divelab/Sys2Bench huggingface dataset:
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
Options:
A)40m3
B)42m3
C)44m3
D)46m3
E)None of these
Rationale: Explanation:
Volume=πr2hVolume=(22/7∗1∗1∗14)m3=44m3
Option C
Answer: C
Question: D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 144:25 and BC=13 cm, then find the length of DE.
Options:
A)12
B)13
C)14
D)11
E)15
Rationale: ABC and ADE are similar triangles.
So (side of ABC/side of ADE)^2=25/169
side of ABC/side of ADE = 5/13
So the length of DE = 5
Answer - C
Answer: C
Question: 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?
Options:
A)20/67
B)20/63
C)20/68
D)20/28
E)20/27
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126
= 20/63
Answer:B
Answer: B
Question: Which of the following inequalities is always true for any non-negative real number 'x' and 'y'?
Options:
A)√(x+y) <= √x + √y
B)√(x-y) <= √x - √y
C)√(x+y) = √x + √y
D)√(x-y) >= √x - √y
E)√(x+y) >= √x + √y
Rationale: Using the principle of subadditivity which we know applies with square roots, we know that evaluating the function for the sum of two elements will always produce something less than or equal to the sum of the function's values at each element. Therefore, the answer is A.
Answer: A
Question: The number 83 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
Options:
A)17
B)16
C)15
D)14
E)13
Rationale: 7^2+5^2+3^2=49+25+9 = 83
7+5+3 =15
Hence answer is C
Answer: C
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
Options:
A)37
B)29
C)11
D)15
E)12
Rationale: Explanation:
i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years.
Answer: D
Answer: D
Question: Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?
Options:
A)55/256
B)255/256
C)155/256
D)5/256
E)201/256
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^5
probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256
Answer : B
Answer: B
Question: If athul rows 16 km upstream and 24 km down steam taking 4 hours each, then the speed of the stream
Options:
A)1kmph
B)2 kmph
C)1.5 kmph
D)12 kmph
E)15 kmph
Rationale: Speed upstream = 16/4 = 4 kmph
Speed down stream = 24/4 = 6 kmph
Speed of stream = ½ (6-4) = 1 kmph
ANSWER:A
Answer: A
Question: The breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape?
Options:
A)520
B)420
C)320
D)550
E)450
Rationale: Sol. 6x * x =7* 4200
x = 70
Length = 6* 70 = 420 B
Answer: B
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?
Options:
A)2P
B)3P
C)4P
D)5P
E)7P
Rationale: P ---- 2P ---- 8 years
3 P ---- 12 years
ANSWER:B
Answer: B
Question: A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
Options:
A)50
B)8
C)60
D)42
E)32
Rationale: in the first case the lady takes up 32 red colour
then he takes up 24 y (cause he should take up pair)
then he takes up 1y+1blue
then 2blue(cause to make sure he has a pair of each color in hand)
32+24+2+2=60
ANSWER:C
Answer: C
Question: What is the greatest positive integer n such that 3^n is a factor of 36^300?
Options:
A)100
B)200
C)300
D)600
E)900
Rationale: 36 = 3^2 * 2^2.
36^300 = 3^600 * 2^600
The answer is D.
Answer: D
Question: 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
Options:
A)II only
B)II,III only
C)I,II and III
D)III only
E)I only
Rationale: 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 multiplication will be odd.
Correct
Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct
Hence all three statements I, II and III are correct
Answer : C
Answer: C
Question: A sum of Rs. 2795 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Options:
A)1642
B)1640
C)1720
D)2795
E)6386
Rationale: (x*8*3)/100 = ((2795 - x)*3*5)/100
24x/100 = 41925/100 - 15x/100
39x = 41925 => x = 1075
Second sum = 2795 – 1075
=1720
Answer:C
Answer: C
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.0 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
Options:
A)63,000
B)2,000,000
C)2,030,000
D)2,040,000
E)2,300,000
Rationale: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
2,030,000
C
Answer: C
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
Options:
A)Four
B)Six
C)Nine
D)Ten
E)Twelve
Rationale: Mean = 8.1
Standard Deviation = 0.4
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.4 = 8.7
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.4 = 7.5
all values are within the range hence, 12 values fall within 1.5 SD from Mean
Answer: Option E
Answer: E
Question: If x/y = 5/z, then 25z^2 =
Options:
A)x²y²
B)25y²/ x²
C)625x²y²
D)y²/ x²
E)625y²/ x²
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 25z²:
x/y = 5/z
x = 5y/z
5y = xz
z = 5y/x.
If we substitute 5y/x into the expression for z, we get:
25(5y/x)² = 25(25y²/ x²) = 625y²/ x².
The correct answer is choice (E)
Answer: E
Question: Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24.
Options:
A)9974
B)9125
C)9565
D)9997
E)None of these
Rationale: Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition.
ANSWER:E
Answer: E
Question: If 50! × 50!/50^n is an integer, what is the largest possible value of n?
Options:
A)36
B)24
C)8
D)4
E)2
Rationale: 50! × 50!/50^n is an integer.
Or 50! × 50!/(5^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 50! = [50/5] + [50/25] = 12
Since there are 2 20!'s, power of 12 in the numerator = 2*12 = 24
Hence the largest value of b for which 50! × 50!/50^n is integer = 24
Correct Option : B
Answer: B
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
Options:
A)56.8 m2
B)82.9 m2
C)52.8 m2
D)17.9 m2
E)72.9 m2
Rationale: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer:C
Answer: C
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3:7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
Options:
A)Rs. 15.50
B)Rs. 16.90
C)Rs. 13.50
D)Rs. 16.50
E)Rs. 16.40
Rationale: Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D
Answer: D
Question: A car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 70 mph. How many hours long is the trip?
Options:
A)6
B)78
C)8
D)9
E)10
Rationale: Let the time for which car averages 60 mph = t
70*(t+4)= 75*4 + 60 t
=>10 t= 20
=> t = 2
Total duration of the trip = 4+2=6
Answer A
Answer: A
Question: Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
Options:
A)7
B)8
C)6
D)5
E)4
Rationale: Explanation:
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
Answer: B
Answer: B
Question: In covering a distance of 42 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options:
A)5 kmph
B)6 kmph
C)6.25 kmph
D)7 kmph
E)7.8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	42/X	-	42/2X	= 3
6x = 42
x = 7 km/hr. Answer: Option D
Answer: D
Question: On a map, 1 inch represents 28 miles. How many C inches would be necessary to represent a distance of 383.6 miles?
Options:
A)5.2
B)7.4
C)13.7
D)21.2
E)28.7
Rationale: C inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: C
Question: Each side of a certain parallelogram has length 8. If the area of the parallelogram is 16. Which of the following is the measure of one of its angles?
Options:
A)14.5
B)45
C)60
D)90
E)120
Rationale: Ans is 30deg
area of a parallelogram = b*h
b*h=16
h=16/8=2
sin theta =opp/hyp = 2/8 = 1/4
theta = sin inv of 1/4 = 14.5 deg
A
Answer: A
Question: Half a number plus 5 is 11.What is the number?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Solution
Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 11
(1/2)x + 5 - 5 = 11 - 5
(1/2)x = 6
2 × (1/2)x = 6 × 2
x = 12
Answer C
Answer: C
Question: How many seconds will a 900 meter 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?
Options:
A)287
B)288
C)500
D)400
E)121
Rationale: Let length of tunnel is x meter
Distance = 900+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
900+x = (65/3) * 60
900+x = 20 * 65 = 1300
x = 1300 - 900 = 400 meters
Answer: D
Answer: D
Question: If 15 students in a class average 70% on an exam and 10 students average 95% on the same exam, what is the average in percent for all 25 students?
Options:
A)77%
B)78%
C)79%
D)80%
E)81%
Rationale: (15*70 + 10*95) / 25 = 80%
The answer is D.
Answer: D
Question: The ages of 2 persons differ by 32 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
Options:
A)30
B)48.5
C)50.4
D)62.6
E)47.9
Rationale: age of the younger person = x
age of the elder person = x+32
6(x-12) = x+32-12
x= 18.4
age of elder person = 18.4+32=50.4
Answer is C
Answer: C
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)12808
B)12800
C)12805
D)12801
E)12802
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: B
Question: A woman is 20 years older than her son. In 5 years, her age will be twice the age of her son. The present age of her son is
Options:
A)15
B)14
C)13
D)12
E)11
Rationale: Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 20) years
=> (x + 20) + 5 = 2(x + 5)
=> x + 25 = 2x +10
So, x = 15. Answer: A
Answer: A
Question: A rectangular with dimensions 40 inches by 65 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
Options:
A)a) 4 inches
B)b) 6 inches
C)c) 7 inches
D)d) 5 inches
E)e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
40=2*2*2*5
65=5*13
GCF = 5
P.S you can make squares with side of 5
Answer : D
Answer: D
Question: If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 30 percent decrease in y would result in which of the following changes in z?
Options:
A)decrease of 7.5%
B)decrease of 26.5%
C)increase of 16.5%
D)increase of 24.5%
E)increase of 32.5%
Rationale: After the changes, z = 1.5x*(0.7y)^2 = (1.5*0.49)xy^2 = 0.735*z
The answer is B.
Answer: B
Question: The greatest ratio out of 2:3, 5:8, 3:2, 8:9 and 8:3 is?
Options:
A)2:3
B)3:2
C)5:8
D)8:9
E)8:3
Rationale: 2/3=0.666
5/8=0.625
3/2=1.5
8/9=0.888
8/3=2.67
ANSWER:E
Answer: E
Question: You keep tossing a fair coin for twenty times. Each time, the coin lands up with tails up.
What is the probability that if you toss it now, the coin will land with heads up this time?
Options:
A)50 %
B)60 %
C)70 %
D)80 %
E)90 %
Rationale: Solution:
50%
Explanation:
The probability will be 50% only as it always was. The next flip of coin is not dependent on what the results were in the previous flips.
Answer A
Answer: A
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
A)18 sec
B)77 sec
C)48 sec
D)28 sec
E)12 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C
Answer: C
Question: The diagonals of a rhombus are 15 cm and 17 cm. Find its area?
Options:
A)277
B)127.5
C)150
D)288
E)212
Rationale: 1/2 * 15 * 17 = 127.5
Answer: B
Answer: B
Question: Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)4 hours 20 min
B)5 hours 49 min
C)3 hours 50 min
D)3 hours 22 min
E)3 hours 42 min
Rationale: Explanation:
Part filled by P in 1 hour = 1/10
Part filled by Q in 1 hour = 1/14
Part filled by (P + Q) in 1 hour = ( 1/10 + 1/14) = (6/35)
Time taken to fill the tank is (35/6) = 5 hours 49 min
ANSWER B
Answer: B
Question: If you add all the numbers on your mobile phone except 8 and 2, what is the answer?
Options:
A)55
B)25
C)85
D)45
E)35
Rationale: We have to add 0,1,3,4,5,6,7 & 9 to find the answer.
Therefore 0+1+3+4+5+6+7+9=35
Answer is E
Answer: E
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If A is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Options:
A) 0<y<4
B) 4<y<10
C) 10<y<20
D) 20<y<30
E) y>30
Rationale: A Smallest prime factor is greater than 29. So answer is E
Answer: E
Question: D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 700. Set D and Set E have how many numbers in common?
Options:
A)None of these
B)1
C)3
D)5
E)12
Rationale: D is a set of multiples of 3.
700 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: A.
Answer: A
Question: There are 6 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 15 other amateurs, what is the total number of chess games possible to be played in the tournament?
Options:
A)10
B)20
C)45
D)60
E)120
Rationale: Each person is one participant of 6 games. So there are in all 6*15 = 90 instances of one participant games. But each game has 2 participants so total number of games = 90/2 = 45
C
Answer: C
Question: There are 27 different three-digit integers that can be formed using only the digits 4, 5 and 6. If all 27 of the integers were listed, what would their sum be?
Options:
A)14,785
B)14,885
C)14,985
D)15,085
E)15,185
Rationale: There must be nine 4's in the hundreds place, nine 4's in the tens place, and nine 4's in the units place. This is also true for the 5's and 6's. Then the sum is:
9(444+555+666)=9*(1665)=14,985.
The answer is C.
Answer: C
Question: A does half as much work as B in three-fourth of the time. If together they take 18 days to complete
the work, how much Ɵme shall B take to do it
Options:
A)40 days
B)35 days
C)30 days
D)25 days
E)None of these
Rationale: Explanation:
Suppose B takes x days to do the work.
As per question A will take
2
∗
34
∗
x=3x2days
(A+B)s 1 days work= 1/18
1/x + 2/3x = 1/18 or x = 30 days
Answer: C
Answer: C
Question: If d is the standard deviation a, b, and c, what is the standard deviation of a +6, b + 6, c + 6 ?
Options:
A)d
B)6d
C)6d+6
D)6d+12
E)6d+18
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 6 is added in each term of set {a, b,c} then the new set {a+6, b+6, c+6} will remain same as the previous standard deviation i.e. d
Answer: A
Answer: A
Question: The distance between 2 cities A and B is 100km. A train starts from A at 8 a.m. and travels towards B at 50 km/hr. Another starts from B at 9 a.m. and travels towards A at 60 km/hr. At what time do they meet?
Options:
A)9.45a.m.
B)10a.m.
C)10.25a.m.
D)11.10am.
E)11.30a.m.
Rationale: Suppose they meet x hrs after 8 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 100
50x + 60 (x-1) = 100
x = 1.45
They meet at 8+1.45 = 9.45 a.m.
Answer is A
Answer: A
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 120 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
Options:
A)50
B)100
C)150
D)200
E)240
Rationale: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 120
Total = 120 + 120 = 240
Answer (E)
Answer: E
Question: In how many ways the letters in the word MANAGEMENT can be arranged such that A’s does not come together.
Options:
A)181440
B)191440
C)171440
D)182440
E)185440
Rationale: Methods to arrange all the letters leaving A = 8*7*6*5*4*3*2*1/(2*1)*(2*1)*(2*1)= 5040
Now between these 8 letters , there are 9 places so methods to place A and A in these positions = 9*8/2*1 = 36
thus total methods are 5040*36 = 181440
ANSWER:A
Answer: A
Question: The average of five numbers id 27. If one number is excluded, the average becomes 24. What is the excluded number?
Options:
A)30
B)40
C)32.5
D)35
E)39
Rationale: Explanation:
Sum of 5 numbers = 5 × 27
Sum of 4 numbers after excluding one number = 4 × 24
Excluded number
= 5 × 27 - 4 × 24
= 135 - 96 = 39
Answer: Option E
Answer: E
Question: Raviraj invested an amount of 100000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
Options:
A)12,310
B)13,2102
C)13,320
D)13,120
E)133100
Rationale: Amount = 100000(1 + 10⁄100)3
= 100000 × 11⁄10 × 11⁄10 × 11⁄10
= 133100
Answer E
Answer: E
Question: The remainder of the division of a number by 66 is 27. What will be the remainder when that number is divided by 7?
Please explain
Options:
A)2
B)5
C)6
D)7
E)8
Rationale: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:
1) Choose a number X that when divided by 66 gives you 27 as a remainder. So I did x = 66 + 27 = 93.
2) Divide that number by 7. 93/7 = 13R2
Since the remainder is 2, the correct answer is choice A.
Answer: A
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
Options:
A)120
B)135
C)185
D)190
E)216
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: C
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
Options:
A)Rs. 8000
B)Rs. 9000
C)Rs. 9800
D)Rs. 9900
E)Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: E
Question: Mohan purchased 15 kgs of rice at the rate of Rs.25 per kg and 8 kgs of pulses at the rate of Rs.25 per kg. Whaat is the total amount that he paid to the shopkeeper?
Options:
A)A)Rs.598
B)B)Rs.575
C)C)Rs.596
D)D)Rs.595
E)None of these
Rationale: Explanation:
Price of 15 kgs of rice at Rs.25/kg = 15x25 = Rs.375
Price of 8 kgs of pulses at Rs.25/kg = 8x25 = Rs.200
Therefore, Total amount = Rs.375+Rs.200 = Rs.575
Answer: Option B
Answer: B