following that will perfectly divide 101100 β 1 is? | [
"9000",
"91000",
"10000",
"11000",
"12000"
] | The easiest way to solve such problems for objective exam purposes is trial and error or by back
substituting answers in the choices given.
1012 = 10,201
1012 β 1 = 10,200.
This is divisible by 100.
Similarly try for 1013 β 1 = 1,030,301β1 = 1,030,300.
So you can safely conclude that (1011 β 1) to (1019 β 1) will be di... | C |
mathematics | Four dice are thrown simultaneously. Find the probability that all of them show the same face. | [
"1/215",
"1/216",
"1/217",
"2",
"2/215"
] | The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6Γ6Γ6Γ6=64
n(S)=64
Let X
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)}
n(X)=6
Hence required probability,
=n(X)n(S)=664
=1/216
Answer is ... | B |
mathematics | A man drive his car to the office at 20miles/hr.
After reaching office, he realize that its a new year holiday so he went back home at a speed of 30miles/hr.
Discounting the time spent in the stoppage what was his average speed of his journey ? | [
"23miles",
"25miles",
"22miles",
"24miles",
"26miles"
] | D
24miles/hr (not 25miles/hr which might be guessed by many)
D : distance traveled
T1 : time of going to office
T2 : time of returning back
Y : Average Speed
D = 20 * T1
T1 = D/20
D = 30 * T2
T2 = D/30
2D = Y(T2 + T1)
2D = Y(D/20 + D/30)
2D = Y(3D/60 + 2D/60)
2D = Y(5D/60)
Y = 120D/5D
=> Y = 24
The answer is: D | D |
mathematics | A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train? | [
"150 meter",
"178 meter",
"209 meter",
"279 meter",
"269 meter"
] | Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
=150 meter
Answer:A
The answer is: A | A |
mathematics | What is the sum of two consecutive even numbers, the difference of whose squares is 84? | [
"34",
"38",
"42",
"46",
"None"
] | EXPLANATION
Let the numbers be x and x + 2.
Then, (x + 2)2 β x2 = 84
4x + 4 = 84
4x = 80
x = 20.
The required sum = x + (x + 2) = 2x + 2 = 42.
Answer C
The answer is: C | C |
mathematics | A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction Y of time taken by the two wide pipes working together to fill the tank? | [
"1/2",
"2/3",
"3/4",
"3/7",
"4/7"
] | I always plug in for these questions.. I find them easier
Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs
now assume the total capacity = 140 lts ( LCM of 20,35)
Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working to... | E |
mathematics | In how many ways can 4 boys and 2girls be arranged ata table if 2 girls are never together? | [
"76",
"74",
"72",
"73",
"79"
] | Total ways of arranging 6 person in a circle = 5! = 120 ways
If we consider two women as one, then we have 4+1=5 persons. Arranging these five persons in circle will take = 4! = 24 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 4!*2! = 48 ways
Total ways in w... | C |
mathematics | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 151 feet long? | [
"8",
"9",
"10",
"11",
"12"
] | Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T
To maximize the number of trees, the number of 14 feet spaces between trees should be 1 less than total number of trees.
For example, If there are 3 trees, then there should be 2 spaces between them.
So the number of 14 feet... | D |
mathematics | The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction? | [
"1/3",
"2/3",
"5/9",
"5/7",
"7/11"
] | Explanation:
Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Hence the fraction is : 5/9
C
The answer is: C | C |
mathematics | One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card? | [
"1/4",
"1/7",
"1/8",
"1/5",
"2/5"
] | Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/48 = 1/4
A
The answer is: A | A |
mathematics | Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0 | [
"If x>y",
"If x>=y",
"If x < y",
"If x<=y",
"x=y or relationship cannot be established"
] | Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
The answer is: B | B |
mathematics | A man counted his animals, 80 heads and 250 legs (ducks and goats). how many goats are there? | [
"30",
"40",
"50",
"45",
"70"
] | let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=250 and divide 2d+4g=250 by 2 we get d+2g=125 -----------> eq2
subtract eq1 from eq2
we get no of goats=45
ANSWER:D
The answer is: D | D |
mathematics | A man buys a cycle for Rs. 1800 and sells it at a loss of 10%. What is the selling price of the cycle? | [
"1410",
"1620",
"1430",
"1440",
"1540"
] | S.P. = 90% of Rs. 1800 = 90/100 x1800= Rs. 1620
answer : B
The answer is: B | B |
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