mathewhe/aqua_rat huggingface dataset:
Question: In Set T, the average (arithmetic mean) equals the median R. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
(A) I only
(B) I and II
(C) II and III
(D) I, II, and III
(E) IV only
Rationale: This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median R you might fall for 'D'.
Ans: E
Answer: (E) IV only
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
(A) 36
(B) 232
(C) 216
(D) 484
(E) None of these
Rationale: Explanation:
number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
Answer: (C) 216
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 10:40 in the morning?
(A) 32.
(B) 36.
(C) 42.
(D) 46.
(E) 60.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
@ 9:30 - 2
@ 10 - 14
@10:30 - 2
totals to E=60
Answer: (E) 60.
Question: Currently guavas cost 60 cents/pound. Due to a disease affecting the guava trees it is expected that next month apples will cost 250% more than they do currently. How much are guavas expected to cost next month?
(A) 110 cents /pound
(B) 150 cents /pound
(C) 180 cents /pound
(D) 200 cents /pound
(E) 210 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (250/100)(60 cents/pound)
= 60 cents/pound + 150 cents/pound
= 210 cents /pound
Answer : E
Answer: (E) 210 cents /pound
Question: A division of a company consists of four men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 2/9
(B) 3/11
(C) 4/15
(D) 5/18
(E) 6/25
Rationale: Total number of ways to select 2 members = 9C2 = 36
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/36 = 5/18
The answer is D.
Answer: (D) 5/18
Question: 8+8
(A) 5
(B) 17
(C) 16
(D) 23
(E) 19
Rationale: C
Answer: (C) 16
Question: Which of the following is/are terminating decimal(s)?
I 299/(32^123)
II 189/(49^99)
III 127/(25^37)
(A) I only
(B) I and III
(C) II and III
(D) II only
(E) I, II, III
Rationale: The fraction will have terminating decimal if and only if the denominator of the fraction is of the form (2^n)(5^m).
If you look at the denominators:
1) (32^123) => (2^(5*123))(5^0) => Terminating Decimal
2) (49^99) => Can't be expressed as (2^n)(5^m) => Non terminating Decimal
3) (25^37) => (2^0)(5^(2*37)) => Terminating Decimal
Hence 1 and 3 are terminating decimals => Choice [B]
Answer: (B) I and III
Question: Which of the following can be a perimeter w of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
(A) I only
(B) III only
(C) II and III only
(D) I, II, and III
(E) Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: w>0.
Answer is D.
Answer: (D) I, II, and III
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22
(B) 30
(C) 48
(D) 99
(E) 12
Rationale: Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer: B
Answer: (B) 30
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
(A) 6:8
(B) 6:4
(C) 6:2
(D) 6:5
(E) 6:2
Rationale: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Answer: (D) 6:5
Question: What percent of a day is seven hours?
(A) 20.83%
(B) 16x1/2%
(C) 29.16%
(D) 22x1/2%
(E) None of these
Rationale: Explanation :
Required percentage = (7/24100)%
= 29.16%.
Answer : C
Answer: (C) 29.16%
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 10 minutes, what part of the cistern will be emptied?
(A) 4/9
(B) 4/3
(C) 4/2
(D) 5/9
(E) 4/1
Rationale: 2/3 ---- 12
? ----- 10 ==> 5/9
Answer: D
Answer: (D) 5/9
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 299
(B) 375
(C) 27878
(D) 288
(E) 212
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375.Answer: B
Answer: (B) 375
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 9/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
(A) 7/17
(B) 14/31
(C) 7/15
(D) 17/35
(E) 9/19
Rationale: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 9/5 units. Total time for Basic would be 10*1=10 and total time for Deluxe would be 5*9/5=9 --> total time for both of them would be 10+9=19 --> deluxe/total=9/19.
Answer: E.
Answer: (E) 9/19
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
(A) Rs.19,828.89
(B) Rs.19,828.80
(C) Rs.19,828.92
(D) Rs.19,822.00
(E) Rs.19,828.24
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2
= (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08
= 17000 Principal + Interest = Rs. 19828.80
Answer:B
Answer: (B) Rs.19,828.80
Question: if 20% of a number is added to second no.,then it increase by 50%.calculate the ratio of these no.
(A) 3:2
(B) 2:3
(C) 5:2
(D) can't be calculated
(E) none of these
Rationale: Answer:	let no. be A and B.
(20%of A)+B=150% of B
A/5=3B/2-B=B/2;A/B=5/2,
A:B=5:2
answer C
Answer: (C) 5:2
Question: A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 3:2
(B) 12:5
(C) 18:10
(D) 18:14
(E) 14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.
A : B
8000*18 : (8000*6) + (4000*12)
14400 : 96000
A:B = 3:2
Answer: A
Answer: (A) 3:2
Question: 8 x 1.6 - 3 x 1.4/1.3 = ?
(A) 21.5
(B) 22
(C) 15.8
(D) 12.8
(E) 25
Rationale: Given Expression
= (12.8 -4.2)/0.4
= 8.6/0.4
= 8.6/0.4
= 21.5
Answer is A.
Answer: (A) 21.5
Question: What is his percentage profit made by Nancy if she purchased 15 dozen pencils at Rs. 20 per dozen. He sold 8 dozens at 12% profit and the remaining 7 dozens with 15% profit?
(A) 10.08%
(B) 18.08%
(C) 15.08%
(D) 12.08%
(E) 16.08%
Rationale: Explanation :
C.P of 15 dozen = Rs.(20 x 15) = Rs.300
C.P of 8 dozen = Rs. (20 x8) = Rs. 160.
C.P of 7 dozen =Rs. (20 x7) = Rs. 140
profit on 8 dozen at 12% = 12/100*160 = 19.2
profit on 7 remaining dozen at 15% = 15/100*140 = 21
total profit = 19.2 + 21 = 40.2
% profit = ?/100*250 = 40.2
= 16.08%
Answer : E
Answer: (E) 16.08%
Question: Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
(A) $270
(B) $280
(C) $290
(D) $300
(E) $310
Rationale: 1.2N + N = 616
2.2N = 616
N = 280
The answer is B.
Answer: (B) $280
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 338
(B) 279
(C) 125
(D) 776
(E) 988
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer:C
Answer: (C) 125
Question: If (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?
(A)  12
(B)  -7
(C)  7
(D)  -1
(E)  -14
Rationale: Rearranging the given expression:
(4x + 7)(x + 2) = 8x^2 + x
i.e. 8x^2 + 15x + 14 = 8x^2 + x
i.e. 14x = -14
i.e. x = -14/14 = -1
Answer: Option D
Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: (D)  -1
Question: If a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be
(A) 1
(B) 3
(C) 2
(D) 5
(E) 4
Rationale: If b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.
Still: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.
Answer: D.
Answer: (D) 5
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,00,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 40,000
(B) Rs. 50,000
(C) Rs. 60,000
(D) Rs. 90,000
(E) None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (100000 – x) respectively. Then,
1/3x=1/2(100000-x)
=> x/3 + x/2 = 50000
=> 5x/6 = 50000
=> x= 50000 x 6 /5= 60000
Savings in Public Provident Fund = Rs. (100000 – 60000) = Rs. 40000
Answer A
Answer: (A) Rs. 40,000
Question: John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, 5, or 6 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?
(A) 1/3
(B) 2/5
(C) 3/5
(D) 4/25
(E) 6/25
Rationale: John will run farther if he runs at 6 mph and Amanda runs at 5 mph, 4 mph, or 3 mph.
In this case, P(John runs farther) = 1/5 * 3/5 = 3/25
John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.
In this case, P(John runs farther) = 1/5 * 2/5 = 2/25
John will run farther if he runs at 4 mph and Amanda runs at 3 mph.
In this case, P(John runs farther) = 1/5 * 1/5 = 1/25
Overall, P(John runs farther) = 3/25 + 2/25 + 1/25 = 6/25
The answer is E.
Answer: (E) 6/25
Question: Calculate the sum of first 19 natural numbers.
(A) 190
(B) 120
(C) 150
(D) 199
(E) 110
Rationale: Solution
We know that(1+2+3+.....+19)	= n(n+1)/2
Therefore (1+2+3+....+19)	=(19×20 / 2)
= 190.
Answer A
Answer: (A) 190
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 60 per cent. The two reductions together are equal to a single reduction of
(A) 45%
(B) 70%
(C) 35%
(D) 32.5%
(E) 30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 60percent is reduced which means the new price is merely 40percent of 3/4P
==> (3/4)x(2/5)P = 6/20P is the new price after both deduction which is 30percent of the original value P. This implies this entire series of deduction is worth having discounted 70% of P. So answer is B = 70%
Answer: (B) 70%
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
(A) 81
(B) 84
(C) 85
(D) 88
(E) 90
Rationale: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8 = 84
B
Answer: (B) 84
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof?
(A) 38.
(B) 40.
(C) 42.
(D) 44.
(E) 45.
Rationale: Let the width= x
x*4x=900
x^2= 225
x= 15
Length= 4*15= 60
difference= 60-15= 45
E is the answer
Answer: (E) 45.
Question: 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job?
(A) 8
(B) 9
(C) 6
(D) 2
(E) 1
Rationale: Explanation:
Solution: It is given that 5/8th of the work is completed in 10 days.
=> Remaining work = 3/8th of total
Applying unitary method:
Total work will be completed in 10 * 8 / 5 days
=> It takes 16 days to complete total work
=> Hence, remaining work days = 16 - 10 = 6 days
ANSWER:C
Answer: (C) 6
Question: Which is the least number that must be subtracted from 1828 so that the remainder when divided by 8, 12, 16 is 4?
(A) 0
(B) 4
(C) 8
(D) 6
(E) 2
Rationale: First we need to figure out what numbers are exactly divisible by 8,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(8,12,16) = 48 = 48
number is to be subtracted is 0
The largest such number less than or equal to 1828 is 48*38+4
A
Answer: (A) 0
Question: Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5y + 3 = 0?
(A) + 5y - 2 = 0
(B) + 5y + 2 = 0
(C) - 5y + 2 = 0
(D) - 5y - 2 = 0
(E) of these
Rationale: The quadratic equation whose roots are reciprocal of 2x2 + 5y + 3 = 0 can be obtained by replacing y by 1/y.
Hence, 2(1/y)2 + 5(1/y) + 3 = 0
=> 3x2 + 5y + 2 = 0
ANSWER:B
Answer: (B) + 5y + 2 = 0
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 60. No two digits of h are identical. How many different numbers are possible values of h?
(A) 20
(B) 22
(C) 24
(D) 30
(E) 36
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 60
a,b,c,d can be 1,2,3,10
Number of ways = 4*3*2 = 24
Answer: (C) 24
Question: Average age of total 80 students from three classes, V, VI and VII, is 13 years. Average age of 30 students of class V is 11 1/2 years. If average age of another 30 students of class VI is 12 1/2 years, what is the average aage of rest of 20 students of class VIII ?
(A) 13 1/2 years
(B) 14 1/2 years
(C) 15 years
(D) 16 years
(E) 5 years
Rationale: Explanation :
Sum of ages of 80 students = 80 x 13 = 1040
Sum of ages of 30 students of class V = 30 x 11.5 = 345
Sum of ages of 30 students of class VI = 30 x 12.5 = 375
∴ Total age of 20 students of class VII = 1040 - 345 - 375 = 320
∴ Average age = 320/20 = 16 years.
Answer : Option D
Answer: (D) 16 years
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 19 seconds. What is the length of the platform in meters?
(A) 220 meters
(B) 360 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 19 * 20 = 380 = Length of train
Length of platform = 600 - 380 = 220
Answer: A
Answer: (A) 220 meters
Question: If W is the set of all the integers between 35 and 64, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 18
(B) 19
(C) 61
(D) 31
(E) 11
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 63, the smallest is 36): 63 - 36 = 27
Step 2. Divide by 3: 27 / 3 = 9
Step 3. Add 1: 9 + 1 = 10.
So there are 10 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 64, the smallest is 36): 64 - 36 = 28
Step 2. Divide by 2: 28 / 2 = 14
Step 3. Add 1: 14 + 1 = 15.
So there are 15 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 10 multiples of 3 and the 15 multiples of 2: 10+15=25.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 10+15=25. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 60 - 30 = 30
Step 2. Divide by 6: 30 / 6 = 5
Step 3. Add 1: 5 + 1 = 6.
So there are 6 multiples of 6 within the range: we counted 6 numbers twice.
Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:
= 10+15 - 6
= 25 - 6
= 19
Therefore, the final number of multiples of 2, 3 or 6 is 19.
Hence, this is the correct answer. (B)
Answer: (B) 19
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40 meters. How many times did the ball bounce?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Division of total distance travelled will be 16+16+8
Ans:2
Answer: (A) 2
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 3 hr
(B) 2 hr
(C) 1 hr
(D) 4 hr
(E) 5 hr
Rationale: 600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
ANSWER C
Answer: (C) 1 hr
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
(A) 14
(B) 16
(C) 21
(D) 25
(E) 27
Rationale: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Answer: (C) 21
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
(A) 5
(B) 4
(C) 8
(D) 12
(E) 32
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 32 + 40 + 10 - (12) - 2x
x = 5
So, answer will be A
Answer: (A) 5
Question: Ratio of two numbers x and y is 1:2. If x is increased by 20% and y is increased by 4 then the new ratio becomes 1:5. What is the ratio 2y:x
(A) 1:3
(B) 3:1
(C) 2:3
(D) 4:1
(E) 1:4
Rationale: Let:
x = 1n
y = 2n
1.2n/(2n+4) = 1/5
6n = 2n+4
n = 1
So, x =1; y=2
2y/x = 4/1 = 4:1
Answer = D
Answer: (D) 4:1
Question: Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
(A) 14 mph
(B) 20 mph
(C) 70/3 mph
(D) 80/3 mph
(E) 30 mph
Rationale: Average speed for first two hours, S1 = 30 mph
Distance travelled in these two hours, D1 = 60 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90
Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30
Hence, the correct answer is E
Answer: (E) 30 mph
Question: In a diving competition, each diver has a 30% 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) 16/125
(E) 71/483
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.3 = 30/100 = 2/7
i.e. Probability of Non-Perfect dive = 0.7 = 70/100 = 2/3
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 = (2/3)*(2/3)*(2/7) = 71/483
E
Answer: (E) 71/483
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.
Answer C
Answer: (C) 8
Question: A warning notice is to be prepared for a building demolition in which the 'warning' is written in 8 differnent languages, including english, french and german. The authority requires you to put french after english and german after french. In how many different order of languages can you prepare the notice?
(A) 4!
(B) 5!
(C) 6!
(D) 7!
(E) 8!
Rationale: The problem requires you to find the total number of arrangements in which 8 object can be arranged paying attention to the given constraints. The constrain is that English, French and German mus follow the order E>F>G. Since there is only one way to arrange E,F and G, we can consider EFG as one object. Therefore 6 object is to be arranged and we can do this in 6! Ways. So the correct option is C. 6!.
Answer: (C) 6!
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many E hours does it currently take Anne to clean the house on her own?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in E=3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: (D) 12
Question: How many cubes of 10 Cm edge can be put in a cubic box of 1 m edge?
(A) 4000
(B) 2000
(C) 3000
(D) 5000
(E) 1000
Rationale: (110×100×100)/10×10×10 = 1000
Answer is E.
Answer: (E) 1000
Question: If 45-[28-{37-(15-*)}]= 56, then * is equal to:
(A) -29
(B) -19
(C) 17
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56
45-[28-37+15-*]=56 => 45[43-37-*]=56
45-[6-*]=56 => 45-6+*=56
39+*=56 => *=56-39
= 17
ANSWER:C
Answer: (C) 17
Question: If a trader bought 9 balls per rupee and sells at the rate of 8 balls per rupee, what is the percentage profit or loss?
(A) 12.5 %
(B) 11.5 %
(C) 23.5 %
(D) 23.5 %x
(E) 14.5 %
Rationale: Let he total number of oranges bought by the shopkeeper be 12.
If he buys 9 a rupee, his CP = 8
He selling at 8 a rupee, his SP = 9
Profit = SP - CP = 9 - 8 = 1
Profit Percent = 1/8 * 100 = 12.5 %
Answer: A
Answer: (A) 12.5 %