mathewhe/aqua_rat huggingface dataset:
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time B will it take to fill the tank now?
(A)  50% less time
(B)  50% more time
(C)  75% less time
(D)  75% more time
(E)  100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is B=50 % less.A
Answer: (A)  50% less time
Question: A cat chases a rat 6 hours after the rat runs. cat takes 4 hours to reach the rat. If the average speed of the cat is 90 kmph, what s the average speed of the rat?
(A) 32kmph
(B) 26kmph
(C) 35kmph
(D) 36kmph
(E) 32kmph
Rationale: cat take 10 hours and rat take 4 hours...then Distance chased by them is 90*4.so speed of rat is (90*4)/10=36kmph.
ANSWER IS D
Answer: (D) 36kmph
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?
(A) 26 sec
(B) 30 sec
(C) 13 sec
(D) 19 sec
(E) 12 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) 30 sec
Question: In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack?
(A) 10
(B) 11
(C) 12
(D) 15
(E) 18
Rationale: This question can be solved by TESTing THE ANSWERS.
Answer C: 12 total cards
With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is...
(11/12)(10/11) = 110/132 ~= 5/6
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
C
Answer: (C) 12
Question: A woman has three blouses of different colors, three skirts of different colors, and thee different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
(A) 8
(B) 12
(C) 25
(D) 17
(E) 18
Rationale: total ways = 3*3*3=27..
now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..
the ways in which the pink blouse and green skirt are together=1*1*2=2..
total ways =27-2=25..
ANSWER:C
Answer: (C) 25
Question: If the sum of five consecutive positive integers is A, then the sum of the next three consecutive integers in terms of A is:
(A) 3A/5
(B) 3A/5 +12
(C) A
(D) 5A/3
(E) 5A/3 +12
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/5 = Mean = Third Integer
First Integer = A/5 - 2
Second Integer = A/5 - 1
Third Integer = A/5
Fourth Integer = A/5 + 2
Fifth Integer = A/5 + 2
i.e.
Sixth Integer = A/5 + 3
Seventh Integer = A/5 + 4
Eighth Integer = A/5 + 5
Now Mean of next 3 Integers = Median = A/5 + 4
i.e. Sum of Next 3 integers = (A/5 + 4)*3 = 3A/5 +12
Answer: option B
Answer: (B) 3A/5 +12
Question: Find value of x: 121 × 54 = x
(A) 34545
(B) 46576
(C) 67887
(D) 57687
(E) 75625
Rationale: 121×54=121×(102)4=121×1000016=7.5625×10000=75625
E
Answer: (E) 75625
Question: What is the smallest no. that should be added to 45454 to make it exactly divisible by 9?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 4+5+4+5+4=22, the next multiple of 9 is 27.
5 must be added to 45454 to make it divisible by 9
C
Answer: (C) 5
Question: The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount?
(A) Rs. 432
(B) Rs. 425
(C) Rs. 412
(D) Rs. 442
(E) None of these
Rationale: Explanation :
F = Rs. 2360
TD = Rs. 360
PW = F - TD = 2360 - 360 = Rs. 2000
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2000 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2360 for unexpired time
=360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B
Answer: (B) Rs. 425
Question: How many cubes of 25 cm edge can be put in a cubical box of 1 m edge.
(A) 177 cm
(B) 100 cm
(C) 86 cm
(D) 64 cm
(E) 87 cm
Rationale: Number of cubes =100âˆ—100âˆ—100/25âˆ—25âˆ—25=64
Note: 1 m = 100 cm
Answer:D
Answer: (D) 64 cm
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 2 km/hr
(B) 5 km/hr
(C) 7.2 km/hr
(D) 9 km/hr
(E) 11 km/hr
Rationale: Explanation:
Speed =(600/5*60)m/sec
= 2 m/sec.
Converting m/sec to km/hr
=(2*18/5)km/hr=7.2 km/hr
ANSWER:C
Answer: (C) 7.2 km/hr
Question: If the cost price of 17 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
(A) 20% loss
(B) 6.25% profit
(C) 33.33 % loss
(D) 30.33% loss
(E) None of these
Rationale: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 17 articles = Rs. 17.
Selling price of 16 articles = Rs. 17
Therefore, Selling price of 17 articles is :-
=>17/16Ã—17
=>18.06
Therefore, Profit = Selling price - Cost price.
=>18.06âˆ’17=1.06
Hence, the percentage of profit = profit x 100/C.P.
=>1.06/17Ã—100.
=>6.25% Profit.
Answer : B
Answer: (B) 6.25% profit
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 228
(B) 162
(C) 5528
(D) 256
(E) 191
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Answer: (B) 162
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) Rs. 12
(B) Rs. 15
(C) Rs. 18
(D) Rs. 21
(E) Rs. 24
Rationale: Dividend on Rs. 20 = Rs.	9/100	x 20 =Rs.	9/5	.
Rs. 12 is an income on Rs. 100.
Rs.	9/5	is an income on Rs.100/12 x 9/5	= Rs. 15.
Answer: Option B
Answer: (B) Rs. 15
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 121
(B) 10
(C) 16
(D) 12
(E) 71
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54 * 60
= 10 min.
Answer: B
Answer: (B) 10
Question: Complete the sequence:
B E J Q ?
(A) M
(B) D
(C) S
(D) D
(E) Z
Rationale: E
B+3=E
E+5=J
J+7=Q
Q+9=Z
Answer: (E) Z
Question: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/3, then x + y =
(A)  4.5
(B)  7
(C)  8
(D)  19/3
(E)  12
Rationale: Line k passes through the origin and has slope 1/3 means that its equation is y=1/3*x.
Thus: (x, 1)=(3, 1) and (10, y) = (10,10/3) --> x+y=3+10/3=19/3.
Answer:D.
Answer: (D)  19/3
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 7.2 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
(A) One
(B) Six
(C) Nine
(D) Ten
(E) Eleven
Rationale: Mean = 7.2
Standard Deviation = 0.3
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 7.2+1.5*0.3 = 7.65
and 1.5 standard deviation BELOW the mean = 7.2-1.5*0.3 = 6.75
hence, 1 value fall within 1.5 SD from Mean
Answer: Option A
Answer: (A) One
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
(A) Rs. 3944
(B) Rs. 3828
(C) Rs. 4176
(D) Cannot be determined
(E) None of these
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
ANSWER:A
Answer: (A) Rs. 3944
Question: If the 5th date of a month is Tuesday, what date will be 3 days after the 3rd Friday in the month?
(A) 17
(B) 18
(C) 20
(D) 22
(E) 33
Rationale: B
18
5th date of a month is Tuesday
Friday will be on = 5 + 3
= 8th of a month
1st Friday is on 1 st of a month
2nd Friday is on 8th of a month
3rd Friday will be on 15th of a month
3 days after 15th = 15 + 3 = 18
Answer: (B) 18
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:48
(C) 39:49
(D) 39:46
(E) 39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer:A
Answer: (A) 39:40
Question: There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability E that the both positions will be taken by members of just one party?
(A) 1/25
(B) 12/49
(C) 1/4
(D) 24/49
(E) 1/2
Rationale: E probability of one party having both spots:
(1/2) * (24/49) = 12/49
(1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.
Since this result can happen for both parties, (12/49) + (12/49) = (24/49)
Answer: D
Answer: (D) 24/49
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
(A) 8:9
(B) 8:7
(C) 8:1
(D) 8:2
(E) 8:8
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
Answer:B
Answer: (B) 8:7
Question: A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid.
The value of the 8th installment is:
(A) Rs 35
(B) Rs 50
(C) Rs 65
(D) Rs 70
(E) Rs 80
Rationale: Explanation :
Let the first installment be 'a' and the common difference between any two consecutive installments be 'd'
Using the formula for the sum of an A.P :-
S=n/2[2a+(n−1)d].
We have,
3600=40/2[2a+(40-1)d].
3600=20[2a+39d].
180 =2a+39d. ----(i)
Similarly,
2400=30/2[2a+(30-1)d].
160=2a+29d. ----(ii)
On solving both the equations we get:
d=2 and a=51
Hence, the Value of 8th installment is :-
=51+(8−1)2.
=65.
Answer : C
Answer: (C) Rs 65
Question: Use distributive property to solve the problem below:
Maria bought 12 notebooks and 6 pens costing 2 dollars each.How much did Maria pay?
(A) 30 dollars
(B) 36 dollars
(C) 50 dollars
(D) 60 dollars
(E) 70 dollars
Rationale: Solution
2 × (12 + 6) = 2 × 12 + 2 × 6 = 24 + 12 = 36 dollars
Answer B
Answer: (B) 36 dollars
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
(A) 19 years
(B) 18 years
(C) 61 years
(D) 14 years
(E) 13 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/3
= 19 years.
Answer:A
Answer: (A) 19 years
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many hours R would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
(A)  22 hours
(B)  30 hours
(C)  44 hours
(D)  60 hours
(E)  It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job R in 44 hours.
Answer: C.
Answer: (C)  44 hours
Question: A can do a piece of work in 8 hours; B and C together can do it in 12 hours, while A and C together can do it in 16 hours. How long will B alone take to do it?
(A) 7 8/5 hours
(B) 5 9/8 hours
(C) 5 6/8 hours
(D) 6 6/7 hours
(E) none of the above
Rationale: A's 1 hour's work = 1/8 ;
(B + C)'s 1 hour's work = 1/12 ;
(B + C)'s 1 hour's work = 1/16
(A + B + C)'s 1 hour's work = (1/8 + 1/12) = 5/24
B's 1 hour's work = (5/24 - 1/16) = 7/48
B alone will take 48/7 hours to do the work.
=6 6/7
Answer = D
Answer: (D) 6 6/7 hours
Question: An electric pump can fill a tank in 7 hours. Because of a leak in the tank, it took 14hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
(A) 10hours
(B) 12hours
(C) 8hours
(D) 5hours
(E) 14hours
Rationale: Work done by the leak in 1 hour = 1/7 - 1/14 = 1/14
The leak will empty the tank in 14hours
Answer is E
Answer: (E) 14hours
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 5, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
(A) 600
(B) 1200
(C) 1500
(D) 1600
(E) 2400
Rationale: Sugar:Flour = 5:5 = 10:10;
Flour:Soda = 10:1 = 10:1;
Thus we have that Sugar:Flour:Soda = 10x:10x:1x.
Also given that 10x/(1x+60) = 8/1 --> x=240 --> Sugar = 10x = 2400
Answer: E.
Answer: (E) 2400
Question: After a storm deposits 115 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 245 billion gallons, the reservoir was approximately what percentage full before the storm?
(A) 45%
(B) 48%
(C) 54%
(D) 58%
(E) 65%
Rationale: When the storm deposited 115 billion gallons, volume of water in the reservoir = 245 + 115 = 360 billion gallons
If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.8 = 450 billion gallons
Therefore percentage of reservoir that was full before the storm = (245/450)*100 = 54.4%
Option C
Answer: (C) 54%
Question: A certain company reported that the revenue on sales increased 20 % from 2000 to 2003, and increased 40 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
(A) 50 %
(B) 40 %
(C) 35 %
(D) 32 %
(E) 17 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 120 and and in 2005 140, so from 2003 to 2005 it increased by (140-120)/120=20/120=17%
Answer: E.
Answer: (E) 17 %
Question: Look at this series: V, __, XI, XIV, XVII, XX, ... What number should fill the blank?
(A) IX
(B) XXIII
(C) XV
(D) VII
(E) None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Answer: (D) VII
Question: A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability K that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: The sum of the three numbers on the balls selected from the box to be odd one should select either three odd numbered balls (Odd+Odd+Odd=Odd) or two even numbered balls and one odd numbered ball (Even+Even+Odd=Odd);
P(OOO)=(1/2)^3;
P(EEO)=3*(1/2)^2*1/2=3/8 (you should multiply by 3 as the scenario of two even numbered balls and one odd numbered ball can occur in 3 different ways: EEO, EOE, or OEE);
So finally K=1/8+3/8=1/2.
Answer: C.
Answer: (C) 1/2
Question: Simple interest at x% for x years will come out to be Rs x on a sum of Rs?
(A) 109/x
(B) 130/x
(C) 100/x
(D) 120/x
(E) 101/x
Rationale: Explanation:
Formula for Simple Interest:
SI = Principal*Rate*Time
SI= x
Rate= x/100
Time= x
=> x= Principal*(x/100)*x
=>Principal Amount= 100/x
ANSWER: C
Answer: (C) 100/x
Question: The average of any 5 consecutive odd natural numbers is k . If two more such numbers , just next to the previous 5 numbers are added , the new average becomes
(A) k+8
(B) k+1
(C) k+9
(D) k+2
(E) k+4
Rationale: Explanation:
The 5 consecutive odd numbers whose average is k are (k-4), (k-2), k, (k+2), (k+4)
Again the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)
Answer: D
Answer: (D) k+2
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 300 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(A) 250
(B) 300
(C) 350
(D) 700
(E) 500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 300 meters, thus second time she runs 2*300 = 600 meters.
Since second time (when they run full circumference) Brenda runs 600 meters and Sally runs 150 meters, thus the circumference is 600 + 150 = 750 meters.
Answer: D.
Answer: (D) 700
Question: What is the remainder when 43717^(43628233) is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: We need to find the units digit of the number.
The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.
Since 43628233 has the form 4a + 1, the units digit is 7.
Then the remainder when dividing by 5 is 2.
The answer is C.
Answer: (C) 2
Question: If 1/4 of the time from midnight plus 1/2 of the time from now to midnight is the present time,then what is the present time ?
(A) 9:36 AM
(B) 9:39 AM
(C) 9:26 AM
(D) 9:46 AM
(E) 9:56 AM
Rationale: Midnight = 12 AM
let the present time is x ( taking the total time from one midnight to other is 24 hours)
so according to the given condition x/4 + (24-x)/2 = x
on solving we will get x = 9.6 means 9 hours 0.6*60 minute = 9:36 AM
ANSWER:A
Answer: (A) 9:36 AM
Question: The profit earned by selling an article for $832 is equal to the loss incurred when the same article is sold for $448. What should be the sale price for making 50% profit?
(A) 780
(B) 490
(C) 960
(D) 690
(E) 500
Rationale: C
$960
Let C.P. = $x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of $640 = 150/100 * 640 = $960.
Answer: (C) 960
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 79% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A)  7/12
(B)  1/4
(C)  1/2
(D)  7/24
(E)  17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
A
Answer: (A)  7/12
Question: A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 36
(B) 35
(C) 34
(D) 33
(E) 31
Rationale: Let the number of notes of each denomination be x
Then, x + 5x + 20x = 312
=> 26x = 312
=> x = 312/26 = 12
the total number of notes that he has = 3x = 3 × 12 = 36
Answer is A.
Answer: (A) 36
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by:
(A) 6
(B) 12
(C) 24
(D) 6 only
(E) 6 and 12 both
Rationale: Explanation:
(6n^2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
E
Answer: (E) 6 and 12 both
Question: When 1/10 percent of 6,000 is subtracted from 1/10 of 6,000, the difference is
(A) 60
(B) 600
(C) 5994
(D) 5940
(E) 594
Rationale: (1/10)*6000 - (1/10)%*6000 =
600 - (1/1000)*6000 =
600 - 6 = 594
The answer is E.
Answer: (E) 594
Question: What is the least number which when divided by 5, 9, 12 and 18 leaves remainder 4 in each care?
(A) 130
(B) 140
(C) 136
(D) 184
(E) 196
Rationale: Explanation:
LCM of 5, 9, 12 and 18 is 180
Required number = 180 + 4 = 184
Answer: Option D
Answer: (D) 184
Question: There are 11 women and 7 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 1155
(C) 1,060
(D) 1,520
(E) 1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 11C2 and 7C2 (55+21=76)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
B
Answer: (B) 1155
Question: How many ways are there to split a group of 6 boys into two groups of 3 boys each? (The order of the groups does not matter)
(A) 8
(B) 10
(C) 16
(D) 20
(E) 24
Rationale: Solution:
Division by 2 has to be made, because in scenarios like
ABC EFG
EFG ABC or,
CBA GFE
GFE CBA,
C(6,3)/2 =B
Answer: (B) 10
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
(A) Rs.4273
(B) Rs.4613
(C) Rs.4064
(D) Rs.4266
(E) None of these
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266
ANSWER:D
Answer: (D) Rs.4266
Question: Out of first 28 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
(A) 1/2
(B) 16/19
(C) 4/5
(D) 22/28
(E) 3/5
Rationale: n(S) = 28
n(Even no) = 14 = n(E)
n(Prime no) = 9 = n(P)
P(EᴜP) = 14/28 + 9/28 - 1/28 = 22/28
ANSWER:D
Answer: (D) 22/28
Question: Mahesh can do a piece of work in 50days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
(A) 45
(B) 25
(C) 37
(D) 41
(E) 50
Rationale: Work done by Mahesh in 50days = 20*1/50 = 2/5
Remaining work = 1 - 2/5 = 3/5
3/5 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*5/3= 50days
Answer is E
Answer: (E) 50
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
(A) 135
(B) 175
(C) 567
(D) 648
(E) 510
Rationale: Let no. of non- officers be x
15 * 460 + x * 110 = (x + 15) 120
x = 510
E
Answer: (E) 510
Question: On a 26 question test, 5 points were deducted for each wrong answer and 8 points were added for right answers. If all the questions were answered how many were correct if the score was zero.
(A) 22
(B) 78
(C) 66
(D) 288
(E) 211
Rationale: Answer:B
Answer: (B) 78