mathewhe/aqua_rat huggingface dataset:
Question: A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
(A) 32 m3
(B) 36 m3
(C) 40 m3
(D) 44 m3
(E) None
Rationale: Sol.
Volume = Πr2h = (22/7 x 1 x 1 x 14)m3
= 44 m3.
Answer D
Answer: (D) 44 m3
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is?
(A) 52:59
(B) 52:53
(C) 52:83
(D) 52:93
(E) 53:53
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer:B
Answer: (B) 52:53
Question: Round off the given number to nearest hundreds
4765
(A) 4800
(B) 4900
(C) 5000
(D) 4600
(E) 4700
Rationale: the given number is 4765
its tens digit is 6. so replace each of the tens and ones digit by 0 and increase the hundreds digit by 1 to get the rounded off number to the nearest hundred.
correct answer (A)
Answer: (A) 4800
Question: What would be the local minimum for the function represented as f(x,y) = x2 +ay+y2 -3x ?
(A) (1,1)
(B) (2,-1)
(C) (-1,1)
(D) (2,2)
(E) (3,2)
Rationale: f(x,y) = x2 + ay + y2 - 3x
= 4 - a + 1 - 6
= -a-1
So the above value will be the minimum if u check for all other options also. therefore, the answer is (2,-1)
ANSWER:B
Answer: (B) (2,-1)
Question: There are 25 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 156
(B) 167
(C) 157
(D) 352
(E) 702
Rationale: The total number of stations = 27
From 27 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.
²⁰P₂ = 27 * 26
= 702.
Answer: E
Answer: (E) 702
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discountoffered on it, find its SP?
(A) Rs. 60
(B) Rs. 65
(C) Rs. 72
(D) Rs. 78
(E) Rs. 85
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: (C) Rs. 72
Question: There are 59 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
(A) 2
(B) 4
(C) 8
(D) 29
(E) 32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 59
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 59=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 29
answer:D
Answer: (D) 29
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 15/7 days
(B) 15/4 days
(C) 25/4 days
(D) 15/9 days
(E) 15/2 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer: B
Answer: (B) 15/4 days
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average Q(arithmetic mean) annual increase in the index over this period?
(A)  (x + 100)/18
(B)  x/18
(C)  (100 − x)/18
(D)  (x − 100)/18
(E)  100x/18
Rationale: CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI Q= (x-100)/18
Answer D
Answer: (D)  (x − 100)/18
Question: What is the difference between the local values of 7 in the number 57407?
(A) 6993
(B) 2997
(C) 3877
(D) 5077
(E) 1211
Rationale: Explanation:
7000 â€“ 7 = 6993
Answer:A
Answer: (A) 6993
Question: Set A = {1, 2, 3, 4, 5, 6, s}
Which of the following possible values for s would cause Set A to have the smallest standard deviation?
(A)  1
(B)  2.5
(C)  3
(D)  3.5
(E)  7
Rationale: I agree. The mean of the set s=1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: (D)  3.5
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time E will it take to fill the bucket to full capacity?
(A) 7/18
(B) 9/18
(C) 2
(D) 18/7
(E) 18/5
Rationale: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank E= 60/7 - 6 = 18/7 mins. ANS D.
Answer: (D) 18/7
Question: If a car goes at 80 km/hr instead of 60 km/hr, he would have walked 30 km more. The time traveled by the car is?
(A) 2 hours
(B) 2.5 hours
(C) 3.5 hours
(D) 1.5 hours
(E) 3 hours
Rationale: Let the actual distance traveled be x km. Then,
x/60 = (x + 30)/80
4x - 3x = 90 =>x = 90 km.
Travel time = 90/60 hours = 3/2 hours = 1.5 hours
Answer :D
Answer: (D) 1.5 hours
Question: Kevin, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 5/9, 2/5 and 1/2, respectively, what is the probability that only Catherine will solve the problem?
(A) 1/6
(B) 1/5
(C) 2/3
(D) 2/15
(E) 1/15
Rationale: P(Kevin will not solve)= 1 - 5/9 = 4/9
P(David will not solve)= 1 - 2/5 = 3/5
P(Catherine will solve) = 1/2
P= (4/9)*(3/5)*(1/2) = 12/90= 2/15
Answer:D
Answer: (D) 2/15
Question: Of the students at a certain high school, 90 percent took a course in arithmatic or geometry and 15 percent took courses in both. If the percent of students who took a course in arithmatic was 2 times the percent of students who took a course in geometry, what percent of the students took a course in arithmatic but not geometry?
(A) 40%
(B) 60%
(C) 55%
(D) 50%
(E) 45%
Rationale: You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
90 = 2X + X - 15
X = 35
2X = 70
This is the number of people who took arithmatic including those who took both. To get the number of people who took only arithmatic, 70 - 15 = 55%
Answer (C)
Answer: (C) 55%
Question: Radha purchased a microwave oven and a washing machine for Rs. 5000 and Rs. 30000 respectively. She sold the microwave oven at a loss of 20 percent and washing machine at a profit of 5 percent. Overall she make a.?
(A) 400
(B) 450
(C) 550
(D) 500
(E) 300
Rationale: Let the SP of the microwave oven and the washing machine be Rs. m and Rs. w respectively.
m = 5000(1 - 20/100) = 5000 - 1000
w = 30000(1 + 5/100) = 30000 + 1500
Total SP - Total CP = m + w - (5000 + 30000) = - 1000 + 1500 = Rs. 500
As this is positive, an overall profit of Rs. 500 was made.
Answer: D
Answer: (D) 500
Question: On dividing a number by 8, we get 8 as quotient and 0 as remainder. On dividing the same number by 5, what will be the remainder?
(A) 10
(B) 4
(C) 8
(D) 6
(E) 5
Rationale: Number = 8 * 8+ 0 = 64
5) 64 (12
60
--------
4
Required number = 4.
ANSWER:B
Answer: (B) 4
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has travelled 60 km more than the other one. The distance between the two stations is?
(A) 222 km
(B) 333 km
(C) 555 km
(D) 444 km
(E) 666 km
Rationale: D
444 km
1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: (D) 444 km
Question: The ratio of the volumes of two cubes is 27: 64. What is the ratio of their total surface areas?
(A) 18:21
(B) 81:13
(C) 8:15
(D) 16:21
(E) 1:13
Rationale: Ratio of the sides
= ³√27 : ³√64 = 3 : 4
Ratio of surface areas
= 32 : 42 = 16:21
Answer:D
Answer: (D) 16:21
Question: If a is a positive integer, then a(a+1)(a+2) is
(A) even only when n is odd
(B) odd whenever n is odd
(C) divisible by 3 only when n is odd
(D) divisible by 4 whenever n is even
(E) even only when n is even
Rationale: a*(a+1)*(a+2)= +ve even integer divisible by 4 ( e.g 6,7&8)
D
Answer: (D) divisible by 4 whenever n is even
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent W above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Good question...2:11 min
Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles-->*afurther loss of 25%to the dealer--> BUT aNET PROFIT of 20%over cost price (C)
0.75* 0.8 * M =1.2 * C
Hence, M/C = 2/1 = 200%=W
From Eqn. A , (C + Mark up)/C = 200% -->Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 54 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 30
(D) 50
(E) 45
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+54) and number of girls were 5x
Hence, 2(5x) = x + 54
=> 10x = x + 54
=> x = 6
Number of girls in the beginning = (5x + 15) = (5×6 + 15) = 45
Answer is E.
Answer: (E) 45
Question: A certain cube floating in a bucket of water has between 70 and 85 percent of its volume below the surface of the water. If between 8 and 20 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: If sides are 7, vol=7^3=343
70%= 240.1, 85%=291.55
so vol above water, between 102.9 and 51.45 -->too big
If side are 4, vol = 64
70%=44.8, 85%=54.4
vol above water between 19.2 and 9.6
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
70%= 87.5, .85%=106.25
vol above water between 18.75-37.5
(Sides are 4 cubic centimeters)
A
Answer: (A) 4
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?
(A) 584000
(B) 504080
(C) 504080
(D) 504000
(E) 504020
Rationale: B's monthly income = 15000 * 112/100
= Rs. 16800
B's monthly income
= 2 parts ----> Rs. 16800
A's monthly income
= 5 parts = 5/2 * 16800
= Rs. 42000
A's annual income
= Rs. 42000 * 12
= Rs.504000
Answer:D
Answer: (D) 504000
Question: If 40% of a number is 36, then the number is
(A) number is 60
(B) number is 70
(C) number is 90
(D) number is 80
(E) None of these
Rationale: Solution:
Let "a" be the number we seek. We get
40% × a = 36
2 × 40% × a = 2 × 36 = 72
80% × a = 72
10% × a = 72 : 8 = 9
100% × a = 9 × 10 = 90
a = 90
Answer C
Answer: (C) number is 90
Question: If "COMPUTER" was given a code of 111, then what is the sum of "VIRUS" and "WORM"?
(A) 123
(B) 22
(C) 20
(D) 160
(E) 158
Rationale: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
VIRUS-89
WORM-69
Answer: E
Answer: (E) 158
Question: In digging a pond 20m*10m*5m the volumes of soil extracted will be ?
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 2000 cu.m
(E) 3000 cu.m
Rationale: 20*10*5=1000Answer : B
Answer: (B) 1000 cu.m
Question: A tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes. The inlet pipe fills water into the tank at the rate of 3 cubic inches/min and the 2 outlet pipes empty it out at the rates of 9 cubic inches/min and 6 cubic inches/min respectively. If all 3 pipes are opened when the tank is full, how many minutes does it take to empty the tank? (1 foot = 12 inches)
(A) 2110
(B) 3210
(C) 4320
(D) 5430
(E) 6540
Rationale: The tank is emptied at this rate: 9 + 6 - 3 = 12 cubic inches/min
The tank has a volume of 30*12*12*12 = 51840 cubic inches.
The time it takes to empty the tank is 51840/12 = 4320 minutes.
The answer is C.
Answer: (C) 4320
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 70 years now, the son's age five years back was:
(A) 50 years.
(B) 40 years.
(C) 30 years.
(D) 35 years.
(E) 45 years.
Rationale: Let the son's present age be x years. Then, (70 - x) = x
2x = 70.
x = 35.Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer: Option A
Son's age 5 years back (35 - 5) = 30 years.
Answer: Option C
Answer: (C) 30 years.
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 1.92 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
(A) $150
(B) $200
(C) $320
(D) $650
(E) $810
Rationale: The volume of each box is 20*20*12 = 4800 cubic inches.
Number of boxes = 1,920,000/4800 = 400 boxes
Total cost = 400×$0.5=$200
The answer is B.
Answer: (B) $200
Question: If 70 honey bees make 70 grams of honey in 70 days, then 1 honey bee will make 1 gram of honey in how many days?
(A) 1
(B) 3.5
(C) 20
(D) 49
(E) 70
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 70 :: 70 : x
Honey 70 : 1
=> 1 x70 x x = 70 x 1 x 70
=> x = 70.
Answer : E
Answer: (E) 70
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 35% of all the employees are men .What % of all the employee went to the picnic?
(A) 33%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: total men in company 35% means total women in company 65%(assume total people in company 100%)
no of men emplyess attended picnic=35x(20/100)=7
no of women empolyees attened picnin=65x(40/100)=26
total percentage of empolyess attened the picnic=7+26=33%
ANSWER:A
Answer: (A) 33%
Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
(A) 3 : 3 : 10
(B) 10 : 11 : 20
(C) 23 : 33 : 60
(D) Cannot be determined
(E) None of these
Rationale: Explanation:
Let A = 2k, B = 3k and C = 5k.
A's new salary =	115/100 of 2k=23k/10
B's new salary =110/100 of 3k =33k/10
C's new salary =	120/100 of 5k =6k
=23:33:60
Answer is C
Answer: (C) 23 : 33 : 60
Question: If x^2=3x+2, then x^3 = ?
(A) 3x+2
(B) 6x+2
(C) 11x+6
(D) 8x-3
(E) 5x+4
Rationale: x^2 = 3x+2
x^3 = x*x^2 = x*(3x+2) = 3x^2 + 2x = 3(3x+2)+2x = 11x+6
The answer is C.
Answer: (C) 11x+6
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
(A) 35.55 km/hr
(B) 36 km/hr
(C) 71.11 km/hr
(D) 71 km/hr
(E) 72 km/hr
Rationale: Total time taken = [160/64 + 160/80 ] hrs. 9/2 hrs
Average speed = [ 320 x 2/9] km/hr = 71.11km/hr
Answer is C
Answer: (C) 71.11 km/hr
Question: The product of n consecutive positive integers is always divisible by
(A) n^2 -1
(B) (n+1)!
(C) 2n +1
(D) n^2 + 1
(E) n!
Rationale: Product of first 2 number is 2*1
Product of first 3 number is 3*2*1
Product of first 4 number is 4*3*2*1
Product of first 5 number is 5*4*3*2*1
So, The product of first n natural numbers is always divisible by n! , answer will be (E)
Answer: (E) n!
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 after six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 8500
(C) 9000
(D) 8000
(E) 8500
Rationale: A : B : C =20000×24:15000×24:20000×18
=20×4:15×4:20×3
=4×4:3×4:4×3
=4:3:3
B's share = 25000×3/10=7500 Answer: Option A
Answer: (A) 7500
Question: A bag contains ten white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/81
(B) 40/91
(C) 40/61
(D) 40/31
(E) 5/1
Rationale: Two balls can be picked from fourteen balls in 14Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (10 * 4) = 40/91
Answer: B
Answer: (B) 40/91
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $42. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 378/(xy)
(B) 11xy/3
(C) 3xy/11
(D) 297/(xy)
(E) 297xy
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 42 / (xy/9) = 378/(xy).
The answer is A.
Answer: (A) 378/(xy)
Question: A tank is filled by 3 pipes A,B,C in 10 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
(A) 20hr
(B) 52hr
(C) 70hr
(D) 66hr
(E) 48hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/10
7/x = 1/10
x = 70 hours
Answer is C
Answer: (C) 70hr
Question: A boat goes 100 km downstream in 10 hours, and 90 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/7
(B) 2
(C) 22 1/2
(D) 22 1/1
(E) 22 1/3
Rationale: 100 --- 10 DS = 10
? ---- 1
90 ---- 15 US = 6
? ----- 1 S = (10 - 6)/2
= 2 kmp Answer: B
Answer: (B) 2
Question: How many different positive integers can be formed using each digit in the set {0,1,3,3,3,7,8} exactly once?(Naturally, the number can't begin with 0)
.
(A) 160
(B) 720
(C) 1440
(D) 4320
(E) 5040
Rationale: Since the first number can't be 0, then there are only 6 possible numbers than there could be. Then the following 6 number are a regular permutation, with 3 of the elements being the same
Number of integers will be 6*6!/3!= 720
ANS:B
Answer: (B) 720
Question: The positive number z is divisible by 4. What is the remainder of dividing z(2+4+z)+3 by 2?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When we solve any of these equations: 28+3 (z=4) or 56+3 (z=8) we end up with numbers to which we have to subtract 1 to end up with a number that is exactly divisible by 2. This is why we know that every result we get is going to have 1 as a remainder. Hence answer is B.
Answer: (B) 1
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction W of the cookies that were placed in the other tins were placed in the green tin?
(A) 15/2
(B) 9/4
(C) 5/9
(D) 7/5
(E) 9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction W= 5N/12 * 12/9N = 5/9 (C)
Answer: (C) 5/9
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 288
(C) 267
(D) 256
(E) 298
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Answer: (A) 230
Question: A boat travels 40 km downstream in 8 hours and 24 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
(A) 8 km/hr, 1 km/hr
(B) 3.5 km/hr, 1.5 km/hr
(C) 1 km/hr, 6 km/hr
(D) 2 km/hr, 1 km/hr
(E) 4 km/hr, 1 km/hr
Rationale: Downstream speed=40km/8hrs
=5 kmph
upstream speed=24km/12hrs
=2 kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(5+2)/2kmph
=3.5kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(5-2)/2kmph
=1.5kmph
ans is 3.5km/hr,1.5km/hr
ANSWER:B
Answer: (B) 3.5 km/hr, 1.5 km/hr
Question: In the xy-plane, the point (2, 1) is the center of a circle. The point (-2, 1) lies inside the circle and the point (2, -5) lies outside the circle. If the radius r of the circle is an integer, then r =
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: An easy way to solve this question will be just to mark the points on the coordinate plane.
You'll see that the distance between the center (2, 1) and the point inside the circle (-2, 1) is 4 units
(both points are on y=1 line so the distance will simply be 2-(-2)=4)
So the radius must be more than 4 units.
The distance between the center (2,1) and the point outside the circle (2,-5) is 6 units
(both points are on x=2 line so the distance will simply be 1-(-5)=6)
So the radius must be less than 6 units, which implies 4 < r < 6, thus as r is an integer then r=5.
Answer: B.
Answer: (B) 5
Question: If there are 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:2, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
(A) 1/25
(B) 2/25
(C) 6/25
(D) 9/25
(E) 21/25
Rationale: 30 red and blue marbles in a jar, and the ratio of red to blue marbles is 3:2
So, 5x=30 ---> x=6
Red marbles = 3*x = 3*6 = 18
Blue marbles = 2*x = 2*6 = 12
Prob to select a red marble = 18/30 = 3/5
Prob to select 2 red marbles with replacement = 3/5*2*5 = 6/25
Hence, answer will be C.
Answer: (C) 6/25
Question: What number has a 5:1 ratio to the number 10?
(A) 22
(B) 50
(C) 88
(D) 52
(E) 12
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: (B) 50
Question: There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
(A) 120
(B) 130
(C) 100
(D) 110
(E) 140
Rationale: The 1st envelope can be filled up in 6 ways.
The 2nd envelope can be filled up in 5 ways and the 3rd envelope can be filled up in 4 ways.
Therefore, by the principle of association, the three envelopes can be filled up in 6 x 5 x 4 = 120 ways
ANSWER:A
Answer: (A) 120
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 5% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
(A) 4 : 5
(B) 5 : 4
(C) 2 : 3
(D) Data inadequate
(E) None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 5% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.05x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.05x
or, 120 = 0.03x
x = 4000
Reqd ratio of population of males and females
4000/9000−4000=4000/5000=4:5
Answer A
Answer: (A) 4 : 5
Question: In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?
(A) 3! 4! 8! 4!
(B) 3! 8!
(C) 4! 4!
(D) 8! 4! 4!
(E) None
Rationale: Solution: Taking all person of same nationality as one person, then we will have only three people.
These three person can be arranged themselves in 3! Ways.
8 Indians can be arranged themselves in 8! Way.
4 American can be arranged themselves in 4! Ways.
4 Englishman can be arranged themselves in 4! Ways.
Hence, required number of ways = 3!*8!*4!*4! Ways.
Answer: Option A
Answer: (A) 3! 4! 8! 4!