mathewhe/aqua_rat huggingface dataset:
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
(A) 35.2
(B) 36.1
(C) 36.5
(D) 39.1
(E) None
Rationale: Sol.
Therefore correct sum
= ( 36 × 50 + 48 – 23)
= 1825.
Therefore correct mean
= 1825 / 50
= 36.5.
Answer C
Answer: (C) 36.5
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 76 m
(B) 17 m
(C) 88 m
(D) 55 m
(E) 44 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer:B
Answer: (B) 17 m
Question: In seven given numbers,the average of first four numbers is 4 and that of last four numbers is also 4. if the average of these seven numbers is 3, the fourth number is?
(A) 3
(B) 4
(C) 7
(D) 11
(E) 12
Rationale: let 7 numbers are a,b,c,d,e,f,g.
given avg of first 4 nums are 4...i.e (a+b+c+d)/4=4
a+b+c+d=16
given avg of last 4 nums are also 4..i.e.(d+e+f+g)/4=4
d+e+f+g=16
e+f+g=16-d
given avg of 7 nums are 3....i.e (a+b+c+d+e+f+g)/7=3
a+b+c+d+e+f+g=21
16+16-d=21
d=32-21
d=11
ANSWER:D
Answer: (D) 11
Question: Which of the following fractions R has a decimal equivalent that is a terminating decimal?
(A) 10/189
(B) 15/196
(C) 16/225
(D) 25/144
(E) 39/128
Rationale: The fraction R will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: (E) 39/128
Question: A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
(A) 42
(B) 210
(C) 420
(D) 840
(E) 5,040
Rationale: we have 7 letters out of which 3 are of one kind, 2 are of another kind..
so total ways = 7!/3!2!=420
ans C
Answer: (C) 420
Question: How many times are the hands of a clock at right angle in a day?
(A) 44
(B) 21
(C) 22
(D) 41
(E) 40
Rationale: A
44
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer: (A) 44
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of A?
(A) 656
(B) 456
(C) 756
(D) 745
(E) 720
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of A = 6/13 * 1638 = Rs. 756
Answer: C
Answer: (C) 756
Question: Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
(A) 60000
(B) 65000
(C) 70000
(D) 75000
(E) None
Rationale: Solution:
Out of 26 alphabets two distinct letters can be chosen in 26P2 ways.
Coming to numbers part, there are 10 ways (any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10 ways to choose the second digit.
Hence, there are totally 10 *10 = 100 ways.
Combined with letters there are,
26P2 *100 = 65000 ways to choose vehicle numbers.
Answer: Option B
Answer: (B) 65000
Question: If a letter is picked randomly from the alphabet, what are the odds of it being in the first 10 letters or being a vowel (a, e, i, o, u, y)?
(A) 6/13
(B) 1/2
(C) 15/26
(D) 11/26
(E) 8/13
Rationale: P(10á´œV) = P(10) + P(V) - P(10âˆ©V), where 10 denotes the first ten letters, and V denotes a vowel.
P(10á´œV) = 10/26 + 6/26 - 3/26
= 1/2
Answer: B
Answer: (B) 1/2
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 31% ryegrass, what percent of the weight of the mixture is from mixture X?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: 31% is 6%-points above 25% and 9%-points below 40%.
Thus the ratio of mixture Y to mixture X is 3:2.
The percent of mixture X is 2/5 = 40%.
The answer is C.
Answer: (C) 40%
Question: A train covers a distance of 100km in 1 hour. If its speed is decreased by 30km/hr, the time taken by the car to cover the same distance will be?
(A) 1hr
(B) 1hr 25min
(C) 50min
(D) 1hr 30min
(E) 1hr 45min
Rationale: Speed = 100/1 = 100km/hr
New speed = 100-30 = 70 km/hr
Time taken = 100/70 = 1hr 25min
Answer is B
Answer: (B) 1hr 25min
Question: In a flower shop there were 5 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
(A) 12
(B) 3
(C) 8
(D) 10
(E) None of these
Rationale: Answer
Now required average
= old average x Multiplicand
= 5 x 2 = 10
Correct Option: D
Answer: (D) 10
Question: (A% of B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 2% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of B + B% of A =AB/100 + AB/100
= 2AB/100 = 2% of AB
Correct Option: C
Answer: (C) 2% of AB
Question: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 6 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.
(A) a) 75m50m
(B) b) 100m50m
(C) c) 50m45m
(D) d) 100/3 m200/3
(E) e) none of these
Rationale: A train running at 50 km/hr takes 9 seconds to pass a platform. Next, it takes 6 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
It's probably best to convert to meters so we can find the length of the platform.
Distance = 50000 meters/h * 9 seconds*(1/60*60)
Distance =(50000*18 / [3600] ) = 125m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is moving forward at a speed of 5km/h while the train is moving forward at a speed of 50km/h. Therefore, the train is moving past the man at a total speed of 45km/h.
distance = speed * time
distance = 45km/h * 12 seconds
distance (length of train) = 75 m
We know the length of the train is roughly 75m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-75 or roughly 50m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.
ANSWER: A) a) 75m50m
Answer: (A) a) 75m50m
Question: Ravi's salary was reduced by 25%. Percentage increase to be effected to bring salary to original level =
(A) 33.38 %
(B) 33.33 %
(C) 83.33 %
(D) 33.35 %
(E) 34.33 %
Rationale: Explanation:
Let the Salary be 100.
Salary was reduced by 25%. So present salary = 75.
Percentage has to be increased in order to get Original level = 2575×1002575×100 = 33.33 %
Answer: B
Answer: (B) 33.33 %
Question: If p and q are positive integers, and 3 is not a factor of q, then q may be which of the following?
(A) (p−1)·p·(p+1)
(B) (p−3)·(p−1)·(p+1)
(C) (p−2)·p·(p+2)
(D) (p−1)·p·(p+2)
(E) (p−3)·(p+1)·(p+2)
Rationale: Plugged in values :
let p=5
A. (p−1)·p·(p+1) --> divisible by 3
B. (p−3)·(p−1)·(p+1) --> divisible by 3
C. (p−2)·p·(p+2) --> divisible by 3
D. (p−1)·p·(p+2) --> not divisible. Hence the answer.
Answer: (D) (p−1)·p·(p+2)
Question: If 7 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 40:15:15
(B) 40:25:18
(C) 40:35:28
(D) 40:25:24
(E) 40:45:11
Rationale: 7A = 8B = 10 C
A:B:C = 1/7:1/8:1/10
= 40:35:28
Answer: C
Answer: (C) 40:35:28
Question: What least number must be added to 686, so that the sum is completely divisible by 5 ?
(A) 2
(B) 3
(C) 5
(D) 4
(E) 6
Rationale: If we divide 686 by 5 remainder is 1
5 - 1 =4
Answer : D
Answer: (D) 4
Question: Dividing by 3⁄6 and then multiplying by 5⁄6 is the same as dividing by what number?
(A) 31⁄5
(B) 16⁄5
(C) 20⁄9
(D) 9⁄20
(E) 5⁄3
Rationale: say X/3/6*5/6 = x*6/3*5/6 = x*5/3
E
Answer: (E) 5⁄3
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
(A) 25/216
(B) 50/216
(C) 25/72
(D) 25/36
(E) 5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 3, there are three ways:
A 3 on the first roll and non 3 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 3 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: (C) 25/72
Question: The cost to park a car in a certain parking garage is $9.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?
(A)  $1.09
(B)  $1.67
(C)  $2.25
(D)  $2.36
(E)  $2.50
Rationale: Total cost of parking for 9 hours = 9$ for the first 2 hours and then 1.75 for (9-2) hours = 9+7*1.75 = 21.25
Thus the AVERAGE parking price = 21.25/9 = 2.36 $
D is the correct answer.
Answer: (D)  $2.36
Question: A bag has 4 blue, 3 yellow and 2 green balls. The balls of the same color are identical. In how many ways can a child picks ball(s) out of the bag? He could even decide to pick ZERO balls.
(A) 60
(B) 1260
(C) 24
(D) 120
(E) 9
Rationale: With the blue ball there are 5 scenarios-->
0 blue ball being selected
1 blue ball being selected
2 blue ball being selected
3 blue ball being selected
4 blue ball being selected
And for each of these cases there is only one possibilty as they are identical.
So there are 5 ways to select the blue ball
Same is the case with 3 yellow (for which we have 4 possibilties) and 2 green balls(we have 3 possibilties)
so in total 5*4*3 = 60 possibilties..
ANS:A
Answer: (A) 60
Question: If it is true that x > -2 and x < 9, which of the following must be true?
(A) x > 2
(B) x < -9
(C) x < 2
(D) -9 < x < 2
(E) none of the above.
Rationale: the range is -2 < x < 9
A. x > 2 - no because x can be between -2 < x < 2
B. x < -9 - no because the values of x are always >-9
C. x < 2 - no because x can be between 2 < x < 9
D. -9 < x < 2 - no because x can be between 2 < x < 9
E. none of the above.
Answer: E
Answer: (E) none of the above.
Question: Roshan is 5 years younger than Raj and they have an age ratio 3:4 respectively. How old is Roshan?
(A) 10
(B) 15
(C) 18
(D) 24
(E) 25
Rationale: Let the age of Roshan be x.( x/x+5)=3/4
on cross multiplication and solving we get x=15
Answer: B
Answer: (B) 15
Question: If A, B and C together can finish a piece of work in 6 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 1
(B) 7
(C) 8
(D) 9
(E) 36
Rationale: C = 1/6 - 1/12 – 1/18 = 1/36 => 36 days'
Answer: E
Answer: (E) 36
Question: An archer is shooting arrows from various distances. She shoots at a target from 50 yards, 60 yards, and 70 yards. The probability that she hits within the bullseye from 50 yards is 3/4, the probability that she hits within the bullseye from 60 yards is 2/3, and the probability that she hits within the bullseye from 70 yards is 3/5. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
(A) 9/10
(B) 14/15
(C) 19/20
(D) 29/30
(E) 39/40
Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 50 yards)*(prob that she misses from 60 yards)*(prob that she misses from 70 yards)
Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5
Thus the probability that she misses all shots = (1/4)*(1/3)*(2/5) = 1/30
Thus the probability that she makes at least one shot = 1 - (1/30) = 29/30
D
Answer: (D) 29/30
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 2/25
(B) 7/14
(C) 9/3
(D) 1/45
(E) 18/35
Rationale: Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
E
Answer: (E) 18/35
Question: There are 10 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 10 points that contain the point A?
(A) 36
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Any 2 points out 9 points will create triangle with third point A, so the answer is 9C2=36.
Answer: A.
Answer: (A) 36
Question: Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
(A) 11/P + 6
(B) 11/P + 7
(C) 11/P + 2
(D) 11/P + 1
(E) 11/P + 8
Rationale: Let Ben’s age now be B
Anita’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B
Answer: A
Answer: (A) 11/P + 6
Question: If I walk at 4 km/h, I miss the bus by 10 minutes. If I walk at 5 km/h, I reach 5 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
(A) 5 km
(B) 4.5 km
(C) 5 1⁄4 km/h
(D) Cannot be determined
(E) None of these
Rationale: d = product of speed difference of time /difference of speed
d = 4×5/60[10−(−5)/5−4]
[Here, –ve sign indicates before the schedule time]
⇒ d = 5 km
Answer A
Answer: (A) 5 km
Question: If Yury has been writing programming code for 16 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
(A) 126(10^2)
(B) 126(10^3)
(C) 144(10^2)
(D) 1.26(10^7)
(E) .126(10^9)
Rationale: 5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
16 HOURS = 900 X 16 = 144(10^2)
ANSWER C
Answer: (C) 144(10^2)
Question: In your classes you counted 130 hands. How many students were at the class?
(A) 65
(B) 61
(C) 85
(D) 86
(E) 88
Rationale: Total number of hands = 130
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 130 by 2
130 ÷ 2 = 65
Therefore, there were 65 students at the class.
ANSWER IS A
Answer: (A) 65
Question: In how many ways can you sit 7 people on a bench if 3 of them must sit together?
(A) 720
(B) 2,160
(C) 2,400
(D) 4,320
(E) 40,320
Rationale: In such questions, always tie the person that have to sit together. So we have effectively 4+1=5 persons to arrange.
They can be arranged in 5! ways.
Now the 3 persons can themselves be arranged in 3! ways.
Total ways: 5!*3! = 720.
A is the answer.
Answer: (A) 720
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability E that the 2 apples selected will include the spoiled one?
(A) a. 1/5
(B) b. 3/10
(C) c. 2/5
(D) d. 1/2
(E) e. 3/5
Rationale: there can be two ways in which one can select a spoiled apple and a good apple.
1. you pick the spoiled one first and the good one later..
Prob of picking bad one = 1/5 (one bad apple)
Prob of picking a good one from the remaining 4 good apples (4/4 =1)
therefore the total prob for case 1 = i/5 * 1 = 1/5
Total prob E= porb1 + prob2 = 1/5+1/5 = 2/5.C
Answer: (C) c. 2/5
Question: The side of a square is increased by 25% then how much % does its area increases?
(A) 56.28
(B) 56.25
(C) 56.2
(D) 56.24
(E) 56.21
Rationale: a = 100 a2 = 10000
a = 125 a2 = 15625
----------------
10000 --------- 5625
100 -------? => 56.25 % Answer:B
Answer: (B) 56.25
Question: Find the total no. of distinct bike no.'s that can beformed using 2 letters followed by 2 no.'s. How many letters need to be distinct?
(A) 59
(B) 89
(C) 94
(D) 100
(E) 110
Rationale: Out of 26 alphabets two distinct letters can be chosen in \inline {\color{Black}26P_2{}} ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are \inline {\color{Black}6P_2{}} X 100 ways = 65000 ways to choose vehicle numbers.
D
Answer: (D) 100
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/28
(B) 2/25
(C) 2/21
(D) 2/08
(E) 2/18
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = 3C2/15C2 = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = 2C2/15C2 = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (3C1 * 2C1)/15C2 = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: (C) 2/21
Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
1/x + 1/(x + 6) = 1/4
x2 - 2x - 24 = 0
(x - 6)(x + 4) = 0 => x = 6.
Answer: C
Answer: (C) 6
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
(A) 1
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: (A) 1
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 60%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
(A) 23
(B) 18
(C) 11
(D) 3
(E) 0
Rationale: Answer:A
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 60%, we can set up the following equation:
60=15+22+x
x=23, choiceA.
Answer: (A) 23
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 6 km in stationary water
(A) 40 min
(B) 1hr
(C) 1hr 15 min
(D) 1hr 30 min
(E) 4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(6/4)=1 1/4=1hr 30 min
Answer(D)
Answer: (D) 1hr 30 min
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 6 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
(A) 10years
(B) 11years
(C) 12years
(D) 13years
(E) 14years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 6 + 16 * 9)]
= (240 - 228) = 12 years.
Answer:C
Answer: (C) 12years
Question: If p is the product of the integers from 1 to 35, inclusive, what is the greatest integer k for which 3^k is a factor of p?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: 35! has 3, 6, 9,....30, 33 as factors, which are 11 multiples of 3.
We need to add 4 more to these 11 because of 9, 18, and 27.
The greatest integer of k is 15.
The answer is C.
Answer: (C) 15
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/8 kmph
(B) 24 3/2 kmph
(C) 22 1/2 kmph
(D) 22 1/5 kmph
(E) 22 9/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer:C
Answer: (C) 22 1/2 kmph
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 2 kmph
(B) 2 kmph
(C) 8 kmph
(D) 9 kmph
(E) 1 kmph
Rationale: Explanation:
S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: Option C
Answer: (C) 8 kmph
Question: A pipe can fill a cistern in 55 minutes. Find the time in which 1/11 part of the cistern will be filled?
(A) 5min
(B) 2min
(C) 3min
(D) 1min
(E) 10min
Rationale: Full cistern filled in = 55 minutes
1/11 part filled in = 55*1/11 = 5minutes
Answer is A
Answer: (A) 5min
Question: Ravi, Ramu and Raja are three partners in business. If Ravi’s capital is equal to twice Ramu’s capital and Ramu’s capital is three times Raja’s capital, the ratio of the capitals of Ravi, Ramu, Raja is
(A) 2:1:3
(B) 1:2:6
(C) 6:3:1
(D) 1:3:6
(E) None of these
Rationale: Explanation:
Let Raja’s capital be Rs. X. Then,
Ramu’s capital = Rs 3x and A’s capital = Rs. 6x
Ravi : Ramu : Raja = 6x : 3x : x = 6 : 3 : 1
Answer: Option C
Answer: (C) 6:3:1
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 3 games?
(A) x + 3y/(n + 3)
(B) x + y/(n + 3)
(C) (x + 3y)/(n + 3)
(D) (nx + 3y)/(n + 3)
(E) (3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 3 games = (nx+3y)/(n+3)
Hence, correct answer will be (D)
Answer: (D) (nx + 3y)/(n + 3)
Question: How should a profit of Rs.500 be divided into two partners, if one of them invested Rs.6000 for 5 months and other invested Rs.5000 for 4 months? (in Rs.)
(A) 1000,5000
(B) 3000,2000
(C) 500,400
(D) 2000,3000
(E) 300,200
Rationale: ratio come as 3:2, pofit become as 300,200.
ANSWER:E
Answer: (E) 300,200
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 7?
(A) 180
(B) 196
(C) 286
(D) 324
(E) 288
Rationale: We have to find the total number of 3-digit odd numbers not having 7 as a digit.
Units digits will be among 1,3,5,9
Tenth digits will be among 0,1,2,3,4,6,5,8,9
Hundredth digits will be among 1,2,3,4,6,5,8,9
So total numbers = 4*9*8 =288
Answer : E
Answer: (E) 288
Question: There are two decks of 11 cards each. The cards in each deck are labeled with integers from 11 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
(A) 0.23
(B) 0.36
(C) 0.4
(D) 0.42
(E) 0.46
Rationale: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:
11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2
Combos that have a 2 and a 3 as factors (first + second card):
12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities
Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100
Probability = 42/100 = 0.46
Answer:E
Answer: (E) 0.46