divelab/Sys2Bench huggingface dataset:
Question: A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top?
Options:
A)20th minute
B)21th minute
C)22th minute
D)24th minute
E)25th minute
Rationale: in every min person climbs up 12m and slips 8m . hence net displacement becomes 4m.
in 19 minutes person would climb (19*4)=76m
in 20th minute person would climb 12m up.. and it will be on top.
hence in 20th minute. person will reach on pole.
ANSWER:A
Answer: A
Question: If z is a multiple of 7899, what is the remainder when z^2 is divided by 9?
Options:
A)0
B)2
C)3
D)6
E)7
Rationale: The sum of the digits is 7+8+9+9=33.
Thus 3 is a factor of 7899, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Answer: A
Question: A bag contains 3 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
Options:
A)6/11
B)27/55
C)31/55
D)91/165
E)109/165
Rationale: P(no red balls) = 8/11*7/10*6/9 = 56/165
P(at least one red ball) = 1 - 56/165 = 109/165
The answer is E.
Answer: E
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?
Options:
A)4/7
B)3/7
C)35/128
D)4/28
E)28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
7C4 (1/2)^4 (1/2)^r
which is 35/128
Answer is C.
Answer: C
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State?
Options:
A)7000
B)8300
C)6000
D)5000
E)4000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 83 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 83
=> total appeared candidates in State B = 83 x 100 = 8300
=> total appeared candidates in State A = total appeared candidates in State B = 8300
Answer: B
Question: What is the Mode of the following data set R- {1,2,7,9,6,6,7,7}
Options:
A)1
B)2
C)7
D)6
E)9
Rationale: Mode of a set is the data point that is repeated the most number of times. In the set given, 7 is repeated.
Answer: C
Answer: C
Question: 624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: firstly factors of 624 = 1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
the question says each row will have people no less than 12 and no more than 52,
therefore, we should be interested in the factors between 12 and 52 (inclusive)
12(in each row) * 52(number of columns) =624, similarly
13 * 48
16 * 39
24 * 26
26 * 24
39 * 16
48 * 13
52 * 12
total possibilities = 8
option C
Answer: C
Question: The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
Options:
A)37 years
B)30 years
C)32 years
D)44 years
E)None of these
Rationale: The total age of 10 students with average 25 = 250
The total age of 12 students with average 27 = 324
The total age of 2 new students = 74
Their average =37
Correct Option A
Answer: A
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)45
B)50
C)55
D)60
E)63
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 4*180/12 = 60 ounces of water
D
Answer: D
Question: A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
Options:
A)48pi/x
B)75x
C)48x
D)24x
E)20x
Rationale: Let's try the explanation. We have two wheels. One with 14pi and the other one with 42pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (42pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 14pi*x=42pi*a.
(14pi*x)/(42pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 20x.
Ans :E
Answer: E
Question: Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case.
Options:
A)170
B)172
C)174
D)176
E)178
Rationale: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(31, 5) + 4 = 174.
ANSWER:C
Answer: C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.79
B)5.77
C)5.76
D)5.72
E)5.71
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer:C
Answer: C
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 39 = 19 + 18 + 12 - 4 - 2x
2x = 19 + 18 + 12 - 4 - 39
= 45 - 39
= 6
x = 3
ANSWER:B
Answer: B
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Options:
A)3/4
B)1/4
C)1/3
D)7/19
E)1/7
Rationale: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E)=7
P(E)=n(E)/n(S)
=7/21
=1/3
The answer should be C
Answer: C
Question: In how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate?
Options:
A)28400
B)28500
C)28600
D)28700
E)28800
Rationale: number of ways = 2*5!*5! = 28800
Answer is E
Answer: E
Question: For how many integers k is (k^2)+3 = 3+(2^k) ?
Options:
A)None
B)1
C)2
D)3
E)4
Rationale: (2^2)+3= 3+(2^2)
(2^4)+3= 3+(4^2)
For k= 2 and 4 the above equality holds true.
Answer:Option C
Answer: C
Question: There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?
Options:
A)30 hours
B)35 hours
C)40 hours
D)42 hours
E)41 hours
Rationale: Explanation:
Lets suppose tank got filled by first pipe in X hours,
So, second pipe will fill the tank in X + 10 hours.
=>1/X+1/X+10=1/12
=>X=20
ANSWER IS A
Answer: A
Question: A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr?
Options:
A)50 km/hr.
B)20 km/hr.
C)30 km/hr.
D)40 km/hr.
E)None
Rationale: Sol.
Speed = [180 + 270 / 54] m/sec = [450 / 54 * 18/5] km/hr =30 km/hr.
Answer C
Answer: C
Question: If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated?
Options:
A)24
B)60
C)720
D)520
E)180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (7-1)! = 6! = 720=C
Answer: C
Question: The number which exceeds 12% of it by 52.8 is:
Options:
A)60
B)77
C)269
D)26
E)91
Rationale: Explanation:
Let the number be x. Then, x – 12% of x = 52.8
x – (12/100)x = 52.8
x (1– 12/100) = 52.8
(88/100)x = 52.8
x = (100 X 52.8) / 88 = 60
ANSWER: A
Answer: A
Question: How many prime numbers are between 15/7 and 131/6?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 15/7= 3-
131/6= 22-
Prime numbers between 3 and 22 are 5, 7, 11, 13, 17, and 19
- sign signifies that the number is marginally less .
Answer D
Answer: D
Question: A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)60
B)110
C)140
D)130
E)120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
A
Answer: A
Question: Find the odd man out. 1, 3, 10, 13, 19, 29
Options:
A)12
B)9
C)1
D)3
E)10
Rationale: 10 is an even number. All other given numbers are odd
Answer : Option E
Answer: E
Question: What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9?
Options:
A)7/6
B)7/9
C)7/8
D)7/10
E)6/7
Rationale: First7 problem is 6C2 = 12 .. Not 20..
Point 2, you sum should be greater than 9, so these are the following possibilities you have
({3,9},{3,12},{3,15},{3,18},{6,9},{6,12},{6,15},{6,18},{9,12},{9,15},{9,18},{12,15},{12,18},{15,18}) which leads to 14 pairs
So the probability is 14 on 12 or 7/6..
ANSWER:A
Answer: A
Question: Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
Options:
A)25/28
B)27/28
C)30/28
D)40/28
E)50/28
Rationale: There are 6 consonants and 2 vowels in KHANTKAR .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : B
Answer: B
Question: Working alone, Jim finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jim alone cleans the entire house in 6 hours. How many hours will it take Nick and Jim to clean the entire house if they work together?
Options:
A)1.5
B)2
C)2.4
D)3
E)3.6
Rationale: Answer is 3.6 hours.
Jim does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: E
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)11758
B)11759
C)11755
D)11750
E)11751
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: D
Question: Choose the missing terms out of the given alternatives.
CMW, HRB, ?, RBL, WGQ, BLV
Options:
A)MWS
B)MWG
C)SJE
D)HHW
E)YSH
Rationale: B
MWG
The letters move five steps forward.
Answer: B
Question: Which of the following will divide evenly into 407,406,520?
Options:
A)11
B)21
C)4
D)31
E)41
Rationale: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: C
Answer: C
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
Options:
A)30 Km/hr
B)36 Km/hr
C)80 Km/hr
D)90 Km/hr
E)None of these
Rationale: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = x.
Then relative velocity = x+x = 2x
2x = distance/time = 240/12 = 20 m/s
Speed of each train = x = 20/2 = 10 m/s
= 10*18/5 km/hr = 36 km/hr
Option B
Answer: B
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)128
B)177
C)199
D)178
E)150
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:E
Answer: E
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)Rs.200
B)Rs.250
C)Rs.300
D)Rs.350
E)Rs.370
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
B)
Answer: B
Question: The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
Options:
A)a) $144
B)b) $150.50
C)c) $159.6
D)d) $158.60
E)e) $160.70
Rationale: total volume * unit cost = total cost
or, 5700 * 0.01 * 2.8 = total cost = 159.6=C
Answer: C
Question: A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)45
B)60
C)75
D)90
E)105
Rationale: Answer : C
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 400
16x = 400
x = 25.
Hence, total number of notes = 3x = 75.
Answer: C
Question: An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?
Options:
A)20
B)40
C)80
D)90
E)100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 9 ways
Hence one chair and one table can be arranged in 10 x 9 ways = 90 ways
D
Answer: D
Question: The perimeter of a square is 52 m. Find the area of the square.
Options:
A)161 m².
B)164 m².
C)166 m².
D)169 m².
E)273 m².
Rationale: Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER : OPTION D
Answer: D
Question: Find the distance covered by a man walking for 36min at a speed of 10km/hr?
Options:
A)1km
B)3km
C)6 km
D)5km
E)6km
Rationale: Distance = 10*36/60 =6 km
Answer is C
Answer: C
Question: A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train?
Options:
A)90
B)60
C)120
D)180
E)360
Rationale: Length = Speed * time
Speed = L/T
S = 2500/100
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A
Answer: A
Question: The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)7%
C)10%
D)12%
E)6%
Rationale: Option E
Explanation:
70*(90/100)*((100-x)/100) = 59.22
x = 6%
Answer: E
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Options:
A)18
B)68
C)67
D)55
E)56
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162
= 18
Answer:A
Answer: A
Question: Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)11n + 2
B)11n + 4
C)11n + 3
D)9n + 3
E)9n + 4
Rationale: its C
n items for $10 each
total price $10n
postage and handling of $4 for 1st item and $1 for the rest
total postage and handling = $ [4+ (n-1)]
= $ n+3
total cost
10n+n+3 = 11n+3
Answer: C
Question: In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
A)A)136
B)B)627
C)C)153
D)D)721
E)E)159
Rationale: 46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A
Answer: A
Question: A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?
Options:
A)2.6 hours
B)3.6 hours
C)4.6 hours
D)5.6 hours
E)None of these
Rationale: Let's first find the rates of the pumps and the drainage hole
pump A: 1 / 5 , pump B: 1 / 8 , drainage hole: 1 / 20
Let t be the time for the pumps to fill the tank. The pumps ,add water into the tank however the drainage hole drains water out of the tank, hence
t ( 1 / 5 + 1 / 8 - 1 / 20) = 1
Solve for t
t = 3.6 hours
Answer B
Answer: B
Question: A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
Options:
A)5%
B)18%
C)33%
D)35%
E)38%
Rationale: Soln:-
Profit in 1995 - 100
Profit in 1996 - 115
%increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38%
ANSWER:E
Answer: E
Question: What is the value of x?
Data 1: x - 2y = 7
Data 2: 4x – 28 = 8y
Options:
A)89
B)10
C)12
D)15
E)no solution exists
Rationale: both are same equations
4X(x-2y=7) is 4x-8y=28
so no solution exists
ANSWER:E
Answer: E
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is
Options:
A)4/5
B)7/11
C)7/13
D)7/15
E)8/11
Rationale: Let the required fraction be x. Then	1	- x =	9
x	20
1 - x2	=	9
x	20
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x =	4/5
A)
Answer: A
Question: A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: P(choosing a red apple 5 times in a row) = 7/8*6/7*5/6*4/5*3/4 = 3/8 < 0.5
The answer is C.
Answer: C
Question: When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth.
Options:
A)2.9
B)2.5
C)2.7
D)2.1
E)2.2
Rationale: Explanation:
Assume distance of sidewalk "x"
Speed 1 (moving on sidewalk)
Speed 2 (moving off sidewalk)
Since both the movements are in same direction, we can do speed 1 + speed 2
Speed 1 = x4x4
Speed 2 = x7x7
Speed 1 + speed 2 = 11x2811x28 = = 0.39286x
Now new time while moving on sidewalk = x0.39286xx0.39286x = 2.54544
Hence, the answer is 2.5
Answer: B
Answer: B
Question: There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
Options:
A)1/12
B)3/4
C)6/9
D)6/7
E)3/4
Rationale: Blue + Red =18
Total number of balls is 14+4+3=21
So the answer is 18/21=6/7
Answer D
Answer: D
Question: A train is walking at 6/7 of its usual speed, the train is 20 minutes too late. Find its usual time to cover the journey.
Options:
A)1 hour
B)30min
C)3 hours 20 min
D)2 hours 30 min
E)2 hours
Rationale: new speed = 6/7 of the usual speed
new time taken = 7/6 of the usual time taken
so, ( 7/6 of the usual time ) - ( usual time ) = 20min
1/6 of the usual time = 20min
usual time = 20*6 = 120 min = 2 hours
correct option is E
Answer: E
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)109 ways
B)908 ways
C)128 ways
D)108 ways
E)104 ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Answer: D
Question: How many meters are there in 770 centimeters?
Options:
A)770 meters
B)7.6 meters
C)700 meters
D)6.5 meters
E)7.7 meter
Rationale: Solution:
1 meter = 100 centimeters
Just divide 770 by 100
770 Ã· 100 = 7.7, so there are 7.7 meters in 770 centimeters
Option E
Answer: E
Question: A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price?
Options:
A)$1000
B)$1500
C)$1850
D)$1600
E)$2000
Rationale: cost price = selling price *100/(100+profit)
C.P. = 1800*100/120 = $1500
Answer is B
Answer: B
Question: For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?
Options:
A)12
B)9
C)3
D)7.5
E)2.5
Rationale: we have 2 equations
1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Answer: B
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)32:45
B)32:47
C)32:45
D)32:41
E)32:42
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45.Answer: A
Answer: A
Question: Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?
Options:
A)350
B)400
C)500
D)550
E)590
Rationale: N * 50 = (325000 - 300000) = 25000
N = 25000 / 50
= 500
C
Answer: C
Question: In how many ways can 12 different gifts be divided among four children such that each child receives exactly three gifts?
Options:
A)16^3
B)(4!)^3
C)12!/(3!)^4
D)12!/4!
E)4^12
Rationale: Total 12 different Gifts, and 4 children.
Thus any one child gets 12C3 gifts,
then the other child gets 9C3 gifts(12 total - 3 already given),
then the third one gets 6C3 gifts,
and the last child gets 3C3 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
12C3 * 9C3 * 6C3 * 3C3 = 12! / (3!)^4
Ans : C.
Answer: C
Question: Find the value of x in (8x-6)=10.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (8x-6)=10
Adding both sides with 6 gives 8x=16
Dividing both sides with 8 gives x=2
Answer: B
Answer: B
Question: The sum of three integers A, B and C is 180. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
Options:
A)120
B)125
C)105
D)115
E)110
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=180.
so 1/3(B+C)+B+C=180
4(B+C)/3= 180
B+C =180*3/4 = 135
A=180-135=45
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=180
so 1/5(A+C)+A+C=180
A+C=180*5/6=150
but A=45, so C=150-45=105
Answer : B
Answer: B
Question: What is (24^7+24) / 24?
Options:
A)159202573
B)160902641
C)172502765
D)182302834
E)191102977
Rationale: (24^7+24) / 24 =
24*(24^6+1) / 24 =
24^6 + 1
Clearly this is a number which ends with a 7 in the units place.
The answer is E.
Answer: E
Question: A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in eight years. Find the compound interest the man will get on twice the principal in two years at the same rate?
Options:
A)s.256.27
B)s.256.29
C)s.205.00
D)s.256.22
E)s.256.25
Rationale: Let the principal be Rs.P
S.I at 5% p.a in 8 years on Rs.P = Rs.400
(P)(8)(5)/100 = 400
P = 1000
C.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years
=2000{ [1 + 5/100]^2 - 1} =
= 2000(41/ 400)
= Rs.205
Answer:C
Answer: C