divelab/Sys2Bench huggingface dataset:
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 20 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
Options:
A)1 hour
B)1 hour 10 minutes
C)2 hours 30 minutes
D)1 hour 20 minutes
E)2 hours 10 minutes
Rationale: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/20)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 20 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (20+60)=80 minutes on the road.
D. 1 hour 20 minutes
Answer: D
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)240
B)88
C)77
D)26
E)22
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: A
Answer: A
Question: A owner of a mart earns an income of Re 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, he earns an income of:
Options:
A)18
B)21
C)22
D)20
E)30
Rationale: 2nd day he earns = 2(2 – 1)
3rd day he earns = 2(3 – 1)
On 10th day he earns 2(10 -1) = 18 rupees
ANSWER:A
Answer: A
Question: What is the value of âˆš64% ?
Options:
A)80%
B)20%
C)40%
D)90%
E)26%
Rationale: Explanation: br>âˆš64%
=âˆš64/âˆš100
=8/10
=80/100=80%
correct answer is A)80%
Answer: A
Question: Three hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 600 selected numbers are odd?
Options:
A)26.67%
B)36.67%
C)25%
D)46.67%
E)56.67%
Rationale: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 300 multiples are odd i.e 150 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (150+0)/(300+300)= 150/600=(1/4) = 25%
Answer C
Answer: C
Question: The calendar of the year 2080 can be used again in the year?
Options:
A)2105
B)1955
C)1945
D)1935
E)2108
Rationale: Explanation:
Given year 2080 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2080 + 28 = 2108
Answer: E
Answer: E
Question: The ratio of three numbers is 1:2:4 and the sum of their squares is 1701. The sum of the numbers is?
Options:
A)A)10
B)B)12
C)C)15
D)D)14
E)E)9
Rationale: Let the numbers be x,2x,4x
then, x^2+4x^2+16x^2 = 1701
21x^2 = 1701
x^2 = 81
x=9
Answer is E
Answer: E
Question: What is the remainder when the number Y=14^2 * 15^8 is divided by 5?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus Y=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: A
Question: The number of six digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that digits do not repeat and the terminal digits are even is
Options:
A)144
B)72
C)288
D)720
E)None of these
Rationale: The first and the last (terminal) digits are even and there are three even digits. This arrangement can be done in 3P2 ways. For any one of these arrangements,two even digits are used; and the remaining digits are 5 (4 odd and 1 even) and the four digits in the six digits(leaving out the terminal digits) may be arranged using these 5 digits in 5P4 ways. The required number of numbers is 3P2 × 5P4 = 6 × 120 = 720.
Answer D
Answer: D
Question: If x is 20 percent greater than 40, then x =
Options:
A)48
B)70.4
C)86
D)105.6
E)108
Rationale: X is 20% greater than 40 means X is 1.2 times 40 (in other words 40 + 20/100 * 40 = 1.2 * 40)
Therefore, X = 1.2 * 40 = 48
ANSWER:A
Answer: A
Question: If the perimeter of a rectangular house is 1400 m, its length when its breadth is 300 m is?
Options:
A)300
B)400
C)500
D)600
E)700
Rationale: 2(l + 300) = 1400 => l = 400 m Answer: B
Answer: B
Question: There are 6 boxes numbered 1, 2,…,.6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
Options:
A)22
B)21
C)45
D)27
E)25
Rationale: List down possibilities: From only 1 box all the way to all 6
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, we have 6 possibilities.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
If 3 of the boxes have green balls, there are 4 possibilities: 123, 234, 345, 456.
If 4 boxes have green balls, there are 3 possibilities: 1234, 2345, 3456.
If 5 boxes have green balls, there are 2 possibilities: 12345, 23456.
If all 6 boxes have green balls, there is just 1 possibility.
Total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21.
Ans: B
Answer: B
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 30 per cent larger than the original. By what percentage has the area of the logo increased?
Options:
A)50
B)80
C)69
D)125
E)250
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 5.2 , so radius is 2.6
New area = 6.76π
Increase in area is 2.76π
% increase in area = 2.76/4*100
So, % increase is 69%
Answer will be (C)
Answer: C
Question: In Town X, 64 percent of the population are employed, and 35 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)25%
C)32%
D)45%
E)52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 35 are employed males,hence 29% are employed females.
(employed females)/(total employed people)=29/64=45%
Answer:D.
Answer: D
Question: A train 60 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
Options:
A)11 s
B)10 s
C)7 s
D)4 s
E)None of these
Rationale: We know from the formula Time = Distance/ Speed
Thus, Time = 60/ 54 x 5/18
or, Time = 4 sec.
ANSWER:D
Answer: D
Question: Four different objects 1,2,3,4 are distributed at random in four places marked 1,2,3,4. What is probability that none of the objects occupy the place corresponding to it's number?
Options:
A)17/24
B)3/8
C)1/2
D)5/8
E)1/3
Rationale: Since, we know there are only 24 possible outcomes in TOTAL, it might not be a big deal just LIST the outcomes where no object is in right place.
We'll list the objects (1, 2, 3, and 4) in an order so that no number is in the correct place.
To begin, we'll place a 2 in the first position to get the following:
2134
2341
2413
There are 3 possible outcomes.
IF we place a 3 in the first position, we should also get 3 possible outcomes.
To confirm:
3142
3412
3421
Yep, 3 possible outcomes
IF we place a 4 in the first position, we should also get 4 possible outcomes.
To confirm:
4123
4312
4321
Yep, 3 possible outcomes
# of outcomes where no object is in right place = 3 + 3 + 3 = 9
---------------------------
So, P(no object is in the right place) = 9/24 = 3/8 = B
Answer: B
Question: A train 110 m long is running with a speed of 90 km/h. In how many seconds will the train pass a man who is running at 9 km/h in the direction opposite to that in which the train is going?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The speed of the train relative to the man = 90 + 9 = 99 km/h.
99000 m/h * 1h/3600 s = (990/36) m/s
(110 m) / (990/36 m/s) = (110 * 36) / 990 = 36/9 = 4 seconds
The answer is B.
Answer: B
Question: The letters C,K,L and U are rearranged to form the word 'Luck'. Find its probability.
Options:
A)1/120
B)1/235
C)1/24
D)1/76
E)1/53
Rationale: Explanation :
There are total 4 letters. The probability that C gets the first position is 1/4.
The probability that K is in the second position is 1/3.
Likewise, probability for L and U are 1/2 and 1/1.
Hence, the required probability is:-
=> (1/4) x (1/3) x (1/2) x 1.
=> 1/24.
Answer : C
Answer: C
Question: Car A leaves the airport at 8:00 am and travels at a constant rate of 40 km per hour. Car B leaves the airport at 8:15 am and travels in the same direction along the same highway at a constant rate of 46 km per hour. At what time will Car B be 11 km ahead of Car A?
Options:
A)10:45 am
B)11:00 am
C)11:15 am
D)11:45 am
E)12:15 pm
Rationale: At 8:15 am, Car A will be 10 km ahead of Car B.
Car B travels at a rate 6 km per hour faster than Car A.
Car B needs to travel 21 km more than Car A in order to be 11 km ahead.
This will take 21 km/6 km per hour=3.5 hours.
Car B will be 11 km ahead at 11:45 am.
The answer is D.
Answer: D
Question: One skirt requires 3.75 yards of cloth. How many skirts you can make from 45 yards
Options:
A)9 skirts
B)10 skirts
C)11 skirts
D)12 skirts
E)13 skirts
Rationale: for 1 shirt --> 3.75 yards reqd
for x skirts --> 45 yards
x=45/3.75 => 45*100/375 = 12
We can make 12 skirts from 45 yards
Ans : 12 skirts
ANSWER:D
Answer: D
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Options:
A)2 : 3 : 4
B)6 : 7 : 8
C)6 : 8 : 9
D)7 : 8 : 9
E)None of these
Rationale: Explanation:
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=>(140/100 X 5X), (150/100 X 7X) and (175/100 X 8X)
The required ratio = 7x :	21x/2 : 14X
=>14x : 21x : 28x
=>2 : 3 : 4
ANSWER IS A
Answer: A
Question: The average ages of three persons is 27 years. Their ages are in the proportion of 1:3:5. What is the age in years of the youngest one among them ?
Options:
A)33
B)77
C)55
D)09
E)41
Rationale: Let the age of three persons be x, 3x and 5x => 9x/3 = 27 = > x = 9
Answer:D
Answer: D
Question: The largest number of six digits
Options:
A)100000
B)222222
C)333333
D)888888
E)999999
Rationale: answer : option E
Answer: E
Question: If the cost price is 94% of sp then what is the profit %
Options:
A)5.07%
B)6%
C)5.7%
D)6.50%
E)6.25%
Rationale: Sol. sp=Rs100 : then cp=Rs 94:profit =Rs 6.
Profit={(6/94)*100}%=6.25%
Answer is E.
Answer: E
Question: The average of five numbers is 100. If one number is excluded, the average becomes 110. The excluded number is?
Options:
A)8
B)6
C)58
D)60
E)96
Rationale: Excluded number
= (100 * 5) - (110 * 4)
= 500 - 440 = 60
Answer:D
Answer: D
Question: If the average (arithmetic mean) of 5b,6b+4,7b,8b-4 and 2b is 140, what is the value of b?
Options:
A)20
B)22
C)25
D)30
E)48
Rationale: AM of 5b,6b+4,7b,8b-4 and 2b=5b+6b+4+7b+8b-4+2b= 28b/5
Given that 28b /5 = 140
b= 25
Answer is C
Answer: C
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit?
Options:
A)3888
B)277
C)29889
D)3000
E)22341
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Answer: D
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 5,000 and at the same time n is a perfect square and a perfect cube?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096.
The answer is C.
Answer: C
Question: Today John, who is 38 years old, and his daughter, who is 13 years old, celebrate their birthdays. How many years will pass before John’s age is twice his daughter’s age?
Options:
A)13
B)14
C)15
D)16
E)12
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes John’s age will be (38+x) years old, and his daughter’s age will be (13+x) years old. Since the John’s age is twice his daughter’s age (38+x)= 2 * (13+x) --->
38+x=26+2x ---> x= 12
The answer is (E).
Answer: E
Question: If n is an integer and 101n^2 is less than or equal to 12100, what is the greatest possible value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 101 * n^2 <=12100
n^2 <=12100/101 which will be less than 121 since 12100/100 = 121 which is the square of 9
Next closest value of n where n^2<=121 is 10
Ans D
Answer: D
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 14 meters. What is the length of the yard if the area of the yard is 6 meters squared?
Options:
A)8
B)6
C)2
D)4
E)3
Rationale: Perimeter of rectangular yard = 2(l + b) = 14 --> l + b = 7
Area = l * b = 6
b = 7 - l
l(7 - l) = 6
7l - l^2 = 6
l^2 - 7l + 6 = 0
Upon simplifying we get l = 1 or 6. Only 6 is there in the answer choice.
Answer: B
Answer: B
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)8 kmph
B)9 kmph
C)2 kmph
D)4 kmph
E)1 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer:E
Answer: E
Question: Set X consists of all two-digit primes and set Y consists of all positive odd multiples of 7 less than 100. If the two sets are combined into one, what will be the range of the new set?
Options:
A) 84
B) 89
C) 90
D) 92
E) 95
Rationale: Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {7, 21, 35,..............., 77, 91,}
Combining two sets, say Set Z
Set Z = {7, 11, 13, 17,21,..................., 77, 83, 89, 91, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 7 = 90
OA C is the answer.
Answer: C
Question: 75 apples on a scale weigh 18.035 kg. When 5 apples are removed from the scale, the average weight of the 70 apples is 240 grams. What is the average weight (in grams) of the 5 apples which were removed?
Options:
A)241
B)243
C)245
D)247
E)249
Rationale: 70*240=16800.
The other 5 apples weigh a total of 1235 grams.
The average weight is 1235/5 = 247 grams.
The answer is D.
Answer: D
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero ?
Options:
A)0
B)1
C)-1
D)-2
E)2
Rationale: Average of 20 numbers = 0.Sum of 20 numbers = (0 * 20) = 0.It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a). Answer : A
Answer: A
Question: The speed of a boat in upstream is 40 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)17 kmph
C)30 kmph
D)17 kmph
E)29 kmph
Rationale: Speed of the boat in still water
= (40+100)/2
= 70 kmph. Speed of the stream
= (100-40)/2
=30 kmph.
Answer: C
Answer: C
Question: The denominator of a fraction is 3 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
Options:
A)A)2/3
B)B)13/19
C)C)4/7
D)D)11/19
E)of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 3
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 3) + 3 => n = 11
d = 2n - 3 => d = 19
Hence the fraction is : 11/19
ANSWER:D
Answer: D
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)647
B)698
C)654
D)847
E)976
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer:C
Answer: C
Question: The average of first 13 natural numbers is?
Options:
A)5.2
B)5.5
C)7
D)9
E)10
Rationale: Sum of 13 natural no. = 182/2 = 91
Average = 91/13 = 7
Answer:C
Answer: C
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
A)40% of 160 + 1⁄3 of 240
B)120% of 1200
C)38 × 12 – 39 × 8
D)1648 – 938 – 566
E)6 1⁄2 of 140 – 2.5 × 306.4
Rationale: Others are equal to 144 whereas (b) equals 1440.
Answer B
Answer: B
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Options:
A)Rs1589
B)Rs654
C)Rs 400
D)Rs1500
E)Rs. 2400
Rationale: Explanation:
1200 * 12: x * 9 = 2:3
x =Rs. 2400
ANSWER:E
Answer: E
Question: In what ratio should a variety of Rice costing Rs. 7 per kg be mixed with another variety of Rice costing Rs. 14.50 per kg to obtain a mixture costing Rs. 9.75 per kg?
Options:
A)19:10
B)19 :11
C)11 :19
D)12 :18
E)11 :20
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (14.50 - 9.75) / (9.75 - 7) = 31/15
ANSWER:B
Answer: B
Question: The sum of two numbers is 84, and one of them is 12 more than the other. What are the two numbers?
Options:
A)36-48
B)50-34
C)60-24
D)42-42
E)21-63
Rationale: In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 84:
word problem = 84
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 84 − 12
= 72.
x = 72/2
= 36.
This is the first number. Therefore the other number is
x + 12 = 36 + 12 = 48.
The sum of 36 + 48 is 84.
Answer: A
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
Options:
A)12
B)14
C)18
D)10
E)6
Rationale: Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER A 12
Answer: A
Question: AB + CD = WWW, where AB and CD are two-digit numbers and WWW is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined
Rationale: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of WWW it's 111.
So, A=1. 1B+CD=111
Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9
Answer: D.
Answer: D
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 4. Find his average after 17th inning.
Options:
A)36
B)39
C)23
D)45
E)None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 4).
∴ 16(x – 4) + 87 = 17x or x = (87 – 64) = 23.
Answer C
Answer: C
Question: Sujit incurred a loss of 45% on selling an article for Rs.3520/-. What was the cost price of the article?
Options:
A)Rs.5725/-
B)Rs.5080/-
C)Rs.6400/-
D)Rs.6750/-
E)None of these
Rationale: Explanation:
45% loss means SP of Rs.3520/- is 55% of CP
:. CP = 3520x100/55 = Rs.6400/-
Answer: Option C
Answer: C
Question: What is the prime factors’ number of 12?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^2*3^1
prime factors’ number will be 2+1 = 3.
Hence, answer is B.
Answer: B
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Options:
A)152400 m^2
B)152500 m^2
C)152600 m^2
D)152800 m^2
E)151000 m^2
Rationale: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
E
Answer: E
Question: A sum of Rs.4300 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)Rs.2520
B)Rs.3120
C)Rs.3320
D)Rs.2795
E)None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4300[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4300 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7095
So the interest = 7095 - 4300 = Rs.2795
ANSWER:D
Answer: D
Question: In a camp, there is a meal for 110 men or 200 children. If 140 children have taken the meal, how many men will be catered to with remaining meal?
Options:
A)41
B)30
C)35
D)33
E)36
Rationale: D
33
There is a meal for 200 children.
140 children have taken the meal.
Remaining meal is to be catered to 60 children.
Now, 200 children 110 men.
60 children = (110/200)x 60= 33 men.
Answer: D
Question: The average weight of 45 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
Options:
A)51 1⁄3
B)52 2⁄3
C)52 1⁄3
D)43.42
E)None of these
Rationale: Total weight of 45 students
= 45 × 52 = 2340 kg
Total weight of 5 students who leave
= 5 × 48 = 240 kg
Total weight of 5 students who join
= 5 × 54 = 270 kg
Therefore, new total weight of 45 students
= 2340 – 240 + 270 = 2370
⇒ New average weight = 2370⁄45 = 522⁄3 kg
Answer B
Answer: B
Question: Martha has 5 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
Options:
A)8
B)9
C)10
D)18
E)20
Rationale: 5 dogs, 4 cats; park/barber shop
1 dog - 2 options - either park or barber shop, so, 5 dogs - 10 options and 4 dogs - 8 options.
Total = 18 options.
ANS:D
Answer: D
Question: A retailer sold an appliance for $70. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?
Options:
A)$14
B)$16
C)$20
D)$24
E)$25
Rationale: Gross Profit = Selling price - Cost = 70-x
70-x = 1/4x
x = 56
GP = 70-56 = 14
Answer: A
Question: If $1000 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?
Options:
A)1000 (1.056)(3)
B)1000 (3+1.056)
C)1000 (1+3(0.056))
D)1000 (1+(0.056)^3)
E)1000 (1.056)^3
Rationale: 1000 * 1.056 * 1.056 * 1.056 = 1000 * 1.056^3.
ANSWER:E
Answer: E
Question: What is the smallest integer a > 0 such that the inequality
1/n + 1
+
1/n + 2
+...+
1/2n + 1
< a - 2010-
1/3
is satisfied for all positive integers n?
Options:
A)2011
B)2012
C)2013
D)2014
E)2015
Rationale: Plugging in n = 1, we see that a > 2011. On the other hand, since there are n + 1
terms, and all of them are at most 1=(n + 1), the expression is at most 1, which means that
a = 2012 works.
correct answer B
Answer: B