mathewhe/aqua_rat huggingface dataset:
Question: When positive integer e is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: the equation that can be formed e is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..
ans 1.. B
Answer: (B)  1
Question: Jim is able to sell a hand-carved statue for $750 which was a 35% profit over his cost. How much did the statue originally cost him?
(A) $496.30
(B) $512.40
(C) $555.56
(D) $574.90
(E) $588.20
Rationale: 750 = 1.35*X
X = 750/1.35 = 555.5555556...
which rounds to $555.56, which is (C).
Answer: (C) $555.56
Question: A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
(A) 500
(B) 700
(C) 750
(D) 900
(E) 950
Rationale: He sells 40% of oranges and still there are 420 oranges remaining.
=> 60% of oranges = 420
=> Total oranges
×
60
100
=
420
×60100=420
=> Total oranges
=
420
×
100
60
=
700
Option B
Answer: (B) 700
Question: The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is
(A) 279
(B) 283
(C) 308
(D) 318
(E) None
Rationale: Solution
Other number	= (11×7700 / 275)
= 308.
Answer C
Answer: (C) 308
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 65000, then the share of B is?
(A) 24008
(B) 24000
(C) 26000
(D) 26000
(E) 30000
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs.65000
Share of B = 6/13 (65000) = Rs. 30000
Answer: E
Answer: (E) 30000
Question: Fred and Sam are standing 55 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 6 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
(A) 5
(B) 9
(C) 25
(D) 30
(E) 45
Rationale: relative distance =55 miles
relative speed =6+5 =11 miles per hour
time taken =55/11=5 hours
distance travelled by sam =5*5=25 miles=C
Answer: (C) 25
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 12 sec, then the speed of each train is?
(A) 11
(B) 27
(C) 36
(D) 99
(E) 108
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (360 + 360)/12 => x = 30
Speed of each train = 10 m/sec.
= 30 * 18/5 =108 km/hr.
Answer: E
Answer: (E) 108
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 700 km/hr
(B) 720 km/hr
(C) 870 km/hr
(D) 869 km/hr
(E) 890 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: (B) 720 km/hr
Question: Two bullet train s are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower bullet train to cross the faster bullet train in seconds is:
(A) 58 sec.
(B) 78 sec.
(C) 68 sec.
(D) 48 sec.
(E) 88 sec.
Rationale: D
48 sec.
Relative speed = (60+ 90) km/hr
= 150x5/18
= 120/3 m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = 2000 x 3/125 = 48 sec.
Answer: (D) 48 sec.
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
(A) 10987
(B) 11755
(C) 17576
(D) 19775
(E) 21899
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Answer: (C) 17576
Question: A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 16 men leave the bus and eight women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
(A) 15
(B) 30
(C) 36
(D) 72
(E) 46
Rationale: Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 16) = (x + 8) or x = 24.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 72.
Answer: D
Answer: (D) 72
Question: Find the amount for Rs. 6000 at 10% per annum, compounded semi-annually for 2 years.
(A) 1293
(B) 1283
(C) 1273
(D) 1263
(E) 1253
Rationale: Solution:
Semi annually means we have to compound the interest for every six months. So we have to calculate interest for 6 months. So R =
10/2= 5% (for half year)
Also, n = 2 years x 2 = 4 periods
Therefore, P = 6000, n = 4, r = 5%
A = 6,000(1+5/100)4 = Rs. 7,293
Interest = Rs.7293 - 6000 = 1293
Answer A
Answer: (A) 1293
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 234
(B) 230
(C) 245
(D) 250
(E) 260
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: Option C
Answer: (C) 245
Question: A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000
(A) 3336,1667
(B) 3339,1667
(C) 3333,1666
(D) 3333,1668
(E) 3333,1669
Rationale: they invested in the ratio 1:2
a's share =1/3*5000=1666
b's share=2/3*5000=3333
ANSWER:C
Answer: (C) 3333,1666
Question: How many positive integers less than 50 are there such that they are multiples of 9?
(A) 5
(B) 6
(C) 4
(D) 8
(E) 3
Rationale: Number of multiples of 9 => 45-9/9+1= 5
Answer is A
Answer: (A) 5
Question: For which of the following functions does f(−u)=−f(u) for all real number values of x?
(A) u^8
(B) −u^6
(C) u^5
(D) u^9/(u^5+1)
(E) 1/(x^2+1)
Rationale: f(-u) = (-u)^5 = -u*u^4
-f(u) = -u^5
C
Answer: (C) u^5
Question: The average of first 10 odd numbers is?
(A) 11
(B) 10
(C) 88
(D) 176
(E) 12
Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer: B
Answer: (B) 10
Question: The ratio between a and y is 7/9; a and y are increased by 4, what is the ratio between the new values of a and y?
(A) 7/9
(B) 14/9
(C) 7/18
(D) 11/13
(E) It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
a and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E
Answer: (E) It Cannot Be Determined
Question: Of the 11 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 11 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
(A) 22
(B) 35
(C) 60
(D) 70
(E) 105
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 6 ways to select one man
so 5*4*3*6 = 360
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 360/3!= 360/6= 60
C
Answer: (C) 60
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability R that exactly two visitors will buy a pack of candy?
(A) 0.343
(B) 0.147
(C) 0.189
(D) 0.063
(E) 0.027
Rationale: 3C2 * (3/10)^2 * 7/10
= 3 * 9/100 * 7/10
= 189/1000
= 0.189=R
Answer - C
Answer: (C) 0.189
Question: A certain industrial loom weaves 0.126 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
(A) 114
(B) 115
(C) 116
(D) 117
(E) 119
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.126 : 15 :: 1 : x
=>0.126*x=15
=>x=15/0.126
=>x=119
ANSWER:E
Answer: (E) 119
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
(A) 4
(B) 8
(C) 16
(D) 20
(E) none
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer = B
Answer: (B) 8
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
(A) W = 35 and L = 31
(B) W = 15 and L = 20
(C) W = 25 and L = 42
(D) W = 27 and L = 37
(E) W = 42 and L = 13
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer B
Answer: (B) W = 15 and L = 20
Question: Calculate 24 x 99
(A) 2673
(B) 2763
(C) 2637
(D) 2736
(E) 2376
Rationale: = 24-1 = 23
= (Decrement each digit of the number obtained from 9) Here we got 23. Now
= 9-2 = 7 and 9-3=6. So we have 76
Just write these numbers together.
That is we have 23 and 76.
Hence answer is 2376
Answer is E.
Answer: (E) 2376
Question: A man buys 50 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
(A) 5.3 %
(B) 7.6 %
(C) 10.6 %
(D) 12 %
(E) None of these
Rationale: Explanation:
Let Marked price be Re. 1 each
C.P. of 50 pens = Rs. 46
S.P. of 50 pens = 99% of Rs. 50 = Rs. 49.50
Profit % = (Profit /C.P.) x 100
Profit% = (3.50/46) x 100 = 7.6 %
ANSWER B
Answer: (B) 7.6 %
Question: The sum of all consecutive odd integers from −23 to 31, inclusive, is
(A) 96
(B) 112
(C) 158
(D) 192
(E) 235
Rationale: The sum of the odd numbers from -23 to +23 is 0.
Let's add the remaining numbers.
25+27+29+31 = 112
The answer is B.
Answer: (B) 112
Question: Jack's toy box contains 13 toy soldiers, 7 model airplanes and 5 dolls. What is the probability that a randomly chosen toy from the box will be either a model airplane or a doll?
(A) 35/252
(B) 12/25
(C) (7/25)+(5/24)
(D) 20/25
(E) 12
Rationale: Probability of selecting either a model airplanes or a doll = 1 - ( Probability of Selecting a Toy )
Probability of selecting either a model airplanes or a doll = 1 - 13C1/ 25C1
Probability of selecting either a model airplanes or a doll = 1 - 13/25
Probability of selecting either a model airplanes or a doll = 12/25
Hence answer will be (B)
Answer: (B) 12/25
Question: If -2<= x <= 2 and 3 <= y <= 5, which of the following represents the range of all possible values of y-x?
(A)  5 <= y-x <= 6
(B)  1 <= y-x <= 7
(C)  1 <= y-x <= 6
(D)  5 <= y-x <= 10
(E)  1 <= y-x <= 10
Rationale: Maximum value of y-x= 5 - (-2)= 7
Minimum value of y-x= 3-2= 1
B mentions the correct range
Answer: (B)  1 <= y-x <= 7
Question: For what value of x between −8 and 8, inclusive, is the value of x^2 − 10x + 16 the greatest?
(A) − 8
(B) − 2
(C) 0
(D) 2
(E) 8
Rationale: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -8 will give the greatest value..
ans A
Answer: (A) − 8
Question: Donovan and Michael are racing around a circular 500-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 500/45 =>100/9
2. Speed/ Rate of Michael = Distance/ time => 500/40 => 50/4
Relative Speed between them = 50/4 -100/9 => 25/36 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 500, Relative Rate = 50/36
Total Time taken by Micheal to surpass Donovan = Distance / rate => 500*36/ 50=> 3600/10 => 360
No. of laps taken by Michael = Total time / Michael's rate => 360/40 => 9
Hence correct answer is 9 Laps.
A
Answer: (A) 9
Question: A committee of 3 people is to be chosen from the chairman and vice chairman of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?
(A) 16
(B) 24
(C) 32
(D) 34
(E) 40
Rationale: Each company can send only one representative to the committee. Let's see in how many ways we can choose 3 companies (as there should be 3 members) to send only one representatives to the committee: 4C3=4.
But these 3 chosen companies can send two persons (either chairman or vice chairman ): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: C.
Answer: (C) 32
Question: There are 26 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
(A) 1 year
(B) 1 year 2 months
(C) 4 years 4 months
(D) 3 years
(E) None
Rationale: Total decrease = 26 * 2 = 52 monthS
= 4 years 4 months
C
Answer: (C) 4 years 4 months
Question: A crate measures 5 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 12
Rationale: We can find the radius of all the three cases of cylinders.
The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.
So r=5 for the surface 8*12 face.
Volume = 125pi
Answer C
Answer: (C) 5
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 10 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 27 sec
(B) 87 sec
(C) 67 sec
(D) 36 sec
(E) 46 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (10 + 20)5/18 = 300 x 18 / 30 x 5 = 36 seconds.
Answer: D
Answer: (D) 36 sec
Question: What is the probability that Company W's advertisement will be one of the first two be shown during the first commercial break?
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
Rationale: W 1/15 + (14/15) * 1/14 = 2/15 D
Answer: (D)  2 / 15
Question: At 1:00, Annie starts to bicycle along a 71 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
(A) 2:00
(B) 2:30
(C) 3:00
(D) 3:30
(E) 4:00
Rationale: In the first 30 minutes, Scott can travel 6 miles, so there are 65 miles left.
Together Annie and Scott can complete 26 miles.
65/26 = 2.5, so they will meet 2.5 hours after 1:00.
The answer is D.
Answer: (D) 3:30
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 10
(B) 28
(C) 277
(D) 299
(E) 22
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Answer: (A) 10
Question: If 50% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
(A) 3:2
(B) 2:3
(C) 1:2
(D) 4:5
(E) 5:3
Rationale: Let 50% of A = 1/3 B. Then,
50A/100 = 1B/3 => 1A/2 = 1B/3
A/B = (1/3 * 2/1) = 2/3
A:B = 2:3.
Answer: B
Answer: (B) 2:3
Question: Elizabeth is interested in dividing the rooms in the house among the family. Unfortunately, they do not divide equally. It turns out that in order for the rooms to be dividable, Elizabeth has to build two more rooms and kick out one of the family members. Which of the following can describe the number of the initial rooms in the house and the initial number of family members (in the order Rooms, family)?
(A) 20; 8.
(B) 30; 9
(C) 15; 6
(D) 10; 5.
(E) 22; 10.
Rationale: Scientists have found new evidence.
Let R be the initial number of rooms and F be the no of members
Then as per the given question : R+2 should be divisible by F-1..
Now check the given values and see which satisfy the above
Only two values satisfy the condition :
10, 5
30,9
10,5 can't be the solution as its already mentioned in statement that the initial no of room are not divisible by the initial no of family members .. hence answer is 30,9
ANSWER:B
Answer: (B) 30; 9
Question: The average of 5 numbers is 7.4. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?
(A)  1.5
(B)  3.0
(C)  3.9
(D)  4.5
(E)  6.0
Rationale: The average of 5 numbers is 7.4
The sum of 5 numbers will be 7.4 x 5 = 37
The average of 5 number after one of the number is multiplied by 3 is 9.2
The sum of the numbers will now be 9.2 x 5 = 46
So the sum has increased by 46-37 = 9
Let the number multiplied by 3 be n
Then,
3n = n+9
or 2n = 9
or n = 4.5
Answer:- D
Answer: (D)  4.5
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers e did Carl drive each way?
(A)  350
(B)  345
(C)  320
(D)  280
(E)  240
Rationale: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try e=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Answer: (D)  280
Question: How many different arrangements of letters are possible if three letters are chosen from the letters A through J and the letters E and A must be among the letters selected?
(A) 36
(B) 39
(C) 42
(D) 45
(E) 48
Rationale: Besides A and E, there are 8 letters and we can choose one of them.
8C1 = 8
Three letters can be arranged in 3! ways.
The number of arrangements is 8*3! = 48
The answer is E.
Answer: (E) 48
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 41, what is the value of K?
(A)  41
(B)  15 3/4
(C)  22
(D)  23
(E)  25 3/10
Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 41
11K = 41 * 4 +1 = 164 +1 = 165
K = 165 / 11 = 15.
Answer A.
Answer: (A)  41
Question: If k^3 is divisible by 540, what is the least possible value of integer k?
(A) 12
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: 540 = 2^2*3^3*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Answer: (B) 30
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 120 m
(B) 240 m
(C) 300 m
(D) 360 m
(E) 280 m
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	(x + 300)/36	= 15
x + 300 = 540
x = 240 m.Answer: Option B
Answer: (B) 240 m
Question: rectangle dimensions were given,2 doors dimensions given, 2 windows dimensions given. 70cm wide wallpaper to be covered on the walls of this room. Cost of wallpaper is 60 per meter.. calculate total cost
(A) 20
(B) 25
(C) 30
(D) 60
(E) 70
Rationale: area of room=(l*b) m^2
area of door+window=(d+w)m^2
Remaining area= ((l*b)-(d+w))m^2
So length=Remaining area/0.70 m
Total cost= length*60---ans
and total cost=60
ANSWER:D
Answer: (D) 60
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/3 of his salary. What fraction of his income came from tips ?
(A) 4/9
(B) 5/4
(C) 5/8
(D) 5/9
(E) 6/9
Rationale: Income = salary (s) +tips = s + s*5/3 = s*8/3
Tips = s*8/3
fraction of his income came from tips = (s*5/3)/(s*8/3)= 5/8
ANSWER:C
Answer: (C) 5/8
Question: Today David is twice as old as Sam and Sam is 3 years younger than Dravid. If David, Sam, and Dravid are all alive 4 years from today, which of the following must be true on that day.
I. David is twice as old as Sam
II. Sam is 3 years younger than Dravid
III. David is older than Dravid
(A) II
(B) I, II & III
(C) III
(D) I
(E) I,II
Rationale: Say Dravid age is 10
Sam age is 7
David age is 14
After 4 years
Dravid age is 14
Sam age is 11
David age is 28
i.e ) after 4 years
Sam is 3 years younger than David
David is twice as old as Sam
David is older than Dravid
Answer : B
Answer: (B) I, II & III
Question: What is the tens' digit E of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
(A) E=2
(B) E=3
(C) 4
(D) 8
(E) 9
Rationale: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Answer: (B) E=3
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 110
(B) 140
(C) 185
(D) 200
(E) 210
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: Can C and can В are both right circular cylinders. The radius of can C is twice the radius of can B, while the height of can C is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can C with the same brand of gasoline?
(A)  $1
(B)  $2
(C)  $4
(D)  $8
(E)  $16
Rationale: Let x be the radius of b and 2h be the height of B. Therefore, radius of C = 2x and height = h
Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h
cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16
Ans E
Answer: (E)  $16
Question: The average height of 35 boys in a class was calculated as 184cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
(A) 187.89 cm
(B) 182.29 cm
(C) 123.98 cm
(D) 149.98 cm
(E) 146.89 cm
Rationale: Calculated average height of 35 boys = 184 cm.
Wrong total height of 35 boys = 184 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 183 cm - (166 cm + 106 cm)/35
= 184 cm - 60 /35 cm
= 184 cm - 1.71 cm = 182.29 cm.
Answer: B
Answer: (B) 182.29 cm