divelab/Sys2Bench huggingface dataset:
Question: Sam ranked 9th from the top and 38th from the bottom in a class. How many students are there in the class ?
Options:
A)22
B)88
C)46
D)299
E)77
Rationale: Explanation:
Number of students in class = (8 + 1 + 37) = 46
Answer: C) 46
Answer: C
Question: A sum is invested for 3 years compounded at 5%, 10% and 20 % respectively. In three years, if the sum amounts to Rs. 1386, then find the sum.
Options:
A)Rs. 1500
B)Rs. 1000
C)Rs. 1200
D)Rs. 1400
E)Rs. 1600
Rationale: Explanation:
1386 = P(1+5/100)(1+10/100)(1+20/100)
1386 = P(21/20)(11/10)(6/5)
P = (1386 × 20 × 10 × 5)/(21 × 11 × 6) = (66 × 20 × 10 × 5)/(11 × 6 = 20 × 10 × 5) = Rs. 1000
i.e., the sum is Rs.1000
Answer: Option B
Answer: B
Question: If $935 are divided between worker A and worker B in the ratio 5:12,what is the share that worker B will get?
Options:
A)62.15%
B)64.26%
C)66.37%
D)68.48%
E)70.59%
Rationale: Worker B will get 12/17 = 70.59%
The answer is E.
Answer: E
Question: The distance between West-Town to East-Town is 16 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
Options:
A)3.
B)7.
C)10.
D)12.
E)16.
Rationale: Time taken by the birds to meet = 16/(5 + 1) = 4 mins
Distance traveled by the bird traveling from West-Town = 4 * 4= 16
Answer: E
Answer: E
Question: At what rate percent of simple interest will a sum of money double itself in 22 years?
Options:
A)6.54 %
B)4.54 %
C)8 .2 %
D)4.94 %
E)5.54 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 22)
= 100/22 = 4.54 %
ANSWER:B
Answer: B
Question: A cylindrical barrel is filled with Kerosene at a rate of 33 cubic meters per hour, the level of kerosene in the barrel rises at a rate of 0.11 meters per hour. Which of the following best approximates the radius of the barrel in meters?
Options:
A)√105/11
B)√102/11
C)12
D)52
E)10
Rationale: Here's my re-worked solution:
volume = 33 = pi (r^2)(0.11)
33 = 22/7 (11/10)(r^2)
r = sqrt(105/11)
Ans: A
Answer: A
Question: Ten men and ten women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Options:
A)5!*6!
B)6!*6!
C)5!*7!
D)9!*10!
E)10!*12!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 10 men in a circle can be arranged in (10-1)! ways and if we place 10 women in empty slots between them then no two women will be together. The # of arrangement of these 10 women will be 10! and not 9! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 9!*10!.
D
Answer: D
Question: 45 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:
Options:
A)20 cm
B)25 cm
C)35 cm
D)50 cm
E)None of these
Rationale: Explanation:
Total volume of water displaced =(4 x 45) m3 = 180 m3
Rise in water level = 180/40Ã—20= 0.225m = 22.5cm
Answer: E
Answer: E
Question: Pat, Kate, and Mark charged a total of 153 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
Options:
A)85
B)36
C)72
D)90
E)108
Rationale: 85
all u do is do
2:1:6=>2x+x+6x=153=>x= 17
34:17:102
102-17=85
Answer A
Answer: A
Question: If 12 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 15
III. 25
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Let x be the length of the third side.
15-12 < x < 15+12
3 < x < 27
The answer is E.
Answer: E
Question: Find the odd man out. 9,18,23,36,99
Options:
A)9
B)18
C)23
D)36
E)99
Rationale: All except 23 are multiples of 9
Answer is C
Answer: C
Question: A circle in the coordinate plane passes through points (-3, -2) and (1, 3). What is the smallest possible area of that circle?
Options:
A)10.5π
B)26π
C)262√π
D)52π
E)64π
Rationale: The distance between the two points is sqrt(41).
radius = sqrt(41)/2
Area= pi*(sqrt(41)/2)^2
A. 10.5π
Answer: A
Question: A shop sells chocolates at re.1 each. U can exchange 3 wrappers for 1 chocolate. If u have Rs.100, how many chocolates can you totally get?
Options:
A)147
B)148
C)149
D)150
E)141
Rationale: 100 chocolates---- 99+1 wrappers
exchanging 99 wrappers;we are left with
33 chocolates+1 wrapper----- 33+1 wrapper
exchanging 33 wrappers,we are left with
11 chocolates +1 wrapper------12 wrappers
exchanging 12 wrappers,we are left with
4 chocolates------3+1 wrappers
exchanging 3 wrappers,we get
1 chocolate
at last we are left wid two wrappers that cannot be exchanged
therfore: no.of chocolates= 100+33+11+4+1=149
ANSWER:C
Answer: C
Question: A and B complete a work in 9 days. A alone can do it in 18 days. If both together can do the work in how many days?
Options:
A)6 days
B)8 days
C)5 days
D)7 days
E)15 days
Rationale: 1/9 + 1/18 = 1/6
6/1 = 6 days
Answer:A
Answer: A
Question: If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
Options:
A)5:3
B)3:5
C)4:5
D)5:4
E)6:4
Rationale: Selling price = 250
profit = 25%
cost price = 250*100/125 = 200
req ratio = 200:250 = 4:5
ANSWER C
Answer: C
Question: Calculate the % profit or loss, if the cost price of 9 apples is equal to the selling price of 11 apples.
Options:
A)29.1%
B)7.2%
C)14.2%
D)12.2%
E)22.2%
Rationale: Let the cost price of 1 apple be Rs 1
Cost of 9 apples = Rs 9
Selling price of 9 apples = 11
Gain/loss = 11 - 9 = 2
%=2/9âˆ—100= 22.2
Answer: E
Answer: E
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?
Options:
A)11 hours
B)76 hours
C)18 hours
D)12 hours
E)16 hours
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.
Answer: B
Answer: B
Question: In a question on division with zero remainder, a candidate took 22 as divisor instead of 11. The quotient obtained by him was 35. The correct quotient is?
Options:
A)A)70
B)B)24
C)C)28
D)D)29
E)E)30
Rationale: Number = (35 * 22) = 770
Correct quotient = 770/11 = 70
A)
Answer: A
Question: A larger cube has 125 cubic inch as a volume and in the cube there are 125 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 125 smaller cubes and the surface area of the larger cube, in square inch?
Options:
A)54
B)600
C)81
D)108
E)120
Rationale: Volume of larger cube = 125 = 5^3
Side of larger cube = 5
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 5^2 = 150
Surface area of 27 smaller cubes = 125 * 6 * 1 = 750
Difference = 750 - 150 = 600
Answer: B
Answer: B
Question: Of the 130 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 30
Answer: Option B
Answer: B
Question: Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's.
What is B's share
Options:
A)Rs 10
B)Rs 20
C)Rs 24
D)Rs 28
E)None of these
Rationale: Explanation:
Let C = x. Then A = (x�20) and B = (x�40).
x + x - 20 + x - 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B's share = Rs. 120*(1/6) = Rs. 20
Answer: B
Answer: B
Question: What is the sum of odd integers from 35 to 75, inclusive?
Options:
A)1,560
B)1,500
C)1,240
D)1,155
E)1,100
Rationale: Number of odd integers = (75-35)/2 + 1
= 40/2 + 1
= 21
Sum of odd integers = (35+75)/2 * 21
= 1155
Answer D
Answer: D
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Options:
A)1:5
B)1:8
C)1:2
D)1:1
E)1:6
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1:1
Answer: D
Answer: D
Question: In Albert house,One tap, working alone at its maximum constant rate, can fill a certain tank in 250 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 254 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to
Options:
A)126 seconds
B)150 seconds
C)177 seconds
D)200 seconds
E)250 seconds
Rationale: Tap 1 : 250 secs
Tap 2 : 254 secs
Considering the average of these 2 taps : 252 secs.
So 1 tap can fill the tank in 252 secs, so 2 taps can fill the tank in 252/2 = 126 secs.
Closest answer is A.
Answer: A
Question: X, Y and Z, each working alone can complete a job in 2, 4 and 6 days respectively. If all three of them work together to complete a job and earn $2000, what will be Z's share of the earnings?
Options:
A)$1080.90
B)$1000.90
C)$1070.90
D)$1050.90
E)$1090.90
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of Z is 1/6 (or 2/12)
1 day work of the combined workforce is (1/2 + 1/4 + 1/6) = 11/12
Z's contribution is 2/9 of the combined effort
Translating effort to $ = 6/11 * 2000 = $1090.90
hence:E
Answer: E
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.20000 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?
Options:
A)1978
B)2707
C)7728
D)4800
E)7291
Rationale: 20:25 => 4:5
9600*10/100 = 960
9600 - 960 = 8640
8640*4/9 = 3840 + 960
= 4800
Answer: D
Answer: D
Question: If 5x + y = 6 and 2y − 4x = 7, then what is the value of x + 3y?
Options:
A)1/7
B)13
C)15
D)52/7
E)60/7
Rationale: 5x + y = 6
−4x + 2y = 7
Adding both the equations --> x + 3y = 13
Answer: B
Answer: B
Question: The ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B?
Options:
A)5
B)3
C)6
D)7
E)8
Rationale: The ratio of A and b is 5x and 3x years.
After 2 years, their ratio will be 3 and 2.
(i.e) (5x+2)/(3x+2)=3/2
10x+4=9x+6
x=2
B's age=3x=3(2)=6 years
Answer is option C
Answer: C
Question: A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
Options:
A)32 minutes
B)28 minutes
C)29 minutes
D)30 minutes
E)31 minutes
Rationale: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 /150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8 * 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
We can also find the final answer as follows
4.5 x 8 = 32 minutes
correct answer A
Answer: A
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.
Options:
A)20/31
B)20/63
C)5/31
D)6/31
E)26/31
Rationale: Required probability = (⁵C₃ . ⁴C₁)/⁹C₄ = (10 * 4)/126 = 20/63
ANSWER:B
Answer: B
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Options:
A)2 8 ½ kmph
B)8 2 ½ kmph
C)2 9 ½ kmph
D)2 2 ½ kmph
E)3 2 ½ kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Answer: D
Question: How many integers between 324,700 and 418,600 have tens digit 1 and units digit 3?
Options:
A)652
B)827
C)939
D)1045
E)1136
Rationale: The integers are:
324,713
324,813
etc...
418,513
The number of integers is 4186 - 3247 = 939
The answer is C.
Answer: C
Question: Suppose you flip a fair coin 7 times. What is the probability that, in 7 flips, you get at least one head?
Options:
A)57/58
B)23/28
C)127/129
D)127/128
E)64/65
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^5
probability of flipping at least 1 head = 1 - (1/2)^7 = 127/128
Answer : D
Answer: D
Question: Find the odd man out. 12, 21, 32, 45, 60, 77, 95
Options:
A)95
B)45
C)32
D)21
E)77
Rationale: Explanation :
12 + 9 = 21
21 + 11 = 32
32 + 13 = 45
45 + 15 = 60
60 + 17 = 77
77 + 19 = 96
Hence, 95 is wrong. 96 should have come in place of 95
Answer : Option A
Answer: A
Question: What is the 56743 rd term in the series 1234567891011121314…….?
Options:
A)1
B)6
C)5
D)4
E)7
Rationale: Explanation:
1 to 9 = 9 no.s 1 digit each no.
9 to 99 = 90 no.s 2 digit each,Total digit = 90 × 2 = 180 terms
99 to 999 = 900 no.s 3 digit each,total digit = 900 × 3 = 2700
999 to 9999 = 9000 no.s 4 digit each,total digit = 9000 × 4 = 36,000
Till Now 999,we have = 9 + 180 + 2700 = 2889 digits
Upto 9999 we have = 2889 + 36000 = 38889 digits
56743 – 38889 = 17854
After 9999 each no. has 5 digit
So 17584/5= 3570 with remainder 4.
3570th no after 9999 =9999+3570=13569
Next term=13570.
4th digit =7 so answer=7
Answer: E
Answer: E
Question: Two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?
Options:
A)85/852
B)45/69
C)18/456
D)13/102
E)23/125
Rationale: let S be the sample space then
n(S)=52C2=(52*51)/(2*1)=1326
let E be the event of getting 1 spade kings and 1 heart
let n(E)=number of ways of chossing 1 spade out of 13 and 1 heart out of 13=(13C1*13C1)=13*13=169
P(E)=n(E)/n(S)
=169/1326
=13/102 Answer(D)
Answer: D
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Options:
A)x
B)x/2
C)2x/3
D)3x/2
E)2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 10 = x/20 hours = 3x minutes
Jessica needs to wait 3x - x = 2x minutes.
The answer is E.
Answer: E
Question: A fruit seller had some oranges. He sells 40% oranges and still has 540 oranges. How many oranges he had originally?
Options:
A)700
B)900
C)720
D)730
E)740
Rationale: 60% of oranges = 540
100% of oranges =(540×100)/6=900
total oranges = 900
ANSWER : B
Answer: B
Question: Count the two-digit whole numbers which yield a remainder of 5 when divided by 10 and also yield a remainder of 0 when divided by 3?
Options:
A)Two
B)Five
C)Three
D)One
E)Six
Rationale: Answer = C) Three
Two digit Numbers giving remainder 5 when divided by 10 = 15, 25, 35, 45, 55, 65, 75, 85, 95
The numbers giving remainder 0 when divided by 3 = 15, 45, 75 = 3
Answer: C
Question: Find the amount on Rs.7000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Options:
A)5568
B)6369
C)5460
D)7644
E)6734
Rationale: 7000 * 104/100 * 105/100
=> 7644
Answer:D
Answer: D
Question: A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
Options:
A)2,250 meters / minute
B)1,250 meters / minute
C)5,250 meters / minute
D)6,250 meters / minute
E)4,250 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 * 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer B
Answer: B
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Options:
A)1000
B)1067
C)1977
D)1056
E)1097
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: A
Answer: A
Question: If two typists can type two pages in two minutes, how many typists will it take to type 49 pages in seven minutes?
Options:
A)3
B)4
C)6
D)12
E)14
Rationale: In 2 minutes 2 typists type 2 pages which means that in 7 minutes they will type 7 pages but to type 49 pages (7 times) we need 7 times more typists i.e. 2 x 7 = 14 typists.
E
Answer: E
Question: If a < 0, c > 0, and b > 5, which of the following is true?
I. a * b * c > 0
II. a * b * (-c) < 0
III. a^2 * b * c > 0
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: I. Not true, example: a = -1, b = 6, and c = 1, so a * b * c= -6
II. Not true, a and (-c) are both negative and b is positive so the product will be positive
III. True, a^2 is positive and so are b and c so the product is positive
C
Answer: C
Question: In a school with 632 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
Options:
A)150
B)200
C)250
D)158
E)None
Rationale: Sol.
Let the number of grils be x.
Then, number of boys = (632 - x).
Then, (11 3/4 × 632)
⇔ 11x + 12(632 - x) ⇔ x = 7584 - 7426 ⇔ 158.
Answer D
Answer: D
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 10 cm, and the point of contact is 12 cm above the ground, what is the radius of the other ball (in centimeters)?
Options:
A)14
B)15
C)16
D)18
E)20
Rationale: A straight line will join the two centers and the point of contact, thus making similar triangles.
2/10 = (r-12)/r
2r = 10r - 120
r = 15
The answer is B.
Answer: B
Question: In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
Options:
A)28000
B)30000 candidates
C)32000
D)33000
E)None of these
Rationale: Explanation :
Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)
Hence total eligible candidates = 95x/100
Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)
Hence Total eligible candidates belonged to other categories
= total eligible candidates × (15/100) = (95x/100) × (15/100)
= (95x × 15)/(100 × 100)
Given that Total eligible candidates belonged to other categories = 4275
⇒ (95x × 15)/(100 × 100) = 4275
⇒ (19x × 15)/(100 × 100) = 855
⇒ (19x × 3)/(100 × 100) = 171
⇒ (x × 3)/(100 × 100) = 9
⇒ x/(100 × 100) = 3
⇒ x = 3 × 100 × 100 = 30000
Answer : Option B
Answer: B
Question: If a = 105 and a^3 = 21 × 25 × 45 × q, what is the value of q?
Options:
A)35
B)42
C)45
D)49
E)54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × q
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x q
=> a^3 = 3^3 * 5^3 * 7 x q
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x q
q = 7^2 = 49
Answer D
Answer: D
Question: The number b yields a remainder p when divided by 15 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of b ?
Options:
A)45
B)52
C)66
D)80
E)96
Rationale: I solved this question in the following way:
Q<7 so Q can be from 0 to 6 and P<15 so P can be from 0 to 14, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 14.
b=15k + P or b= 15k + 7 to 14 and look at the answer as, place different values for k, B will give 52 which is 15*3 + 7, the other answers are out of the range
Answer: B
Question: A trader bought a car at 20% discount on its original price. He sold it at a 55% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)17%
B)24%
C)12%
D)82%
E)16%
Rationale: Original price = 100
CP = 80
S = 80*(155/100) = 124
100 - 124 = 24%
Answer:B
Answer: B
Question: The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 45 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
Options:
A)17
B)18
C)22
D)26
E)36
Rationale: The total sum of the numbers should be increased by 20.
Then the average will increase by 20/10 = 2.
The correct average is 18.
The answer is B.
Answer: B
Question: A fill pipe can fill 1/2 of cistern in 10 minutes. In how many minutes, it can fill 1/2 of the cistern?
Options:
A)1 min
B)4 min
C)6 min
D)10 min
E)25min
Rationale: Required time = 10*2*1/2 = 10 minutes
Answer is D
Answer: D
Question: 20 carrots on a scale weigh 3.64 kg. When 4 carrots are removed from the scale, the average weight of the 16 carrots is 180 grams. What is the average weight (in grams) of the 4 carrots which were removed?
Options:
A)160
B)170
C)180
D)190
E)200
Rationale: 16*180=2880.
The other 4 carrots weigh a total of 760 grams.
The average weight is 760/4 = 190 grams.
The answer is D.
Answer: D
Question: For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $5. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day?
Options:
A)$24960
B)$25920
C)$28080
D)$28350
E)$29160
Rationale: From 9:00 in the morning to 5:55 in the afternoon, inclusive there are 9*12=108 five-minute intervals, thus total of 108*30 tickets were sold.
Say x student and 3x regular tickets were sold, then x+3x=108*30 --> x=27*30 and 3x=3*(27*30)=27*90.
Therefore, the total revenue from ticket sales that day was 27*30*5+27*90*10=$28,350.
Answer: D.
Answer: D
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
Options:
A)150
B)152
C)278
D)267
E)261
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer:A
Answer: A
Question: If a - b =4 and
a2+b2=52
, find the value of ab.
Options:
A)8
B)26
C)18
D)42
E)36
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2ab=52âˆ’16=36
=>ab=18
Option C
Answer: C
Question: The Simplistic language has only 2 unique values and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
Options:
A)9
B)12
C)36
D)72
E)108
Rationale: The nouns have fixed structure C-V-C-V-C. Now, each C can take 3 values (let's say X, Y or Z) and each V can take 2 values (let's say A or E), so there will be 3*2*3*2*3=108 nouns possible.
Answer: E.
Answer: E