mathewhe/aqua_rat huggingface dataset:
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates X apply to what fraction of a week?
(A)  1/2
(B)  5/8
(C)  9/14
(D)  16/21
(E)  9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates X/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: (C)  9/14
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $8 and the price of a student ticket was $4. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
(A) $20960
(B) $21920
(C) $22680
(D) $28500
(E) $29160
Rationale: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.
Therefore, the total revenue from ticket sales that day was 27*30*4+27*90*8=$22,680.
Answer: C.
Answer: (C) $22680
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 22
(B) 25
(C) 77
(D) 99
(E) 12
Rationale: 800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Two pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
(A) 5
(B) 12
(C) 24
(D) 32
(E) 120
Rationale: The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 12.
Answer: option B
Answer: (B) 12
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) 285
(B) 665
(C) 999
(D) 255
(E) 121
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Answer: (D) 255
Question: Sara bought both German chocolate and Swiss chocolate for some cakes she was baking. The Swiss chocolate cost $3.5 per pound, and German chocolate cost $2.5 per pound. if the total the she spent on chocolate was $70 and both types of chocolate were purchased in whole number of pounds, how many total pounds of chocolate she purchased?
(A) 7
(B) 8
(C) 10
(D) 24
(E) 15
Rationale: If there were all the expensive ones,3.5....
There would be 70/3.5 or 20 of them but since 2.5$ ones are also there, answer has to be >20....
If all were 2.5$ ones, there will be 70/2.5 or 28..
So ONLY 24 is left
Ans D..
Answer: (D) 24
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 225,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
(A) a) 500
(B) b) 750
(C) c) 1,000
(D) d) 1,250
(E) e) 1,500
Rationale: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 225,000 = 56,250
So required ratio = 56,250/75 = 750
Answer B
Answer: (B) b) 750
Question: What was the day of the week on, 17th July, 1776?
(A) Tuesday
(B) Wednesday
(C) Monday
(D) Saturday
(E) SUNDAY
Rationale: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 3 days)
Total number of odd days = (0 + 3) = 3.
Required day was 'Wednesday'.
Answer:B
Answer: (B) Wednesday
Question: Two trains 110 meters and 140 meters long are running in the same direction with speeds of 102 km/hr, 66 km/hr. In how much time will the first train cross the second
(A) 22 sec
(B) 25 sec
(C) 27 sec
(D) 23 sec
(E) 30 sec
Rationale: Explanation:
Relative speed of the trains = (102 - 66) km/hr = 36 km/hr
= (36Ã— 5/18) m/sec = 10 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (110 + 140) m at 10 m /sec = (250/10) sec = 25 sec.
Answer: Option B
Answer: (B) 25 sec
Question: f (x + y)/(2x + y) = 4/5, then find (2x + y)/(3x + y) ?
(A) 5/9
(B) 5/6
(C) 5/7
(D) 5/4
(E) 5/1
Rationale: (x + y)/(2x + y) = 4/5
=> 5x + 5y = 8x + 4y => y = 3x
Now, (2x + y)/(3x + y) = 5x/6x = 5/6.
Answer: B
Answer: (B) 5/6
Question: Rectangular tile each of size 20cm by 30cm must be laid horizontally on a rectangular floor of size 100cm by 150cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 40
(B) 15
(C) 25
(D) 32
(E) 45
Rationale: Area of tile = 20*30 = 600
Area of floor = 100*150 = 15000
No of tiles = 15000/600 =25
So, the no of tile =25
ANSWER:C
Answer: (C) 25
Question: How many integers between 300 and 1200 are there such that their unit digit is odd?
(A) 250
(B) 350
(C) 450
(D) 550
(E) 650
Rationale: There are 900 numbers from 301 to 1200 (inclusive).
Half of the numbers are odd, so there are 450 odd numbers.
The answer is C.
Answer: (C) 450
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 7,000 meters of fabric?
(A) $13,360
(B) $14,450
(C) $15,720
(D) $16,780
(E) $17,240
Rationale: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*3500 = $6510
The total price is $4000 + $2850 + $6510 = $13,360
The answer is A.
Answer: (A) $13,360
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 4 women and 30 children together complete the piece of work?
(A) 5 days
(B) 15 days
(C) 28 days
(D) 4 days
(E) 7 days
Rationale: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
4 women’s 1 day’s work = 1/192 × 4 = 1/48
1 child’s 1 day’s work = 1/240
30 children’s 1 day’s work = 1/8
Therefore, (10 men + 4 women + 30 children)’s 1 day’s work = 5/48 + 1/48 + 1/8
=1/4
The required No. of days = 4 days
Answer: Option D
Answer: (D) 4 days
Question: Abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If abi's savings by the end of the year from these monthly savings were six times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 6/9
(B) 5/3
(C) 2/3
(D) 4/3
(E) 5/3
Rationale: Let Abi 's monthly savings = S
Abi 's monthly pay = P
Abi 's monthly expenditure = P-S
Abi 's savings by the end of the year from these monthly savings were six times the amount she spent per month
12S = 6*(P-S)
=>2S = P-S
=> P = 3S
Abi 's monthly expenditure = P-S = 3S-S = 2S
fraction of her salary that Abi spent each month = 2S / 3S=P-S/P = 2/3. Answer is C
Answer: (C) 2/3
Question: A present value of a machine is $148000. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
(A) A)$54000
(B) B)$48000
(C) C)$36520
(D) D)$62437.5
(E) E)$42500
Rationale: P= $148000
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=148000*3/4 * 3/4 * 3/4
=$62437.5
Answer is D
Answer: (D) D)$62437.5
Question: A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?
(A) 8kmph
(B) 6kmph
(C) 4kmph
(D) 5 kmph
(E) 1kmph
Rationale: Explanation:
Speed of the boat in still water: 15 km/hr
Speed of boat downstream: (15+x)km/hr where x is speed of the current.
The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.
Total time= Time taken to travel downstream + Time taken to travel upstream
=> 4/5= (30/(15+x))+(30/(15-x))
=>x= 5
ANSWER:D
Answer: (D) 5 kmph
Question: How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph ?
(A) 60 sec
(B) 70 sec
(C) 80 sec
(D) 50 sec
(E) 90 sec
Rationale: 72 kmph=72*5/18 mps=20mps.
54 kmph=54*5/18 mps=15 mps.
The train has to travel (200+100)m=300m to overtake the other one.
Resultant velocity=(20-15)mps=5 mps
time it takes to travel 300m at a velocity of 5 mps is 60 sec..
Ans 60 sec.
ANSWER:A
Answer: (A) 60 sec
Question: 3,6,13,26,33,66,?
(A) 70
(B) 71
(C) 72
(D) 73
(E) 74
Rationale: 3*2=6
6+7=13
13*2=26
26+7=33
33*2=66
so next will be
66+7=73
ANSWER:D
Answer: (D) 73
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
(A) 180°
(B) 154°
(C) 160°
(D) 170°
(E) 150°
Rationale: We know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6×36012=180°
Answer is A.
Answer: (A) 180°
Question: Find the slope of the line perpendicular to the line y = x - 7
(A) 1
(B) 2
(C) -1
(D) 4
(E) 5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1. If m is the slope of the line perpendicular to the given line, then
m × 1 = -1
Solve for m
m = - 1
correct answer C) -1
Answer: (C) -1
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 8.8%
(B) 9.75%
(C) 9.2%
(D) 8.6%
(E) 8.4%
Rationale: The amount of chromium in the new 35+45=80 kg alloy is 0.12*35+0.08*45=7.8 kg, so the percentage is 7.8/80*100=9.75%.
Answer: B.
Answer: (B) 9.75%
Question: Look at this series: 55, 55, 40, 40, 25, 25, ... What number should come next?
(A) 14
(B) 15
(C) 17
(D) 10
(E) 11
Rationale: In this series, each number is repeated, then 15 is subtracted to arrive at the next number.
The next number should be 10
Answer : D
Answer: (D) 10
Question: In order to obtain an income of Rs. 1250 from 10% stock at Rs. 210, one must make an investment of
(A) 5363
(B) 26250
(C) 28678
(D) 29002
(E) 2732
Rationale: To obtain Rs. 10, investment
= Rs. 210.
To obtain Rs. 1250, investment =
= Rs. 26250.
Answer: B
Answer: (B) 26250
Question: In a certain city each of 17 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)
(A) 5
(B) 10
(C) 6
(D) 20
(E) 40
Rationale: B.6:
if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15. This is less than the number of girl scout groups.
if we have 6 colors we can choose pairs in 6C2 ways = 15 and single color flags are 6. Therefore total number of flags = 21.
ANS C.
Answer: (C) 6
Question: A tank can supply water to a village for 60 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 45 days only. For how many days will the supply last if the leak drains out 20 liters per day?
(A) 15
(B) 18
(C) 20
(D) 24
(E) 36
Rationale: Losing 10 liters per day results in a loss of 450 liters in 45 days. So, those 450 liters were for 15 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*60 = 1800 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 1800/50 = 36 days.
The answer is E.
Answer: (E) 36
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 11
(B) 8
(C) 12
(D) 99
(E) 17
Rationale: T = 9/45 * 60
= 12
Answer: C
Answer: (C) 12
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 331/8%
(B) 331/3%
(C) 338/3%
(D) 391/3%
(E) 311/3%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
Answer: B
Answer: (B) 331/3%
Question: In a group of ducks and cows, the total number of legs are 48 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 28
(B) 12
(C) 24
(D) 16
(E) 19
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 48
=> 2x = 48 => x = 24
C
Answer: (C) 24
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
(A) 84 m
(B) 88 m
(C) 120 m
(D) 137 m
(E) None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 66 ⇔ = [66 * 20 * 20 * 7 / 22] = 8400cm = 84 m.
Answer A
Answer: (A) 84 m
Question: Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 15% and its breadth is decreased by 10%?
(A) 3.5 percent increase
(B) 9.5 percent increase
(C) 1.5 percent increase
(D) 3.9 percent increase
(E) 3.5 percent increase
Rationale: let L and B be 100 each
100 * 100 = 10000
L increase by 15% = 115
B decrease by 10% = 90
115 * 90 = 10350
3.5 percent increase
ANSWER:E
Answer: (E) 3.5 percent increase
Question: Which of the following is equal to 10^-(-2)^2?
(A) 1/(10^6)
(B) 1/(10^7)
(C) 1/(10^8)
(D) 1/(10^9)
(E) 1/(10^4)
Rationale: 10^-(-2)^2 => 10^-(-2^2) => 10^-(4) = 1/(10^4)
Answer : E
Answer: (E) 1/(10^4)
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 4 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
(A) 27
(B) 36
(C) 72
(D) 18
(E) 422
Rationale: {1}{2}{greater than 6}{divisible by 4}{3x}{x}:
The third digit can take 3 values: 7, 8, or 9.
The fourth digit can take 2 values: 4, or 8.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 3*2*3 = 18.
Answer: D.
Answer: (D) 18
Question: Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many H miles will Tom drive before Karen wins the bet?
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: Let K and T be the speeds of Karen and Tom respectively.
t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.
Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours
Thus the distance traveled by Tom when Karen is 4 miles ahead of him H: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. D is the correct answer.
Answer: (D) 24
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 25 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $8,662.50
(C) $10,500
(D) $11,500
(E) $12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.75 = 10,395
Answer B is correct.
Answer: (B) $8,662.50
Question: Markov bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
(A) $10
(B) $11
(C) $12
(D) $13
(E) $14
Rationale: From the given information,we can conclude that Markov bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: (B) $11
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
(A) 33
(B) 20
(C) 28
(D) 36
(E) 11
Rationale: (9*12)/3 = 36
Answer: D
Answer: (D) 36
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
(A) 1/8
(B) 1/7
(C) 1/0
(D) 1/6
(E) 1/1
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: B
Answer: (B) 1/7
Question: Five boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
(A) A)5^30
(B) B)2^30
(C) C)1^30
(D) D)3^30
(E) E)6^30
Rationale: Each Mango can be given to any one of the five people or in other words..1 mango can be divided into 5 ways...so all 30 can be divided in 5^30 ways
ANS:A
Answer: (A) A)5^30
Question: The value of x + x(xx) when x = 2 is:
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
ANSWER : (B) +10
Answer: (B) 10
Question: It takes Jim three hours to wash the gym and it takes Julia two hours to wash the gym. Working together, how many minutes will it take them to wash the gym?
(A) 70
(B) 72
(C) 74
(D) 76
(E) 78
Rationale: Jim can wash (1/3) of the gym per hour.
Julia can wash (1/2) gym per hour.
Together they can wash 1/3+1/2=5/6 of the gym per hour.
1 gym / (5/6) of the gym per hour = 6/5 hours = 72 minutes.
The answer is B.
Answer: (B) 72
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
(A) 4/15
(B) 4/18
(C) 4/16
(D) 4/13
(E) 4/11
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer: D
Answer: (D) 4/13
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
(A) 1/39
(B) 1/36
(C) 1/35
(D) 1/34
(E) 1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Answer: (B) 1/36
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
(A) $5
(B) $10
(C) $14
(D) $28
(E) $29
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $52
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 52
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 52
i.e. x = 24
i.e. Fixed Monthly Charge, y = 28
Answer: Option
D
Answer: (D) $28
Question: If a sum of money doubles itself in 10 years at simple interest, the ratepercent per annum is
(A) 10
(B) 12.5
(C) 13
(D) 13.5
(E) 14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 10) = 10
Option A
Answer: (A) 10
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) 3909
(B) 3907
(C) 3905
(D) 3900
(E) 3901
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
25. The length of a rectangl.Answer:D
Answer: (D) 3900
Question: What is the perimeter of a square with area 4p^2/9 ?
(A) 8p/3
(B) 3p^2/4
(C) 3p
(D) 3p^2
(E) 4p/3
Rationale: Area of square, (side)^2 = (2p/3)^2
Therefore side of the square = 2p/3
Perimeter of square = 4*side = 4* (2p/3) = 8p/3
Answer is A.
Answer: (A) 8p/3
Question: For what value(s) of n is the following equation satisfied: 2n-6-n = 5n+6-4n
(A) a. -5
(B) b. 0 only
(C) c. 5/2 only
(D) d. No value
(E) e. Any value
Rationale: 2n-6-n = 5n+6-4n
n - 6 = n + 6
-6 = 6, which is false.
So, no n satisfies given equation.
Answer: D.
Answer: (D) d. No value
Question: Ages of two persons differ by 4 years. If 3 years ago, the elder one was 3 times as old the younger one, find their present age
(A) 5,9
(B) 14,18
(C) 16,20
(D) 18,22
(E) 19,23
Rationale: Explanation:
Let the age of the younger person be x,
Then the elder person's age is (x+4)
=> 3(x-3) = (x+4-3) [3 years before]
=> 3x-9 = x+1
=> x = 5.
So the elder person's age is x + 4 = 9
Answer: Option A
Answer: (A) 5,9
Question: If the Average of 10 consecutive integers is 19.5 then the 10th integer is :-
(A) 15
(B) 20
(C) 23
(D) 24
(E) 25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 19, integer 6 = 20.
Counting up to the tenth integer
we get 24.
ANSWER:D
Answer: (D) 24
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many W hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
(A)  22 hours
(B)  30 hours
(C)  44 hours
(D)  60 hours
(E)  It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job W in 44 hours.
Answer: C.
Answer: (C)  44 hours
Question: Evaluate: 40 - 12*3*2 = ?
(A) 62
(B) 52
(C) 32
(D) 12
(E) 22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
40 - 12*3*2 = 40 - 8 = 32
correct answer C
Answer: (C) 32