divelab/Sys2Bench huggingface dataset:
Question: Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 20000 at the end of the year, what should be the share of Narendra?
Options:
A)A)Rs.7000
B)B)Rs.8000
C)C)Rs.8500
D)D)Rs.8600
E)E)Rs.16000
Rationale: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.
:. Narendra’s share on profit of Rs.20000 = 20000 × 4/5 = Rs.16000.
E)
Answer: E
Question: A train 120 m long crosses a platform 120 m long in 6 sec; find the speed of the train?
Options:
A)144 kmph
B)58 kmph
C)54 kmph
D)94 kmph
E)59 kmph
Rationale: D = 120 + 120 = 240
T = 6
S = 240/6 * 18/5 = 144 kmph
Answer: A
Answer: A
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,15
Options:
A)9700
B)9710
C)9720
D)9730
E)None of these
Rationale: Explanation:
LCM of 27-18-12-15 is 540.
After dividing 9999 by 540 we get 279 remainder.
So answer will be 9999-279 = 9720
Answer: Option C
Answer: C
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
Options:
A)three times as much
B)twice as much
C)a third as much
D)half as much
E)the same
Rationale: et speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: B
Question: The contents of a certain box consist of 24 oranges and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be oranges?
Options:
A) 24
B) 26
C) 30
D) 46
E) 50
Rationale: oranges = (oranges + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: B
Question: A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32
B)28
C)29
D)44
E)21
Rationale: S = (250 + 300)/45 = 550/45 * 18/5 =44
Answer: D
Answer: D
Question: A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled?
Options:
A)4x
B)3x
C)1x
D)2x
E)6x
Rationale: If the parameter before it was tripled 3x, one of the sides must have been 3x/3. This reduces to 1x. Answer option C.
Answer: C
Question: If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
Options:
A)22
B)24
C)26
D)28
E)None of them
Rationale: Let 3 engines of former type consume 1 unit in 1 hour.
Then, 4 engines of latter type consume 1 unit in 1 hour.
Therefore 1 engine of former type consumes(1/3) unit in 1 hour.
1 engine of latter type consumes(1/4) unit in 1 hour.
Let the required consumption of coal be x units.
Less engines, Less coal consumed (direct proportion)
More working hours, More coal consumed (direct proportion)
Less rate of consumption, Less coal consumed(direct prportion)
Number of engines 9: 8
Working hours	8 : 13 } :: 24 : x
Rate of consumption (1/3):(1/4)
[ 9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) = 24x = 624 = x = 26.
Hence, the required consumption of coal = 26 metric tonnes.
Answer is C.
Answer: C
Question: An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing?
Options:
A)Rs.500000
B)Rs.50000
C)Rs.5000
D)Rs.15000
E)Rs.6000
Rationale: let x amount he has then 20% of 25% of 30% of x=750
so x=50000
ANSWER:B
Answer: B
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
Options:
A)117/2Â°
B)64Â°
C)135/2Â°
D)145/2Â°
E)155/2Â°
Rationale: Apply the formula:
30h-11/2m=Angle
30*5-11/2*15
150-165/2=135/2
ANSWER:C
Answer: C
Question: A man walks a certain distance and rides back in 6 1⁄4h. He can walk both ways in 7 3⁄4h. How long it would take to ride both ways ?
Options:
A)5 hours
B)4 1⁄2 hours
C)4 3⁄4 hours
D)6 hours
E)None of these
Rationale: We know that, the relation in time taken with two different modes of transport is
twalk both + tride both = 2 (twalk + tride)
31⁄4 + tride both = 2 × 25⁄4
⇒ tride both = 25⁄2 - 31⁄4 = 19⁄4 = 43⁄4 hours
Answer C
Answer: C
Question: It is only in the second option we find the sentence A in continuation with the opening sentence D. Sentence A alone explains, why the fear has such enormous effect on the human beings.
Options:
A)28
B)99
C)728
D)27
E)271
Rationale: Answer:B
Answer: B
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
Options:
A)266
B)500
C)287
D)26
E)281
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer: B
Answer: B
Question: If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 1/(2x^2 − x)
III. 1/(x + 1)
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 20
x=3-> 3+9 = 12 ...decreased
ST2:x= 4-> 2*16-4 = 1/28
x=3->2*9-3 = 1/15
increased
St3: x=4-> 1/4 = .25
x=3->1/3 = .33
Ans: A
Answer: A
Question: the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: For the 5 minutes the cyclist continues to overtake the hiker, she is going at 21 miles per hour faster than the hiker.
Once the cyclist stops, the hiker is going at 7 miles per hour while the cyclist is at rest
So the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 21/7 * 5 or 15 minutes
Answer is (B)
Answer: B
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 12 meters, and the interior of tank B has a height of 12 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Options:
A)80%
B)90%
C)100%
D)110%
E)120%
Rationale: The radius of tank A is 12/(2*pi).
The capacity of tank A is 10*pi*144 / (4*pi^2) = 360 / (pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 12*pi*100 / (4*pi^2) = 300 / (pi)
Tank A / Tank B = 360/300 = 12/10 = 120%
The answer is E.
Answer: E
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)186 sq.units
C)176 sq.units
D)865 sq.units
E)143 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square
= √1225 = 35 units
The radius of the circle
= side of the square
= 35 units Length of the rectangle
= 2/5 * 35
= 14 units
Given that breadth
= 10 units
Area of the rectangle
= lb = 14 * 10
= 140 sq.units
Answer:A
Answer: A
Question: Which of the following is a prime number ?
Options:
A)33
B)81
C)93
D)97
E)95
Rationale: Explanation:
Clearly, 97 is a prime number.
ANSWER IS D
Answer: D
Question: A man buys an article for $10. and sells it for $30. Find the gain percent?
Options:
A)25%
B)50%
C)20%
D)150%
E)300%
Rationale: C.P. = $10
S.P. = $30
Gain = $20
Gain% = 20/10 *100 = 300%
Answer is E
Answer: E
Question: The average age of 19 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
Options:
A)9
B)71
C)85
D)92
E)90
Rationale: Age of the 15th student = 19*15 - (14*5+16*9) = 285-214 = 71 years
Answer is B
Answer: B
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
Options:
A)208 km
B)637 km
C)342 km
D)300 kilometre
E)543 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11
=> x/60 + x/50 = 11 => (5x + 6x)/300
= 11 => x = 300 km
Answer:D
Answer: D
Question: What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?
Options:
A)10/216
B)12/216
C)21/216
D)23/216
E)25/216
Rationale: Sum of 12 can be achieved in following ways
6,5,1---Total cases = 3! = 6
6,4,2---Total cases = 3!= 6
6,3,3---Total cases = 3!/2! = 3
5,5,2---Total cases = 3!/2! = 3
5,4,3---Total cases = 3! = 6
4,4,4---Total cases = 3!/3! = 1
Total cases = 25
Probability = 25 * (1/6 * 1/6 * 1/6) = 25/216
ANSWER:E
Answer: E
Question: A sum of Rs.7000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)A)282
B)B)4550
C)C)8383
D)D)8383
E)E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 7000[1 + 10/100][1 + 20/100][1 + 25/100]
A = 7000 * 1.65
A = Rs.11550
So the interest = 11550 - 7000 = Rs.4550
Answer: B
Answer: B
Question: In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)800
B)820
C)880
D)960
E)840 eight hundred forty
Rationale: three letters can be arranged in 3! ways.
only one combination AEI is required.
7 letters can be arranged in 7! ways.
thus 7!/ 3! * 1 = 840.
Answer: E
Question: There are 3 numbers A, B and C. If A:B = 3/5, B:C = 5/4, C:D = 4/8, then A:D will be?
Options:
A)1 : 2
B)3 : 5
C)5 : 7
D)6 : 11
E)3:8
Rationale: Sol. A : B = 3 : 5, B : C = 5 : 4, C : D = 4 : 8
∴A∶B∶C∶D= 3 : 5:4 : 8
Thus, A : D = 3 : 8
E
Answer: E
Question: If y exceeds x by 28%, then x is less than y by?
Options:
A)16 2/8%
B)16 8/3%
C)21 7/8%
D)76 2/3%
E)17 2/3%
Rationale: X=100	y=128
128------28
100-------? => 21 7/8%
Answer:C
Answer: C
Question: If 14 men do a work in 80 days, in how many days will 20 men do it?
Options:
A)18 days
B)38 days
C)42 days
D)48 days
E)56 days
Rationale: 14 * 80 = 20 * x
x = 56 days
ANSWER:E
Answer: E
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.1446 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Options:
A)32200
B)41897
C)58799
D)60000
E)62782
Rationale: P(11/10)^4 - P(6/5)^2 = 1446
P = 60000
Answer: D
Answer: D
Question: A soccer team played 160 games and won 65 percent of them. How many games did it win?
Options:
A)84
B)94
C)104
D)114
E)124
Rationale: 65% of 160 =x
0.65*160 = x
104=x
answer :C
Answer: C
Question: If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ?
Options:
A)1/2
B)3/5
C)5/7
D)9/11
E)3/4
Rationale: Let the original fraction be x/y
Then, 115% of x/92% of y = 15/16
115x/92y = 15/16
x/y = 3/4
Answer is E
Answer: E
Question: A driver goes on a trip of 50 kilometers, the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour. What is the average speed of the entire trip in kilometers per hour?
Options:
A)38
B)40
C)44
D)45
E)48
Rationale: The time for the first part of the trip was 25/66 hours.
The time for the second part of the trip was 25/33 hours.
The total time fro the trip was 25/66 + 25/33 = 75/66 = 25/22 hours.
The average speed for the trip was 50 / (25/22) = 44 kph
The answer is C.
Answer: C
Question: The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?
Options:
A)16
B)18
C)13
D)20
E)22
Rationale: We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r.
The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s. Since s must be greater than r, r can be 10+3 = 13 and s can be 10+4 = 14.
So r is 13.
Answer (C)
Answer: C
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number R?
Options:
A)a. 2^96 + 1
B)b. 2^16 - 1
C)c. 2^16 + 1
D)d. 7 * 2^33
E)e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of R=(a+b) is a factor of (a³ + b³)
Henca A
Answer: A
Question: If the product of 10 integers is negative, at most how many of the integers can be negative?
Options:
A)2
B)3
C)4
D)9
E)6
Rationale: The product of 10 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 9
Correct Option : D
Answer: D
Question: A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
Options:
A)20 hours
B)19 hours
C)90 hours
D)80 hours
E)None of these
Rationale: Explanation:
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour
=1/9−1/10=1/90
We used subtraction as it is getting empty.
So total time to empty the cistern is 90 hours
Option C
Answer: C
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?
Options:
A)111.12 m
B)111.19 m
C)111.82 m
D)113.12 m
E)211.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: A
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 95 m is?
Options:
A)286 m
B)899 m
C)200 m
D)205 m
E)187 m
Rationale: 2(l + 95) = 600 => l
= 205 m
Answer: D
Answer: D
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,800 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
Options:
A)38,000
B)40,000
C)42,500
D)45,800
E)48,500
Rationale: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.8
So, answer is D.
Answer: D
Question: FOG + FOG + FOG + FOG = 1464.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: given,FOG + FOG + FOG + FOG = 1464
4(FOG)=1464
=>FOG=366
Face value of F is:3
Face value of O is:6
Face value of G is:6
so F+O+G=3+6+6=15
ANSWER:E
Answer: E
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 64) square inches. What is the perimeter of the photograph, in inches?
Options:
A)16
B)24
C)32
D)40
E)48
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+6)(y+6)=M and so (2) xy + 6x + 6y + 36 = M+64
Let's subtract equation (1) from equation (2).
4x + 4y + 32 = 64
2x + 2y = 16, which is the perimeter of the photograph.
The answer is A.
Answer: A
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)65 sec
B)30 sec
C)87 sec
D)88 sec
E)55 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Answer: B
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible?
Options:
A)252
B)1,680
C)2,340
D)362,880
E)592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: B
Question: How many coins of 0.5 dollars each and 0.7 dollars each together make exactly 4.6 dollars?
Options:
A)  1,6
B)  2,7
C)  3,5
D)  4,3
E)  5,3
Rationale: Straightaway use answer options ( Ignoring the decimal point ) -
(A)  1,6
1*5 + 6*7 => 47 ( Incorrect )
(B)  2,7
2*5 + 7*7 => 59 ( Incorrect )
(C)  3,5
3*5 + 5*7 => 50 ( Incorrect )
(D)  4,3
4*5 + 3*7 => 41 ( Incorrect )
(E)  5,3
5*5 + 3*7 => 46 ( Correct )
Hence answer will be (E)
Answer: E
Question: An investment of d dollars at k percent simple annual interest yields $500 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,000 over a 4 year period?
Options:
A)2d
B)(3d)/4
C)(4d)/3
D)(3d)/2
E)(8d)/3
Rationale: 500 dollars in 2 years means 250 dollars in 1 year.
To get 2000 dollars' it will take 8 years.
To get 2000 in 4 years, we need 8/4 =2 times money. Answer is A
Answer: A
Question: The price of a jacket is reduced by 35%. During a special sale the price of the jacket is reduced another 10%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)70.9
B)75
C)48
D)65
E)67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 35% , therefore bringing down the price to $65.
3) Again it is further discounted by 10%, therefore bringing down the price to $58.5
4) Now 58.5 has to be added byX %in order to equal the original price.
58.5 + ( X% ) 58.5 = 100.
Solving this eq for X, we get X = 70.9
Ans is A.
Answer: A
Question: (469 + 174)(power 2) - (469 - 174)(power 2) / (469 x 174) = ?
Options:
A)2
B)6
C)4
D)8
E)10
Rationale: Formula = (a + b)(power 2) - (a - b)(power 2) / ab
= 4ab/ab
= 4 (where a = 469, b = 174.)
Answer is D.
Answer: D
Question: Yukou enjoys reading science-fiction. It is the New Year and he has made a resolution to read a book every week for this year. He has a collection of monster books and space travel books in the ratio of 4:5. He presently has 20 space travel books. How many more books (of each genre) does he need to buy to keep his resolution, without changing the ratio?
Options:
A)6 monster, 10 space
B)8 monster, 10 space
C)8 monster, 9 space
D)4 monster, 10 space
E)7 monster, 12 space
Rationale: There are 52 weeks in a year. Youku has 20 space travel books, so 4:5 is 4/5:1 means (4/5)(20) = 16 monster books. So, he has 20 + 16 = 36 books. Youku needs 52 - 36 = 16 more books.
Keeping with the ratio of 4:5 and allowing for the fact that we can not have a fraction of a book, the minimum ratio that satisfies these restrictions is 8:10 giving 18 books, of which 8 are monster books and 10 space travel books.
Answer: B
Answer: B
Question: Sripad has scored average of 65 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
Options:
A)79
B)28
C)38
D)27
E)21
Rationale: Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 65.
i.e (58+58+x)/3 = 65
116 + x = 195
x = 79 marks.
Therefore, the maximum marks he can score in maths is 79.
Answer: A
Answer: A
Question: How many odd 4-digit positive integers T that are multiples of 5 can be formed without using the digit 3?
Options:
A)648
B)729
C)900
D)1296
E)3240
Rationale: I choose A.
Possible n° of 1st digit: 8 (0 can't be the first number, or else it wouldn't have 4 digits. 3 is exlcuded)
Possible n° of 2nd digit: 9 (3 is excluded)
Possible n° of 3rd digit: 9 (3 is excluded)
Possible n° of 4th digit: 1 (a number is a multiple of 5 if it ends in 5 or 0, here we are asked for the odd numbers, hence the last digit can't be 0)
So, T=8*9*9*1=648 (A)
Answer: A
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different K sets can be produced by this process?
Options:
A) 41
B) 89
C) 125
D) 243
E) 512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total K: 1+5+10+10+15=41 => Answer: A
Answer: A
Question: A cylindrical bucket of height 36 cm and radius 21 cm is filled with sand. The bucket is emptied on the ground and a conical heap of sand is formed, the height of the heap being 12 cm. The radius of the heap at the base is :
Options:
A)63 cm
B)53 cm
C)56 cm
D)66 cm
E)None of these
Rationale: Volume of the bucket = volume of the sand emptied
Volume of sand = π(21)2 × 36
Let r be the radius of the conical heap.
Then, 1⁄3πr2 × 12 = π(21)2 × 36
or r2 = (21)2 × 9 or r = 21 × 3 = 63
Answer A
Answer: A
Question: Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compunded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Options:
A)333
B)383
C)402
D)433
E)483
Rationale: Let the monthly payment be xx.
After the 1st month there will be 1,000∗1.1−x dollars left to repay;
After the 2nd month there will be (1,000∗1.1−x)∗1.1−x=1,210−2.1 x dollars left to repay;
After the 3rd month there should be 0 dollars left to repay: (1,210−2.1x)∗1.1−x=0--> 1331=3.31x--> x≈402x≈402
Answer: C.
Answer: C
Question: 10x + 2y = -6
8x + y = 3
In the system of equations above, what is the value of x?
Options:
A)-6
B)-4
C)-2
D)2
E)4
Rationale: 10x + 2y = -6 can be written as 5x + y = -3
Let's subtract the second equation from this equation.
-3x = -6
x = 2
The answer is D.
Answer: D
Question: How many minutes are there in two right angles?
Options:
A)21
B)22
C)17
D)2888
E)2880
Rationale: E
2880
They are the hour-minute, hour-second, and minute-second. Each hour, the minute hand will be at a right angle twice, so that's 48 right angles -- 2 for each hour of the day. Each hour, the second hand will go around 60 times and have 2 right angles for each, that's 120 right angles per hour or 120 * 24 = 2880
Answer: E
Question: A cycle is bought for Rs.900 and sold for Rs.1150, find the gain percent?
Options:
A)15
B)20
C)27.77
D)40
E)12
Rationale: 900 ---- 250
100 ---- ? => 27.77%
Answer: C
Answer: C