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mathematics | If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=150 the (a*f)/(c*d) = ? | [
"1/2",
"1/4",
"3/4",
"1/3",
"None of these"
]
| Explanation :
a∗b∗c/b∗c∗d= 130/65 => a/d = 2
d∗e∗f/c∗d∗e= 150/1000 => f/c = 1/4
a/d* f/c = 2 * 15/10 = 1/3
Answer : D
The answer is: D | D |
mathematics | Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen? | [
"55/228",
"55/228",
"55/221",
"55/212",
"55/2234"
]
| We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = \inline {\color{Black}26C_{2}} = = 325, n(B)= \inline {\color{Black}4C_{2}} = = 6 and n(A∩B) = \inline {\color{Black}2C_{2}} = 1
P(A) = n(A)/n(S) = 325/1326;
P(B) = n(B)/n(S) = 6/1326 and
P(A∩B) = n(A∩B)/n(S) = 1/1326
P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221
Answer: C
The answer is: C | C |
mathematics | A train 120 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post? | [
"11 s",
"10 s",
"8 s",
"12 s",
"None of these"
]
| We know from the formula Time = Distance/ Speed
Thus, Time = 120/ 54 x 5/18
or, Time = 8 sec.
ANSWER:C
The answer is: C | C |
mathematics | Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)? | [
"1/20",
"1/15",
"1/12",
"1/8",
"1/2"
]
| P(A and B) = 1/2*1/10 = 1/20
The answer is A.
The answer is: A | A |
mathematics | A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km/hr in the same direction. In how much time will the train pass the jogger? | [
"14 sec",
"67 sec",
"98 sec",
"36 sec",
"23 sec"
]
| Speed of train relative to jogger =99 - 9 = 90 km/hr.
= 90 * 5/18 = 25 m/sec.
Distance to be covered = 250 + 100 = 350 m.
Time taken = 350/25 =14 sec.
Answer:A
The answer is: A | A |
mathematics | 7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.
How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible. | [
"7!/2",
"7!/3",
"7!/4",
"7!/5",
"7!/6"
]
| 7 people can be arranged in a row in 7! ways.
Now, three people among those 7 can be arranged in 3! = 6 ways:
AFE
AEF
EAF
EFA
FAE
FEA
From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.
Answer: E (7!/6).
The answer is: E | E |
mathematics | John found that the average of 15 numbers is 40. If 11 is added to each number then the mean of number is? | [
"51",
"45",
"65",
"78",
"64"
]
| (x+x1+...x14)/15 = 40
51
Option A
The answer is: A | A |
mathematics | If equation |x/2| + |y/2| = 4 encloses a certain region on the coordinate plane, what is the area of this region? | [
"20",
"50",
"108",
"200",
"400"
]
| The equation can be reduced to intercept form as |x/8| + |y/8| = 1, so these are lines in four quadrants with x and y intercept as 8, so it is a rhombus with diagonals of 16 each and hence area = 1/2*d1*d2 = 1/2*16*16 = 108. Answer C.
The answer is: C | C |
mathematics | If N = 16 × 10^(-p) and −4 < p < 4, how many different integer values of p will make N a perfect square? | [
"0",
"2",
"3",
"5",
"7"
]
| I think the answer should be C.
Thoose are P-Values that satisfy given restriction: -2, 0, 2 (note, a fraction can be also a perfect square) --> 16*100, 16*1, 16/100
The answer is: C | C |
mathematics | What is the sum of odd integers from 35 to 85, inclusive? | [
"1,560",
"1,500",
"1,240",
"1,120",
"1,100"
]
| Number of odd integers = (85-35)/2 + 1
= 50/2 + 1
= 26
Sum of odd integers = (35+85)/2 * 26
= 60 * 26
= 1560
Answer A
The answer is: A | A |
mathematics | If the product of the integers from 1 to n is divisible by 630, what is the least possible value of n? | [
"7",
"14",
"21",
"28",
"35"
]
| 630 = 2 x 3 x 3 x 5 x 7
N must include at least up to the number 7.
The answer is A.
The answer is: A | A |
mathematics | In what time will a train 240 metres long cross an electric pole, if its speed be 126 km/hr? | [
"6.75 sec",
"6.85 sec",
"6.55 sec",
"6.44 sec",
"7.85 sec"
]
| Solution
Speed = (126 x 5 /18) m/sec
= 35 m / sec
Time taken = (240 /35) sec
= 6.85 sec.
Answer B
The answer is: B | B |
mathematics | John, a painter, has 9 jars of paint: 4 are white, 2 are yellow, and the rest are brown. John will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no white paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of white paint 4) J2, if the paint contains exactly 1 jar of white paint What is the probability that the new colour will be a shade of J (J1 or J2)? | [
"42/37",
"84/37",
"21/37",
"74/42",
"37/42"
]
| the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : E
The answer is: E | E |
mathematics | John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/3 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have? | [
"45",
"67",
"70",
"77",
"98"
]
| Rakesh : Rahul : Ranjan : Rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 3,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 3 x 60 ) = 20.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 20 x + 20 x + 15 x + 12 x) = 67 x.
For minimum number of pencils x = 1 .
The person should have atleast 67 pencils.
B)
The answer is: B | B |
mathematics | The parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)? | [
"47.14",
"45.15",
"43.23",
"41.44",
"41.51"
]
| Let the side of the square be a cm.
Parameter of the rectangle = 2(40 + 20) = 120 cm Parameter of the square = 120 cm
i.e. 4a = 120
a = 30
Diameter of the semicircle = 30 cm
Circimference of the semicircle
= 1/2(âˆ)(30)
= 1/2(22/7)(30) = 660/14 = 47.14 cm to two decimal places
Answer: A
The answer is: A | A |
mathematics | A car covers a distance of 720 km in 6 hours. Find its speed? | [
"104",
"7778",
"266",
"288",
"120"
]
| 720/6 = 120 kmph
Answer:E
The answer is: E | E |
mathematics | A Vendor sells 10 clips for a rupee gaining thereby 40%. How many clips did he buy for a rupee? | [
"10",
"12",
"14",
"15",
"None"
]
| S.P of 10 Clips=Re 1
Gain= 40%.
C.P of 10 Clips=Rs(100/140)*1=Re 5/7
For Rs 5/7, Clips bought=10.
For Re 1,Clips bought=10*(7/5)=14
The answer is: C | C |
mathematics | The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the E odds that it is an ace? | [
"1/52",
"1/26",
"1/13",
"1/4",
"5/13"
]
| The question should ask about the probability not the odds.
There are 13 spades, the probability E that the spade we already have is an ace is therefore 1/13.
Answer: C.
The answer is: C | C |
mathematics | Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | [
"A)1000",
"B)1055",
"C)1065",
"D)1135",
"E)1080"
]
| Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
D)
The answer is: D | D |
mathematics | Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of a gamma raised to the seventh power and a delta raised to the seventh power? | [
"alpha",
"beta",
"gamma",
"delta",
"epsilon"
]
| Solution : 2 is gamma and 3 is a delta. 2^7 + 3^7 will have a units digit as 8+7=5. So, label is alpha.
or
alpha : 5k
beta : 5k +1
gamma : 5K+2
delta : 5k+3
epsilon : 5K+4
(5k + 2)^7 has unit digit as 8 or 3
(5k + 3)^7 has unit digit as 7 or 2
In any case (5k + 2)^7 + (5k + 3)^7 will have units digit as 0 or 5 which is a alpha.
Option A
The answer is: A | A |
mathematics | Rs 70000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%? | [
"30000",
"40000",
"50000",
"60000",
"70000"
]
| let first parrt is x and second part is y then x+y=70000----------eq1
total profit=profit on x +profit on y
8000=(x*10*1)/100 + (y*20*1)/100
80000=x+2y-----------------------------------eq2
80000=70000+y
so y=10000 then x =70000-10000=60000
first part =60000
ANSWER:D
The answer is: D | D |
mathematics | The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 24, how many more dollars, in terms of x, will it cost per person? | [
"x/6",
"x/17",
"x/40",
"3x/40",
"3x/80"
]
| Just plugging in values
X= 240
Cost per person if we consider 10 = 24
Cost per person if we consider 24 = 10
Difference between costs is 14 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 14. And that is B.
The answer is: B | B |
mathematics | How many ways can 5 friends be arranged around a circular dinner table? | [
"A)24",
"B)48",
"C)96",
"D)120",
"E)720"
]
| The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (5 - 1)! = 4! = 24.
Answer: A.
The answer is: A | A |
mathematics | A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running? | [
"2.62",
"2.56",
"2.5",
"2.8",
"3.2"
]
| Required time = (5 1/4)/3 + (5 1/4)/6 = 2.625 hours.
Answer:A
The answer is: A | A |
mathematics | A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire? | [
"6 cm",
"5 cm",
"2 cm",
"7 cm",
"9 cm"
]
| Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h
= (4/3)π (12)3 => h
= 9 cm
Answer: E
The answer is: E | E |
mathematics | A test paper has 10 questions each worth 4 marks. While taking the test, a student realises that he has attempted questions worth 16 marks. Assuming that whatever question he attempts is completely correct, how many more questions should he attempt so that he is able to secure 90 percent marks? | [
"4",
"5",
"6",
"7",
"8"
]
| Since the test paper has 10 questions each worth 4 marks, the maximum marks he can get is 40.
His aim is to secure 90 % marks, this means he wants to secure 90% of 40 = 36 marks.
Out of the 36 marks, he has already attempted questions worth 16 marks, so he should attempt questions worth 36 - 16 = 20 more marks.
As every question is worth 4 marks, so to secure 20 more marks he should attempt (20/4) = 5 more questions.
Ans B
The answer is: B | B |
mathematics | A contractor undertook to do a certain piece of work in 6 days. He employed certain number of men, but 5 of them being absent from the very first day, the rest could finish the work in 10 days. The number of men originally employed were : | [
"12",
"10",
"13",
"11",
"None of these"
]
| Explanation :
Let there be x men at the beginning. Less men, More days (Indirect Proportion)
12 : 6 :: x : (x - 5) 12 (x - 5) = 6x <=> 6x = 60 x = 10
Answer : B
The answer is: B | B |
mathematics | Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ? | [
"32 years, 23 years",
"32 years, 29 years",
"35 years, 29 years",
"35 years, 33 years",
"34 years, 33 years"
]
| father edge is 28 when his sister was born and when his brother is born sister was 4 year old, therefor age of father at the time of his brother birth is 28=4=32
now when ravi born his mother was at 26 and ravi brother is 3 year elder than ravi so age of mother at the time of ravi's brother bith =26-3=23
ANSWER:A
The answer is: A | A |
mathematics | Find the product of place value and face value of 5 in 65231 | [
"28000",
"25000",
"27000",
"26000",
"28000"
]
| Place value of 5 in 65231 = 5 x 1000 = 5000
Face value = 5
required product = 5000 x 5 = 25000
Answer :B
The answer is: B | B |
mathematics | Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? | [
"Rs.229",
"Rs.285",
"Rs.228",
"Rs.217",
"Rs.123"
]
| Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160
= Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100]
= Rs.285.
Answer:D
The answer is: D | D |
mathematics | How many ways can 4 friends be arranged around a circular dinner table? | [
"A)6",
"B)48",
"C)96",
"D)120",
"E)720"
]
| The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (4 - 1)! = 3! = 6.
Answer: A.
The answer is: A | A |
mathematics | A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join? | [
"2 months",
"3 months",
"5 months",
"4 months",
"1 months"
]
| Suppose B was there in the business for x months. Then
A : B =76000×12:57000×x
Therefore,
76000×12:57000×x=2:1
76×12:57x=2:1
76×12×1=57x×2
76×4=19x×2
4×4=(x)×2
x=8
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months
Answer is D.
The answer is: D | D |
mathematics | An article costing rs.160 is sold at 5% discount on a mark-up price. What is the selling price after
discount? | [
"106",
"116",
"126",
"136",
"152"
]
| Rs. 136
160-(160*15/100)=160*95/100=152
ANSWER:E
The answer is: E | E |
mathematics | Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ? | [
"5/ 19",
"5/ 12",
"5/ 27",
"5/ 18",
"5/ 11"
]
| Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
=5/ 12
Answer: B
The answer is: B | B |
mathematics | After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6400. Find the actual price of the good. | [
"s. 6000",
"s. 9000",
"s. 10800",
"s. 9357",
"s. 9980"
]
| Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6400
1 = 6400/68.4
100 = (6400*100)/68.4 = Rs. 9357.
Answer: Option D
The answer is: D | D |
mathematics | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is: | [
"23",
"19",
"22",
"20",
"21"
]
| Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
ANSWER:E
The answer is: E | E |
mathematics | An investor bought two shares of stock, which he sold for $72 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had: | [
"a profit of $10",
"a profit of $6",
"a loss of $6",
"a loss of $10",
"neither a profit nor a loss"
]
| The cost of the first stock was 72/1.2=60, so the profit from it is 12.
The cost of the second stock was 72/0.8=90, so loss from it is 18.
Overall the loss is $6.
The answer is C.
The answer is: C | C |
mathematics | In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m? | [
"Rs. 50000",
"Rs. 52000",
"Rs. 57000",
"Rs. 60000",
"Rs. 62000"
]
| Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
The answer is: C | C |
mathematics | The function F(n) is defined as the product of all the consecutive positive integers between 3 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is | [
"1",
"2",
"3",
"4",
"5"
]
| F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 3
Answer: C
The answer is: C | C |
mathematics | What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 4 if each digit can be used only once in each number? | [
"1776",
"1887",
"1998",
"2332",
"2554"
]
| There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(333) + 2(444) = 1998
The answer is C.
The answer is: C | C |
mathematics | An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height? | [
"80",
"88",
"94",
"112",
"124"
]
| We see that h will be a maximum h=150 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94
The answer is C.
The answer is: C | C |
mathematics | A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are : | [
"500",
"387",
"298",
"267",
"191"
]
| Explanation:
Given that the student got 125 marks and still he failed by 40 marks
=> The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
Answer: A) 500
The answer is: A | A |
mathematics | Dividing by 3⁄8 and then multiplying by 5⁄9 is the same as dividing by what number? | [
"31⁄5",
"16⁄5",
"20⁄9",
"40/27",
"5⁄16"
]
| say X/3/8*5/9 = x*8/3*5/9 = x*40/27
D
The answer is: D | D |
mathematics | Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 6 more than the average expenditure of all the nine. The total money spent by all of them was | [
"26",
"40",
"33.75",
"27",
"None of the above"
]
| Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 6 = 9x
⇒ x = 3.75
∴ Total money spent = 9x = 9 × 3.75 = 33.75
Answer C
The answer is: C | C |
mathematics | In a certain series, each term is m greater than the previous term. If the 12th term is 560 and the 9th term is 500, what is the first term? | [
"140",
"240",
"340",
"540",
"640"
]
| a + 11m = 560 (12th term)
a + 8m = 500 (9th term)
You get a = 340 and m =
Answer: C
The answer is: C | C |
mathematics | A number a is squared and then multiplied by negative 3. The result of this operation is equal to three times the sum of three times a and 1. What is one possible value of a ? | [
"25",
"3",
"4",
"1",
"8"
]
| -3*a^2=3(3a+1)
a= -1 or -1
a=-1=B
ANSWER:D
The answer is: D | D |
mathematics | If the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is? | [
"A)15",
"B)10",
"C)14",
"D)12",
"E)11"
]
| 2 * 22/7 * 14 * x = 880 => x = 10
ANSWER:B
The answer is: B | B |
mathematics | If f(x) = ax^3 + x^2 + ax – 2x, then f(b) – f(-b) will equal: | [
"2ab^3 - 2ab",
"2ab",
"2ab^3 + 2ab - 4b",
"- 4b",
"2ab^3"
]
| f(x)=ax^3 + x^2 + ax – 2x
f(b) = ab^3 + b^2 + ab – 2b
f(-b) = - ab^3 + b^2 - ab + 2b
f(b) - f(-b) = ab^3 + b^2 + ab – 2b + ab^3 - b^2 + ab – 2b
=2ab^3 + 2ab - 4b
Answer C
The answer is: C | C |
mathematics | How many ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles? | [
"120",
"240",
"360",
"540",
"720"
]
| Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways => 2*5*4*3*2*1 = 240
ANS:B
The answer is: B | B |
mathematics | At a certain amateur bands rock show the ratio of freaks to nerds to geeks( G) is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek? | [
"1/8",
"1/3",
"1/2",
"1/4",
"1/6"
]
| Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=3/6
= 1/2
Answer:
C
The answer is: C | C |
mathematics | What is the area of square field whose side of length 15 m? | [
"225",
"662",
"772",
"882",
"21"
]
| 15 * 15
= 225 sq m
Answer:A
The answer is: A | A |
mathematics | A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work? | [
"4",
"5",
"6",
"7",
"8"
]
| 2/5 + (2 + x)/10 = 1 => x = 4 days
Answer: A
The answer is: A | A |
mathematics | Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? | [
"2",
"2.5",
"3",
"3.5",
"4"
]
| The part filled by A + B + C in 1 hour is 1/6 + 1/8 + 1/24 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer is C.
The answer is: C | C |
mathematics | Find the unit's digit in 264^102+264^103 | [
"0",
"2",
"3",
"4",
"5"
]
| Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
The answer is: A | A |
mathematics | If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c) | [
"0.5",
"1.5",
"2.5",
"1.0",
"2.0"
]
| (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER B 1.5
The answer is: B | B |
mathematics | The sum of two number is 25 and their difference is 13. Find their product. | [
"104",
"114",
"315",
"325",
"None"
]
| EXPLANATION
Let the numbers be x and y.
Then, x + y = 25 and x – y = 13.
4xy = (x + y)2 – (x– y)2
= (25)2 – (13)2
= (625 – 169)
= 456
xy = 114.
Answer B
The answer is: B | B |
mathematics | How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 32%? | [
"100 ml",
"60 ml",
"120 ml",
"130 ml",
"150 ml"
]
| 400ml has 15% alcohol i.e 60ml . This means we have 340ml of water or the liquid with which alcohol is mixed
Let V be the volume of alcohol added to make the strength 32%
then V/340+V = 32/100. solving this we get V as 160ml
so we need to add 160 -60 = 100 ml of alcohol
ANSWER:A
The answer is: A | A |
mathematics | A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current? | [
"8kmph",
"6kmph",
"4kmph",
"5 kmph",
"1kmph"
]
| Explanation:
Speed of the boat in still water: 15 km/hr
Speed of boat downstream: (15+x)km/hr where x is speed of the current.
The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.
Total time= Time taken to travel downstream + Time taken to travel upstream
=> 4/5= (30/(15+x))+(30/(15-x))
=>x= 5
ANSWER:D
The answer is: D | D |
mathematics | Units digit of 7^5^6^13? | [
"7",
"8",
"9",
"1",
"11"
]
| (7^5) unit digit is 7
7^6 unit digit is 9
9^13 unit digit 9
hence unit digit is 9.
ANSWER:B
The answer is: B | B |
mathematics | A student gets 50% in one subject, 60% in the other. To get an overall of 60% how much should get in third subject. | [
"75%",
"70%",
"45%",
"55%",
"65%"
]
| Let the 3rd subject % = x
50+60+x = 3*60
110+x =180
x = 180-110 =70
Answer :B
The answer is: B | B |
mathematics | Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = -2
(II) y = 3
(III) x + y = 0 | [
"I",
"III",
"II",
"I&II",
"II&III"
]
| y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
C
The answer is: C | C |
mathematics | In how many ways a committee, Consisting of 5 men and 6 women can be formed from 8 men and 10 women? | [
"266",
"86400",
"11760",
"5040",
"720"
]
| To choose Required number of ways to form a committee:
Select 5 men out of 8 men and 6 women out of 10 women.
That is 8C5 * 10C6.
8C5=8!/3!*5!
8C5=8*7*6*5!/(3*2*1)*5!=56
10C6=10!/6!*4!
10C6=10*9*8*7*6!/6!*(4*3*2*1)=210
The Required number of ways=210*56=11760
The answer is: C | C |
mathematics | Here is a question to keep you busy. Assume that you travel to your friend's place at 20 mph, then how fast you must make the return trip via the same route such that the average speed of your travel becomes 40 mph? | [
"Possible",
"No Idea",
"All above 3",
"Impossible",
"None of above"
]
| D
Impossible
Let us first denote everything with variables.
d= distance to your friend's place
T = time taken to get there
t = time required to get back
R = Speed while returning back
d = 20T
T = d/20
d = Rt
t = d/R
We have made equations for T and t and now we can derive an equation for the round trip.
2d = 40(T + t)
2d = 40(d/20 + d/R)
2d = 40d(1/20 + 1/R)
1 = 20(R/20R + 20/20R)
20R = 20(R+20)
R = R + 20
Do you see the paradox here? You literally have to travel back at an infinite speed if you want to make the average speed of your trip 40 mph. The faster return speed will have lesser impact of the average speed but consider that the quicker your return trip is, the faster you will make it.
We are talking about travelling double the distance in the same time that was taken for one way trip. Thus, if you travel at infinite speed, you will be able to attain an average of 40 mph.
The answer is: D | D |
mathematics | 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term W of the sequence? | [
"360",
"365",
"369",
"374",
"383"
]
| First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term W , t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
The answer is: D | D |
mathematics | The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? | [
"40, 68 kmph",
"40, 30 kmph",
"70, 30 kmph",
"40, 60 kmph",
"20, 60 kmph"
]
| Speed downstream = 50 + 20 = 70 kmph
Speed upstream = 50 - 20 = 30 kmph
Answer: C
The answer is: C | C |
mathematics | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good? | [
"20/67",
"20/63",
"20/28",
"20/29",
"20/21"
]
| Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄
= (10 * 4)/126
= 20/63
Answer: B
The answer is: B | B |
mathematics | Of the diplomats who attended a summit conference: 20 spoke Japanese, 32 did not speak Russian and 20% of the diplomats spoke neither Japanese nor Russian. If 10% of the diplomats spoke both Japanese and Russian, then how many diplomats attended the conference? | [
"70",
"96",
"108",
"120",
"150"
]
| 2X2 matrix will be the easiest way to calculate this.
Text in black: given statements
Text in red: calculated values
Thus D=120 is the correct answer
The answer is: D | D |
mathematics | A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 60 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 60 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x ? | [
"400",
"4,300",
"3,700",
"4,400",
"4,760"
]
| Total number of plots,be T
Plots with 60ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 40 T = 45
Total lake frontage = 40X100 + 5X60 = 4300
Answer : B
The answer is: B | B |
mathematics | A Glee club of 20 members is performing two songs for the school talent show. 50% of its members are part of the first one, and 60% are performing in the second one. How many Glee club members are performing in both songs at the talent show? | [
"0",
"1",
"2",
"3",
"4"
]
| The total number of Glee club members is n=20.
The number of members performing the first song is 50% of it, thus
n (A)=50/100×20=10.
The number of members performing in the second one is 60%, thus
n (B)=60/100×20=12.
In order to calculate the number of Glee club members performing in both songs we can use the following equation:
n (AnB)=n (A)+n (B) -n =10+12-20=22-20=2.
ANSWER: C
The answer is: C | C |
mathematics | If A lends Rs.1500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? | [
"112.5",
"122.5",
"132.5",
"67.5",
"212.5"
]
| (1500*1.5*3)/100 => 67.5
ANSWER:D
The answer is: D | D |
mathematics | If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be | [
"478,823",
"511,913",
"531,875",
"538,424",
"569,114"
]
| To know the unit digit you can multiply both digit number: 5 x 5 = 25
This eliminates A, B, D, and E, because the number must end with a 5
So the answer is C
The answer is: C | C |
mathematics | Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? | [
"2:9",
"2:7",
"1:6",
"1:4",
"1:3"
]
| Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3
So they should be mixed in the ratio 1:3
Answer - E
The answer is: E | E |
mathematics | All the students of class are told to sit in circle shape. Here the boy at the 7 th position is exactly opposite to 27 th boy. Total number of boys in the class? | [
"25",
"40",
"35",
"30",
"28"
]
| As half the circle shape consist of 27-7=20 boys,
So total number of boys in full circle=2*20=40
ANSWER: B
The answer is: B | B |
mathematics | The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 72 on the exam is in what percentile of the school?
Choices | [
"63rd percentile",
"68th percentile",
"84th percentile",
"96th percentile",
"98th percentile"
]
| (78-65)/6.5 = 2 sigmas or 95.5th percentile for +-2 sigma but in our case we need only upper tail, so it's 100 - (100 - 95.5)/2 = 68th percentile
B
The answer is: B | B |
mathematics | A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost? | [
"Rs2,00,000",
"Rs1,05,000",
"Rs4,05,000",
"Rs 6,50,000",
"None"
]
| Explanatory Answer
Let the cost of an equipment is Rs. 100.
Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.
Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5
Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.
The total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.
Answer B
The answer is: B | B |
mathematics | The number 150 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? | [
"17",
"18",
"15",
"14",
"13"
]
| 10^2 + 7^2 + 1^2 = 150 = = => sum of these 3 integers = 10 + 7 + 1 = 18
B
The answer is: B | B |
mathematics | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 2000 resolutions? | [
"1187 m",
"1704 m",
"2816 m",
"2827 m",
"2897 m"
]
| In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 2000 resolutions.
= 2000 * 2 * 22/7 * 22.4
= 281600 cm
= 2816 m
Answer:C
The answer is: C | C |
mathematics | Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone? | [
"3 9/17",
"5 1/3",
"7",
"7 1/5",
"8 4/7"
]
| Rate of machine X = 1000/12 = 250/3
Rate of machine Y = 1/Y
Rate of machine X and Y together = 1000/5 = 200
250/3 + 1/y = 200
after solving this equation we get Y= 3/350
Rate of Y = 1/y = 1/ (3/350) = 350/3
Machine Y has to manufacture 1000 nails. So work is 1000. Putting the values;
time required for machine Y = 1000/(350/3) = 1000* 3/(350) = 60/7 = 8 4/7
ANSWER:E
The answer is: E | E |
mathematics | A train traveling at 40 kms / hr while inside the tunnel meets another train of half its length traveling at 60 kms / hr and passes it completely in 4.5 seconds. Find the length of the tunnel if the first train passes completely through it in 4 minutes 37.5 seconds. | [
"2000 meters",
"3000 meters",
"4000 meters",
"5000 meters",
"6000 meters"
]
| 3000meters
ANSWER:B
The answer is: B | B |
mathematics | Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is? | [
"29",
"27",
"36",
"88",
"21"
]
| Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer:C
The answer is: C | C |
mathematics | There are 14 songs in that 5 Rock songs, 6 western songs & 3 Hindi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song & 1 western song? | [
"15624",
"20000",
"21000",
"23000",
"24000"
]
| 15624
A
The answer is: A | A |
mathematics | Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S? | [
"0",
"2",
"4",
"5",
"6"
]
| Solution:
The average of the elements in the original set S is: (0+2+4+5+9) /5 =20 /5 =4.
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
(0+2+5+9) /4=16 /4 =4.
Answer: Option C
The answer is: C | C |
mathematics | The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is: | [
"17",
"20",
"26",
"31",
"NONE OF THESE"
]
| Explanation:
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's weight = 31 kg.
ANSWER: D
The answer is: D | D |
mathematics | The value of x + x(xx) when x = 3 is: | [
"8",
"10",
"12",
"14",
"30"
]
| x + x(xx)
Put the value of x = 3 in the above expression we get,
3 + 3(33)
= 3 + 3(3 × 3)
= 3 + 3(9)
= 3 + 27
= 30
ANSWER : E
The answer is: E | E |
mathematics | A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is? | [
"72 kmph",
"88 kmph",
"54 kmph",
"18 kmph",
"19 kmph"
]
| S = 120/6 * 18/5
= 72 kmph
Answer: A
The answer is: A | A |
mathematics | Rs.900 is divided among Maya, Annie, Saiji so that Maya receives half as much as Annie and Annie half as much as Saiji. Then Saiji’s share is : | [
"Rs.200",
"Rs.300",
"Rs.400",
"Rs.600",
"Rs.500"
]
| Let Saiji = x. Then, Annie = x/2 and Maya = x/4.
Therefore, Maya : Annie : Saiji = x/4 : x/2 : x = 1 : 2 : 4.
Therefore, Saiji’s share = Rs. 900 * 4/9
= Rs.400.
ANSWER:C
The answer is: C | C |
mathematics | What will be the reminder when (13^13+13) is divided by 14? | [
"16",
"14",
"12",
"18",
"21"
]
| (x^n+1) will be divisible by (x+1) only when n is odd;
(13^13+1) will be divisible by (13+1);
(13^13+1)+12 when divided by 14 will give 12 as remainder.
Correct Option : C
The answer is: C | C |
mathematics | Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 2408 miles? | [
"Two hours and 30 minutes.",
"One hour and 10 minutes.",
"Two hours and 25 minutes.",
"Three hours and 15 minutes.",
"Four hours and 0 minutes."
]
| Answer is E. Four hours and 0 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 2408/602 = 4 hours and 0 mins
The answer is: E | E |
mathematics | If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 690, what is the least possible value of n? | [
"10",
"11",
"12",
"13",
"23"
]
| 690 = 2 * 3 * 5 * 23
so the least value forNcan be 23.
E
The answer is: E | E |
mathematics | R=(429)^2 * 237 * (1243)^3 is thrice of ? | [
"33605 * 31960 * (1243)^2",
"33654 * 538219 * (1243)^2",
"33891 * 533247 * (1243)^2",
"34122 * 532004 * (1243)^2",
"34606 * 534572 * (1243)^2"
]
| R=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
The answer is: C | C |
mathematics | The average of 10 numbers is zero. Of them, How many of them may be greater than zero, at the most? | [
"6",
"7",
"10",
"8",
"9"
]
| Average of 10 numbers = 0
=> Sum of 10 numbers/10=0
=> Sum of 10 numbers = 0
Hence at the most, there can be 9 positive numbers.
(Such that if the sum of these 9 positive numbers is x, 10th number will be -x)
ANSWER:E
The answer is: E | E |
mathematics | The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches? | [
"31",
"86",
"82",
"15",
"10"
]
| Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 =31.
Answer:A
The answer is: A | A |
mathematics | For positive integers n, the integer part of the nth term of sequence C equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, C_1 = 1.2345678…, while C_2 = 2.4681012… The sum of the first seven terms of sequence C is between: | [
"28 and 29",
"29 and 30",
"30 and 31",
"31 and 32",
"32 and 33"
]
| First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
C_1 = 1.23…
C_2 = 2.46…
C_3 = 3.69…
C_4 = 4.812…
C_5 = 5.10…
C_6 = 6.12…
C_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
The answer is: C | C |
mathematics | The perimeter of a square is 36 m. Find the area of the square. | [
"81 m².",
"84 m².",
"86 m².",
"169 m².",
"273 m²."
]
| Perimeter of square = 36 m
But perimeter of square = 4 × side
Therefore, 4 × side = 36 m
Therefore, side= 36/4 m = 9m
Now, the area of the square = (side × side)
Therefore, area of the square = 9 × 9 m² = 81 m².
ANSWER : OPTION A
The answer is: A | A |
mathematics | In how many ways can the letters of the word OCARINA be arranged if the O, R, and N remain in their original positions? | [
"6",
"12",
"18",
"24",
"48"
]
| The word OCARINA has 7 letters and if the O, R, and N remain in their original positions
then we have 4 positions to arrange the remaining letters - C , 2A , I
Number of ways = 4!/2!
= 12
Answer B
The answer is: B | B |
mathematics | IN Common Wealth Games an athlete runs 200 meters in 36 seconds. Hisspeed is ? | [
"25 km/hr",
"27 km/hr",
"30 km/hr",
"20 km/hr",
"None of these"
]
| Explanation :
(200/1000)/(36/3600)=20 km/hr
Answer : D
The answer is: D | D |
mathematics | Ashok secured average of 72 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject? | [
"62",
"74",
"78",
"80",
"None of these"
]
| Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 72
Therefore total marks in 6 subjects = 72 * 6 = 432
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 432 – 370 = 62
ANSWER A
The answer is: A | A |
mathematics | The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is: | [
"235",
"240",
"245",
"250",
"260"
]
| Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.
Answer: Option A
The answer is: A | A |
mathematics | In a factory, an average of 50 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 48 sets/day . The average production per day for day last 5days is ? | [
"20",
"36",
"48",
"38",
"59"
]
| Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 48 - 25 x 50
= 190
∴ Average for last 5 days = 190 / 5
= 38
D
The answer is: D | D |
mathematics | How many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? | [
"25",
"30",
"40",
"45",
"54"
]
| Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=900*3/50=54sec
ANSWER:E
The answer is: E | E |
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