mathewhe/aqua_rat huggingface dataset:
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.43, b = 2.98, and c = 3.76, what is y – x?
(A) 0
(B) 0.04
(C) 0.05
(D) 0.1
(E) 0.2
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.43 + 2.98 + 3.76 = 12.17, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 3.0 + 3.8 = 12.2.
We are looking for y - x, which gives us 12.2 - 12.2 = 0, or
answer choice A.
Answer: (A) 0
Question: If a certain sample of data has a mean of 15 and a standard deviation of 2, which of the following is not within 2 standard deviations?
(A) 11
(B) 15
(C) 10
(D) 12
(E) 14
Rationale: If a data distribution is normal then the 68% data values are within one standard deviation of the mean (i.e., μ ± σ), and about 95 percent are within two standard deviations (μ ± 2σ).
Here, mean = 15 and standard distribution is 2.
Numbers which are within two standard distribution will be in the range of 15±(2*2) i.e. 11 to 19.
Only only which does not follow this range is 10
Answer is C
Answer: (C) 10
Question: In the manufacture of a certain product, 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.15%
(B) 0.45%
(C) 0.8%
(D) 1.25%
(E) 2.0%
Rationale: 0.09*0.05 = 0.0045 = 0.45%
The answer is B.
Answer: (B) 0.45%
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) 50
(B) 87
(C) 17
(D) 98
(E) 16
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: (A) 50
Question: Find the remainder W when 12^190 is divided by 1729 ?
(A) 12
(B) 1
(C) 1728
(D) 1717
(E) 4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder W -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: (D) 1717
Question: A team of eight entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
(A) 525
(B) 665
(C) 412
(D) 235
(E) 856
Rationale: Answer: Option B
8 * 84 = 672 â€“ 7 = 665
Answer: (B) 665
Question: Two trains for Palwal leave Kanpur at 10 a.m and 10:30 am and travel at the speeds of 60 Kmph and 75 Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
(A) 150
(B) 160
(C) 170
(D) 180
(E) 190
Rationale: Let two train meet at X km distance.
Time taken by first train to cover X km=x/75 h
Time taken by 2nd train to cover X km=x/60 h
Now, x/60 - x/75=1/2
thus, x=150.
ANSWER:A
Answer: (A) 150
Question: Which of the following values is the greatest?
(A) 11% of 89
(B) 22% of 78
(C) 33% of 67
(D) 44% of 56
(E) 55% of 45
Rationale: Now, 89 < 78*2 < 67*3 < 56*4 < 45*5;as we can see option E, has the highest value for 11% , hence the answer must be E.
ANSWER:E
Answer: (E) 55% of 45
Question: If the number is divided by 3, it reduced by 30. The number is
(A) A)51
(B) B)50
(C) C)45
(D) D)40
(E) E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 30 => 2x/3 = 30
=> x = 45
Answer: Option C
Answer: (C) C)45
Question: The least number which when increased by 6 each divisible by each one of 24, 32, 36 and 54 is :
(A) 858
(B) 859
(C) 869
(D) 4320
(E) None of these
Rationale: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 5 = 864 - 6 = 858. Answer A
Answer: (A) 858
Question: Tom covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
(A) 15 Kmph
(B) 29 Kmph
(C) 25 Kmph
(D) 30 Kmph
(E) 34 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A
Answer: (A) 15 Kmph
Question: Find the fourth proportion to 5,6,15
(A) 18
(B) 12
(C) 6
(D) 9
(E) 2
Rationale: Explanation:
5:6 :: 15:x
=> 5/6 = 15/x
=> x = 15*6/5
=> x = 18
Answer:A
Answer: (A) 18
Question: In what time will a train 20 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 0.5 sec
(D) 2.3 sec
(E) 1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 20/40
= 0.5 sec.
Answer:C
Answer: (C) 0.5 sec
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 84, 60, then the average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.58
(E) 65.56
Rationale: Explanation:
(55Ã—50)+(60Ã—84)+(45Ã—60) / 55+60+45
10490 / 160=65.56
Option E
Answer: (E) 65.56
Question: Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 3/4 were basic and the rest were deluxe. If it takes 7/5 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) 6/22
(B) 5/22
(C) 7/22
(D) 4/22
(E) 3/22
Rationale: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
C
Answer: (C) 7/22
Question: If the ratio of x to y is 3 to 7, then (y-x)/(x+y)?
(A) -7/3
(B) -3/7
(C) 4/10
(D) 1
(E) 7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 3 to 7 means
(x/y)=(3/7)
Cross-multiply
3x = 7y
x = (3/7)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (3/7)*y) / ((3/7)*y + y)
= ((4/7)*y) / ((10/7)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(4/7) / (10/7)
= (4/7) * (10/7)
The 7s cancel each other out, and you are left with 4/10.
Answer: (C) 4/10
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 6
(B) 8
(C) 16
(D) 24
(E) 32
Rationale: Packages can be prepared in following 2 ways:
1) 3 notepads of same size and same color
2) 3 notepads of same size and of 3 different colors
Lets go step by step.
1) 3 notepads of same size and same color:
We know that there are 2 sizes of pads and 4 colors in total. We want to keep the size and color same. so there are 2*4 = 8 ways to create package.
2) 3 notepads of same size and of 3 different colors:
We want to select 3 colors out of 4 available = 4C3 = 4
And there are 2 sizes of notepad available. So the total ways in which a package can be created is = 4C3*2 = 8
So total 8+8 = 16 packages can be created. Answer is C.
Answer: (C) 16
Question: What is the remainder when 4^8707 is divided by 5 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 4^0 = 1
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = .....4
4^6 = .......6
And so on in a distinct last-digit pattern of 4,6,4,6... after ignoring the first last-digit of 1
8707/2 = 4353 (with a remainder of 1) So the last number is a 4.
Alternatively, 8707 is an odd number and hence the last digit is a 4
When 4^8707 is divided by 5 the remainder is 4, ANS = E
Answer: (E) 4
Question: A grocer has a sale of Rs. 7435, Rs. 7927, Rs. 7855, Rs. 8230 and Rs. 7562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?
(A) Rs. 1991
(B) Rs. 2991
(C) Rs. 3991
(D) Rs. 4991
(E) Rs. 5991
Rationale: Explanation:
Total sale for 5 months = Rs. (7435 + 7927 + 7855 + 8230 + 7562) = Rs. 39009.
Required sale = Rs. [ (7500 x 6) â€“ 39009 ]
= Rs. (45000 â€“ 39009)
= Rs. 5991.
Answer E
Answer: (E) Rs. 5991
Question: Out of 7 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
(A) 1/21
(B) 10/21
(C) 20/21
(D) 11/21
(E) 2/21
Rationale: The number of exhaustive events = 7C2 = 21.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/21.
ANSWER:A
Answer: (A) 1/21
Question: A man covers a certain distance on bike. Had he moved 4 kmph faster, he would have taken 72 minutes less. If he moves slow by 4 kmph, he will take hours more to cover the distance. What is the distance travelled by him ?
(A) 48 km
(B) 56 km
(C) 64 km
(D) 96 km
(E) 106 km
Rationale: Explanation :
Let the distance be 'D' and the speed be 'x' kmph.
D/x + 4 = D/x - 72/60
D/x - D/(x - y) = 6/5 = D(x + 4 - x)/x(x - 4) = 6/5
∴ D/x(x + 4) = 3/10 ......(i)
D/x - 4 - D/x = 2
∴ Dx - Dx + 4D/x(x - 4) = 2
∴ D/x(x - 4) = 1/2 .....(ii)
From equation (i) and (ii):
3/10 x (x + 4) = 1/2 x(x - 4)
∴ 3(x + 4) = 5(x - 4) = 3x + 12 = 5x - 20
2x = 32 ∴ x = 16 kmn-1
∴ D = x(x - 4)/2 = 16x12/2 = 16x6 = 96 km
Answer : Option D
Answer: (D) 96 km
Question: Amita is taller than Rita but not as tall as Sapna, who is shorter than Farida. Sumedha is shorter than Farida but not as short as Rita. Who is the shorest among them?
(A) Amita
(B) Sumedha
(C) Rita
(D) Cannot be determined
(E) None of these
Rationale: here sumedha is shorter than Farida but not as short as rita
So sumedhaa will be placed in between farida and rita
hence rita is shortest among them
ANSWER:C
Answer: (C) Rita
Question: A scale 7 ft. 12 inches long is divided into 4 equal parts. Find the length of each part.
(A) 20 inches
(B) 77 inches
(C) 24 inches
(D) 97 inches
(E) 66 inches
Rationale: Explanation:
Total length of scale in inches = (7*12) + 12 = 96 inches
Length of each of the 4 parts = 96/4 = 24 inches
ANSWER:C
Answer: (C) 24 inches
Question: When a number is divided by 6 &then multiply by 12 the answer is 12 what is the no.?
(A) 4.5
(B) 5
(C) 5.5
(D) 5.8
(E) 6
Rationale: if $x$ is the number, x/6 * 12 = 12
=> 2x = 12
=> x = 6
E
Answer: (E) 6
Question: Winson's shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
(A) 0.8
(B) 0.75
(C) c) 8/9
(D) 5/7
(E) 6/8
Rationale: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Winson's shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Answer: (D) 5/7
Question: In a stack of cards, 6 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 8/11. What is the number of cards in the stack?
(A) 7
(B) 11
(C) 12
(D) 15
(E) 18
Rationale: This question can be solved by TESTing THE ANSWERS.
We're told that we have 6 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 8/11. We're asked for the TOTAL number of cards.
Probability of pulling two blue cards is...
(6/7)(5/6) = 30/42~ 8/11
A
Answer: (A) 7
Question: In a renowned city, the average birth rate is 4 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A)  43,100
(B)  43,200
(C)  43,300
(D)  43,400
(E)  43,450
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 4-3 = 1 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 1 = 43,200. Hence B.
Answer: (B)  43,200
Question: A train running at the speed of 20 km/hr crosses a post in 10 seconds. What is the length of the train?
(A) 150
(B) 250
(C) 415
(D) 200
(E) 312
Rationale: Speed=(20x5/18)=50/9 m/sec.
Length of the train=(Speed x Time).
Length of the train=50/9 x10m=200 m.
Answer: D
Answer: (D) 200
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in an ideal case scenario?
(A) 1652
(B) 1651
(C) 1653
(D) 1654
(E) None
Rationale: Solution:
1653
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 49th over. In the last over, he can hit a six in the last ball as well as that will be the last ball of the match.
Thus runs for the last over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 49 + 36 = 1653
Answer C
Answer: (C) 1653
Question: Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce,making a profit of 20 percent. What was the ratio of the mixture?
(A) 1:10
(B) 1:5
(C) 2:7
(D) 3:8
(E) 5:7
Rationale: Let x ounce of ist be mixed with y ounce of 2nd
thus total CP = 5x+6y
Sly SP = 7x+7y
Now profit % = 20, its very easy to solve profit n loss problems using Fraction rule.
SP = CP * 120/100 ( since profit so SP >CP n hence multiplied by 120/100 which is > 1
thus 7x+ 7y= (5x+6y) * 120/100
or, x:y = 1:5
ANSWER:B
Answer: (B) 1:5
Question: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: It's almost always better to solve "at least one" combinations/probability questions with {at least one}={total}-{none}.
Total # of selections of 4 books out of 8: C48=70C84=70;
Total # of selections of 4 hardback books out of 8 (so none paperback): C46=15C64=15;
{at least one}={total}-{none}=70-15=55.
Answer: D
Answer: (D) 55
Question: If n is the greatest positive integer for which 4^n is a factor of 10!, then n =?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 10! = 3628800
E. 4^10 = 1048576 (3628800/1048576) - this is not a factor of 10!
D. 4^8 = 65536 (3628800/65536) - this is not a factor of 10!
C. 4^6 = 4096 (3628800/4096) - this is not a factor of 10!
B. 4^4 = 256 (3628800/256) - this is a factor of 10!
B is answer
Answer: (B) 4
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 17/25
(B) 17/29
(C) 17/21
(D) 17/20
(E) 17/24
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20
=17/20
Answer: D
Answer: (D) 17/20
Question: √530493 ,493 is between
(A) 300 and 600
(B) 200 and 400
(C) 600 and 800
(D) 100 and 300
(E) 800 and 1000
Rationale: 530493 is greater than 49,0000 (700^2) and smaller than 64,0000 (800^2)
700 < √530493 < 800. Only option satisfying this condition is 600 < √530493 < 800.
Answer:C
Answer: (C) 600 and 800
Question: Which of the following equations passes through the points (2,4) and (-3,-6)
(A) y = (1/2)x - 2
(B) y = 2x + 3
(C) y = (-1/2)x + 2
(D) y = 2x + 4
(E) y = 4x - 4
Rationale: Find slope first = (y1-y2)/(x1-x2) = (-6-4)/(-3-2) = 2
Using the point (2,4) in options
we get,
y = 4x - 4 as right answer.
Ans- E
Answer: (E) y = 4x - 4
Question: How many figures are required to number the pages the pages of a book containing 1000 pages?
(A) 2793
(B) 2333
(C) 2993
(D) 2893
(E) 2693
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 999 = 900 * 3 = 2700
1000 = 4
-----------
2893
ANSWER:D
Answer: (D) 2893
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 2 2/3 days
(B) 2 6/3 days
(C) 2 2/7 days
(D) 6 2/3 days
(E) 2 8/3 days
Rationale: Work done by all three of them in one day
= 1/6 + 1/8 + 1/12 = 3/8.
The number of days required
= 8/3
= 2 2/3 days
Answer:A
Answer: (A) 2 2/3 days
Question: Of the employees in a company, 20 % are female who have a master degree. If 10 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 27.24%
(B) 26.22%
(C) 25.22%
(D) 22.25%
(E) 22.22%
Rationale: Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.2 x E (From the question)
No. of female employees without masters = 0.1 x F (From the question)
Therefore No. of female employees with masters = F - 0.1 F = 0.9 F
The 2 expressions equal each other therefore 0.9F = 0.2E; F/E = 0.2/0.9 = 22.22%
Ans: E
Answer: (E) 22.22%
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 20 sec
(B) 30 sec
(C) 40 sec
(D) 50 sec
(E) 60 sec
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
ANSWER:C
Answer: (C) 40 sec
Question: A man has some hens and cows. If the number of heads be 46 and the number of feet equals 136, then the number of hens will be
(A) 22
(B) 24
(C) 26
(D) 20
(E) 28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 46
=> h + c = 46 ---(Equation 1)
number of feet = 136
=> 2h + 4c = 136
=> h + 2c = 68 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 68 - 46
=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 46
=> h = 46 - 22 = 24
i.e., number of hens = 24
Answer : B
Answer: (B) 24
Question: The mall charges 60 cents for the first hour of parking and $4 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If Edward parked his car in the mall for 7 hours and 30 minutes, how much is he going to pay?
(A) $25.2
(B) $22.
(C) $13.
(D) $14.5.
(E) $15.5
Rationale: 0.60+4*4+2*4+0.60= $25.2
Answer :$25.2
Answer: (A) $25.2
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $660 (before payroll deductions)?
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) 1200
Rationale: total pay = 40*$12.50 + $0.16*x = 660
x = 160 / 0.16 = 1000
The answer is C.
Answer: (C) 1000
Question: Pat, Kate, and Mark charged a total of 135 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
(A) 18
(B) 36
(C) 75
(D) 90
(E) 108
Rationale: 75
all u do is do
2:1:6=>2x+x+6x=135=>x= 15
30:15:90
90-15=75
Answer C
Answer: (C) 75
Question: A group of store managers must assemble 280 displays for an upcoming sale. If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour?
(A) 70
(B) 98
(C) 126
(D) 168
(E) 182
Rationale: During the first hour 0.25*280 = 70 displays were assembled.
During the second hour 0.4*(280-70) = 84 displays were assembled.
Thus, 280 - (70+84) = 126 displays had not been assembled by the end of the second hour.
Answer: C.
Answer: (C) 126
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 60% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
(A) 10.5%
(B) 12.5%
(C) 15%
(D) 22%
(E) 25%
Rationale: 0.1 M = 0.40 E
=> E/M = 1/4 * 100 = 25%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: (E) 25%
Question: A certain ball team has an equal number of right- and left-handed players. On a certain day, one-third of the players were absent from practice. Of the players at practice that day, one-third were right handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left handed players who were not at practice?
(A) 1/3
(B) 5/1
(C) 5/7
(D) 7/5
(E) 3/2
Rationale: Say the total number of players is 18, 9 right-handed and 9 left-handed.
On a certain day, two-thirds of the players were absent from practice --> 6 absent and 12 present.
Of the players at practice that day, one-third were right-handed --> 12*1/3=4 were right-handed and 8 left-handed.
The number of right-handed players who were not at practice that day is 9-4=5.
The number of left-handed players who were not at practice that days is 9-8=1.
The ratio = 5/1.
Answer: B
Answer: (B) 5/1
Question: If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 10km more. The actual distance traveled by him is?
(A) 50 km
(B) 30 km
(C) 18 km
(D) 16 km
(E) 97 km
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 10)/15
5x - 150 =>x = 30 km.
Answer: B
Answer: (B) 30 km
Question: If Q is an odd number and the median of Q consecutive integers is 150, what is the largest of these integers?
(A) Q/2 + 150
(B) Q/2 + 149
(C) (Q - 1)/2 + 150
(D) (Q + 149)/2
(E) (Q + 150)/2
Rationale: Consider the easiest case, say Q=3, then;
Set = {149, 150, 151};
The largest integer = 151.
Now, plug Q=3 into the answers to see which yields 151.
Answer: C.
Answer: (C) (Q - 1)/2 + 150
Question: If the number 5 * 2 is divisible by 6, then * = ?
(A) 2
(B) 5
(C) 3
(D) 1
(E) 6
Rationale: 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
ANSWER A
Answer: (A) 2
Question: If p and q are both odd integers, which of the following must be an odd integer?
(A) p+q
(B) 2p+q
(C) p+3q
(D) 2p+q+1
(E) p+q^2
Rationale: p is odd; for this assume p=1
q is odd; for this assume q = 1
1+1 = 2 Even
(2*1)+1 = 3 Odd
1 + (3*1) = 4 Even
(2*1)+1+1 = 4 Even
1+(1^2) = 1 Even
Answer:B
Answer: (B) 2p+q
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
(A) 1 : 5
(B) 1 : 4
(C) 1 : 2
(D) 1 : 1
(E) 1 : 9
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1.Answer: D
Answer: (D) 1 : 1