mathewhe/aqua_rat huggingface dataset:
Question: In how many different number of ways a Committee of 3 person of can be selected from 3boys and 3girls such that at least 1 girl is included in the committe
(A) 15
(B) 17
(C) 16
(D) 20
(E) 19
Rationale: 1G 2B 2G 1B 3G
= (3C1*3C2)+(3C2*3C1)+3C3
= (3*3)+(3*3)+1
= 9+9+1=19
Total 3M 3W
6C3=20
3C3=1
At least one girl = total - with out girl
At least one girl = 20-1=19
E)
Answer: (E) 19
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1000 resolutions?
(A) 1077 m
(B) 804 m
(C) 978 m
(D) 1048 m
(E) 878V
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 1000 resolutions.
= 1000 * 2 * 22/7 * 22.4 = 104800 cm
= 1408 m
Answer: D
Answer: (D) 1048 m
Question: One side of a rectangular field is 15 m and one of its diagonal is 18 m. Find the area of the field.
(A) 100
(B) 120
(C) 150
(D) 148.5
(E) None
Rationale: Solution
Other side = √(18)2 - (15)2
= √324 - 225
= √99
= 9.9 m.
∴ Area = (15 x 9.9)m2 = 148.5 m2.
Answer D
Answer: (D) 148.5
Question: What is the maximum area that can be enclosed by a wire 44cm long ?
(A) 77
(B) 154
(C) 308
(D) 318
(E) None of these
Rationale: Perimeter of circle=2*22/7*r=44cm
From this r=7
then area of circle=22/7*r^2=154
ANSWER:B
Answer: (B) 154
Question: A father is now three times as old as his son. Three years back, he was four times as old as his son. The age of the son (in years) is
(A) A)12
(B) B)9
(C) C)18
(D) D)20
(E) E)22
Rationale: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Three years ago, father's age = (3x - 3) years and son's age = (x - 3) years.
So, 3x - 3 = 4 (x - 3)=> 3x - 3 = 4x - 12=> x = 9.
Answer: B
Answer: (B) B)9
Question: The angles of a triangle are in the ratio 3: 4 : 2. Find the measurement of the 3 angles of triangle.
(A) 40°
(B) 25°
(C) 30°
(D) 75°
(E) 90°
Rationale: If the ratio of the three angles is 3:4:2, then the measures of these angles can be written as 3x, 4x and 2x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
3x + 4x + 2x = 180
Solve for x
9x = 180
x =20
The measures of the three angles are
3x =3 x20=60°
4x = 4 × 20= 80°
2x = 2 × 20 = 40°
A
Answer: (A) 40°
Question: How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately f ollowed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6
(A) 1
(B) 2
(C) 3 three
(D) 4
(E) More than four
Rationale: A is followed by B means : A comes first,B comes next
A preceded by B means : B comes first, A comes next
The sets which satisfy the condition is: 5 3 8
1 3 8
7 3 4
ANSWER:C
Answer: (C) 3 three
Question: On a summer camp, 25% of the campers paid $120 each, 35% paid $60 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $60?
(A) 18%
(B) 27.27%
(C) 26%
(D) 33.3%
(E) 37.5%
Rationale: let the total no of campers be 100
total amount = (25*120)+(35*60)+(40*65) = 3000+2100+2600= $7700
required percentage = (21/77)*100=27.27%
B
Answer: (B) 27.27%
Question: If there are 26 laborers in a crew, and on a certain day, 10 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
(A) 39.5%
(B) 38.5%
(C) 36.5%
(D) 37.5%
(E) 30.5%
Rationale: 10/26*100=38.46
38.5%
correct answer B
Answer: (B) 38.5%
Question: Peter got married 0.8 decades ago. His current age is (6/5) times his age at the time of his marriage. Peter’s brother was ten years younger to him at the time of his marriage. What is the age of Peter’s Brother?[0.8 decades = 8 years]
(A) 38 years
(B) 34 years
(C) 28 years
(D) 43 years
(E) 41 years
Rationale: A
38 years
Let Peter’s current age is A years.
Then, his age at the time of marriage = (A – 8) years
A = (6/5)(A – 8)
5A = 6A – 48
A = 48
Peter’s sister’s age at the time of his marriage = (A – 8) – 10
= (A – 18) = 30 years.
Peter’s sister’s current age = (30 + 8) years
= 38 years.
Answer: (A) 38 years
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?
(A) (A+ Ax/100) - Y/100 ( A +Ax/100)
(B) (10,000z + 100z(y – x) – xyz)/10,000
(C) (100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by Y% on Total Y/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - Y/100 ( A +Ax/100)
A
Answer: (A) (A+ Ax/100) - Y/100 ( A +Ax/100)
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 15 and 41 inclusive.
(A) 351
(B) 392
(C) 410
(D) 424
(E) 450
Rationale: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 15 to 41, inclusive. We're asked for the SUM of this group.
1) Start with the sum of the smallest and the biggest: 15 + 41 = 56
2) Now look at the 'next smallest' and the 'next biggest': 17 + 39 = 56
Now we have proof that there is no middle term. We have 7 bunches of 56.
7(56) = 392
B
Answer: (B) 392
Question: A car takes 6 hours to cover a distance of 450 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 65
Rationale: Time = 6
Distance = 450
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 450/9 = 50 Kmph
Answer B.
Answer: (B) 50
Question: If a and b are digits, and the number a,11b is evenly divisible by 88, what are the values of a and b?
(A) a = b = 9
(B) a = b = 7
(C) a = b = 5
(D) a = b = 2
(E) a = b = 1
Rationale: a,11b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
11b/8 => 112/8 = 14 => b = 2
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a11-2 => a09 => 209/11 = 19.
So a = 2.
Answer: D
Answer: (D) a = b = 2
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n*n is odd
(C) n is even
(D) n is odd
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.3
(C) 62.7
(D) 62.2
(E) 64.5
Rationale: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(92/100)
= 59.375
MP = 64.5
Answer:E
Answer: (E) 64.5
Question: The sum of three consecutive even numbers multiples of 3 is 72. what is the largest number ?
(A) 21
(B) 24
(C) 27
(D) 36
(E) None
Rationale: Solution
let the number be x and x + 2.
Then, (x + 2)2 - x2 = 84 ⇔ 4 x + 4 = 84 ⇔ 4 x = 80 ⇔ x = 20.
∴ Required sum = x + (x + 2) = 2 x + 2 = 42.
Answer C
Answer: (C) 27
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
(A) 1: 8
(B) 1: 6
(C) 1: 9
(D) 1: 3
(E) 1: 2
Rationale: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1: 9
Answer:C
Answer: (C) 1: 9
Question: Seller selling an apple for Rs.17, a Seller loses 1/6th of what it costs him. The CP of the apple is?
(A) 10
(B) 12
(C) 18
(D) 19
(E) 20
Rationale: SP=17Loss=CP18Loss=CP−SP=CP−17⇒CP18=CP−17⇒17 CP18=17⇒CP18=1⇒CP=18
C
Answer: (C) 18
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 25%?
(A) 20%
(B) 26%
(C) 42%
(D) 27%
(E) 12.5%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 =75
2/3 SP1 = 75
SP1 = 112.50
100 --- 12.5 => 12.5%
Answer: E
Answer: (E) 12.5%
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 1/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 30 vehicles that are not Speedsters, how many Speedster convertibles are there?
(A) 13
(B) 18
(C) 12
(D) 15
(E) 17
Rationale: Total Vehicle = 1/3 of speedster + 2/3 of others.
Speedster convertibles = 1/3 total vehicle * 4 /5
Given : 2/3 constitutes 30 Vehicles. hence 1/3 constitutes 15
Speedster convertibls = 15 * 4/5 = 12
C
Answer: (C) 12
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 6
(B) 5
(C) 3
(D) 4
(E) 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Answer: (D) 4
Question: The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
(A) 197
(B) 198
(C) 199
(D) 200
(E) 201
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient * divisor + remainder = 15 * 13 + 2 = 197
correct answer A
Answer: (A) 197
Question: Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?
(A) 35
(B) 55
(C) 39
(D) 40
(E) 60
Rationale: After 30 mins, Richard travels 15 miles ahead Carla.
x = mph Carla need to catch up Richard in 3 hours. --> relative speed of them = x-30
Carla needs to catch up 15 miles in 3 hours --> (x−30)3=15--> x=35
Answer: A
Answer: (A) 35
Question: An bus covers a certain distance at aspeed of 210 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 560 km/h
(B) 567 km/h
(C) 779 km/h
(D) 723 km/h
(E) 630 km/h
Rationale: Distance = (210 x 5) = 1050 km.
Speed = Distance/Time
Speed = 1050 /(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1050 x 3/5 km/hr = 630 km/hr.
E
Answer: (E) 630 km/h
Question: what is the probability of getting atmost one head when Two unbiased coin are tossed ?
(A) 3/4
(B) 3/2
(C) 4/3
(D) 1/2
(E) 2/6
Rationale: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Option A
Answer: (A) 3/4
Question: Pipe A fills a tank of capacity 850 liters at the rate of 40 liters a minute. Another pipe B fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is open for a minute and then closed and then pipe C is open for a minute and then closed and the cycle is repeated, when will the tank be full?
(A) 42 minutes
(B) 51 minutes
(C) 39 minutes
(D) 40 minutes 20 seconds
(E) None of these
Rationale: In one cycle they fill 40+30-20 = 50 liters
850 = 50*n => n = 17
here n = number of cycles.
total time = 17*3 = 51 as in one cycle there are 3 minutes.
thus 51 minutes
ANSWER:B
Answer: (B) 51 minutes
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/5 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
(A) 1/7
(B) 1/8
(C) 2/5
(D) 3/4
(E) 7/8
Rationale: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
We're told that 1/5 of the garden is green, so, since all the flowers must be either green or yellow, we know that 4/5 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 4/5 * 1/2 = 2/5, or C.
Answer: (C) 2/5
Question: You hold some gold in a vault as an investment. Over the past year the price of gold increases by 60%. In order to keep your gold in the vault, you must pay 10% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.
(A) 45%
(B) 46%
(C) 50%
(D) 55%
(E) 44%
Rationale: (100%+60%)*(100%-10%) = 160*0.90 = 144% an increase of 44%
Your gold holdings have increased in value by 44%.
The Answer is E
Answer: (E) 44%
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 22
(B) 27
(C) 20
(D) 99
(E) 78
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
(A) Rs. 8400
(B) Rs. 11,900
(C) Rs. 13,600
(D) Rs. 14,700
(E) Rs. 13700
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 x	21/50) = Rs. 14,700.
THE CORRECT ANSWER IS D.
Answer: (D) Rs. 14,700
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 26%
(B) 23%
(C) 85%
(D) 45%
(E) 25%
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit
= 10/40 * 100
= 25%
Answer: E
Answer: (E) 25%
Question: If the sum of two positive integers is 22 and the difference of their squares is 44, what is the product of the two integers?
(A) 108
(B) 119
(C) 120
(D) 135
(E) 143
Rationale: Let the 2 positive numbers x and y
x+ y = 22 -- 1
x^2 - y^2 = 44
=> (x+y)(x-y)=44 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 12
y= 10
Product = 12*10 = 120
Answer C
Answer: (C) 120
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train.
(A) 150
(B) 278
(C) 179
(D) 300
(E) 191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 18 = 300 meter
Answer:D
Answer: (D) 300
Question: In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
(A) 14
(B) 12
(C) 13
(D) 15
(E) 16
Rationale: Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.
Now, according to the question,
nC2 = 105;
Or, n!/[2!*(n-2)!] = 105;
Or, n*(n-1)/2 = 105;
Or, n2-n = 210;
Or, n2-n-210 = 0;
Or, n = 15, -14;
But, we cannot take negative value of n.
So, n = 15 i.e. number of persons in the party = 15.
Option D
Answer: (D) 15
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) 28,077
(B) 28,019
(C) 28,019
(D) 28,000
(E) 28,001
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000.Answer: D
Answer: (D) 28,000
Question: Of the diplomats who attended a summit conference: 20 spoke French, 32 did not speak Hindi and 20% of the diplomats spoke neither French nor Hindi. If 10% of the diplomats spoke both French and Hindi, then how many diplomats attended the conference?
(A) 70
(B) 96
(C) 108
(D) 120
(E) 150
Rationale: 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
Answer: (D) 120
Question: if 6 coins are tossed simultaneously what is the probability of getting atleast four heads
(A) 11/32
(B) 12/32
(C) 13/32
(D) 15/32
(E) 19/32
Rationale: n(S)= 2^6= 64
n(E)= 6C4 + 6C5 + 6C6 = 15+6+1= 22
p(E)= n(E)/n(S)= 22/64= 11/32
ANSWER:A
Answer: (A) 11/32
Question: The average of temperatures at noontime from Monday to Friday is 40; the lowest one is 30, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 50
(D) 45
(E) 75
Rationale: Average=40, Sum of temperatures=40*5=200
As the min temperature is 30, max would be 200-4*30=80 --> The range=80(max)-30(min)=50
Answer: C
Answer: (C) 50
Question: List L: ABC, BCA, CAB
In list L above, there are 5 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
(A) 47
(B) 114
(C) 152
(D) 161
(E) 488
Rationale: Let's try to sum the 3 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
D
Answer: (D) 161
Question: One copy machine can make 30 copies a minute, and a second copy machine makes 20 copies a minute. If the two copiers work together, how long would it take them to make 2,000 copies?
(A) 20 minutes
(B) 40 minutes
(C) 45 minutes
(D) 50 minutes
(E) 55 minutes
Rationale: Total work done by both machines in a minute = 30 + 20 = 50 copies
Total number of copies required = 2000
Time = 2000/50 = 40 mins
Answer B
Answer: (B) 40 minutes
Question: if log 2 = 0.30103, the number of digits in 2128 is
.
(A) 38
(B) 39
(C) 40
(D) 41
(E) 56
Rationale: log(2128) = 128log(2) = 128 × 0.30103 ≈ 38.4
ie, its characteristic = 38
Hence, number of digits in 2128 = 38+1 = 39
Answer: Option B
Answer: (B) 39
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
(A) 3:9
(B) 3:0
(C) 3:5
(D) 3:2
(E) 3:1
Rationale: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
Answer: C
Answer: (C) 3:5
Question: There are 5,280 feet in 1 mile and 11 inches in one foot. How many inches are in a mile?
(A) 5,280 - 12
(B) 5,280/12
(C) 12(5,280)
(D) 11(5,280)
(E) 12/5,280
Rationale: 1 feet = 11 inches
1 mile = 5280 feet
1 mile = 5280*11 inches
Ans: D
Answer: (D) 11(5,280)
Question: How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
(A) 256
(B) 24
(C) 12
(D) None of these
(E) Cannot be determined
Rationale: Solution:
Let the 3 boys be B1, B2, B3 and 4 prizes be P1, P2, P3 and P4.
Now B1 is eligible to receive any of the 4 available prizes (so 4 ways).
B2 will receive prize from rest 3 available prizes(so 3 ways).
B3 will receive his prize from the rest 2 prizes available(so 2 ways).
So total ways would be: 4*3*2*1=24 Ways.
Hence, the 4 prizes can be distributed in 24 ways.
Answer B
Answer: (B) 24
Question: A reduction of 40% in the price of bananas would enable a man to obtain 60 more for Rs.40, what is reduced price per dozen?
(A) 1.2
(B) 2.2
(C) 3.2
(D) 4.2
(E) 5
Rationale: 40*(40/100) = 16 --- 60
? --- 12 => Rs.3.2
Answer: C
Answer: (C) 3.2
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 30%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
(A) 15%
(B) 25%
(C) 33.33%
(D) 40%
(E) 35%
Rationale: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.30(85)
so;
total weight=100g
fat=20g
20%
A
Answer: (A) 15%
Question: If a drawing has an outer circle of diameter 30 and an inner circle of diameter 24, then what fraction of outer circle's surface is not covered by the inner circle?
(A) 3/6
(B) 8/24
(C) 14/16
(D) 9/25
(E) 2/3
Rationale: The questions asks us to find the surface which is not covered by the inner circle i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the inner circle=pi* r^2, where r=12
=>pi*144
Area of the outer circle=pi*225
Surface not covered by the inner circle=pi*225-pi*144=Pi*81
fraction of outer circle's surface is not covered by the inner circle= Pi*81/total area of the outer circle
=>Pi*81/Pi*225=9/25
Answer is D
Answer: (D) 9/25
Question: 1/2+[(2/9*9/32)+1]-9/16=
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Rationale: 1/2 - [(2/9*9/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: (E) 0
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 2/3 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
(A) 1/6
(B) 1/8
(C) 1/4
(D) 3/4
(E) 7/8
Rationale: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
we're told that 2/3 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/3 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 1/3 * 1/2 = 1/6, or A.
Answer: (A) 1/6
Question: Simple interest on a sum at 5% per annum for 2 years is Rs.140. The C.I. on the same sum for the same period is?
(A) 141.5
(B) 142.5
(C) 143.7
(D) 144.6
(E) 178.4
Rationale: SI = 70 + 70
CI = 70 + 70 + 1.5 = 141.5
Answer: A
Answer: (A) 141.5
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 11.9
(B) 11.2
(C) 11.6
(D) 11.5
(E) 11.1
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer: D
Answer: (D) 11.5
Question: At what rate percent on simple interest will Rs.600 amount to Rs.950 in 5 years?
(A) 3.33%
(B) 5.93%
(C) 4.33%
(D) 9.33%
(E) 11.67%
Rationale: 350 = (600*5*R)/100
R = 11.67%
ANSWER:E
Answer: (E) 11.67%
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 16th highest price and the 23rd lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: There were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio. Including the radio, there were 15 + 22 + 1 = 38 items sold.
The answer is D.
Answer: (D) 38
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/72 of the area of the field. What is the length of the field?
(A) 73
(B) 32
(C) 34
(D) 43
(E) 96
Rationale: Explanation:
A/72 = 8 * 8 => A = 8 * 8 * 72
x * 2x = 8 * 8 * 72
x = 48 => 2x = 96
Answer: Option E
Answer: (E) 96