mathewhe/aqua_rat huggingface dataset:
Question: If a boat is rowed downstream for 500 km in 5 hours and upstream for 240 km in 6 hours, what is the speed of the boat and the river?
(A) 70 , 30
(B) 30 , 70
(C) 70 , 70
(D) 30 , 30
(E) 80 , 50
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 100 ; Us = 40
x = (100 + 40) / 2 = 140/2 = 70 km/hr
y = (100 - 40)/2 = 60/2 = 30 km/hr
ANSWER: A
Answer: (A) 70 , 30
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent L of her bushes have only yellow roses?
(A) 20
(B) 30
(C) 50
(D) 70
(E) 80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so,L= 0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B
Answer: (B) 30
Question: If |x – 9/2| = 5/2, and if y is the median of a set of q consecutive integers, where q is odd, which of the following must be true?
I. xyq is odd
II. xy(q^2 + q) is even
III. x^2y^2q^2 is even
(A) I only is true
(B) II only is true
(C) I and III
(D) II and III
(E) I, II, and III
Rationale: given:
q is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: q = O, y = O and x = O or E
Statement I = x*y*q = y*q*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(q^2 + q) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2q^2 is even. E/O x O x O = Odd or even. Hence False.
Answer =B.
Answer: (B) II only is true
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:49
(C) 39:42
(D) 39:47
(E) 39:41
Rationale: Explanation:
3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer:A
Answer: (A) 39:40
Question: The sub-duplicate ratio of 1:9 is
(A) 4:3
(B) 1:2
(C) 1:3
(D) 1:4
(E) 2:3
Rationale: root(1):root(9)=1:3
ANSWER:C
Answer: (C) 1:3
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 10,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) 3,000,000,000
Rationale: number of cars sold = x=800000-50y
y=10000
x=800000-500000=300000
revenue from 300000 cars=10000*300000=3000000000 E
Answer: (E) 3,000,000,000
Question: What is the sum of all even numbers from 1 to 501?
(A) 122821
(B) 281228
(C) 281199
(D) 62750
(E) 128111
Rationale: Explanation:
500/2 = 250
250 * 251 = 62750
Answer: D
Answer: (D) 62750
Question: A, B and C enter in partnership. A invests some money at the beging, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs 39,000/-, C’s Share is:
(A) Rs. 12655/-
(B) Rs. 13,000/-
(C) Rs. 9000/-
(D) Rs. 10800/-
(E) None of these
Rationale: Explanation:
Suppose A, B, C invest Rs. X, Rs. 2x and Rs. 3x respectively
A : B : C = (x * 12) : (2x * 6) : (3x * 4)
= 12x : 12x : 12x = 1: 1: 1
C’ Share = Rs. (39000 * 1/3) =Rs. 13000/-
Answer: Option B
Answer: (B) Rs. 13,000/-
Question: A student finds the sum 1 + 2 + 3 + ... as his patience runs out. He found the sum as 575. When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed?
(A) 16
(B) 18
(C) 14
(D) 20
(E) 22
Rationale: Explanation :
Sum of 1st 10 natural numbers (1 – 10) = 1 + 2 + …10 = 55.
Sum of next 10 natural numbers (11 – 20) = 10 + 11 + 12 +…20 = 100 + 55 = 155.
Sum of next 10 natural numbers (31 – 40) = 255.
Sum of numbers from 31 – 40 = 355 and so on and on.
So, we have here 55 + 155 + 255 = 465.
If we add 355 to 465, it will be way more than 575.
So, we can add one by one.
465 + 31 + 32 + 33 = 561.
465 + 31 + 32 + 33 +34 = 595.
Thus, the sum should be 595 instead of 575, and the missing number is 20.
Answer : D
Answer: (D) 20
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn $90 only. Men’s wages are?
(A) $4
(B) $6
(C) $7
(D) $9
(E) $3
Rationale: B
$6
5M = xW = 8B
5M + xW + 8B ----- $90 Rs.
5M + 5M + 5M ----- $90 Rs.
15M ------ $90 => 1M = $6.
Answer: (B) $6
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3312, how much was it in the beginning?
(A) A)3800
(B) B)4200
(C) C)4400
(D) D)4500
(E) E)4600
Rationale: X * (90/100) * (80/100) = 3312
X = 4600
ANSWER:E
Answer: (E) E)4600
Question: Aniket deposited two parts of a sum of 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?
(A) 9000
(B) 18000
(C) 15000
(D) Data inadequate
(E) None of these
Rationale: Let the amount deposited at the rate of 15% per annum be x.
15% of x + 18% of (25000 – x) = 4050
or, 15% of x + 18% of 25000 – 18% of x = 4050
or, 3% of x = 4500 – 4050 = 450 ⇒ x = 15000
\ Amount deposited at 18% = (25000 – 15000 ) = 10000
Answer E
Answer: (E) None of these
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 108 kmph. In how much time will the trains cross each other?
(A) 80/8
(B) 80/7
(C) 80/5
(D) 80/3
(E) 80/11
Rationale: Relative speed = (90 + 108)* 5/18 = 11 * 5 = 55 mps.
The time required = d/s = (100 + 100 + 200)/55
= 400/55 = 80/11 sec.
Answer: E
Answer: (E) 80/11
Question: Convert the following unit:
2.2 hectares in ares
(A) 200 ares.
(B) 210 ares.
(C) 220 ares.
(D) 230 ares.
(E) 240 ares.
Rationale: 2.2 hectares in ares
1 hectare = 100 ares
Therefore, 2.2 hectares = 2.2 × 100 ares
= 220 ares.
ANSWER : OPTION C
Answer: (C) 220 ares.
Question: If a 3-number code is formed of the integers from 1 to 17 inclusively, and each of the numbers in the code is different, how many possible codes are there?
(A) 3970
(B) 4080
(C) 4190
(D) 4200
(E) 4310
Rationale: 17*16*15=4080
The answer is B.
Answer: (B) 4080
Question: A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
(A) 71.12
(B) 71.19
(C) 71.11
(D) 71.132
(E) 71.16
Rationale: Total time taken = (160/64 + 160/8) = 9/2 hrs.
Average speed = 320 * 2/9 = 71.11 km/hr.
Answer:C
Answer: (C) 71.11
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
(A) 22 days
(B) 68 days
(C) 77 days
(D) 11 days
(E) 88 days
Rationale: (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Answer: (D) 11 days
Question: Find 125/14*6
(A) 2.4658
(B) 6.398
(C) 1.488
(D) 5.687
(E) 9.652
Rationale: Answer=125/14*6
=125/84=1.488
Option C is correct
Answer: (C) 1.488
Question: When the stock market opened yesterday, the price of a share of stock X was 10 1/2. When the market closed, the price was 11 1/4. Of the following, which is closest to the percent increase in the price of stock X?
(A) 0.5%
(B) 1.0%
(C) 6.7%
(D) 7.1%
(E) 7.5%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the percent increase in the price of stock X is (45/4−21/2)/(2/12)∗100=50/7
Answer: D.
Answer: (D) 7.1%
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $70,000?
(A) $38,796.
(B) $40,000.
(C) $38,976.
(D) $39,679.
(E) $68,208.
Rationale: 70,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.
Only option E fulfills the condition and hence is the answer
Answer: (E) $68,208.
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 60?
(A) 10
(B) 12
(C) 14
(D) 18
(E) 24
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
60=2*3*5*2 is divisible by 12. therefore the greatest common divisor is 12
B
Answer: (B) 12
Question: P is 10% more efficient than Q. P can complete a work in 21 days. If P and Q work together, how many days will it take to complete the same work?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: The work done by P in 1 day = 1/21
Let work done by Q in 1 day = q
q × (110/100) = 1/21
q = 100/(21×110) = 10/(21×11)
The work done by P and Q in 1 day = 1/21 + 10/(21×11) = 21/(21×11)= 1/11
P and Q together can do the work in 11 days.
The answer is C.
Answer: (C) 11
Question: A train running at the speed of 126 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 286 meter
(C) 186 meter
(D) 315 meter
(E) 265 meter
Rationale: Speed = 126*(5/18) m/sec
= 35 m/sec
Length of Train (Distance)
= Speed * Time
(35) * 9 = 315 meter
Answer:D
Answer: (D) 315 meter
Question: There are two cars. One is 60 miles north of the other. Simultaneously, the car to the north is driven westward at 15 miles per hour and the other car is driven eastward at 25 miles per hour. How many miles apart are the cars after 2 hours?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 60 and a height of 80. The hidden pattern here is a 3/4/5 right triangle (the 60 lines up with the '3' and the 80 lines up with the '4'). In this way, you can deduce that each side is '20 times' bigger than it's corresponding side:
3/4/5 becomes
60/80/100
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer: C
Answer: (C) 100
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 30 Km/hr. His average speed during the whole journey in km/hr. is :
(A) 34
(B) 43
(C) 40
(D) 38
(E) 29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*60*30 / 60+30
=40
Answer : C
Answer: (C) 40
Question: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
(A) 256
(B) 432
(C) 512
(D) 640
(E) None of these
Rationale: Explanation:
Let total number of children be x.
Then, x x	1/8x=x/2x 16 x = 64.
Number of notebooks =	1/8x2 = (1/8	x 64 x 64)= 512.
ANSWER IS C
Answer: (C) 512
Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y =	1/8	and 3x + 7y =	1/10	.
Solving the two equations, we get: x =11/400, y =1/400
1 woman's 1 day's work =	1/400	.
10 women's 1 day's work =	1/400 x 10 =	1/40	.
Hence, 10 women will complete the work in 40 days.
Answer : B
Answer: (B) 40
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
12 minutes more to walk to work than to ride his bicycle, then x equals
(A) 4
(B) 7
(C) 10
(D) 18
(E) 20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 12 mins or 12*60 secs in 12*60/40 =18 km
ANSWER:D
Answer: (D) 18
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Unit digit in (6374)1793 = Unit digit in (4)1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
A)
Answer: (A) 0
Question: If y exceeds x by 20%, then x is less than y by?
(A) 86 2/3%
(B) 16 2/7%
(C) 16 2/3%
(D) 16 3/3%
(E) 16 2/3%
Rationale: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 6% dividend at the end of the year,then how much does he get ?
(A) Rs. 500
(B) Rs. 600
(C) Rs. 650
(D) Rs. 720
(E) None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(6/100x12000) = Rs. 720.
Answer D
Answer: (D) Rs. 720
Question: Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 90 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
(A) 45
(B) 50
(C) 60
(D) 75
(E) 81
Rationale: AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 90
y - 90 + (y/4) = 90
5y/4 = 180
y = 144
2x/3 = 144 - 90 = 54
x = 162/2 = 81
Answer: E
Answer: (E) 81
Question: Awordis defined as a sequence of two dots arranged in a row. Each dot is colored any one of the three colours. How many distinct words can be formed?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Each dot can be coloured any of the three colours, so 3 options for each dot: 3*3 = 9.
Answer: E
Answer: (E) 9
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 1/2
(B) 3/4
(C) 3/5
(D) 3/7
(E) 4/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: In a mayoral election, Candidate X received 1/2 more votes than candidate Y, and Candidate Y received 2/5 fewer votes than Z. If Z received 25,000 votes how many votes did candidate X received?
(A) 18000
(B) 22500
(C) 24000
(D) 26000
(E) 32000
Rationale: Z=25 --> Y received 2/5 fewer votes than Z --> Y=Z- 2/5*Z=15;
X received 1/2 more votes than Y --> X=Y+1/2*Y=22,5.
Answer: B.
Answer: (B) 22500
Question: 12.1212+17.0005 - 9.1100 = ?
(A) 20.0015
(B) 20.0117
(C) 20.0115
(D) 20.1015
(E) None
Rationale: Solution
Given expression
=(12.1212+17.0005)-9.1100
= (29.1217 - 9.1100)
=20.0117.
Answer B
Answer: (B) 20.0117
Question: If the population of a certain country increases at the rate of one person every 20 seconds, by how many persons does the population increase in 1 hour?
(A) 100
(B) 120
(C) 150
(D) 180
(E) 160
Rationale: Answer = 3 * 60 = 180
Answer is D
Answer: (D) 180
Question: Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 40%. What fraction of the original paint was replaced?
(A) 1/30
(B) 1/5
(C) 2/5
(D) 3/4
(E) 4/5
Rationale: 40% is 15%-points above 25% and 10%-points below 50%.
Thus the ratio of 25%-solution to 50%-solution is 2:3.
2/5 of the original paint was replaced.
The answer is C.
Answer: (C) 2/5
Question: The average of first 10 odd numbers is?
(A) 11
(B) 10
(C) 99
(D) 77
(E) 65
Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer: B
Answer: (B) 10
Question: The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 350, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
(A) 60
(B) 90
(C) 120
(D) 150
(E) 240
Rationale: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 2/5 x = 350
Hence, x = 250. So, number of timeshare condos available at Playa del Mar = 250
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 2/5x = 3/5x = 3/5(250) = 150
The correct answer is D
Answer: (D) 150
Question: If 'A' means '-', 'B' means '/', 'C' means '+', and 'D' means 'X' then
Find the value of the following:
21 B 7 C 9 D 10 A 13
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: Solution:
80
Explanation:
21 B 7 C 9 D 10 A 13
= 21 / 7 + 9 X 10 - 13
= 3 + 90 - 13
= 80
Answer C
Answer: (C) 80
Question: Find the average of all prime numbers between 20 and 30
(A) 15
(B) 20
(C) 18
(D) 32
(E) 26
Rationale: Prime numbers between 20 and 30 are 23,29
Required average = (23+29)/2 = 52/2 = 26
Answer is E
Answer: (E) 26
Question: Ram professes to sell his goods at the cost price but he made use of 700 grms instead of a kg, what is the gain percent?
A. 11%
(A) 11 1/9%
(B) 11 1/8%
(C) 11 9/9%
(D) 11 5/9%
(E) 42.85%
Rationale: 700 --- 300
100 --- ? => 42.85%
Answer:E
Answer: (E) 42.85%
Question: A trader marked the selling price of an article at 60% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :
(A) 10 %
(B) 10.5 %
(C) 6.8 %
(D) 12.5 %
(E) None
Rationale: Sol.
Let C.P. = Rs. 100. Then, Marked Price = Rs. 160, S.P. = Rs. 99.
∴ Discount % = [11/160 * 100] % = 6.8 %
Answer C
Answer: (C) 6.8 %
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
(A) 8/15
(B) 5/14
(C) 7/15
(D) 16/7
(E) 4/3
Rationale: .let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Ans: C
Answer: (C) 7/15
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 40 litres of tomato juice?
(A) 2.8 liters.
(B) 2.5 liters.
(C) 5 liters.
(D) 2.6 liters.
(E) 2.1 liters.
Rationale: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
â‡’â‡’ 10%(40) = 80%(x)
â‡’â‡’ x = 5 liters.
Answer:C
Answer: (C) 5 liters.
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for7 years and that for 9 years.
(A) 7:5
(B) 2:5
(C) 2:9
(D) 7:9
(E) None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗7/100) /(P∗R∗9/100)]
=7PR /9PR=7:9
Option D
Answer: (D) 7:9
Question: In how many ways can you seat 8 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 720
(B) 1720
(C) 2880
(D) 5040
(E) 25200
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 5 chairs to sit. The remaining 7 people can sit in 7! ways. Thus the # of arrangements is 5*7! = 25,200.
Answer: E.
Answer: (E) 25200
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 40% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $37.80
(B) $38.50
(C) $39.20
(D) $44.33
(E) $40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 40% discount then the original price of it was x*0.6=$14 --> x=$23,33.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 23,33+21=$44,33.
Answer: D.
Answer: (D) $44.33
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 238, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 22
(B) 33
(C) 55
(D) 42
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 238 => .1x + 3/4x = 238 => x = 280
280 - 238 = pure gala = 42.
Answer D
Answer: (D) 42
Question: If 14 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
(A) 95
(B) 90
(C) 85
(D) 80
(E) 56
Rationale: Let x be the number of students in the school. 0.14x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.14x/0.25=0.56x students went to the camping which is 56%.
The answer is E
Answer: (E) 56
Question: In a diving competition, each diver has a 40% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)
(A) 1/5
(B) 1/15
(C) 4/25
(D) 18/125
(E) 61/125
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.4 = 40/100 = 2/5
i.e. Probability of Non-Perfect dive = 0.6 = 60/100 = 3/5
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect
Method-1:
i.e. Probability of First two being Imperfect and Third being Perfect dive = (3/5)*(3/5)*(2/5) =18/125
D
Answer: (D) 18/125
Question: The average age of 36 students in a group is 15 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 45 years
(C) 52 years
(D) 54 years
(E) None of these
Rationale: Explanation:
Age of the teacher = (37 * 16 - 36 * 15) years = 52 years. Answer: C
Answer: (C) 52 years
Question: A fair coin with sides marked heads and tails is to be tossed seven times. What is the probability that the coin will land tails side up more than five times?
(A) 37/256
(B) 56/256
(C) 65/256
(D) 70/256
(E) 8/128
Rationale: More than 5 times tails = 6times +7times = 7C6 + 7C7 = 8
2 2 2 2 2 2 2
2^8 times total events and 8 events where tails side up .
So probability = 8/2^7 = 8/128 (Answer E)
Answer: (E) 8/128
Question: In a group of ducks and cows, the total number of legs are 26 more than thrice the number of heads. Find the total number of cows.
(A) A)14
(B) B)13
(C) C)16
(D) D)8
(E) E)6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 26 more than twice the number of heads
=> 2(d + 2c) = 26 + 2(c + d)
=> d + 2c = 13 + c + d
=> 2c = 13 + c
=> c = 13
i.e., total number of cows = 13
Answer : B
Answer: (B) B)13