mathewhe/aqua_rat huggingface dataset:
Question: S1 = 7 S2 = 10 ... Sn = 3n + 4 For the sequence above, in which any term n is defined as 3n + 4, what is the value of n for the first term in the sequence to exceed 50?
(A) 13
(B) 12
(C) 16
(D) 14
(E) 15
Rationale: term 16 = 3*16+4 = 52
Answer : C
Answer: (C) 16
Question: In a particular library there are 5 computer clusters open for public use. Each Computer Clusters has 40 Tablets. In the 1st week, 75 tablets are used, while 155 tablets are used in the second week, 30 in the third week & 140 in 4th week. Approximately what fraction of the library's computer facilities are in use per month?
(A) 1/3
(B) 1/4
(C) 1/2
(D) 2/3
(E) 2/5
Rationale: Total number of tablets = 40*5 = 200
Fraction of library's computer facilities used,
1st week = 75/200 = 3/8
2nd week = 155/200 = 31/40
3rd week = 30/200 = 3/20
4th week = 140/200 = 7/10
Fraction of library's computer facilities used per month
= (3/8+31/40+3/20+7/10)/4
=1/2
ANSWER:C
Answer: (C) 1/2
Question: If 4a = 16b and 6b = 13c, Find a:b:c?
(A) 52:13:6
(B) 13:7:52
(C) 7:13:52
(D) 7:13:54
(E) None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (6b = 13c ==> b/c = 13/6)
==> a:b = 16:4 and b:c = 13:6
a:b:c = 52:13:6
Answer: Option A
Answer: (A) 52:13:6
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 66 years
(C) 77 years
(D) 44 years
(E) 99 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years .Answer: A
Answer: (A) 20 years
Question: Palindromes are words or phrases that read the same in both directions, e.g. EYE Now consider the word LEVEL, such a word is known as palindromes. Find the maximum possible number of five letter palindromes.
(A) 17515
(B) 17566
(C) 17576
(D) 17655
(E) None
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets. Having chosen this, the second letter can be chosen in 26 ways. => The first two letters can be chosen in 26*26=676 ways Having chosen the first two letters, the third letter can be chosen in 26 ways. => All the three letters can be chosen in 676*26=17576 ways. It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer C
Answer: (C) 17576
Question: The sum of 77 consecutive integers is 7777. What is the greatest integer in the set?
(A) 139
(B) 141
(C) 143
(D) 145
(E) 147
Rationale: Let x be the first integer in the set. Then x+76 is the largest integer.
The sum is: x+(x+1)+(x+2)+...+(x+76)
= 77x + 76*77/2
= 77(x+38)
Then x+38=101
x=63
The largest integer in the set is 63+76=139
The answer is A.
Answer: (A) 139
Question: The sum of two numbers is 40 and their product is 400. What will be the sum of their reciprocals?
(A) 1/40
(B) 8/75
(C) 75/4
(D) 75/8
(E) 1/10
Rationale: (1/a)+(1/b)=(a+b)/ab=40/400=1/10
ANSWER:E
Answer: (E) 1/10
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 25 years. The present age of the husband is
(A) 40
(B) 30
(C) 45
(D) 55
(E) 65
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (25 * 2 + 5 * 2) years = 60 years.
Husband's present age = (90 - 60) years =30 years
Option B
Answer: (B) 30
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 297 cm
(B) 178 cm
(C) 800 cm
(D) 287 cm
(E) 976 cm
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer:C
Answer: (C) 800 cm
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 9 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 25
(C) 30
(D) 45
(E) 50
Rationale: Ans.(D)
Sol. Number of choices to go by ship = 9 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 9 x 5 = 45 ways
Answer: (D) 45
Question: By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(A) 116.68
(B) 116.11
(C) 116.19
(D) 116.66
(E) 116.1
Rationale: Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer: D
Answer: (D) 116.66
Question: In a game of 100 points, A can give B 20 points and C 25 points. then how many points can B give C in a game of 70?
(A) 4.38
(B) 6.38
(C) 7.38
(D) 8.38
(E) 9.38
Rationale: In a game of 100 points,A give B 20 points and c 25 points means B=80,C=75
In 80 points B give 5 since 80-75=5
In 70 points B gives=70*5/80=4.38
ANSWER:A
Answer: (A) 4.38
Question: Y is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in Y?
I. 9
II. 15
III. 27
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Ans: C
Y->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: (C) I and II only
Question: How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?
(A) 134
(B) 144
(C) 154
(D) 164
(E) 174
Rationale: divisible by 4 means last two digit should always div by 4.
unit place=(04,20,40,12,24,32,52)
_ _ _04
_ _ _ 20
_ _ _40
total no=4x3x2x3=72
_ _ _12
_ _ _24
_ _ _32
_ _ _52
total no=3x3x2x4=72
total n0 = 72+72=144
ANSWER:B
Answer: (B) 144
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) 10 min
(B) 15 min
(C) 24 min
(D) 12 min
(E) 8 min
Rationale: Explanation:
T = 9/45 * 60 = 12 min
D)
Answer: (D) 12 min
Question: If m, n, and o are positive numbers such that (m/(m+n))(10) + (n/(m+n))(20)=o and if m<n which of the following could be the value of o?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 36
Rationale: The answer is D. For any positive m and n, o is a number between 10 and 20. Since m < n, weight of 10 is inferior of weight of 20 -> o is > 15 -> 18 is the answer.
Answer: (D) 18
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 48km/h, what is the circumference of the tire?
(A) 2 meters
(B) 6 meters
(C) 5 meters
(D) 3 meters
(E) 7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 48,000 m : C is the circumference
C = 2 meters
correct answer A
Answer: (A) 2 meters
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 18 Kmph
(B) 17 Kmph
(C) 72 Kmph
(D) 18 Kmph
(E) 16 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: (C) 72 Kmph
Question: A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?
(A) 0.75
(B) 1
(C) 0.25
(D) 0.5
(E) 0.58
Rationale: radius of inner dartboard/overall radius of dartboard
((r/2)^2)/(r^2)=1/4=0.25
ANSWER:C
Answer: (C) 0.25
Question: If a man walks at a rate of 5kmph, he misses a train by 7minutes. However, if he walks at the rate of 6kmph, he reaches the station 5minutes before the arrival of the train. Find the distance covered by him to reach the station.
(A) 8
(B) 4
(C) 15
(D) 6
(E) 12
Rationale: Let the required distance x km
difference in the times taken at two speeds = 12min = 1/5 hr
(x/5)-(x/6) = 1/5
x = 6
the required distance is 6 km
Answer is D
Answer: (D) 6
Question: Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?
(A) 33
(B) 98
(C) 25
(D) 29
(E) 27
Rationale: Explanation:
Let Varun's age today = x years.
Then, Varun's age after 1 year = (x + 1) years.
Therefore x + 1 = 2 (x - 12) x + 1 = 2x - 24 x = 25
Answer: C) 25 years
Answer: (C) 25
Question: A sum of money becomes double itself in 6 years at simple interest. How many times will it become 10 years at the same rate?
(A) 2 1/3
(B) 3 1/3
(C) 2 1/4
(D) 3 1/4
(E) 4
Rationale: P ---- 2P ---- 6 years3 1/3 P ---- 10 years Answer: B
Answer: (B) 3 1/3
Question: Pipe A fills a tank in 12 minutes. Pipe B can fill the same tank 3 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
(A) 4 mins
(B) 6 mins
(C) 5 mins
(D) 3 mins
(E) 7 mins
Rationale: A's rate is 1/12 and B's rate is 1/4.
The combined rate is 1/12 + 1/4 = 1/3
The pipes will fill the tank in 3 minutes.
The answer is D.
Answer: (D) 3 mins
Question: Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/16
Rationale: Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).
Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.
Answer: D.
Answer: (D) 1/8
Question: Holly,Paul,Anne and Jim are rehearsing a dance routine. How many different ways can you arrange the 4 dancers in a line if Anne must be first or second
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Anne first: three others follow in any order; 3P3 = 3! ways = 6
Anne 2nd: three other positions assigned in 3!ways = 6 ways.
TOTAL: 12 possible arrangements
Answer B
Answer: (B) 12
Question: There are 25 students in a class. Find the numbers of ways in which a committee of 3 students is to be formed?
(A) 1250
(B) 1800
(C) 2300
(D) 3256
(E) 2863
Rationale: Required number of ways = 25C3 = 25*24*23 / 6 = 2300
Answer is C
Answer: (C) 2300
Question: Which of the following options represents an approximate value for the question mark (?) in the following equation? 65.321 + 22.4 × 3.2 + ? = 502.871
(A) 509.2
(B) 529.2
(C) 504.2
(D) 549.2
(E) 506.2
Rationale: 65.321 + 22.4 × 3.2 + ? = 502.871
or, ? = 502.871 – 65.321 + 22.4 × 3.2
? = 502.871 – 65.321 + 71.68
≈ 509.2
Answer A
Answer: (A) 509.2
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 12 more photos than Claire. How many photos has Claire taken?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Explanation:
L = R
L = 3C
R = C + 12
We can substitute R for L in the second equation: R = 3C. If R is equal to both 3C and C + 12, we can say 3C = C + 12, and solve for C.
3C = C + 12
2C = 12
C = 6
Answer : (A)
Answer: (A) 6
Question: A red ant is sitting on one side of a table (point X) and a black ant is sitting on the opposite side of the table (point Y). Now both of them decides to exchange their places and starts crawling. On the way, both of the ants meet and after that, it takes 20 seconds for the Red ant to move to point Y and it takes 5 seconds for the Black ant to reach point X.
Find out the total time taken by the Red and the Black ant to make the journey.
(A) 30 and 15 seconds
(B) 10 and 15 seconds
(C) 20 and 15 seconds
(D) 25 and 15 seconds
(E) 5 and 15 seconds
Rationale: Solution:
Let the speed of red ant be R.
Speed of Black ant be B.
Time at which they cross their paths be T.
Now we will apply the basic formula of distance
Distance = Speed * Time
The Red ant travels R * T distance before meeting and R * 20 after meeting.
The Black ant travels B * T distance before meeting and B * 5 after meeting.
Now as per the question,
The distance traveled by red ant before they both meet will be equal to the distance covered by black ant after they meet. We can say the same for the vice versa case as well.
Thus
R * T = B * 5 and B * T = R * 20
Using both the quations
T = 10
Thus the red ant will require 10 + 20 = 30 seconds to travel the distance.
And the black ant will take 10 + 5 = 15 seconds to travel the distance.
Answer A
Answer: (A) 30 and 15 seconds
Question: The sum of the ages of 5 children born at the intervals of 1 year each is 50 years. what is the age of the youngest child ?
(A) 22
(B) 8
(C) 10
(D) 99
(E) 38
Rationale: Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3, x+4.
We know that the sum of their ages is 50 .
so, x+(x+1)+(x+2)+(x+3)+(x+4) = 50
therefore The youngest child is 8 years old
Answer: B
Answer: (B) 8
Question: In the recent, religious conference in India, out of 1100 men, 900 women, 600 children present inside the building premises, 50% of the men, 40% of the women and 30% of the children were Christian. Find the percentage of people who were not Christian?
(A) 58.08%
(B) 59.23%
(C) 55.23%
(D) 63.25%
(E) 61.45%
Rationale: Solution: Number of Christian men present there = 1100*50/100 = 550
Christian women = 900*40/100 = 360
Christian children = 600*30/100 = 180.
Total member present in religious conference = 1100+900+600 = 2600
Total Christian = 550+360+180 = 1090
Hence, % of Christian present there = 1090*100/2600 = 41.92%
% of people who were not Christian = 100-41.92 = 58.08%.
Answer A
Answer: (A) 58.08%
Question: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 12% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
(A) 117%
(B) 120%
(C) 121%
(D) 133%
(E) 140%
Rationale: Since Michelle earns 12% interest compounded semiannually, then she earns 6% interest every 6 months.
Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 6%*5=30%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 30%, only answer choice D fits.
Answer: D
Answer: (D) 133%
Question: Machine–A produces 50% of the total output and Machine-B produces 75% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 250 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
(A) 0.06
(B) 0.006
(C) 0.07
(D) 0.08
(E) 0.09
Rationale: Suppose machine A produce 1000 units
total defective = 9
Machine B then produces=1500 units
total defective=6
probability=15/2500
=0.006
Answer : B
Answer: (B) 0.006
Question: A bag contains equal number of 25 paise, 50 paise and one rupee coins respectively. If the total value is Rs 105, how many types of each type are present?
(A) 75 coins
(B) 60 coins
(C) 30 coins
(D) 25 coins
(E) 15 coins
Rationale: EXPLANATION:
Bag consists of 25 paise, 50 paise and 1 rupee (100 paise) so the ratio becomes 25 : 50 : 100 or 1 : 2 : 4
Total value of 25 paise coins =(1 / 7 ) x 105 = 15
Total value of 50 paise coins = (2 / 7) x 105 = 30
Total value of 100 paise coins = (4 / 7) x 105 = 60
No. of 25 paise coins = 15 x 4 = 60 coins
No. of 50 paise coins = 30 x 2 = 60 coins
No. of 1 rupee coins = 60 x 1 = 60 coins
Therefore, there are 60 number of coins of each type.
ANSWER IS B
Answer: (B) 60 coins
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 40% on the cost price?
(A) 62.5
(B) 69.5
(C) 67.5
(D) 62.5
(E) 70
Rationale: CP = 47.50
SP = 47.50*(140/100) = 66.5
MP*(95/100) = 66.5
MP = 70
Answer:E
Answer: (E) 70
Question: A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
(A) Rs.60
(B) Rs.57
(C) Rs.55
(D) Rs.52
(E) Rs.53
Rationale: 2 *3(15 + 4) = 114
114 * 1/2 = Rs.57
ANSWER:B
Answer: (B) Rs.57
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
(A) 253 mph.
(B) 275 mph.
(C) 296 mph.
(D) 278 mph.
(E) 235 mph.
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253
Therefore, the speed of the plane in still air = 253 mph.
correct answer A
Answer: (A) 253 mph.
Question: A man can row upstream at 10kmph and downstream at 12kmph. Find man's rate in still water ?
(A) 11km/hr
(B) 15km/hr
(C) 10km/hr
(D) 20km/hr
(E) 7.5km/hr
Rationale: Rate in still water = 1/2 (10+12) = 11km/hr
Answer is A
Answer: (A) 11km/hr
Question: A lump of two metals weighing 18 g is worth Rs. 87 but if their weight is interchanged, it would be worth Rs. 78.60. If the price of one metal be Rs. 6.70 per gram, find the weight of the other metal in the mixture.
(A) 8g
(B) 12g
(C) 15g
(D) 18g
(E) None
Rationale: Solution: Cost of (18 g of 1st metal + 18 g of 2nd metal) = Rs. 165.60
Cost of (1 g of 1st metal + 1 g metal of 2nd metal) = Rs. 9.20
Hence cost of 1 g of 2nd metal,
= 9.20 - 6.70
= Rs. 2.5
Mean price = Rs. 87/18
quantity of 1st metal /quantity of 2nd metal = 14/6:56/30 = 5:4
Quantity of 2nd metal = (18*4)/9 = 8 g.
Answer: Option A
Answer: (A) 8g
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) 33
(B) 77
(C) 20
(D) 99
(E) 71
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: In a deck of 52 cards, how many ways are there to select 13 Spade and 13 heart cards without repetition?
(A) 169
(B) 170
(C) 171
(D) 172
(E) 173
Rationale: 13*13=169 ways
ANSWER:A
Answer: (A) 169
Question: A completes a work in 10 days and B complete the same work in 15 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 10 days
(D) 6 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 15/ 25 = 6 days.
D
Answer: (D) 6 days
Question: By selling 20 pencils for a rupee a man loses 60%. How many for a rupee should he sell in order to gain 60%?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 40% --- 20
160% --- ?
40/160 * 20 = 5
Answer: E
Answer: (E) 5
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.9 sec
(C) 3.8 sec
(D) 6.9 sec
(E) 2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 150/40
= 3.8 sec.
Answer: C
Answer: (C) 3.8 sec
Question: If x is a whole number, then x2(x2-1) is always divisible by:
(A) 12
(B) 24
(C) 36
(D) 48
(E) 26
Rationale: Putting x=2, we get 22(22-1)= 12.
So, x2(x2-1) is always divisible by 12.
ANSWER:A
Answer: (A) 12
Question: If each and every term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
To illustrate consider adding:
*7
*7
...
77
77
----
=350
So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
Answer: C.
Answer: (C) 40
Question: 6) A marketing firm determined that , of 260 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
(A) a) 15
(B) b) 20
(C) c) 30
(D) d) 40
(E) e) 45
Rationale: 180 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 180
=> 4x = 120
=> x = 30
Answer - C
Answer: (C) c) 30
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
(A) 480
(B) 520
(C) 360
(D) 280
(E) 420
Rationale: Let the total no of mangoes in the crate be X.
Then the no of bruised mango = 1/30 X
Let the no of unsaleable mangoes =3/4 (1/30 X) ==> 3/120 X = 12
1/40 X =12
X=480
so the answer is Option A) 480.
Answer: (A) 480
Question: Solve the quickfire maths brain teaser âˆš4% = ?
(A) 30%
(B) 40%
(C) 85%
(D) 19%
(E) 20%
Rationale: âˆš4%
=> âˆš4/âˆš100
=> 2/10
=> 20/100
=> 20%
E
Answer: (E) 20%
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,250 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: C for me.
Let managers comminsion rate be M.
m*5000+ 2*0.05*5000=2250
5000*m=1750
m=35/100=35%
Answer: (C) 35%
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 2:1
(B) 1:2
(C) 1:3
(D) 3:1
(E) 1:4
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9
=45×12:30×9
=3×12:2×9
=2:1
Correct Answer is 2:1
Answer: (A) 2:1
Question: In a public show 62 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
(A) 100
(B) 110
(C) 120
(D) 140
(E) 228
Rationale: 75 % of 600
= 62/100 × 600
= 372
Therefore, the number of vacant seats = 600 - 372 = 228.
Answer:E
Answer: (E) 228
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability Q that the new color will be one of theJaunecolors?
(A) 5/42
(B) 37/42
(C) 1/21
(D) 4/9
(E) 5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune Q= (40 + 34)/84 = 37/42
Answer: (B) 37/42