mathewhe/aqua_rat huggingface dataset:
Question: Randy'sbar serves customers every weeknight from 5 pm to 2 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?
(A) Monday, 7:30 pm
(B) Monday, 9 pm
(C) Monday, 7 pm
(D) Monday, 7:45 pm
(E) Monday, 9:30 pm
Rationale: Let the keg be a 150 Litre keg
At 5 pm.. There are 75 litres
At 6:30 pm there are 50 litres.
So, consumption rate is 25 litres per 1.5 hours.
So it will take 3 hours to finish 50 litres at this rate.
During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.
So, keg becomes empty at 6:30 + 1 hour = 7:45 pm
Answer is D
Answer: (D) Monday, 7:45 pm
Question: If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b - c ?
(A) 6
(B) 2
(C) -1
(D) -3
(E) -4
Rationale: consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) - (X+4)
doing this leaves us with X -2
what even number can we substitute in X to yield an answer choice
B works 2 (plug in 4 for X)
Answer: (B) 2
Question: The cost of producing x tools by a company is given by
C(x) = 600 x + 5500 (in $)
a) What is the cost of 100 tools?
(A) 65500 $
(B) 125800 $
(C) 125900 $
(D) 6500 $
(E) 122500 $
Rationale: Solution
C(100) = 600*100 + 5500 = 125500 $
Answer A
Answer: (A) 65500 $
Question: Instead of multiplying a number by 3, the number is divided by 5. What is the percentage of error obtained ?
(A) 92.33%
(B) 91.33%
(C) 95.33%
(D) 93.33%
(E) 94.33%
Rationale: let the number be x
the right number is 3x
the wrong number is x/5
error is(3x-x/5)=14x/5
percentage of error is((14x/5)/3x)*100=93.33%
ANSWER:D
Answer: (D) 93.33%
Question: Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1⁄3 as efficiently as he actually did, the work would have completed in 3 days. Find the time for A to complete the job alone.
(A) 6 1⁄4 days
(B) 5 3⁄4 days
(C) 5 days
(D) 3 days
(E) None of these
Rationale: (A + B)’s one day’s work 1⁄5th work
Let A can do job in x days.
Then,A’s one day’s work = 1⁄x th work.
and B’s one day’s work = 1⁄5 - 1⁄x = x−5/5xth work.
Now, (2A)'s work + (1⁄3) B's work = 1⁄3 rd work.
⇒ 2/x+1/3(x−5/5x)=1/3⇒ x = 25⁄4 = 61⁄4 days
Answer A
Answer: (A) 6 1⁄4 days
Question: 4 liters of a 25 percent solution of alcohol in water are mixed with 3 liters of a 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
(A) 18.2%
(B) 18.6%
(C) 19.0%
(D) 19.4%
(E) 19.8%
Rationale: The total amount of alcohol is 0.25(4) + 0.11(3) = 1.33 liters.
The percentage is 1.33 / 7 = 133 / 700 = 19 / 100 which is 19%
The answer is C.
Answer: (C) 19.0%
Question: {5, 6, 3, 8, 4}
If we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values?
(A) 5
(B) 7
(C) 15
(D) 12
(E) 13
Rationale: Median is the middle number of a sorted distribution. In case of even number of items, Median will be the average of middle two values.
The question asks fora new number that will cause the median of new set at 10.
Mentionable that given set is already sorted and number of items of new set will be 5+1 = 6.
To get median 10,the sum of 3th4th Term should be 20 i.e. 3+7.
So to keep the median 10,the new item should be >=7
Answer is B
Answer: (B) 7
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the "sport" formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the "sport" formulation contains 3 ounces of corn syrup, how many ounces of water does it contain?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 63
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 3*180/12 = 45 ounces of water
ANSWER:A
Answer: (A) 45
Question: A car takes 6 hours to cover a distance of 450 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 50 Kmph
(C) 52 Kmph
(D) 56 Kmph
(E) 60 Kmph
Rationale: Time = 6
Distence = 450
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 450/9 = 50 Kmph
B
Answer: (B) 50 Kmph
Question: If radius of a circle is diminished by 10% then its area is diminished by
(A) 22
(B) 19
(C) 877
(D) 26
(E) 271
Rationale: Explanation:
Let old radius = 10 units.
New radius is diminshed by 10%. So new radius = 90% (10) = 9 units.
Old area = π × r2 = 100π
New area = π × 92 = 81π
Change = 19π/100π ×100 = 19%
Answer: B
Answer: (B) 19
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 30
(D) 50
(E) 40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+45) and number of girls were 5x
Hence, 2(5x) = x + 45
=> 10x = x + 45
=> x = 5
Number of girls in the beginning = (5x + 15) = (5×5 + 15) = 40
Answer is E.
Answer: (E) 40
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 7 baseball cards. How many baseball cards do you have at the end?
(A) 11
(B) 12
(C) 13
(D) 9
(E) 15
Rationale: Solution
Start with 16 baseball cards.
John takes 7 baseball cards from you: 16 - 7 = 9 baseball cards.
So you have 9 at the end.
Correct answer : D
Answer: (D) 9
Question: The current birth rate per Two thousand is 52, whereas corresponding death rate is 21 per two thousand. The net growth rate in terms of population increase in percent is given by
(A) 1.80%
(B) 1.45%
(C) 1.25%
(D) 1.35%
(E) 2.10%
Rationale: Sol.
Net growth on 1000 = (52 - 21) = 31.
Net growth on 100 = (27/2000 Ã— 100)% = 1.35%.
Answer D
Answer: (D) 1.35%
Question: A circular rim 28 inches in a diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes D revilutions per second, how many revilutions per minute does the larger rim makes in terms of D?
(A) a) 48pi/D
(B) b) 75m
(C) c) 48D
(D) d) 24D
(E) e) D/75
Rationale: distance covered by a circular wheel per sec* = 2*pi* r * n
where n is number of revolution
So we know the smaller rim makes D rev per sec so the inches coverd SR per sec = 28 * pi* D
the problem the say SR rotates the same number of inches as the LR.
The inches covered by the LR per sec = 35 * pi*Y
So equate both u will get Y = 4/5 D
Theis is in sec we need the answer in min so 48 D
answer is C
Answer: (C) c) 48D
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 9 consecutive days in Rwanda?
(A) 4/7
(B) 3/7
(C) 63/256
(D) 4/28
(E) 28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
9C4 (1/2)^4 (1/2)^r
which is 63/256
Answer is C.
Answer: (C) 63/256
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 24mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
(A) 20
(B) 30
(C) 56
(D) 60
(E) 72
Rationale: Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 24
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 24*t2 = 80
t1 + 3*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> 2t2 = 2 , t2=1and t1 = 8 - 1 = 7
Walking distance = s1*t1 = 8*7 = 56
Answer: C
Answer: (C) 56
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 110.12 meters
(B) 111.12 meters
(C) 112.12 meters
(D) 113.12 meters
(E) None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 800 meters.
Therefore, B runs 900 meters while C runs 800 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 800)/900 = 8000/9 = 888.88 meters
Thus, B can give C (1000 - 888.88) = 111.12 meters start
Answer: B
Answer: (B) 111.12 meters
Question: The cash realised on selling a 14% stock is Rs.120.50, brokerage being 1/4% is
(A) 120.25
(B) 120.35
(C) 106.5
(D) 156
(E) 240
Rationale: Explanation:
Cash realised= Rs. (120.50 - 0.25)
= Rs. 120.25.
Answer: A
Answer: (A) 120.25
Question: In how many ways the letters of the word RAIXBON be arranged?
(A) 2476
(B) 4432
(C) 3532
(D) 5040
(E) 7349
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
D)
Answer: (D) 5040
Question: In a kilometer race, A beats B by 51 meters or 11 seconds. What time does A take to complete the race?
(A) 22
(B) 190
(C) 277
(D) 204
(E) 208
Rationale: Time taken by B run 1000 meters = (1000 * 11)/51 = 215 sec.
Time taken by A = 215 - 11 = 204 sec.Answer:D
Answer: (D) 204
Question: If 75 percent of 600 is 50 percent of x, then x=?
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) 1200
Rationale: 0.75 * 600 = 0.5 * x
x = 7.5/5 * 600 = 900
Answer: (B) 900
Question: How many integers are divisible by 9 between 10! and 10! + 100 inclusive?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: E - 7
10! is divisible by 9
There are 11 numbers between 10! and 10!+ 100 that are divisible by 9.
Hence 10
Answer: (E) 10
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
(A) 4229
(B) 4220
(C) 4211
(D) 4200
(E) 4212
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer:D
Answer: (D) 4200
Question: A customer purchased a package of ground beef at a cost of $1.95 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 35 percent less than the package of ground beef. What was the cost per pound of the steak?
(A) $2.50
(B) $2.75
(C) $3.00
(D) $3.25
(E) $3.50
Rationale: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.95.
Let x be the price per pound for the steak.
Then 0.65x = 195
x = 195/0.65 = $3.00
The answer is C.
Answer: (C) $3.00
Question: In a single throw of a die, what is probability of getting a number greater than 4?
(A) 1/3
(B) 2/3
(C) 4/6
(D) 1/6
(E) 5/6
Rationale: E= {5,6}
n(E)=2
P(S)=n(E)/n(S)
=2/6
=1/3
ANSWER A 1/3
Answer: (A) 1/3
Question: What is the average of 1/2, 3/5 and 3/10?
(A) 7/15
(B) 3/10
(C) 2/5
(D) 1/2
(E) 6/5
Rationale: Sum of 1/2,3/5,3/10 =14/10
Average = 14/10*1/3 =7/15
Answer A 7/15
Answer: (A) 7/15
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
(A) 170Rs
(B) 108Rs
(C) 100Rs
(D) 160Rs
(E) 103Rs
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x =100Rs.
Answer:C
Answer: (C) 100Rs
Question: During a Pizza buffet where A eats more times 5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat
(A) 35
(B) 45
(C) 25
(D) 28
(E) 42
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 5:1 and as B eat 7 times less the C the the ratio of B : C is 1:7 the the least number of times all three has eat is the LCM of A,B,C that is 35 ..
ANSWER:A
Answer: (A) 35
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 1 buckles is how many times that of 5 buckles and 6 buttons?
(A) 7/15.
(B) 2/5.
(C) 6/11.
(D) 5/9.
(E) 8/15.
Rationale: 2buttons + 2buckles = 1/3(11buckles + 3buttons)
6buttons + 6buckles = 11buckles + 3buttons
3buttons = 5buckles
Weight of 3buttons and 1buckles = 5buckles + 1buckles = 6buckles
Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
6 = x*15
x = 6/15=2/5
Answer: B
Answer: (B) 2/5.
Question: The average of the first five multiples of 9 is:
(A) 20
(B) 27
(C) 28
(D) 30
(E) None of these
Rationale: Solution: Required average = (total sum of multiple of 9)/5
= (9+18+27+36+45)/5
= 27
Note that, average of 9 and 45 is also 27.
And average of 18 and 36 is also 27.
Answer: Option B
Answer: (B) 27
Question: Find the ratio in which wheat of inferior quality (Rs.14/kg) be mixed with wheat of superior quality (Rs.28/kg) so that the shopkeeper gains Rs.2 by selling the resulting mixture at Rs.20/kg.
(A) 5 : 2
(B) 5 : 9
(C) 5 : 3
(D) 5 : 1
(E) 5 : 8
Rationale: Explanation:
Let the resulting mixture be 1 kg, and x kg be the amount of wheat of inferior quality.
Therefore, (1-x)kg is the amount of wheat of superior quality.
As the shopkeeper gains Rs.2, the cost of the mixture is Rs.18
14*x + 28*(1-x) = 18
14x - 28x + 28 = 18
14x = 10
x = 5/7
(1 – x) = 2/7
x : (1-x) = 5/7 : 2/7
= 5 : 2
ANSWER: A
Answer: (A) 5 : 2
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 10 days before the project is completed, in how many days total will the project be completed?
(A) 18
(B) 27
(C) 26
(D) 16
(E) 12
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 10 days, A can do 1/2 of the project.
Thus A and B must complete 1/2 of the project, which takes 6 days.
The total number of days is 6 + 10 = 16.
The answer is D.
Answer: (D) 16
Question: In a certain parking lot, 3% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What % of cars in the parking lot are parked illegally.'
(A) 11
(B) 13
(C) 15
(D) 60
(E) 75
Rationale: So Total no. of cars parked illegally: 300
Total no. of cars: 2000
300/2000*100, So 15%
ANSWER:C
Answer: (C) 15
Question: What is the sum of the first 21 natural numbers (starting from 1)?
(A) 191
(B) 201
(C) 211
(D) 221
(E) 231
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 21*22/2 = 231
The answer is E.
Answer: (E) 231
Question: If the perimeter of a square and a rectangle is equal to one another, find out the ratio of the area of both these shapes in case the sides of the rectangle are in the
ratio of 2 :5.
(A) 40 : 49
(B) 24 : 25
(C) 4 : 5
(D) 5 : 6
(E) 4 : 9
Rationale: Let side of square=a
length of rectangle=l
breadth of rectangle=b
l/b=2/5------->l=2b/5-----(1)
given 4a=2(l+b)-------->4a=2(2b/5+b)
a=7b/10------(2)
we have to find l*b/a^2
substituting from (1) &(2)
(b*2b/5)/49b^2/100------40/49
Answer: A
Answer: (A) 40 : 49
Question: If, when the two parties of knights encounter one another after a month, exactly one knight changes from one travelling party to the other travelling party, that knight must be
(A) P
(B) Q
(C) R
(D) S
(E) T
Rationale: Q because Q always have to travel in northern route
ANSWER:B
Answer: (B) Q
Question: By selling an article at Rs.400, a profit of 25% is made. Find its cost price?
(A) 228
(B) 320
(C) 287
(D) 480
(E) 811
Rationale: SP = 400
CP = (SP)*[100/(100+P)]
= 400 * [100/(100+25)]
= 400 * [100/125] = Rs.320
Answer: B
Answer: (B) 320
Question: The price of an article has been reduced by 35%. In order to restore the original price the new price must be increased by ?
(A) 51.8 %
(B) B) 49.25 %
(C) 47.2 %
(D) 53.84 %
(E) None of these
Rationale: Explanation:
100
65
-------
65 ------- 35
100 ------ ? => 53.84 %
ANSWER IS D
Answer: (D) 53.84 %
Question: which of the following inequalities indicates the set of all values of d for which the lengths Q of the three sides of a triangle can be 3,4, and d?
(A) 0<d<1
(B) 0<d<5
(C) 0<d<7
(D) 1<d<5
(E) 1<d<7
Rationale: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer.
Answer: (E) 1<d<7
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 35. He was allowed to drop his lowest score. After doing so, his average test score improved to 40. What is the lowest test score that was dropped?
(A) 20
(B) 25
(C) 55
(D) 65
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 35. So what we can assume is that we have 4 test scores, each 35.
He dropped his lowest score and the avg went to 40. This means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 35.
So the lowest score =35 - 15 = 20
Answer (A)
Answer: (A) 20
Question: When Rajeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev's brother is 6 years older than Rajeev and his mother is 3 years younger than his father, how old was Rajeev's sister when Rajeev was born?
(A) 10 years
(B) 11 years
(C) 12 years
(D) 13 years
(E) 14 years
Rationale: his brother is x years old
thn his father is 6+32=38 when rajeev was born
and his mother is 3 years yonger thn hi father so his mother was 35 years old whn rajeev was born
and his sister is 25 year younger thn his mother
so rajeev's sister was 10 years old when rajeev was born.
ANSWER:A
Answer: (A) 10 years
Question: If (x^2 + 1)y=4, which of the following is not a possible value for y?
(A) 3/2
(B) 2
(C) 4/3
(D) 4
(E) 9/2
Rationale: Its simple
equation is (x^2 +1)y = 4 ===> x^2 = (4/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (4/y) - 1>= 0 ===> y =< 4. Now only option E has greater value of 'y' than 4.
Thus, correct ans is E
Answer: (E) 9/2
Question: The ratio of the area of a square to that of the square drawn on its diagonal is?
(A) 4/16
(B) 4/13
(C) 4/11
(D) 4/19
(E) 4/12
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:B
Answer: (B) 4/13
Question: Find the surface area of a 10 cm × 4 cm × 3 cm brick.
(A) 84 sq. cm
(B) 124 sq. cm
(C) 164 sq. cm
(D) 180 sq. cm
(E) None of these
Rationale: Solution
Surface area = [2(10 × 4 + 4 × 3 + 10 × 3)] cm2 = (2 × 82)cm2 = 164 cm2
Answer C
Answer: (C) 164 sq. cm
Question: Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
(A) 22m
(B) 77m
(C) 88m
(D) 17m
(E) 16m
Rationale: Explanation:
Length of longest pole = Length of the diagonal of the room
\inline {\color{Black}\sqrt{12^2+8^2+9^2}=\sqrt{289}=17m}
Answer: D
Answer: (D) 17m
Question: A man swims downstream 60 km and upstream 40 km taking 4 hours each time; what is the speed of the current?
(A) 3 kmph
(B) 2.5 kmph
(C) 13 kmph
(D) 6.5 kmph
(E) 7:3kmph
Rationale: Explanation:
60 --- 4 DS = 15
? ---- 1
40 ---- 4 US = 10
? ---- 1 S = ?
S = (15 - 10)/2 = 2.5
Answer: Option B
Answer: (B) 2.5 kmph
Question: A Cone and a sphere have equal radii and equal volumes. Find the ratio of the sphere of the diameter of the sphere to the height of the cone.
(A) 1:2
(B) 1:3
(C) 1:6
(D) 1:7
(E) 1:8
Rationale: Let radius of each be R and height of the cone be H.
Then, (4/3) ∏ R3 = (1/3) ∏ R2H (or) R/H = ¼ (or) 2R/H = 2/4 =1/2
Required ratio = 1:2.
ANSWER A 1:2
Answer: (A) 1:2
Question: The speed of a boat in upstream is 85 kmph and the speed of the boat downstream is 185 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10
(B) 99
(C) 77
(D) 50
(E) 22
Rationale: Speed of the boat in still water = (85+185)/2 = 135 kmph. Speed of the stream
= (185-85)/2
= 50 kmph.
Answer: D
Answer: (D) 50
Question: If the height of a cone is increased by 160% then its volume is increased by?
(A) 100
(B) 777
(C) 998
(D) 729
(E) 160
Rationale: 160%
Answer:E
Answer: (E) 160
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 176 votes. Find the total number of valid votes?
(A) 440
(B) 438
(C) 436
(D) 434
(E) 422
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 176 => 4x/10 = 176
=> 4x = 1760 => x = 440.
Answer:A
Answer: (A) 440
Question: If P, Q, and R are distinct positive digits and the product of the two-digit integers PQ and PR is 221, what is the sum of the digits P, Q, and R?
(A) 5
(B) 11
(C) 13
(D) 21
(E) 23
Rationale: Factor out 221
221=13*17
Thus PQ=13 & PR = 17 or vice versa
Thus P=1, Q=3 & R=7
Sum=1+3+7=11
Answer: B
Answer: (B) 11
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
(A) 71 days
(B) 55 days
(C) 21 days
(D) 77 days
(E) 44 days
Rationale: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
Answer: C
Answer: (C) 21 days
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 22 kmph
(B) 24 kmph
(C) 20 kmph
(D) 27 kmph
(E) 83 kmph
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20 kmph
Question: A train 50 m long passes a platform 100 m long in 10 seconds. The speed of the train in m/sec is ?
(A) 150
(B) 50
(C) 10
(D) 15
(E) 12
Rationale: Speed of train = distance covered / time.
= (50 + 100) / 10
= 15 m/sec.
Answer : D
Answer: (D) 15
Question: If 1/3 of the passengers on a ship are from North America, 1/8 are Europeans, 1/5 are from Africa, 1/6 are from Asia and the remaining 42 people are citizens of other continents, then how many passengers are on board the ship?
(A) 240
(B) 250
(C) 280
(D) 300
(E) 320
Rationale: 1/3 + 1/8 + 1/5 + 1/6 = (40+15+24+20)/120 = 99/120
Let x be the number of passengers on the ship.
42 = (21/120)x = 7x/40
x = 240
The answer is A.
Answer: (A) 240
Question: Exactly 36% of the numbers in set S are even multiples of 3. If 40% of the even integers in set S are not multiples of 3, what percent of the numbers in set S are not even integers?
(A) 76%
(B) 60%
(C) 50%
(D) 40%
(E) 24%
Rationale: Let S be the total number of elements in set S.
We know that 0.36*S is the number of even multiples of three.
Let N be the number of even numbers.
We know 0.40*N are even numbers not multiple of three. This also means, 0.60*N are even numbers that are multiples of three.
Therefore:
0.06*N = 0.36*S
N = (0.36/0.60)*S = (36/60)*S = (6/10)*S = 0.60*S = 60% of S
So even numbers are 60% of S. That means, 40% of S are not even integers. Answer = D
Answer: (D) 40%
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/29
(C) 5/23
(D) 5/24
(E) 5/26
Rationale: Number of ways of (selecting at least two couples among five people selected) = (5C2 * 6⁶C1)
As remaining person can be any one among three couples left.
Required probability = (5C2 * 6C1)/10C5
= (10 * 6)/252 = 5/21
Answer:A
Answer: (A) 5/21
Question: Billy and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: Billy always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Billy bids up first, and Bonnie follows. Billy bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?
(A) 464
(B) 46
(C) 90
(D) 466
(E) 4673
Rationale: Initial bid = p$
Billy = p+40
Bonnie = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus C is the correct answer.
Answer: (C) 90