mathewhe/aqua_rat huggingface dataset:
Question: A 5% stock yields 10%. The market value of the stock is:
(A) Rs.56
(B) Rs.55
(C) Rs.50
(D) Rs.90
(E) Rs.75
Rationale: Explanation:
For an income of Rs. 10, investment = Rs. 100.
For an income of Rs 5, investment =Rs.100/10 X5 =Rs 50
Market value of Rs. 100 stock = Rs.50
Answer is C
Answer: (C) Rs.50
Question: If two numbers are in the ratio 2:3. If 5 is subtracted from both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 5
(B) 10
(C) 20
(D) 40
(E) 90
Rationale: Given Ratio -> 2:3
2x - 5 : 3x - 10 = 3 : 4
4[2x - 5] = 3[3x - 5]
8x - 20 = 9x - 15
9x - 8x = 20 - 15
x = 5
Then smallest number is = 2x
2x = 10
Ans - B
Answer: (B) 10
Question: The average of numbers 0.44204, 0.44203, 0.44202 and 0.44201 is ?
(A) 0.44202
(B) 0.44204
(C) 0.442022
(D) 0.442025
(E) None
Rationale: Answer
Average = (0.44204 + 0.44203 + 0.44202 + 0.44201)/ 4
=1.7681/ 4
=0.442025
Correct Option: D
Answer: (D) 0.442025
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 245 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2
=> 2(130 + x)
= 750 => x = 245 m.
Answer: C
Answer: (C) 245 m
Question: How long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length?
(A) 15
(B) 17
(C) 15
(D) 16
(E) 18
Rationale: D = 200 + 200 = 400 m
S = 80 * 5/18 = 200/9
T = 400 * 9/200 = 18 sec
Answer:E
Answer: (E) 18
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 896 grams per kg, what is his percent?
(A) 22%
(B) 25%
(C) 77%
(D) 99%
(E) 11.6%
Rationale: 896 --- 104
100 --- ? => 11.6%
Answer: E
Answer: (E) 11.6%
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 22
(B) 87
(C) 66
(D) 28
(E) 61
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Answer: (D) 28
Question: In a classroom, the average age of boys (b) is g and the average age of girls (g) is b. The average age of all is b+g. At the time of calculation, the class teacher, who is 42 years old was also present in the class. Can you find the value of b+g?
(A) 8
(B) 3
(C) 7
(D) 9
(E) 10
Rationale: A
b+g = 8
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)
(b,g)=(3,5) => b+g=8
Answer: (A) 8
Question: 6 friends visited a book stall and brought 6 books, and everyone decided to contribute equally to the total bill of $400. If one of the friends had a coupon for 5% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) 62.12
(B) 63
(C) 63.33
(D) 64
(E) 65
Rationale: At the non-discounted price, each friend would pay $66.66, as $400 divided by 6 friends is $66.66 per friend. But if the bill is 5% off, then each friend would pay 5% less. 5% of $66.66 is $3.33, so each friend saves $3.33 and pays the remaining $63.33
CORRECT OPTION:OPTION C
Answer: (C) 63.33
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
(A) 76 years
(B) 31 years
(C) 45 years
(D) 13 years
(E) 15 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row
= 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102
= 31 years.
Answer: B
Answer: (B) 31 years
Question: Bob wants a bunch of bananas and insists that the bunch contains a prime number of bananas. The bunches contain the following number of bananas. Which bunch should Bob buy?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Bunch B has a prime number of bananas.
Answer: (B) 5
Question: Two trains travelling in the same direction at 58 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 110 m, what is the length of the second train?
(A) 800 m
(B) 110 m
(C) 600 m
(D) 490 m
(E) 710 m
Rationale: RS = 58 â€“ 22= 36 * 5/18 = 10 mps
T = 60 sec
D = 10 * 60 = 600 m
110
--------
490 m
Answer: D
Answer: (D) 490 m
Question: By selling an umbrella for Rs. 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper alows a discount of 10% on the marked price. His gain percent during the sale is :
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Sol.
Marked price = Rs. 300. C.P. = Rs. [100 / 120 * 300] = Rs.250.
Sale price = 90% of Rs. 300 = Rs. 270.
∴ Required gain% = [20 / 250 * 100] % = 8%.
Answer C
Answer: (C) 8
Question: Which among the following represents a sum of 3 consecutive even integers?
(A) 200
(B) 303
(C) 400
(D) 564
(E) 571
Rationale: Sum of three consecutive Even Integers must be a multiple of 2 as well as a multiple of 3 because such a sum is always 3 times the middle number (applicable to all equally spaced numbers)
Divisibility of 3: Sum of the digits of the number must be divisible by 3
Divisibility of 2: Unit digit of the number must be divisible by 2
A. 200NOT A MULTIPLE OF 3 SO RULED OUT
B. 303NOT A MULTIPLE OF 2 SO RULED OUT
C. 400NOT A MULTIPLE OF 3 SO RULED OUT
D. 564 A MULTIPLE OF 3 and 2 THE CORRECT ANSWER!!!
D
Answer: (D) 564
Question: The probability that A speaks truth is 4/5 and that of B speaking truth is 3/4. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 12/35
(C) 9/10
(D) 19/35
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 4/5 * 3/4 + 3/5 * 2/4
= 12/20 + 6/20 = 18/20 = 9/10
ANSWER:C
Answer: (C) 9/10
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 10 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N in one hour, where N is a positive integer?
(A) 12 + 50N
(B) 12 + 2N
(C) 10 + 2N
(D) 37N
(E) 25
Rationale: 25 units = 1 worker;
50N units = 50N/25 = 2N workers.
So, the answer is 2N workers plus 10 managers.
Answer: C.
Answer: (C) 10 + 2N
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned
(A) 19828.88
(B) 19828.8
(C) 19828.87
(D) 19828.81
(E) 19828.82
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer: B
Answer: (B) 19828.8
Question: Income of A is 25% more than the income of B. What is the income of B in terms of income of A?
(A) 80%
(B) 8%
(C) 82
(D) 27
(E) 81
Rationale: Explanation:
One of the most basic questions.
Let income of B be 100. Income of A is 25% more than income of B which means Income of A becomes 125
Now income of B in terms of A = 100/125 *100 = 80%
ANSWER: A
Answer: (A) 80%
Question: A solution is made of water and pure acid. If 75% of the solution is water, how many litters of pure acid are in 20 litters of this solution?
(A) 10
(B) 35
(C) 27
(D) 5
(E) 13
Rationale: If 75% of the solution is water then
100% - 75% = 25% is acid.
If the solution is 20 litters, then
25% of 20 = 25% * 20 = 5 litters are pure acid.
correct answer D
Answer: (D) 5
Question: Find compound interest on $ 16000 at 15% per annum for 2 years 4 months, compounded annually.
(A) 6109
(B) 6209
(C) 6218
(D) 6107
(E) 6100
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = $ [16000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]
=$ [16000 * (23/20) * (23/20) * (21/20)]
= $ 22218	.
:. C.I. = Rs. (22218 - 16000) = $ 6218
Answer C.
Answer: (C) 6218
Question: sue has 3 apples. Billy has 10 apples. If billy steals all of sues apples and eats 4 how many does he have left?
(A) 2
(B) 5
(C) 6
(D) 4
(E) 9
Rationale: 9 E
Answer: (E) 9
Question: Tough and Tricky questions: Exponents.
If 3^m3^m3^m = 7^n, then m/n =
(A) 1/3
(B) 2/3
(C) 1
(D) 3/2
(E) 3
Rationale: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=1/3.A
Answer: (A) 1/3
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 3/7?
(A) -15/4
(B) -1/6
(C) -1/15
(D) 3/5
(E) 15/1
Rationale: Solving for y/x gives, -1/6 (B)
Answer: (B) -1/6
Question: If x : y = 3 : 5, find the value of (2x + 4y) : (3x – y)
(A) 13 : 2
(B) 11 : 2
(C) 13 : 3
(D) 13 : 4
(E) 13 :5
Rationale: Explanation:
Given: x/y = 3/5
(2x + 4y)/(3x – y)
= (2*3 + 4*5) : (3*3 – 5)
= 26:4
= 13 : 2
ANSWER: A
Answer: (A) 13 : 2
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 840, what is the least possible value of n?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 840 = 2*2*2*3*5*7, so n must be at least 7.
The answer is C.
Answer: (C) 7
Question: What is the median from the below series 90, 93, 93, 88, 95, 88, 97, 87, and 98
(A) 80
(B) 85
(C) 93
(D) 97
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 93, 93, 95, 96, 98
The median quiz score was 93. (Four quiz scores were higher than 93 and four were lower.)
C
Answer: (C) 93
Question: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
(A) 222
(B) 300
(C) 99
(D) 88
(E) 67
Rationale: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300
Answer:C
Answer: (C) 99
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number R of races we need to conduct to get the top 3 fastest horses?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: R=7 is the correct answer.
Good solution Buneul.B
Answer: (B) 7
Question: Calculate the value of n from the below equation: y^4âˆ’20y+1=22
(A) 5
(B) 3
(C) 6
(D) 2
(E) 1
Rationale: Use elimination method to find the correct option. you find that of all the options 3 is the correct value for y
Answer: B
Answer: (B) 3
Question: Find the area of trapezium whose parallel sides are 18 cm and 12 cm long, and the distance between them is 14 cm?
(A) 288 cm2
(B) 277 cm2
(C) 224 cm2
(D) 226 cm2
(E) 227 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (18 + 12) * (14)
= 224 cm2
Answer: C
Answer: (C) 224 cm2
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) Rs.500
(B) Rs.750
(C) Rs.1250
(D) Rs.1500
(E) Rs.1520
Rationale: Explanation:
(5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
ANSWER IS D
Answer: (D) Rs.1500
Question: The sum of the two numbers is 12 and their product is 35.What is the sum of the reciprocals of these numbers?
(A) 12/35
(B) 12/38
(C) 12/31
(D) 12/32
(E) 12/33
Rationale: Explanation:
Let a and b are the numbers.Then a+b is 12 and ab is 35.
Answer: A
Answer: (A) 12/35
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 70 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 36
(C) 48
(D) 99
(E) 23
Rationale: Relative speed = 70 + 30 = 100 km/hr.
100 * 5/18 = 250/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/250= 36 sec
Answer: B
Answer: (B) 36
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors A?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have A=2*3*5*7 = 840
Thus, answer B
Answer: (B) 3
Question: The population of a village is 13400. It increases annually at the rate of 21% p.a. What will be its population after 2 years?
(A) 10000
(B) 12000
(C) 19619
(D) 18989
(E) 14400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
13400 × 121/100 × 121/100 = 19619
C
Answer: (C) 19619
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
(A) 12 hours
(B) 24 hours
(C) 36 hours
(D) 48 hours
(E) None
Rationale: Sol.
Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.
∴ total time taken = [210/7.5 + 210/10.5] hours = 48 hours.
Answer D
Answer: (D) 48 hours
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 7 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $10,395
(C) $10,593
(D) $11,500
(E) $12,705
Rationale: the amount at the end of first year will become the principle for 2nd year, applying this trick and calculating we get the amount at the end of third year to be 10593. So the answer is (C).
Answer: (C) $10,593
Question: What is the sum of all three digit integers formed using the digits 3,4 and 5 (repetition is allowed)
(A) 11982
(B) 11984
(C) 11985
(D) 11988
(E) 11986
Rationale: n = 3*3*3 = 27
= (555 + 333) / 2 = 444
Sum = number of integers x average value
n * = 27 * 444 = 11988
answer = D
Answer: (D) 11988
Question: What is the remainder when 7^74 - 5^74 is divided by 12?
(A) 1
(B) 0
(C) 2
(D) 3
(E) None of these
Rationale: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (12*4+1)^37 - (12*2+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans : B
Answer: (B) 0
Question: 40 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?
(A) 47
(B) 46
(C) 54
(D) 58
(E) 62
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=40
orange+mango+apple=4
40+10+4-7=47 like apple
ANSWER:A
Answer: (A) 47
Question: Which of the following numbers is divisible by 12?
(A) 1332
(B) 1021
(C) 3221
(D) 4211
(E) 3233
Rationale: 1332. This is the only option with last two digits divisible by 12
Answer:A
Answer: (A) 1332
Question: An advertising agency finds that, of its 200 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
(A) 100
(B) 70
(C) 90
(D) 98
(E) 95
Rationale: Total=200
Television=115
Radio=110
Magazine=130
All the three =200-115-110-130+85+75+95=100
ANSWER A
Answer: (A) 100
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 180 square feet and its length is 8 feet longer than its width. If the uniform width between the rug and room is 8 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
(A) 32
(B) 36
(C) 704
(D) 46
(E) 104
Rationale: Rug's area = 180
which is (x) x (8+x) = 180
so x= 10
rug maintains a uniform distance of 8 feet
so room has dimension 10+16 and 18+16 i.e. 26 and 34
area of room 26x34 = 884 area covered is 180
so uncovered area is 884-180=704 (ANSWER C)
Answer: (C) 704
Question: Gita, Hussain, Inge, Jeong, Karen, and Leila are seated in a row of six chairs. How many seating arrangements are possible if Gita cannot sit next to Inge and Jeong must sit next to Leila?
(A) 288
(B) 240
(C) 144
(D) 120
(E) 96
Rationale: taking he initials of each for reference... Since, J and L have to be together, lets combine them into 1. So, now we have 5 things which can be arranged in 5! ways. ALso, J and L can be arranged in two ways (JL, LJ) .
This gives total ways, 5! * 2 = 240
Now, we are given G and I can not be together, therefore subtract the cases when they (G and I) are together. Now, see we have 4 people (JL and GI) are combined as one. Total no of arrangement = 4!
But, J and L can be arranged internally in 2 ways (JL and LJ). Similarly, G and I can be internally arranged in two ways (GI and IG).
Therefore, total such cases will be 4! * 2 * 2 = 96. Subtract this from 240.
240 - 96 = 144. Hence, C
Answer: (C) 144
Question: How many such pairs of digits are there in the number 421579368 each of which has as many digits between them in the number as when they are arranged in ascending order?
(A) 4
(B) 5
(C) 6
(D) 3
(E) 1
Rationale: Explanation:
Given Number: 4 2 1 5 7 9 3 6 8
Ascending order: 1 2 3 4 5 6 7 8 9
Hence the required pairs are
Answer: D) Three
Answer: (D) 3
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
(A) 10.21
(B) 10.27
(C) 10.25
(D) 10.23
(E) 60.25
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer: E
Answer: (E) 60.25
Question: If the speed of a man is 63 km per hour, then what is the distance traveled by him in 25 seconds ?
(A) 275m
(B) 360m
(C) 375 m
(D) 437.5 m
(E) 440 m
Rationale: The distance traveled in 25 sec = 63*(5/18) *25 =437.5m
ANSWER:D
Answer: (D) 437.5 m
Question: What is the product of the greatest 2 digit multiple of 3 and the greatest 2 digit prime number?
(A) 9,312
(B) 9,603
(C) 9,506
(D) 9,649
(E) 9,702
Rationale: the greatest 2 digit multiple of 3: 99
the greatest 2 digit prime numebr: 97
97*99.
9603
B
Answer: (B) 9,603
Question: If X is the sum of first 30 positive even integers and Y is the sum of first 30 positive odd integers, what is the value of x-y?
Please try to explain your answers
(A) 10
(B) 25
(C) 30
(D) 75
(E) 100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 30 positive even integers minus the sum of first 30 positive odd integers will be 30.
Answer: C.
Answer: (C) 30
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in ?
(A) 3 days
(B) 4 days
(C) 4 days
(D) 6 days
(E) 7 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
Option 'D'
Answer: (D) 6 days
Question: What is the units digit of 33^2 * 17^3 * 49^3?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The units digit of 33^2 is the units digit of 3*3 = 9 which is 9.
The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.
The units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9.
The units digit of 9*3*9 = 243 is 3.
The answer is B.
Answer: (B) 3
Question: 10x + 2y = -6
6x + y = 1
In the system of equations above, what is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 10x + 2y = -6 can be written as 5x + y = -3
Let's subtract the second equation from this equation.
-x = -4
x = 4
The answer is C.
Answer: (C) 4
Question: There are 9color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?
(A) 434562
(B) 546563
(C) 567343
(D) 566748
(E) 345600
Rationale: Total number of ways in which 9 different colour balls can be arranged in a row
=9! ⋯(A)
Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.
We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways.
We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways.
Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together
=6!×4! ⋯(B)
From (A) and (B),
Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together
=9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600
E
Answer: (E) 345600
Question: In how many ways can the letters of wordINTELLIGENTbe arranged such that all the Consonants always appear together?
(A) 9!
(B) 5!*4!
(C) 5!*5!
(D) 5!*7!
(E) 6!*4!
Rationale: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (11 letters, 4 vowels I, E, I, E and 7 consonant N, T, L, L, G, N, T)
For all consonants together, consider them as 1 group {N, T, L, L, G, N, T} I E I E --> this gives us 5! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways
Thus total arrangements with all consonants together = 5!*7! --> D is the correct answer.
Answer: (D) 5!*7!
Question: In a garden , there are 10 rows and 12 columns of mango trees. the distance between the two trees is 2 m and a distance of one meter is left from all sides of the boundary of the length of the garden is :
(A) 450 sq mtrs
(B) 460 sq mtrs
(C) 480 sq mtrs
(D) 490 sq mtrs
(E) 470 sq mtrs
Rationale: length of garden = 1+2*11+1= 24 m
breadth of garden = 1+9*2+1= 20 m
area = 24*20 =480 sq mtrs
ANSWER:C
Answer: (C) 480 sq mtrs
Question: Caleb and Frank are partners in a business. Caleb runs the business and receives 8% of the profit for managing the business, the rest is divided in proportion of their capitals. Caleb invested Rs.5000 and Frank invested Rs.10000. the rest is divided in proportion of their capitals. Out of a total profit of Rs.6000, how much did Caleb receive?
(A) 1197.6
(B) 3097.6
(C) 1097.6
(D) 5097.6
(E) 2097.6
Rationale: ratio of their investments Rs.5000:10000=1:2
8% of the profit for managing the business =8/100*6000=480
remaining profit=6000-480=5520
share profit in ratio of investment 5520/3 =323.52
Moses's ratio share=5*323.52=1617.6
total money Moses collects=1617.6+480=2097.6
Answer: E
Answer: (E) 2097.6
Question: 34.	The side surface of a cylinder can is rolled with a rectangular plate. If the height of a cylinder tank is 8 feet and the perimeter of the circular base Is 6 feet, what is the diagonal of the rectangular plate?
(A) 10
(B) 12
(C) 8
(D) 14
(E) 9
Rationale: Think of a can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, use pythagoreans theorem or properties of 3-4-5 triangles to solve for the hypothenuse, 10. (Correct answer: A)
Answer: (A) 10
Question: A car finishes a journey in ten hours at the speed of 60 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
Rationale: Distance covered by the car = 64 × 10 = 640 km
\ Speed = 640⁄8 = 80 km/hr
\ Speed gain = 80– 64 = 16 km/hr
Answer D
Answer: (D) 16 km/hr