mathewhe/aqua_rat huggingface dataset:
Question: If, in a baseball game, a single picher can decide to throw either a 100mph fastball or 60 mph knuckleball on any pitch, how much less time, in seconds, does the batter have from when the ball is released as a fastball than when the ball is released as a knuckle ball? (Assume where the batter's point of contact is exactly 60ft away from the pitcher's release point. 5280 ft = 1 mile.)
(A) 6/22s
(B) 7/22s
(C) 8/22s
(D) 9/22s
(E) 15/22s
Rationale: One conversion to know is = 1 mile = 5280 ft
Time taken for fastball = (60 / (100 * 5280)) * 60 * 60 = 9/22
Time taken for knuckle ball = (60 / (60 * 5280)) * 60 * 60 = 15/22
Qn is the difference between the time taken by the two balls => 15/22 - 9/22 = 6/22
Option A
Answer: (A) 6/22s
Question: It takes 8 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 8 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 5:00 pm?
(A) 6:06 pm
(B) 6:12 pm
(C) 6:24 pm
(D) 6:42 pm
(E) 6:56 pm
Rationale: Each student paints at a rate of 1/80 of the house per hour.
In 8 hours, the 8 students can paint 64/80 of the house.
From 5 pm to 6 pm, 9 students paint another 9/80 for a total of 73/80.
10 students can paint the remaining 7/80 of the house in 7/10 of an hour = 42 minutes.
The house is completed at 6:42 pm.
The answer is D.
Answer: (D) 6:42 pm
Question: A cylindrical can has a radius of 3 centimeters and a height of 12 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
(A) 16 pi
(B) 72 pi
(C) 96 pi
(D) 192 pi
(E) 576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*3*12=72 pi
Answer is B.
Answer: (B) 72 pi
Question: What profit percent is made by selling an article at a certain price, if by selling at 1/3rd of that price, there would be a loss of 20%?
(A) 140%
(B) 29%
(C) 70%
(D) 27%
(E) 28%
Rationale: SP2 = 1/3 SP1
CP = 100
SP2 = 80
1/3 SP1 = 80
SP1 = 240
100 --- 240 => 140%
Answer: A
Answer: (A) 140%
Question: Firm A's revenues are described by the equation Ra = 15.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
(A) 20%
(B) 30%
(C) 60%
(D) 50%
(E) 33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 50%
D
Answer: (D) 50%
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students E in the class?
(A) A)10
(B) B)12
(C) C)15
(D) D)20
(E) E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: (C) C)15
Question: A man can row 8.4 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
(A) 2.8 km/hr
(B) 12.5 km/hr
(C) 1 2.6 km/hr
(D) 22.5 km/hr
(E) 22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=8.4
3x = 16.8
x = 5.6
i.e., speed upstream = 5.6 km/hr
Rate of stream = 1/2(2x−x)=x/2=5.6/2=2.8 km/hr
Answer is A
Answer: (A) 2.8 km/hr
Question: A train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 288
(B) 195
(C) 881
(D) 1277
(E) 121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 23 = 345 m.
Let the length of the platform be x m . Then,
(x + 345)/36 = 15 => x = 195 m.
Answer: B
Answer: (B) 195
Question: In a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course
(A) 4 min
(B) 3 min 3 sec
(C) 4 min 4 sec
(D) 5 min 3 sec
(E) 4 min 3 sec
Rationale: Clearly, B covers 28 m in 7 seconds.
:. B's time over the course = (278 x 1000) sec = 250 seconds.
:. A's time over the course = (250 - 7-) sec = 243 sec
= 4 min. 3 sec.
ANSWER E 4 min 3 sec
Answer: (E) 4 min 3 sec
Question: What is the units digit of the product of the first 3 primes?
(A) 1
(B) 3
(C) 6
(D) 0
(E) 2
Rationale: 1*2*3 =6
Answer : C
Answer: (C) 6
Question: If 5 < x < 9 and y = x + 7, what is the greatest possible integer value of x + y?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: x+y = x+x+7 = 2x+7
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 8.5
Then x+y = 8.5 + 15.5 = 24.
The answer is D.
Answer: (D) 24
Question: The price of lunch for 12 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A) 11.73
(B) 12
(C) 13.8
(D) 14
(E) 15
Rationale: Clearly E is the answer
I used POE here
Lets consider option (E)
12*15= 180 now 180(115/100)=207
=> possible ANSWER IMO E
Answer: (E) 15
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.4500. How much third person will get?
(A) 2400
(B) 2429
(C) 2980
(D) 2000
(E) 2872
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 4500 = 2000
Answer:D
Answer: (D) 2000
Question: A river 3m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
(A) 4500
(B) 3200
(C) 3400
(D) 2761
(E) 2882
Rationale: (2000 * 3 * 32)/60
= 3200 M3
Answer:B
Answer: (B) 3200
Question: A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 50%
(B) 40%
(C) 60%
(D) 57%
(E) 80%
Rationale: Number of runs made by running = 140 - (3 x 4 + 8 x 6)
= 140 - (60)
= 80
Now, we need to calculate 80 is what percent of 140.
=> 80/140 x 100 = 57 %
ANSWER:D
Answer: (D) 57%
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.28
(C) 6.11
(D) 6.19
(E) 6.21
Rationale: Required run rate
= [282 - (3.2 * 10)]/40
= 250/40
= 6.25
Answer:A
Answer: (A) 6.25
Question: Find the odd man out
1,25, 31,37, 127, 503,
(A) 503
(B) 37
(C) 31
(D) 1
(E) 25
Rationale: 25 is square of 5 which is a square number where as all others are prime numbers.
ANSWER:E
Correct Option:	C) E . Answer : E
Answer: (E) 25
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 115 Kmph
(B) 100 Kmph
(C) 102 Kmph
(D) 105 Kmph
(E) 108 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
ANSWER:E
Answer: (E) 108 Kmph
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
(A) 535 m
(B) 178 m
(C) 250 m
(D) 168 m
(E) 150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 15
= 250 m
Answer:C
Answer: (C) 250 m
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
(A) 1
(B) 9
(C) 12
(D) 14
(E) 15
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: (A) 1
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 432 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: Let rate = R% and time = R years.
Then,1200 x R x R/100= 432
12R2 = 432
R2 = 36
R = 6.
Answer:B
Answer: (B) 6
Question: What will be the compound interest on Rs. 40000 after 3 years at the rate of 12 % per annum
(A) Rs 16123.20
(B) Rs 16123.30
(C) Rs 16197.12
(D) Rs 16123.50
(E) None of these
Rationale: Explanation:
(40000×(1+12/100)3)
=>40000×28/25×28/25×28/25
=>56197.12
So Compound interest will be 56197.12 - 40000
= Rs 16197.12
Option C
Answer: (C) Rs 16197.12
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 72, how many more green disks than blue disks are in the bag?
(A) 20
(B) 28
(C) 30
(D) 35
(E) 40
Rationale: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 72 --> x= 4.
G - B = 8x - 3x = 5x = 20.
The answer is A.
Answer: (A) 20
Question: How much is 90% of 40 is greater than 4/5 of 25?
(A) 22
(B) 16
(C) 88
(D) 12
(E) 66
Rationale: (90/100) * 40 – (4/5) * 25
= 16
Answer: B
Answer: (B) 16
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  7
Rationale: Given that (10a + b) - (10b + a) = 45 --> 9a - 9b =45 --> a - b = 5.
Answer: C.
Answer: (C)  5
Question: On Monday, Lou drives his vehicle with 27-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?
(A) Decrease by 14.3%
(B) Decrease by 16%
(C) Increase by 14.3%
(D) Increase by 12.5%
(E) Cannot be determined with the given information.
Rationale: 864 is the LCM
On Tuesday 864/32 =27
On Monday 864/27 = 32
Therefore, 27-32/32 = -1/6=-16% decrease
Answer is B
Answer: (B) Decrease by 16%
Question: The ratio of boys to girls in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two-third of the girls in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)272 degree
(E) e)192 degree
Rationale: let the common ratio be x.. so B=2x and G=3x and Total=5x
1/3 of M= 2x/3 and 2/3 of F= 2x..
Total preferring that carrer = 2x/3+2x=8x/3..
Now 5x= 360, so x=360/5=72..
so x*8/3= 72*8/3=192
ans 192
E
Answer: (E) e)192 degree
Question: Working together, printer A and printer B would finish the task in 10 minutes. Printer A alone would finish the task in 30 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?
(A) 125
(B) 150
(C) 175
(D) 200
(E) 225
Rationale: 10*A + 10*B = x pages
in 10 mins printer A will print = 10/30 * x pages = 1/3*x pages
thus in 10 mins printer printer B will print x - 1/3*x = 2/3*x pages
Also it is given that printer B prints 5 more pages per min that printer A. In 10 mins printer B will print 50 more pages than printer A
thus 2/3*x - 1/3*x = 50 => x = 150 pages
Answer : B
Answer: (B) 150
Question: If d= (b-1)(b+2), then what is the least possible value of d?
(A) 1
(B) 2
(C) 3
(D) 4
(E) -9/4
Rationale: Answer : E
Answer: (E) -9/4
Question: Papaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papaya and natural lemon juice makes 1/3 of Papaya. The amounts of sugar and papaya puree in Papaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?
(A) 7/30
(B) 7/21
(C) 2/5
(D) 12/29
(E) 4/7
Rationale: Soda water = 12/21
Natural lemon juice = 7/21
The quantities of sugar and papaya puree are equal. Total units are 21 of which 12 + 7 = 19 are used up by above two. Remaining is 2 which is equally divided between sugar and papaya puree:
Sugar = 1/21
Papaya puree = 1/21
Thus ratio of soda:lemon:sugar:puree = 12:7:1:1
Now, lemon is doubled, puree is three times and remaining are the same.
Resultant ratio is = 12:14:1:3
Ratio of soda water in the resultant mixture = 12/(12+14+1+3) = 12/30 = 2/5
ANSWER:C
Answer: (C) 2/5
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 15 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 12 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 15 = 7(x-1) + 12
4x = 20
x= 5
The answer is A.
Answer: (A) 5
Question: Which is a better investment 9% stock at 580 or 6 2/5 stock at 312?
(A) 9% stock at 580
(B) Both are equally good
(C) 6 2/5 stock at 312
(D) None
(E) Cannot be compared, as the total amount of investment is not given
Rationale: Let investment in each case be Rs. (580 x 312).
Income in 1st case = Rs. 9 x 580 x 312/580= Rs. 2808.
Income in 2nd case = Rs.32 x 580 x 312/(5*312)= Rs. 3712
Clearly, 6 2/5 stock at 312 is better.
ANSWER:C
Answer: (C) 6 2/5 stock at 312
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 165∏ cm
(B) 65∏ cm
(C) 12∏ cm
(D) 14∏ cm
(E) 16∏ cm
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: (C) 12∏ cm
Question: An urn contains 6 black and 2 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/5
(B) 3/7
(C) 2/5
(D) 3/5
(E) 15/28
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 6/8
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 5 black balls and eight white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 5/7
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 6/8× 5/7 = 15/28
E
Answer: (E) 15/28
Question: What number has a 15:1 ratio to the number 10?
(A) 130
(B) 100
(C) 200
(D) 150
(E) 120
Rationale: 15:1 = x: 10
x = 10*15
x=150
ANSWER:D
Answer: (D) 150
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 6?
(A) 1/45
(B) 2/45
(C) 4/45
(D) 2/15
(E) 1/5
Rationale: The number of ways to choose two cards is 10C2=45.
There are 4 ways, {1,2},{1,3}, {1,4} and {2,3}, to get a sum less than 6.
P(sum less than 6)=4/45
The answer is C.
Answer: (C) 4/45
Question: Siddharth wants to borrow Rs.7000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.21.60
(B) s.21.68
(C) s.25.2
(D) s.21.98
(E) s.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.7,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 7,000{ [1 + 6/100]2 - 1 - 12/100}
= 7,000 {(1.06)2- 1 - 0.12} = 7,000(1.1236 - 1 - 0.12)
= 7,000 (0.0036) = 7 * 3.6
= Rs.25.2
Answer: C
Answer: (C) s.25.2
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?
(A) 42
(B) 52
(C) 62
(D) 72
(E) 82
Rationale: Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Answer: (E) 82
Question: Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes
(A) 1700
(B) 7570
(C) 1576
(D) 17576
(E) 500
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26Ã—26=67626Ã—26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676Ã—26=17576676Ã—26=17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
ANSWER D
Answer: (D) 17576
Question: The distance from Springville to Franklin is 400 Km. Travelling at 120 Km/h from Springville to Franklin, Teresa arrives two hours faster than her return trip, which took five hours. What speed was Teresa travelling on the return trip?
(A) 50 Km/h
(B) 55 Km/h
(C) 62 Km/h
(D) 72 Km/h
(E) 80 Km/h
Rationale: distance=speed*time
d1=s1t1
d2=s2t2
The distance from point A to point B is the same for each trip so,
d1=d2 and
t1=3
t2=5
thus,
s1t1=s2t2
120(3)=s2(5)
s2=72 Km/h
Answer: D
Answer: (D) 72 Km/h
Question: What least number should be added to 1054, so that the sum is completely divisible by 23
(A) A)4
(B) B)1
(C) C)2
(D) D)3
(E) E)5
Rationale: Explanation:
(1054 / 23) gives remainder 19
19 + 4 = 23, So we need to add 4
Answer: Option A
Answer: (A) A)4
Question: What is the remainder when you divide 2^200+1 by 7?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: answer is E. this is very similar to the 32^32^32+1 divided by 7 question.
Answer: (E) 5
Question: 3,8,24,48,120,?
(A) 166
(B) 167
(C) 168
(D) 198
(E) 178
Rationale: 2^2 =(4) -1 =3
3^2=(9) -1 =8
5^2 =(25) -1 =24
7^2 =(49) -1 =48
11^2 =(121) -1 =120
So, next
13^2 =(169) -1=168
ANSWER:C
Answer: (C) 168
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 55 minutes?
(A) 80
(B) 100
(C) 150
(D) 180
(E) 220
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 55 minutes the population increases by 55 x 4 = 220 people.
Answer. E.
Answer: (E) 220
Question: P persons have decided to rent a van to tour while on holidays. The price of the van is x dollars and each person is to pay an equal share. If D persons cancel their trip thus failing to pay their share, which of the following represents the additional number of dollars per person that each remaining person must pay in order to still rent the van?
(A) Dx
(B) x/(P −D)
(C) Dx/(P −D)
(D) Dx/(P(P −D))
(E) x/(P(P −D))
Rationale: Share per person =x/p
When D person left, share per person = x/(p-D)
So the additional share per person is =x/(D-p) - x/p = (px-Dx+px)/p(D-p)=Dx/p(D-p)
Answer D
Answer: (D) Dx/(P(P −D))
Question: What percent of a day is 6 hours?
(A) 12%
(B) 12.5%
(C) 25%
(D) 11.3%
(E) None of these
Rationale: Explanation :
Solution: required percentage = (6/100 * 24) = 25%
Answer : C
Answer: (C) 25%
Question: If a(n) is to be entered following the rule [a(n)^2 - 1] then what are the next three entries.
(A) 0,-1,0
(B) 2,3,4
(C) 1,2,3
(D) 0,-1,2
(E) 0,-1,1
Rationale: It only satisfies the rule, when a(n) = -1,0,1
ANSWER:A
Answer: (A) 0,-1,0
Question: John has purchased an item on sale for $25.00. A few days later John sees the price is now $32.00. By what percentage of the price John paid has the price risen?
(A) 5
(B) 7
(C) 15
(D) 20
(E) 28
Rationale: C.P.=25.00
N.P.=32.00
markup%=(N.P.-C.P.)/C.P.*100=(32-25)/25*100=28%
ANSWER:E
Answer: (E) 28
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 30 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
(A) 3%
(B) 5%
(C) 9%
(D) 10%
(E) 12%
Rationale: Bob's time = 630 secs.
His sis' time = 576 secs.
Percent increase needed = (630-576/630) * 100 = 54/640 * 100 = 9%. Ans (C).
Answer: (C) 9%
Question: Of 45 applicants for a job, 28 had at least 5 years of prior work experience, 24 had advanced degrees, and 20 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees?
(A) 9
(B) 13
(C) 18
(D) 20
(E) 23
Rationale: Had advanced degrees and 5 years work experience: 20
Only had 5 years work experience: 28-20 = 8
Only had advanced degrees: 24-20 = 4
45-20-8-4=13
Answer: B
Answer: (B) 13
Question: In a 200-mile trip, the first 50 miles were completed at 40 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 150 miles?
(A) 592/11 mph
(B) 594/11 mph
(C) 596/11 mph
(D) 598/11 mph
(E) 600/11 mph
Rationale: The time to complete the first 50 miles was (50 miles / 40 mph) = (5/4) hours.
The time to complete the whole trip was (200 miles / 50 mph) = (4) hours.
The time to complete the last 150 miles was (4) - (5/4) = (11/4) hours.
The average speed in the last 150 miles was (150 miles / (11/4) hours) = 600/11 mph.
The answer is E.
Answer: (E) 600/11 mph