mathewhe/aqua_rat huggingface dataset:
Question: If x is a positive integer, and two sides of a certain triangle have lengths x and y respectively, where x is greater than y, which of the following could be the length of the third side of the triangle?
I. AB < x + y
II. AB > x - y
III. AB < y - x
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Let the third side of triangle be AB
Triangle rule states that:
Difference of other 2 sides < any side < sum of other two sides
So x - y < AB < x + y
I. AB < x + y ; could be a possible value.
II. AB > x - y ; could be a possible value.
III. AB < y - x ; could not be a possible value.
Answer: C
Answer: (C) I and II only
Question: A train covers a distance of 100km in 1 hour. If its speed is decreased by 12km/hr, the time taken by the car to cover the same distance will be?
(A) 1hr
(B) 1hr 8min
(C) 50min
(D) 1hr 30min
(E) 1hr 45min
Rationale: Speed = 100/1 = 100km/hr
New speed = 100-12 = 88 km/hr
Time taken = 100/88 = 1hr 8min
Answer is B
Answer: (B) 1hr 8min
Question: Jane makes toy bears. When she works with an assistant, she makes 60 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 70%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 70%
A
Answer: (A) 70%
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:4. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:8
(B) 8:9
(C) 3:2
(D) 2:3
(E) 16:9
Rationale: The ratio of economy to luxury cars is 3:4 --> E:L = 3:4 = 12:16.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.
Thus, L:S = 16:9.
Answer: E.
Answer: (E) 16:9
Question: If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+17 is divided by 41?
(A) 3
(B) 5
(C) 6
(D) 22
(E) 18
Rationale: X can be written as 82K + 5 or X = 5,87,169,etc.
X + 17 = 82K + 5+17= 82K +22 or X + 17 = 22,104, 186 etc.
When divided by 41, we will get the remainder 22.
D
Answer: (D) 22
Question: When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 54
(E) 67
Rationale: If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
54
Answer: D
Answer: (D) 54
Question: A man covers a certain distance A in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?
(A) 200 km
(B) 50 km
(C) 20 km
(D) 60 km
(E) 80 km
Rationale: Not really. When you solve the 2 equation above, you get,
6T-4/3 = 5R/6 from simplifying equation 1
4T-2=R/2 from simplifying equation 2
You can now multiply equation 2 by 5 to get
5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance A= R*T=20*3=60 km.D
Answer: (D) 60 km
Question: The present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?
(A) Rs. 480
(B) Rs. 420
(C) Rs. 120
(D) Rs. 240
(E) None of these
Rationale: TD = √PW × BG
=√5760×10
=√57600
= Rs. 240
ANSWER:D
Answer: (D) Rs. 240
Question: How much time will take for an amount of Rs. 150 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 7
(B) 4
(C) 5
(D) 12
(E) 2
Rationale: Time = (100 * 81) / (150 * 4.5) = 12 years'
Answer:D
Answer: (D) 12
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
(A) 13 1/7 days
(B) 13 1/3 days
(C) 13 2/3 days
(D) 13 1/7 days
(E) 13 3/3 days
Rationale: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer:B
Answer: (B) 13 1/3 days
Question: The price for a loaf of bread in April was $1.14, in May the price was $1.35, and in June the price was $1.05. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
(A) $1.13
(B) $1.14
(C) $1.15
(D) $1.16
(E) $1.17
Rationale: Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(114) + 135x + (4x/3)(105) / (2x/3 + x + 4x/3) =
(76 + 135 + 140) / (3) = 351/3 = $1.17
The answer is E.
Answer: (E) $1.17
Question: ¹⁵/₇₁, ⁴¹/₇₁, ⁶²/₇₁ etc. are like/unlike fractions
(A) unlike fraction
(B) like fraction
(C) both
(D) none
(E) Can't determined
Rationale: Fractions having the same denominators are called like fractions.
denominators of all fractions are 71 so like fraction
ANSWER :B
Answer: (B) like fraction
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 7 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
(A) 20 km
(B) 35 km
(C) 40 km
(D) 50 km
(E) 60 km
Rationale: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 7 = 35 km
IMO, correct answer is "B."
Answer: (B) 35 km
Question: 12 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
(A) 80
(B) 160
(C) 720
(D) 1600
(E) 1848
Rationale: No. of ways of picking 2 biology books(from 12 books) = 12C2 = (12*11)/2 = 66
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 66*28 =1848
(Option E)
Answer: (E) 1848
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference Q between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference Q= 10k - 3 - (10k - 7)
= 4
Answer - D
Answer: (D) 4
Question: There are 5 boys and 3 girls. In how many ways can they be seated in a row so that all the three girls do not sit together?
(A) 24000
(B) 36000
(C) 54200
(D) 32560
(E) 45100
Rationale: Total number of persons = 5+3 = 8
they can be seated in a row in 8! ways
Treat 3 girls as 1 so we have 6 people can be arranged in 6! ways
Three girls can be arranged among themselves in 3! ways
Required number of ways = 8!-6!*3! = 36000
Answer is B
Answer: (B) 36000
Question: Adams's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Adams makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?
(A)  15
(B)  24
(C)  25
(D)  26
(E)  13
Rationale: day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now Adams can still use the internet till her debt reaches $5 which means total of 5*2=10 days.
now the question states for how many days, including today, will she be connected to the internet without any additional paymentsi.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C
Answer: (C)  25
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 18 pages.
(A) 8
(B) 10
(C) 2
(D) 14
(E) 16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(5/2.5)=2 hrs
ANSWER:C
Answer: (C) 2
Question: If cost of sugar increases by 10%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
(A) 22%
(B) 50%
(C) 20%
(D) 9.1%
(E) 30%
Rationale: 100
110
-----
110 ----- 10
100 ------ ? => 9.1%
Answer: D
Answer: (D) 9.1%
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:7
(C) 2:2
(D) 2:1
(E) 2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer: A
Answer: (A) 2:5
Question: What annual installment will discharge a debt of Rs. 1260 due in 3 years at 12% simple interest?
(A) 315
(B) 345
(C) 325
(D) 375
(E) None of them
Rationale: Let each Installment be Rs. x
Then, ( x+ ((x*12*1)/100)) + (x+ ((x*12*2)/100) ) + x = 1260
=((28x/25) + (31x/25) + x) = 1260 ïƒ› (28x+31x+25x)=(1260*25)
x= (1260*25)/84 = Rs.375.
Therefore,	Each installment = Rs. 375.
Answer is D.
Answer: (D) 375
Question: (7.5 × 7.5 + 37.5 + 2.5 × 2.5) is equal to :
(A) 30
(B) 60
(C) 80
(D) 100
(E) None of these
Rationale: Solution
Given expression = (7.5 × 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5)
=(a 2 + 2ab + b 2) = (a + b)2 = (7.5 + 2.5)2 = 102 = 100 . Answer D
Answer: (D) 100
Question: x = y - (20/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
(A) decrease
(B) stay the same
(C) increase four fold
(D) double
(E) triples
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (20/y)
Or, x = 10 - (20/10) =8
Let y = 20
So, x = y - (20/y)
Or, x = 20 - (20/20) =19
So, x increases from 8 to 19
Hence the number increases 2.2 times, thus the correct answer will be (D)
Answer: (D) double
Question: The area of a square is equal to five times the area of a rectangle of dimensions 25 cm * 5 cm. What is the perimeter of the square?
(A) 100
(B) 800
(C) 500
(D) 600
(E) 700
Rationale: Area of the square = s * s = 5(25 * 5)
=> s = 25 cm
Perimeter of the square = 4 * 25 = 100 cm.
Answer: Option A
Answer: (A) 100
Question: If 75 percent of a class answered the first question on a certain test correctly, 45 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 10%
(B) (8) 40%
(C) 30%
(D) 50%
(E) 65%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (45 - x)] = 20 .......... values are in percent
x = 20 - 100 + 120
x = 40
Ans: B
Answer: (B) (8) 40%
Question: A sum of money deposited at C.I. amounts to Rs.9000 in 10 years and to Rs.9990 in 11 years. Find the rate percent?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 13%
Rationale: 9000 --- 990
100 --- ? => 11%
Answer: C
Answer: (C) 11%
Question: In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race?
(A) 180 sec
(B) 190 sec
(C) 290 sec
(D) 490 sec
(E) 390 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/25
= 400 sec.
Time taken by A = 400 - 10
= 390 sec.
Answer:E
Answer: (E) 390 sec
Question: What is the most powerful tool used by the Reserve Bank of India to control inflation?
(A) FDS
(B) Reduce interest rates
(C) Raise interest rates
(D) Raise current supply
(E) Reduce current supply
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: (C) Raise interest rates
Question: A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 49 grams of protein daily, how many grams of food X are in the mixture?
(A) 160
(B) 180
(C) 200
(D) 220
(E) 240
Rationale: Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 49
0.05x = 11
x = 220
The answer is D.
Answer: (D) 220
Question: A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. However, already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately, he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90.
What is the overall profit the man makes?
(A) $10
(B) $60
(C) $20
(D) $50
(E) $60
Rationale: C
$20
In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10.
In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.
Conclusion: The man makes an overall profit of $10 + $10 = $20.
You can also look at the problem as follows: the total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140 = $20.
Answer: (C) $20
Question: A given positive integer is divided by 9 with a remainder of 5. The same integer when divided by 12 has a remainder of 3. What is the remainder if the it integer is divided by 35.
(A) Between 1 and 4, inclusive
(B) Between 5 and 7, inclusive
(C) Between 8 and 10, inclusive
(D) 5
(E) 1
Rationale: Put in real numbers.
Let the integer be x
9x+5= 12x+3
Start 9x+5 -->14, 23, 32,....41...
Of these only 41 fit the description 12x+3. The remainder when divided by 35 is 6. So answer is B).
Answer = B)
Answer: (B) Between 5 and 7, inclusive
Question: In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
(A) 15
(B) 21
(C) 25
(D) 30
(E) 36
Rationale: Total number of entries 6*6(6rows*6columns) =36
Now 6 entries are representing mileage with the city itself so subtract that => 36-6
Minimum entries required = half the Total = 30/2 = 15
ANSWER:B
Answer: (B) 21
Question: Which is not a leap year?
(A) 2004
(B) 2012
(C) 1700
(D) 1704
(E) 2008
Rationale: the answer is 1700,
becz if the year is centurial ,that should be divisible by 400 for leap year
ex:400,800,1200
ANSWER:C
Answer: (C) 1700
Question: Of the 800 employees of Company X, 80 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 70 percent ?
(A) 200
(B) 266.67
(C) 112
(D) 80
(E) 56
Rationale: The # oflong-termemployees is 80%*800=640.
After y of them retire new # oflong-termemployees would become 640-y.
Total # of employees would become 800-y.
We want 640-y to be 70% of 800-y --> 640-y=(800 -y)*70% --> y = 266.67.
Answer: B.
Answer: (B) 266.67
Question: What is the average of 1/2, 4/5 and 7/10?
(A) 1/5
(B) 3/10
(C) 2/3
(D) 1/2
(E) 6/5
Rationale: Sum of 1/2,4/5,7/10 =20/10
Average = 20/10*1/3 =2/3
Answer C 2/3
Answer: (C) 2/3
Question: add 10% of 30 and 15% of 50.
(A) 9.5
(B) 10.5
(C) 11.5
(D) 12
(E) 15
Rationale: 10% of 30 + 15% of 50
30*10/100+50*15/100
3+7.5=10.5
answer B
Answer: (B) 10.5
Question: What annual payment will discharge a debt of Rs. 6450 due in 4 years at 5% per annum?
(A) 1500
(B) 1400
(C) 1700
(D) 1800
(E) 1600
Rationale: Explanation :
he amount needs to be repaid in 4 years = Rs.6450
Suppose Rs.x is paid annually to repay this debt
Then, amount paid after 1st year = Rs.x
Interest for this Rs.x for the remaining 3 years = x × 5×3/100=15x/100
Then, amount paid after 2nd year = Rs.x
Interest for this Rs.x for the remaining 2 years = x × 5 × 2 /100=10x/100
Amount paid after 3rd year = Rs.x
Interest for this Rs.x for the remaining 1 year = x × 5 ×1/100=5x/100
Amount paid after 4th year = Rs.x and this closes the entire debt
=>x+15x/100+x+10x/100+x+5x/100+x=6450
=>4x+30x/100=6450
=>4x+3x/10=6450
=>40x+3x=64500
=>43x=64500
=>x=1500
Answer : Option A
Answer: (A) 1500
Question: What is the greatest of 3 consecutive integers whose sum is 33 ?
(A) 12
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 33;
=> 3n = 30;
=> n = 10
The greatest of the three numbers is therefore 10+ 2 = 12 Answer: A
Answer: (A) 12
Question: It was calculated that 75 men could complete a piece of work in 25 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
(A) 28 days.
(B) 30 days.
(C) 37.5 days.
(D) 40 days.
(E) 36 days.
Rationale: One day work = 1 / 25
One man’s one day work = 1 / ( 25 * 75)
Now:
No. Of workers = 50
One day work = 50 * 1 / ( 25 * 75)
The total no. of days required to complete the work = (75 * 25) / 50 = 37.5
Answer:C
Answer: (C) 37.5 days.
Question: In a 100 m race,A covers the distance in 30 seconds and B in 45 second.In this race A beats B by :
(A) 33.33 m
(B) 25 m
(C) 45 m
(D) 30 m
(E) None of these
Rationale: Solution
Distance covered by B in 15 sec. = (100/45x15)m =33.33m.
∴ A beats B by33.33 metres.
Answer A
Answer: (A) 33.33 m
Question: A bowl contains many kinds of fruit. In the bowl there are twice as many apples then there are bananas, and three times as many oranges as bananas. If the total number of pieces of fruit is X, then how many apples are in the bowl as a fraction of X
(A) X/2
(B) X/3
(C) 2*X
(D) X/6
(E) X/4
Rationale: Since X is the total number of fruit: X = apples + bananas + oranges.
Since there are three times as many oranges as bananas then 1*orange = 3*bananas
Thus X = apples + bananas + (3*bananas); which simplifies to X = apples + 4*bananas
Since there are twice as many apples as bananas then 1*apple = 2*bananas; which converts to bananas=apple/2
Thus X = apples + 4*(apples/2); which simplifies to X = 2*apples.
Thus apples = X/2
Answer: A
Answer: (A) X/2
Question: If x : 0.25 : : 3 : 5, then x is equal to :
(A) 0.25
(B) 0.15
(C) 0.2
(D) 0.3
(E) None of these
Rationale: Explanation :
Solution: x : 0.25 : : 3 : 5
=> x*5 = 3*0.25 => x = 0.75/5 = 0.15
Answer : B
Answer: (B) 0.15
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 16 sec
(B) 12 sec
(C) 41 sec
(D) 09 sec
(E) 15 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20
=12 sec.
Answer: B
Answer: (B) 12 sec
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 5% 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.(5/100x12000) = Rs. 600.
Answer B
Answer: (B) Rs. 600
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 105?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 105
5x -20 = 105
5x = 125
x = 25
The answer is B.
Answer: (B) 25
Question: if radius of a circle is reduced by 10%,then how much % of its area will be reduced?
(A) 10%
(B) 19%
(C) 20%
(D) 36%
(E) 30%
Rationale: let initial radius=a then,area=πa^2.
new radius=90% of a=9a/10.new area=π*81a^2/100=81/100πa^2
reduce in area=[πa^2-81/100πa^2]=19/100πa^2
% reduce=[(19*πa^2/100)*(1*100/πa^2)]%=19%
answer B
Answer: (B) 19%
Question: A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability G that the first ball picked up is odd numbered?
(A) 	0
(B) 	1/3
(C) 	1/2
(D) 	2/3
(E) 	1
Rationale: Answer-D
Selecting the balls either Even or Odd is having probability 50/100=1/2
We have already selected 3 balls with 2 odd numbers and 1 even number.
So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability G is 2/3.D
Answer: (D) 	2/3
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
(A) 1/48
(B) 5/16
(C) 11/12
(D) 11/16
(E) 23/48
Rationale: Probability of event not happening is equal to (1 - Probability of event happening)
So, Probability NO heads=1/2
Probability NO number 6 =5/6
Probability NO picking a spades card =3/4
so, Probability NO winning = 1/2*5/6*3/4 = 15/48=5/16
Probability NO winning = 1 - 5/16 = 11/16 .
answer is D
Answer: (D) 11/16
Question: In a library, there are certain number of books on a shelf, ranging between 75 and 100. 1/6th of them are fiction and 12.5% of them are non-fiction. Find the number of books.
(A) 376
(B) 96
(C) 26
(D) 198
(E) 178
Rationale: Explanation:
12.5% can be written as 1/8th
Since 1/6th of the books are fiction and 1/8th are non-fiction, the total number of books must be exactly divisible by 6 and 8 and should be between 75 and 100.
Therefore, 96 is the only number, which fulfills the above criteria.
Note that the question doesn't imply that there are ONLY two varieties of books.
ANSWER: B
Answer: (B) 96
Question: There are 16 bees in the hive , then 9 more fly. How many bees are there in all?
(A) 7
(B) 33
(C) 12
(D) 17
(E) 25
Rationale: 16+9=25 . Answer is E.
Answer: (E) 25
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 289
(C) 267
(D) 261
(E) 552
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 841 = 261
Answer: D
Answer: (D) 261
Question: Of the 100 people in a room, 4/5 are women. If 3/5 of the people are married, what is the maximum number of women in the room who could be unmarried?
(A) 32
(B) 34
(C) 36
(D) 38
(E) 40
Rationale: women = 4/5 * 100 = 80
married = 3/5 * 100 = 60
unmarried = 40
max(un-married women) = 40
E
Answer: (E) 40
Question: Alfred buys an old scooter for $4400 and spends $800 on its repairs. If he sells the scooter for $5800, his gain percent is?
(A) 5.45%
(B) 6.23%
(C) 7%
(D) 8.12%
(E) 11.5%
Rationale: C.P. = 4400+800 = $5200
S.P. = $5800
Gain = 5800-5200 = $600
Gain% = 600/5200 * 100 = 11.5%
Answer is E
Answer: (E) 11.5%
Question: In a mayoral election, Candidate X received 2/3 more votes than candidate Y, and Candidate Y received 1/3 fewer votes than Z. If Z received 27,000 votes how many votes did candidate X received?
(A) 18000
(B) 22000
(C) 24000
(D) 26000
(E) 30000
Rationale: Z=27 --> Y received 2/3 fewer votes than Z --> Y=Z-1/3*Z=18;
X received 2/3 more votes than Y --> X=Y+2/3*Y=30.
Answer: E.
Answer: (E) 30000