RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If a4 +(1/a4)=119 then a power 3-(1/a3)
A.22
B.36
C.27
D.18
Answer: B.36
Explanation: Explanation:
Given that a4+1a4=119a4+1a4=119 , adding 2 on both sides, we get : (a2+1a2)2=121(a2+1a2)2=121
⇒a2+1a2=11⇒a2+1a2=11
Again, by subtracting 2 on both sides, we have, ⇒(a−1a)2=9⇒(a−1a)2=9
⇒a−1a=3⇒a−1a=3
Now, ⇒a3−1a3⇒a3−1a3 = (a−1a)(a2+1a2+1)(a−1a)(a2+1a2+1) = 12×3 = 36
Answer:B
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
A.35
B.25
C.40
D.52
Answer: A.35
Explanation: Excluded number = 27*5-25*4 = 135-100 = 35
Answer is A
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 6 Ohms?
A.7/30
B.11/30
C.11/15
D.30/11
Answer: D.30/11
Explanation: 1/R = 1/x + 1/y
1/R = 1/5+1/6 = 11/30
R = 30/11
The answer is D.
Question: probability Like between 100 and 999 how many no have the probability that they does not contain 7 ?
A.646/900
B.648/900
C.649/900
D.658/900
Answer: B.648/900
Explanation: There are 900 numbers between 100 and 999.
those that contain 7 are.....
107, 117, 127, ........ -- 10 of these
207, 217, 227, ........ -- 10 of these too
307, 317, 327, .......
....
9*10 numbers that end in 7.
170, 171, 172, 173, 174, 175, 176, (NOT 177 WE ALREADY COUNTED IT), 178, 179 -- 9 of these
270, 271, 272, 273, 274, 275, 276, (NOT 277 WE ALREADY COUNTED IT), 278, 279 -- 9 of these
...
and so on
so 9*9 numbers that have a middle digit of 7
and finally
700, 701, 702, 703, 704.................., but NOT
(707, 717, 727,....) or (770, 771, 772, 773, ....)
So that's (100 - 10 - 9) = 81 numbers that start with 7.
We had 900 numbers.
N = 900 - 90 - 81 - 81 = 648
So the probability is 648/900 = 0.72
ANSWER:B
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?
A.190
B.105
C.200
D.205
Answer: B.105
Explanation: This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 200, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
20(10) = 200
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 200 = 210
20 + 190 = 210
30 + 180 = 210
Etc.
Since there are 20 total terms, this pattern will create 10 'pairs' of 210.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(10)(210)/(20) =105
Answer : B
Question: The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
A.57.6
B.51.6
C.51.4
D.51.1
Answer: C.51.4
Explanation: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 = 51.4.
Answer: C
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 11 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
A.1,260
B.2,520
C.9,240
D.6,020
Answer: C.9,240
Explanation: 5 students can be selected out of 11 students in 11C5 ways.
out of the remaining 5 students,Note taker can be chosen in 5 ways.
Finally only 4 students remain from which we can choose a treasurer in 4 ways.
Total number of ways = 462 * 5 *4 = 9240
correct answer - C
Question: How much water should be added to 12 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
A.28 liters
B.27 liters
C.30 liters
D.32 liters
Answer: A.28 liters
Explanation: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=12+x)))
2=5%*(12+x)-------->x=28
Ans A
Question: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C
A.2
B.4
C.8
D.16
Answer: B.4
Explanation: It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 4
B
Question: If n is the smallest integer such that 54 times n is the square of an integer, what is the value of n?
A. 2
B. 1
C. 6
D. 12
Answer: B. 1
Explanation: 54 can written as = 2 * 3 * 3 * 3 --> 2^1 * 3^3 ---(1)
so for 54 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 2 to make the power of 1 in (1) even
Option B is correct
Question: In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?
A.160
B.170
C.190
D.210
Answer: D.210
Explanation: 7p3 = 7 × 6 × 5 = 210
Option 'D'
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
A.32778
B.50000
C.27798
D.27799
Answer: B.50000
Explanation: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000.Answer:B
Question: A publishing company advertisd the job opening.The response was good. One hundred people applied for the post. The company wanted someone expert in both physics and chemistry. Out of which 10 did not had any specalization.70 of them had got physics training and 82 got training in chemistry.how many applicants had got training in both
physics and chemistry?
A.60
B.61
C.62
D.63
Answer: C.62
Explanation: (100-10)=90-82=8,70-8=62
ANSWER:C
Question: 20 litres of a mixture contains milk and water in the ratio 3:1. How much milk must be added to this mixture to have a mixture containing milk and water in the ratio 4 :1 ?
A.2
B.5
C.6
D.7
Answer: B.5
Explanation: Quantity of milk in the given mixture = \inline \frac{20\times 3}{4}=15 lts
Quantity of water in this mixture = 20 - 15 = 5 lts
Let x litres of milk be added to given mixture to have the requisite ratio of milk and water
Then
\inline \Rightarrow 15 + x =20
\inline \therefore x = 5
\inline \therefore Milk to be added = 5 litres
Answer:B
Question: A cube of side 4 meter length is cut into small cubes of side 25 cm each. How many such small cubes can be obtained?
A.4069
B.6048
C.1000
D.4096
Answer: D.4096
Explanation: Along one edge, the number of small cubes that can be cut
= 400/25=16
Along each edge 16 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 16 * 16 * 16= 4096
Answer:D
Question: The mass of 1 cubic meter of a substance is 300 kg under certain conditions. What is the volume in cubic centimeters of 1 gram of this substance under these conditions? (1 kg =1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
A.3.33
B.3.34
C.3.53
D.5.32
Answer: A.3.33
Explanation: 300 kg - 1 cubic meter;
300,000 g - 1 cubic meter;
300,000 g - 1,000,000 cubic centimeters;
1 g - 1,000,000/300,000 = 10/3 = 3.33 cubic centimeters.
Answer: A.
Question: A train running at the speed of 90 km/hr crosses a pole in 6 seconds. Find the length of the train.
A.150 meter
B.100 meter
C.105 meter
D.120 meter
Answer: A.150 meter
Explanation: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
(25) * 6 = 150 meter
Answer:A
Question: The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?
A.P=1/3+1/5*3
B.P=1/3+1/5*4
C.P=1/3+1/5*2
D.P=1/8*(1/8-3)
Answer: A.P=1/3+1/5*3
Explanation: The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true?
a)P=1/3+1/5*3 b)P=1/5*(1/8-3)
P=1/3+1/5*3 is true.
ANSWER:A
Question: What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 20 ?
A.-1
B.6
C.7
D.12
Answer: B.6
Explanation: First of all |x - 3|^2 = (x - 3)^2, so we have: (x - 3)^2 + |x - 3| = 20.
When x < 3, x - 3 is negative, thus |x - 3| = -(x - 3). In this case we'll have (x - 3)^2 - (x - 3) = 20 --> x = -1 or x = 8. Discard x = 8 because it's not in the range we consider (< 3).
When x >= 3, x - 3 is non-negative, thus |x - 3| = x - 3. In this case we'll have (x - 3)^2 + (x - 3) = 20 --> x = -2 or x = 7. Discard x = -2 because it's not in the range we consider (>= 3).
Thus there are two solutions: x = -1 and x = 7 --> the sum = 6.
Answer: B.
Question: A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?
A.1/16
B.1/2
C.3/16
D.11/16
Answer: D.11/16
Explanation: Let's find the probability of the opposite event and subtract this value from 1.
The opposite event would be getting zero tails (so all heads) or 1 tail.
P(HHHH)=(12)4=116P(HHHH)=(12)4=116.
P(THHH)=4!3!∗(12)4=416P(THHH)=4!3!∗(12)4=416, we are multiplying by 4!3!4!3! since THHH scenario can occur in number of ways: THHH, HTHH , HHTH, or HHHT (notice that 4!3!4!3! basically gives number of arrangements of 4 letters THHH out of which 3 H's are identcal).
P(T≥2)=1−(116+416)=1116P(T≥2)=1−(116+416)=1116.
Answer: D.
Question: A train running at the speed of 80 km/hr crosses a pole in 9 sec. What is the length of the train?
A.298 m
B.200 m
C.208 m
D.988 m
Answer: B.200 m
Explanation: Speed = 80 * 5/18 = 200/9 m/sec
Length of the train = speed * time = 200/9 * 9
= 200 m
Answer:B
Question: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.30 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
A.0.40x
B.4.20x
C.1.40x
D.1.60x
Answer: B.4.20x
Explanation: because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.3 * 4X * 7/8
In May they pay for the storage 0.3 * 4X * 6/8
In Jun they pay for the storage 0.3 * 4X * 5/8
In Jul they pay for the storage 0.3 * 4X * 4/8
In Aug they pay for the storage 0.3 * 4X * 3/8
In Sep they pay for the storage 03 * 4X * 2/8
In Oct they pay for the storage 0.3 * 4X * 1/8
total = 0.3 * 4X * 1/8 * [ 1+2+3+4+5+6+7]
= 0.3 * X/2 * (28)
= 4.2X
(B)
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 7 years hence?
A.22
B.77
C.74
D.98
Answer: C.74
Explanation: A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
7 years, their ages will be 47 and 27.
Sum of their ages = 47 + 27 = 74.
Answer: C
Question: A certain sum of money at simple interest amounted Rs.890 in 10 years at 3% per annum, find the sum?
A.681.61
B.682.61
C.683.61
D.684.61
Answer: D.684.61
Explanation: 890 = P [1 + (10*3)/100]
P = 684.61
Answer: D
Question: 1,000^2 + 1,001^2 =
A.6,030,053
B.6,002,001
C.6,030,055
D.6,030,056
Answer: B.6,002,001
Explanation: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
Total -> *1
Answer B.
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
A.2000
B.2100
C.2200
D.2300
Answer: B.2100
Explanation: Explanation:
Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 5200 = Rs. 25200
So, Average monthly income = 25200/12 = Rs. 2100
Answer B
Question: In the Biotechnology class of 2000, there were E graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is E equal to?
A.69.
B.71.
C.73.
D.75.
Answer: C.73.
Explanation: Total = 32 +45 -13 +9 = 73 .... My first post on the forum... I hope I am correct
C is correct choice.
Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
A.180 min
B.144 min.
C.126 min
D.114 min
Answer: A.180 min
Explanation: Explanation:
Let time taken by the faster pipe to fill the tank =x minutes.
Then, time taken by the slower pipe to fill the tank =4x minutes.
Time taken by both pipes together to fill the tank=x x 4x /x+4 x=4 x / 5
4x/5=36
⇒x=45
Time taken by the slower pipe to fill the tank=4x=180 minutes.
Answer: Option A
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
A.400 km
B.500 km
C.360 km
D.550 km
Answer: C.360 km
Explanation: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Question: How many even three-digit integers greater than 700 are there such that all their digits are different?
A.40
B.72
C.80
D.112
Answer: D.112
Explanation: Case 1: Numbers starting with 7
7 _ _
The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8*5=40
Case 2: Numbers starting with 8
8 _ _
The unit digit can take 4 numbers (0,2,4,6) to be EVEN so 4 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8*4=32
Case 3: Numbers starting with 9
9 _ _
The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8 *5 = 40
Hence 40+32+40=72, correct answer is D
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
A.33 1/3%
B.43 1/3%
C.83 1/3%
D.36 1/3%
Answer: A.33 1/3%
Explanation: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer:A
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
A.288
B.200
C.279
D.992
Answer: D.992
Explanation: (800*3*3)/100 = 72
920 + 72 = 992
Answer: D
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
A.11 days
B.16 days
C.13 days
D.15 days
Answer: B.16 days
Explanation: B
16 days
P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days.
Question: If the price of a certain bond on May 1st was 3/4 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
A.50%
B.75%
C.118.5%
D.133 1/3%
Answer: C.118.5%
Explanation: The price on June 1st = 12 (assume);
The price on May 1st = 3/4*12 = 9;
The price on July 1st = 9*1.25 = 11.25.
The average price of the bond on May 1st and July 1st = (9+11.25)/2 = 10.125.
The price of the bond on June 1st (12) is 32/27 times (118.5%) the average price of the bond on May 1st and July 1st.
Answer: C.
Question: What should come in place of the question mark (?) in the following equation?
17 2⁄3 of 180 + 1⁄4 of 480 = ?
A.3180
B.3420
C.3200
D.3300
Answer: D.3300
Explanation: 17 2⁄3 of 180 + 1⁄4 of 480 = ?
or, ? = 53⁄3 of 180 + 1⁄4 of 480 = = 3180 + 120 = 3300
Answer D
Question: Present ages of Kiran and Shyam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Shyam's present age in years?
A.12
B.18
C.24
D.32
Answer: C.24
Explanation: Ratio of the present age of Kiran and Syam = 5 : 4
=Let the present age of Kiran = 5x
Present age of Shyam = 4x
After 3 years, ratio of their ages = 11:9
= (5x + 3) : (4x + 3) = 11 : 9
= (5x+3) / (4x+3) = 11/9
= 9(5x + 3) = 11(4x + 3)
= 45x + 27 = 44x + 33
= x = 33-27 =6
Shyam's present age = 4x = 4×6 = 24
answer :C
Question: Four persons can cross a bridge in 3,7,13,17 minutes.Only two can cross at a time.Find the minimum time taken by the four to cross the bridge ?
A.20 minutes.
B.25 minutes.
C.30 minutes.
D.40 minutes.
Answer: A.20 minutes.
Explanation: Explanation:
First send 17 and 7. After 7 minutes, 7 is at finish and 17 needs 10 more minutes to complete his travel. now send 13. After 10 minutes 17 reaches finish and 13 needs 3 more minutes to complete. now send 3. both 3 and 13 reach destination at the same time after 3 minutes. hence the time taken is 7+10+3=20 minutes.
Answer A
Question: 16.02 Ã— 0.01 = ?
A.0.1602
B.0.001602
C.1.6021
D.0.01602
Answer: A.0.1602
Explanation: 16.02 Ã— 0.01 = 0.1602
The answer is A.
Question: A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is?
A.1 kmph
B.2 kmph
C.6 kmph
D.8 kmph
Answer: C.6 kmph
Explanation: DS = 25
US = 13
S = ?
S = (25 - 13)/2 = 6 kmph
Answer:C
Question: The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score.
A.172
B.173
C.174
D.175
Answer: C.174
Explanation: Total runs = 40 × 50 = 2000
Let his highest score be = x
Then his lowest score = x – 172
Now 200−x−(x−172)/38=48
⇒ 2x = 2172 – 1824
⇒ x = 174
Answer C
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 8 km each. Then they turned left and ran for another 6 km.
What is the distance (in kilometers) between the the two twins when they stop?
A.18
B.20
C.22
D.24
Answer: B.20
Explanation: The distance between them is the hypotenuse of a right angle triangle with sides 12 km and 16 km. The hypotenuse = sqrt(12^2 + 16^2) = 20
The answer is B.
Question: A bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is
A.10%
B.15%
C.20%
D.22%
Answer: B.15%
Explanation: Solution
Rate of discount	= (12 / 80 x 100)%
= 15%.
Answer B
Question: A woman introduces a man as the son of the brother of her mother. How is the man, related to the woman ?
A.Nephew
B.Son
C.Cousin
D.Uncle to Grandson
Answer: C.Cousin
Explanation: Explanation:
Brother of mother — Uncle: Uncle's son — Cousin
Answer: C) Cousin
Question: 3 candidates in an election and received 6136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
A.46%
B.49%
C.57%
D.59%
Answer: A.46%
Explanation: Total number of votes polled = (6136 + 7636 + 11628) = 25400
So, Required percentage = 11628/25400 * 100 = 46%
A
Question: An empty fuel tank with a capacity of 204 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
A.160
B.150
C.100
D.66
Answer: D.66
Explanation: Say there are A gallons of fuel A in the tank, then there would be 204-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 204-A gallons of fuel B is 0.16(204-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(204-A)=30 --> A=66.
Answer: D.
Question: X can do 1/4 of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first?
A.X
B.Y
C.Z
D.N
Answer: C.Z
Explanation: Whole work will be done by X in 10*4 = 40 days.
Whole work will be done by Y in (40*100/40) = 100 days.
Whole work will be done by Z in (13*3) = 39 days
Therefore, Z will complete the work first.
Answer : C.
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
A.8
B.7
C.6
D.5
Answer: A.8
Explanation: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%.Answer: A
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
A.1100
B.1134
C.1349
D.1430
Answer: C.1349
Explanation: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Question: In a particular 100 meter race, 8 athletes are participating that are numbered 1-8. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
A.14,540
B.16,580
C.18,920
D.20,160
Answer: D.20,160
Explanation: The total number of ways for the athletes to finish is 8! = 40,320.
#4 will be ahead of #2 in exactly half of these possibilities.
40,320/2 = 20,160
The answer is D.
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
A.
B.
C.
D.
E.
A.15/64
B.30/64
C.1/2
D.1/4
Answer: A.15/64
Explanation: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days = 15/64
Ans A
Question: The profit earned by selling an article for 892 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
A.960
B.1005
C.1,200
D.920
Answer: B.1005
Explanation: Let the profit or loss be x
and 892 – x = 448 + x or, x = 444⁄2 = 222
\ Cost price of the article = 892 – x = 448 + x = 670
\ SP of the article = 670 × 150⁄100 = 1005
Answer B
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers E are there between 6* + 2 and 6* + 6, inclusive?
A.None
B.One
C.Two
D.Three
Answer: A.None
Explanation: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes E in this range.
Answer: A.
Question: Seven people enter a race. There are 4 types of medals. Winner - platinum, runner up - gold, next two racers - silver and the last 3 - bronze. Ways to do it?
A.7!/3!
B.7!/2!3!
C.1*1*2!*3!
D.7*6*2!*3!
Answer: B.7!/2!3!
Explanation: let me take the approach adopted by you..
platinum-7 different people..
gold- remaining 6 different people..
silver- 2 out of remaining 5=5C2= 5!/2!3!...
bronze - 1 as all the three remaining are getting it..
total ways= 7*6*5!/2!3!=7!/2!3!.
ANS:B