mathewhe/aqua_rat huggingface dataset:
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 388
(B) 2769
(C) 177
(D) 150
(E) 821
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Answer: (D) 150
Question: If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following?
(A) 2
(B) 4
(C) 12
(D) 18
(E) 24
Rationale: a^2=24n
a^2=2^2∗6n
Least value of n to make "a" a perfect square is 6
Answer = A = 2
Answer: (A) 2
Question: If 5 persons can do 5 times of a particular work in 5 days, then, 7 persons can do 7 times of that work in
?
(A) 3 days
(B) 7 days
(C) 5 days
(D) 11 days
(E) 15 days
Rationale: That is, 1 person can do one time of the work in 5 days.
Therefore, 7 persons can do 7 times work in the same 5 days itself.
Option 'C'
Answer: (C) 5 days
Question: Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
(A) 14.5
(B) 14.1
(C) 14.2
(D) 14.8
(E) 14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be M, N and R respectively.
M/N = 5/x --- (1)
M = R - 18 --- (2)
R + 9 = 47 --- (3)
M - N = R --- (4)
(3) => R = 47 - 9 = 38 years
(2) => M = 38 - 18 = 20 years
(1) => 20/N = 5/x => N = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: (E) 14.5
Question: Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, 63, 63, ? ... What number should fill the blank?
(A) 51
(B) 39
(C) 75
(D) 15
(E) None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option C
Answer: (C) 75
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder Q when N is divided by 30?
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder Q when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: (C) (c) 11
Question: In the list 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
(A) 2/9
(B) 1/8
(C) 2/5
(D) 2/3
(E) 7/9
Rationale: Mode: The mode of any set is the term which has the highest frequency (Occurrence)
Highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
ONE term (4) out of a total of 8 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 1/8
Answer: Option B
Answer: (B) 1/8
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 3 1/89%
(B) 3 7/3%
(C) 3 1/3%
(D) 2 1/3%
(E) 3 5/3%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 3 1/3%
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 6/63
(B) 2/63
(C) 125/126
(D) 1/126
(E) 1/63
Rationale: Required probability = 1 - 1/126 = 125/126
ANSWER:C
Answer: (C) 125/126
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 14 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
(A) 6
(B) 16
(C) 20
(D) 30
(E) 174
Rationale: The number of integers that belong to set X ONLY is 14-6=8;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 8+12=20.
Answer: C.
Answer: (C) 20
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 5:30 am. They shall first cross each other at ?
(A) 7:15 am
(B) 7:30 am
(C) 5: 42 am
(D) 7:50 am
(E) 7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 5:30 + 12 mins = 5:42
Option C
Answer: (C) 5: 42 am
Question: If an amount of Rs 24,705 is divided equally among
61 students, approximately how much amount will
each student get?
(A) Rs 405
(B) Rs 415
(C) Rs 450
(D) Rs 218
(E) None
Rationale: Amount received by each student = 24705/61 â‰ˆ Rs
405
Answer A
Answer: (A) Rs 405
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 5.2 hrs
(B) 2.9 hrs
(C) 1.9 hrs
(D) 4.8 hrs
(E) 1.4 hrs
Rationale: Net part filled in 1 hour = (1/3 - 1/8) = 5/24
The cistern will be filled in 24/5 hrs i.e., 4.8 hrs.
Answer:D
Answer: (D) 4.8 hrs
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
(A) 33 years
(B) 34 years
(C) 35 years
(D) 36 years
(E) 37 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*25 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 75+84+90+2x+11=308
so 2x = 48
so x = 24.
Age of the captain = (x+11)
= 35 years.
Answer : C
Answer: (C) 35 years
Question: A boat can travel with a speed of 15 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 68 km downstream?
(A) 3 hours 30 minutes
(B) 3 hours
(C) 4 hours
(D) 5 hours
(E) None
Rationale: Solution
Speed Downstream	= (15 + 4) km/hr
= 19 km/hr.
Time taken to travel 68 km downstream	=(68 / 19)hrs
= 3 hrs 30 mins.
Answer A
Answer: (A) 3 hours 30 minutes
Question: Two employees X and Y are paid a total of Rs.750 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.200.90
(B) s.250.90
(C) s.290.90
(D) s.300.90
(E) s.340.90
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 750
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 750
⇒ y[12/10 + 1] = 750
⇒ 22y/10 = 750
⇒ 22y = 7500
⇒ y = 7500/22 = Rs.340.90
E)
Answer: (E) s.340.90
Question: Ganesh spends 30% of his monthly salary on food, 5% of the remaining on personal use and saves 80% of the remaining amount. If his monthly salary is Rs.12,000, how much money does he save every month ?
(A) Rs.3500
(B) Rs.4200
(C) Rs.2000
(D) Rs.1245
(E) Rs. 6384
Rationale: Explanation:
Ganesh's monthly income = Rs.12,000
He spends 30% on food.
The total money spent on food = 30/100 * 12000 = Rs. 3600
Now, his monthly remaining income = Rs.12000 – Rs.3600 = Rs. 8400
Out of Rs. 8400, he spends 5% for his personal use
The total money spent on his personal use = 5/100 * 8400 = Rs. 420
Now, his monthly remaining income = Rs.8400 – Rs.420 = Rs. 7980
Out of Rs. 7980, he saves 80%.
Amount saved = 80/100 * 7980 = Rs. 6384
ANSWER:E
Answer: (E) Rs. 6384
Question: What percent of 75 is 45?
(A) 0.25%
(B) 4%
(C) 25%
(D) 40%
(E) 60%
Rationale: 75*x /100 = 45
x = 4*45/3
x=60
Ans: E
Answer: (E) 60%
Question: If x and y are integers such that (x+1)^2 is less than or equal to 64 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
(A)  -16
(B)  -18
(C)  0
(D)  14
(E)  16
Rationale: (x+1)^2 <= 64
x <= 7
x >= -9
(y-1)^2 < 64
y < 9
y > -7
Max possible value of xy is -9 × -6 = 54
minimum possible value of xy is -9 × 8 = -72
-72 + 54 = -18
Answer : B
Answer: (B)  -18
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 40 worth of diesel fuel?
(A) 20 seconds
(B) 1 minute
(C) 1 minute 20 seconds
(D) 20 minutes
(E) 1 hour 20 minutes
Rationale: No. of gallons = 40 / 1.25 = 32
for 2 gallons it takes 5 secs
for 32 gallons it will take 80 secs = 1 min and 20 secs
Answer: C
Answer: (C) 1 minute 20 seconds
Question: The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 8800 for a computer table, then what was the cost price of the computer table?
(A) Rs.6725
(B) Rs.6727
(C) Rs.8000
(D) Rs.6725
(E) Rs.6728
Rationale: CP = SP * (100/(100 + profit%))
= 8800(100/110) = Rs.8000.
Answer: C
Answer: (C) Rs.8000
Question: Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
(A) 639
(B) 2079
(C) 3791
(D) 37911
(E) None of these
Rationale: 639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
Answer: Option B
Answer: (B) 2079
Question: Find out the wrong number in the given sequence of numbers.
1, 2, 6, 15, 30
(A) 2
(B) 6
(C) 15
(D) 30
(E) 91
Rationale: 1(result) + (1*1) = 2.
2(result) + (2*2) = 6.
6(result) + (3*3) = 15.
15(result) + (4*4) = 31.
Now we are getting 31 not 30.. So 30 is the wrong number of the given.
answer : D
Answer: (D) 30
Question: How many terminating zeroes does 200! have?
(A) 40
(B) 48
(C) 49
(D) 55
(E) 64
Rationale: we must realize that the trailing zeros depend on the number of 10s (i.e. 10s or its multiples) in the factorial. 10=5*2, so we are looking for 5s and 2s. By virtue of being the more frequent number, we don't need to count the number of 2s, because there will always be equal or more 2s than 5s in a factorial. So, essentially we are looking for 5s and its exponents.
Start with finding 5s. 200/5= 40. So we have 40 fives (and 40 twos) which means we'll have 40 zeros. If the answer was a decimal, such as 201/5, round down.
Now look for two 5s, that is 25. So, 200/25= 8, so we have eight more zeros.
Lastly, 5^3= 125, and we have one such number in 200!, which gives us one more trailing zero. Therefore, we have 40+8+1=49 trailing zeros.
ANSWER:C
Answer: (C) 49
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 39288
(C) 288
(D) 266
(E) 1881
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.Answer: A
Answer: (A) 3944
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
(A) Rs. 50000
(B) Rs. 52000
(C) Rs. 57000
(D) Rs. 60000
(E) Rs. 67000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
Answer: (C) Rs. 57000
Question: A train 125 m long passes a man running at 5 km/hr in the same direction in which the train is going in 10 sec. The speed of the train is?
(A) 33 km/hr
(B) 50 km/hr
(C) 77 km/hr
(D) 65 km/hr
(E) 99 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Answer: (B) 50 km/hr
Question: A train passes a station platform in 50 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?
(A) 550
(B) 400
(C) 700
(D) 600
(E) 850
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Length of the train = 20 * 20 = 400 m.
Let the length of the platform be x m . Then,
(x + 400)/50 = 20 => x = 600 m.
Answer: D
Answer: (D) 600
Question: The L.C.M. of two numbers is 30. The numbers are in the ratio 2 : 3. Then sum of the number is:
(A) 25
(B) 32
(C) 40
(D) 53
(E) 54
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 30 or x = 5.
The numbers are 10 and 15.
Hence, required sum = (10 + 15) = 25.
Answer: Option A
Answer: (A) 25
Question: A certain country is divided into 5 provinces. Each province consists entirely of Progressives and Traditionalists. If each province contains the same number of Traditionalists and the number of Traditionalists in any given province is 1/15 the total number of Progressives in the entire country, what fraction of the country is Traditionalist?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: Let P be the number of Progressives in the country as a whole.
In each province, the number of traditionalists is P/15
The total number of traditionalists is 5P/15 = P/3.
The total population is P + P/3 = 4P/3
P / (4P/3) = 3/4
The answer is E.
Answer: (E) 3/4
Question: A train running at the speed of 36 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 90 metres
(E) 100 meters
Rationale: Speed=36x5/18m/sec=30/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	30/3	x 9m = 90 m.
ANSWER:D
Answer: (D) 90 metres
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 125 mangoes.
(A) 360
(B) 380
(C) 400
(D) 416
(E) 412
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 125 mangoes = 125*3.33 = 416.
Answer D
Answer: (D) 416
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
(A) 2999
(B) 2789
(C) 3700
(D) 1032
(E) 1000
Rationale: 2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer:E
Answer: (E) 1000
Question: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train.
(A) 200/3m
(B) 100m
(C) 50m
(D) 100/3
(E) none of these
Rationale: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
The man is moving forward at a speed of 5km/h while the train is moving forward at a speed of 25km/h. Therefore, the train is moving past the man at a total speed of 20km/h.
distance = speed * time
distance = 20km/h * 12 seconds
distance (length of train) = 66.6 m
ANSWER: A) 200/3m
Answer: (A) 200/3m
Question: 45 x ? = 10% of 900
(A) 2
(B) 4
(C) 5
(D) 500
(E) None
Rationale: Answer
Let 45 x A = (10 x 900)/100
∴ A = (10 x 9)/45 = 2
Correct Option: A
Answer: (A) 2
Question: Three table runners have a combined area of 208 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
(A)  22 square inches
(B)  20 square inches
(C)  24 square inches
(D)  28 square inches
(E)  30 square inches
Rationale: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 208 - 24 - 2*(all three) + 0
2*(all three) = 208 - 24 - 140
all three = 22
Answer: A
Answer: (A)  22 square inches
Question: If f is a function defined for all k by f(k) = k^5/16, what is f((6/4)*k) in terms of f(k)?
(A) 1/8 f(k)
(B) 7.6 f(k)
(C) 2 f(k)
(D) 10 f(k)
(E) 32 f(k)
Rationale: f(k) = k^5/16
f((6/4)*k) = ((6/4)*k)^5/16 = 7.6 * (k^5/16) = 7.6 (k^5/16) = 7.6 f(k).
So answer is B.
Answer: (B) 7.6 f(k)
Question: George's car calls for 8 ounces of oil for each cylinder used. His car's engine has 6 cylinders. If 16 ounces of oil has already been put into the engine used, then how many additional ounces of oil are needed?
(A) 16
(B) 48
(C) 64
(D) 32
(E) 8
Rationale: Number of ounces per cylinder 8
Number of cylinders 6
Ounces needed 48
Ounces used 16
Answer D
Answer: (D) 32
Question: The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 4.9 min
(B) 5.28 min
(C) 5.5 min
(D) 6 min
(E) 7 min
Rationale: Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.
ANSWER:B
Answer: (B) 5.28 min
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -13?
(A) -13
(B) 7
(C) 13
(D) 14
(E) 20
Rationale: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
t10 = -4
t11 = -7
t12 = -10
t13 = -13
So, ourANS is C.
Answer: (C) 13
Question: In 1979 approximately 1/3 of the 32.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
(A)  18.6
(B)  9.3
(C)  6.2
(D)  1.33
(E)  1.6
Rationale: number of
passengers using Kennedy airport = 32/3 =~10.67
Passengers using Miami airport = 10.67/2=~5.34
passengers using logan airport = 5.34/4 =~1.33
so D
Answer: (D)  1.33
Question: Of the teams competing in the world archery championships, 10 percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 13/20
(B) 15/20
(C) 13/15
(D) 16/20
(E) 13/17
Rationale: Assume 100 total people.
10% of 100 = 10 --->Europeans
1/2 of 10 ---> 5 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 20= 80. So, 80 people out of 100 are not EU, US or Africans. 80/100 is also equal to 16/20.
So therefore, the answer is D
Answer: (D) 16/20
Question: A batsman in his 12th innings makes a score of 80 and thereby increases his average by 3 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 47
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 3) + 80
∴ x = 47
Answer E
Answer: (E) 47
Question: Diane sold a book worth $ 850 at a loss of $ 180. Find the selling price of the book.
(A) $ 670
(B) $ 680
(C) $ 600
(D) $ 700
(E) $ 710
Rationale: Cost Price = $ 850
Loss = $ 180
Since, Selling Price = Cost Price + Loss
Selling Price = 850 - 180
= $670
Therefore, selling price of the book = $ 670
Answers: A
Answer: (A) $ 670
Question: In a group of 80 people,40 like movie,10 like both movie and series. How many like Series?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Make a Venn diagram, and enter your data.
Let the number of people who like series be x
x + 10 + 30 = 80
x = 40
so number who like series = 10+40 = 50
Answer E
Answer: (E) 50
Question: X, 1320 , 1070 , -180, -6430
(A) 1370
(B) 6530
(C) 6630
(D) 6730
(E) 6830
Rationale: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Answer: (A) 1370
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 5%
(B) 3 1/2%
(C) 4%
(D) 5 1/2 %
(E) 6 %
Rationale: Explanation:
150 = (750*5*R)/100
R = 4%
ANSWER IS C
Answer: (C) 4%
Question: The average (arithmetic mean) of six numbers is 7. If 3 is subtracted from each of four of the numbers, what is the new average?
(A) 1.5
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Sum of 6 numbers = 6*7 =42
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 42 - 12 = 30
New average = 30/6 = 5
Answer E
Answer: (E) 5
Question: A and B are two multiples of 36, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 9, how many multiples of 4 are there in Q?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: Now given that Q is set the consecutive integers between A and B.
and Q contains 9 multiples of 9
Let take A as 36.
then 36 45 54 63 72 81 90 99 108...So B will 108.
Now let's check the multiples of 4 among this set
108 - 36 / 4 + 1 => 18 + 1 => 19
ANS option B.
Answer: (B) 19
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 9/11
(B) 5/6
(C) 7/20
(D) 11/20
(E) 9/20
Rationale: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = (E)/(S)
= 9 / 20
E
Answer: (E) 9/20
Question: Jim drove 384 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 113 miles
(B) 432 miles
(C) 456miles
(D) 816 miles
(E) 767 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 384 = 816 miles
correct answer D
Answer: (D) 816 miles
Question: A big container is 40% full with water. If 14 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container in liters?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Rationale: 14 liters is 35% of the capacity C.
14 = 0.35C
C = 14/0.35 = 40 liters.
The answer is C.
Answer: (C) 40
Question: P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q × (130/100) = 1/23
=> q = 100/(23×130) = 10/(23×13)
Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13
=> P and Q together can do the work in 13 days
Answer is C.
Answer: (C) 13
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320,660,1056
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 8 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: E
Answer: (E) 8
Question: Dimitri weighs 3x-2x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
(A) y - x/2
(B) 2x - y/2
(C) (y - x)/2
(D) y - 2x
(E) 2x - y
Rationale: These type of multi-variable story problems are usually perfect for TESTing VALUES.
Here, we're told that Dimitri weighs 3X-2X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.
IF....
Dimitri = 30
Allen = 20
X = 10
Y = 50
We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.
Answer A: 50 - (10/2) = 45 NOT a match
Answer B: 20 - (50/2) = -5 NOT a match
Answer C: (50-10)/2 = 20 This IS a match
Answer D: 50 - 20 = 30 NOT a match
Answer E: 20 - 50 = -30 NOT a match
Final Answer:
C
Answer: (C) (y - x)/2
Question: The ratio of radius of a circle and the side of a square is 2 : 9. Find the ratio of their areas:
(A) 2 : 1
(B) 4 : 7
(C) 8 : 77
(D) 4 : 81
(E) None
Rationale: radius/side = 2/9
â‡’ area of circle/area of square= 4/81
Answer: D
Answer: (D) 4 : 81