mathewhe/aqua_rat huggingface dataset:
Question: If an object travels at nine feet per second, how many feet does it travel in one hour?
(A) 30
(B) 300
(C) 720
(D) 1800
(E) 32400
Rationale: Speed = 9 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X9 = 32400
Answer E
Answer: (E) 32400
Question: A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
(A) 5 minutes
(B) 6 minutes
(C) 8 minutes
(D) 9 minutes
(E) 10 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;
Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;
d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.
Interval=\frac{d}{b}=\frac{6b}{b}=6
Answer: B (6 minutes).
Answer: (B) 6 minutes
Question: P software has coding line 5% more than N, N software has coding line 1/3 more than M. M software has 90 lines of coding. find P lines.
(A) 106
(B) 107
(C) 126
(D) 109
(E) 110
Rationale: M s/w has 90 line of code
N s/w has = 90+90*1/3= 120 line of code
P s/w 5% more N' code 120+6=126
ANSWER:C
Answer: (C) 126
Question: In a locality, the prevailing price of a 700 square feet property last year was US Dollar 1000. The owner made some additions and the 900 square feet property is now fetching a price of US Dollar 1500. By approximately what percent did the ratio of price to size increase from the previous year's price?
(A) 12
(B) 14
(C) 17
(D) 21
(E) 19
Rationale: Initial price/area ratio = 1000/700 = 9000/6300
Revised mileage/weight ratio = 1500/900 = 10500/6300
Answer: C
Answer: (C) 17
Question: On dividing 271 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
(A) A)12
(B) B)15
(C) C)16
(D) D)17
(E) E)30
Rationale: d = (D-R)/Q
= (271 - 1)/9
= 270/9 = 30
E)
Answer: (E) E)30
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 10 to produce 80 units?
(A) 63
(B) 20
(C) 42
(D) 65
(E) 84
Rationale: 5 machines would produce 80 units in 40 hours. Increasing the amount of machines by 2 would mean dividing 40 hours by 2.
40/2 = 20
Answer : B
Answer: (B) 20
Question: There is a square with sides of 9. What is the area of the biggest circle that can be cut out of this square?
(A) 72.83
(B) 63.62
(C) 81
(D) 254.47
(E) 100
Rationale: Area of a circle = area=Ï€r^2
Square is 9 wide, so circle's diameter would be 9, and radius would be 4.5
area=Ï€4.5^2 which is approximately 63.62
Answer is B
Answer: (B) 63.62
Question: There are 8 stations between Vijayawada and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 100
(B) 90
(C) 190
(D) 110
(E) 105
Rationale: The total number of stations = 10
From 10 stations we have to choose any two stations and the direction of travel (i.e.,Vijayawada to Chennai is different from Chennai to Vijayawada) in 10P2 ways.
10P2= 10 * 9 = 90
ANSWER: B
Answer: (B) 90
Question: In how many ways can the letters of the English alphabets be arranged so that there are seven letters between the letters A and B, and no letter is repeated?
(A) 24P7*2*18!
(B) 24P7*2*20!
(C) 18*24!
(D) 36*24!
(E) 36*25!
Rationale: first we can arrange 7 letter b/w in 24p7 way
then A and B can be arrenge in *2 way so total is 24p7*2
no consider this 9 letter as 1 number so remainin number can be arrange in
(26-9+1)!
so ans = 24p7*2*18!
ANSWER:A
Answer: (A) 24P7*2*18!
Question: Which of the following CANNOT be a product of two distinct positive integers X and Y?
(A) X
(B) Y
(C) 3Y + 2X
(D) Y - X
(E) YX
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take X = 1 and Y = 2 and work with the options
XY = 2
A) X take X =2, Y = 1
B) Y take X = 1 Y = 2
C) 3Y + 2X Seems tricky, lets see other options and then come back to it.
D) Y - X take Y = 1 and X = 2 --> Y - X = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) YX Always true
You don't even have to worry what C is !
ans D
Answer: (D) Y - X
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
(A) 10
(B) 100
(C) 1000
(D) 10000
(E) None of these
Rationale: Explanation:
number of cubes=(100 x 100 x 100)/(10 x 10 x 10)=1000
Answer: C
Answer: (C) 1000
Question: In what time a sum of money double itself at 5% per annum simple interest?
(A) 33 1/8%
(B) 20%
(C) 83 1/3%
(D) 33 4/3%
(E) 73 1/3%
Rationale: P = (P*5*R)/100
R = 20%
Answer:B
Answer: (B) 20%
Question: 3 years before age of A was double than age of B.after 7 years the sum of their ages will 83.calculate the age of A.
(A) 24
(B) 21
(C) 40
(D) 45
(E) 42
Rationale: Let 3 years before age of B=x year and age of A=2x year
present age of B=(x+3) and present age of A=(2x+3)
after 7 years age of B=(x+10) year and age of A=(2x+10) year
(x+10)+(2x+10)=83,3x=63,x=21.
present age of A=(2x+3)=45 years
answer D
Answer: (D) 45
Question: A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1
(A) After 3 months
(B) After 4 months
(C) After 6 months
(D) After 2 1⁄2 months
(E) None of these
Rationale: Let B joined after x months.
Then, 4500 × 12 : 3000 (12 – x) = 2 : 1
Ratio of their investments
4500×12/3000(12−x)=2/1 ⇒ x = 3
Answer A
Answer: (A) After 3 months
Question: A total of 525 players participated in a single tennis knock out tournament. What is the total number of matches played in the tournament? (Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
(A) 511
(B) 512
(C) 256
(D) 524
(E) 1023
Rationale: There are 525 players, only 1 person wins, 524 players lose. in order to lose, you must have lost a game.
524 games.
Ans- D
Answer: (D) 524
Question: A retail item is offered at a discount of x percent (where x > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of x, would result in the same final price?
(A) x+5/1.05
(B) x/1.05 +5
(C) 1.05x-5
(D) x-5/1.05
(E) 1.05(x – 5)
Rationale: Let y be the price of the item.
Final price after discount and sales tax = y * (1 - x/100) * 1.05
Let z be the percent discount which would result in the same final price.
Then,
y * (1 - x/100) * 1.05 = y * (1 - z/100)
=> 1.05 - 1.05x/100 = 1 - z/100
=> z/100 = 1.05x/100 - .05
=> z = 1.05x - 5
Hence ,option C is correct.
Answer: (C) 1.05x-5
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance W that he will have a matched pair?
(A) W=2/5
(B) W=3/5
(C) W=1/5
(D) 1/2
(E) 7/5
Rationale: P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: (A) W=2/5
Question: 0.0005521/0.0000110 x 15.05=?
(A) 7534
(B) 255.4
(C) 756.4
(D) 755.4
(E) 752.4
Rationale: Explanation :
? = 0.0005521/0.0000110 x 15.05 = 755.4
Answer : Option D
Answer: (D) 755.4
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 18%
(B) 22%
(C) 12%
(D) 92%
(E) 14%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 12%
Question: M is the sum of the reciprocals of the consecutive integers from 601 to 700, inclusive. Which of the following is true?
(A) 1/7 < M < 1/6
(B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/12 < M < 1/9
Rationale: M = 1/601 + 1/602 + 1/603 + ...... + 1/700
If we replace the first 99 terms by 1/700, then we get a sum = 100/700 = 1/7. Since the actual terms are larger than 1/700, the sum is larger than 1/7.
If we replace the all the 100 terms by 1/600, we get a sum = 100/600 = 1/6. Since the actual terms are smaller than 1/600, the sum is less than 1/6.
Therefore 1/7 < M < 1/6
Choice A
Answer: (A) 1/7 < M < 1/6
Question: 16.036 divided by 0.04 gives :
(A) 40.09
(B) 4.06
(C) 40.06
(D) 400.9
(E) 400.6
Rationale: = 16.036/0.04
= 1603.6/4
= 400.9
Answer is D.
Answer: (D) 400.9
Question: Donovan and Michael are racing around a circular 300-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) 6
(B) 9
(C) 8
(D) 7
(E) 10
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 300/45 =>60/9
2. Speed/ Rate of Michael = Distance/ time => 300/40 => 30/4
Relative Speed between them =30/4 - 60/9 => 270 -240/36 = 30/36 =5/6 (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 = 300, Relative Rate = 5/6
Total Time taken by Micheal to surpass Donovan = Distance / rate => 300*6/5 => 1800/5 => 360
No. of laps taken by Michael = Total time / Michael's rate => 360/40 => 9
Hence correct answer is 9 Laps.
B
Answer: (B) 9
Question: A wheel rotates 10 times every minute and moves 40 cm during each rotation. How many metres does
the wheel move in one hour?
(A) 123 metre
(B) 240 metre
(C) 120 metre
(D) 1200 metre
(E) 2200 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *40) cm = 24000 cm
In metres = 240 metre
Answer: B
Answer: (B) 240 metre
Question: The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 70,30 kmph
(B) 80,40 kmph
(C) 10,40 kmph
(D) 80,80 kmph
(E) 84,40 kmph
Rationale: Speed downstream = 50 + 20
= 70 kmph
Speed upstream = 50 - 20
= 30 kmph
Answer: A
Answer: (A) 70,30 kmph
Question: A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certain green paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
(A) 2.8
(B) 3.5
(C) 4.2
(D) 5
(E) 7
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each.
Thus 5 grams a piece. Out of the 5 grams of the violet paint, 70% is red.
Therefore, 5*.7 = 3.5 Grams of red pigment
ANSWER:B
Answer: (B) 3.5
Question: Arun and Amit started walking from two different points 'A' and 'B' respectively.Arun walks 2 kms North and turns to the East and walks 3 kms and again turns to North walks 4 kms and finally turns to East and Walks 5kms to reach point 'C'. Similarly, Amit walks 2 kms North and turns to west and walks 3 kms and finally turns to North, walks 4 kms and meets Arun at point 'C'. What is the distance between Arun and Amit's starting points?
(A) 5 km
(B) 8 km
(C) 11 km
(D) 13 km
(E) 15 km
Rationale: Explanation:
Where A= Arun's starting point; B = Amit's starting point; C = The point where Arun and Amit meet
PQ + RC + ST = 3 + 5 + 3 = 11 kms.
ANSWER IS C
Answer: (C) 11 km
Question: Find the missing number in the given sequence : 1,2,3,5,?,13,21,?
(A) 8 & 34
(B) 7 & 34
(C) 9 & 34
(D) 7 & 35
(E) 7 & 36
Rationale: 1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34
ANSWER:A
Answer: (A) 8 & 34
Question: What is 7 1/4 - 4 2/3 divided by 7/8 - 3/4 ?
(A) 87/36
(B) 36/17
(C) 7/6
(D) 62/3
(E) 5/4
Rationale: 7 1/4 - 4 2/3 = 29/4 - 14/3 = (87 - 56 )/12 = 31/12
7/8 - 3/4 = (7-6)/8 = 1/8
So 31/12/1/8 = 31/12 * 8 = 62/3
Answer - D
Answer: (D) 62/3
Question: The average of 11 numbers is 9.6. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 9.5
(B) 10
(C) 10.5
(D) 11.5
(E) 25.8
Rationale: Explanation:
1 to 11 = 11 * 9.6 = 105.6
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 105.6 = 25.8
6th number = 25.8
Option E
Answer: (E) 25.8
Question: Set C consists of 19 elements. The average of set C is L. If a new element is added to the set and the average grows by K, what is the value of the new element?
(A) a) L(1 + K / 5)
(B) b) L * (K/100) - 20L
(C) c) 20L(1+K/100)
(D) d) 20(1+K/100)-19L
(E) e) L*(K/5)-19
Rationale: Let's assume the value of new element to bea. So converting the word problem into equation,
(19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K
But according to the answer options, problem writer wanted to conveyk% percent rise in average value.
If we consider this case than resulting equation will be,
(19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]
==> a= 20L + KL/5 -19L
==> a= L + KL/5 , which is equivalent to option [A]
Answer: (A) a) L(1 + K / 5)
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/6, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
(A) 1/32
(B) 7/8
(C) 9/64
(D) 5/64
(E) 3/64
Rationale: P(Xavier will solve)=1/6
P(Yvonne will solve)=1/2
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/6)*(1/2)*(3/8) = 1/32.
Ans. A.
Answer: (A) 1/32
Question: The bankers discount and the true discount of a sum at 15% per annum simple interest for the same time are Rs.120 and Rs.60 respectively. What is the sum and the time?
(A) Sum = Rs.160 and Time = 6.6 years
(B) Sum = Rs.120 and Time = 6.6 years
(C) Sum = Rs.140 and Time = 6.6 years
(D) Sum = Rs.200 and Time = 6 years
(E) None of these
Rationale: Explanation :
BD = Rs.120
TD = Rs.60
R = 15%
F = BD ×TD/(BD – TD)=120×60/(120–60)=120×60/60=Rs. 120
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒120 = (120×T×15)/100
⇒1200 = 12 × T × 15 ⇒100 = 15 × T
⇒ T = 100/15 = 6.6 years Answer : Option B
Answer: (B) Sum = Rs.120 and Time = 6.6 years
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 9 3/6
(B) 9 3/4
(C) 9 3/8
(D) 5 3/2
(E) 9 3/2
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer:C
Answer: (C) 9 3/8
Question: There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 987
(B) 177
(C) 357
(D) 267
(E) 380
Rationale: The total number of stations = 20
From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.
²⁰P₂ = 20 * 19
= 380.
Answer:E
Answer: (E) 380
Question: A sells a bicycle to B and makes a profit of 25%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.
(A) 237
(B) 126
(C) 971
(D) 611
(E) 144
Rationale: Explanation:
Let CP be 100
A sells at 25% profit so SP=125
B sells at 25% profit = 125 x (1+25/100) = 156.25
CP SP
100--- 156.25
x --- 225
CP = 225 x 100/156.25 = 144
ANSWER: E
Answer: (E) 144
Question: Average of first five multiples of 4 is
(A) 12
(B) 11
(C) 13
(D) 15
(E) 16
Rationale: Explanation:
Average=4(1+2+3+4+5)/5=12
Answer: Option A
Answer: (A) 12
Question: A card shop contains 5 birthday cards, 4 holiday cards, and 3 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be graduation cards?
(A) 1/33
(B) 6/264
(C) 1/44
(D) 1/264
(E) 1/1320
Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 3/12
Probability of choosing 2nd card of the same type: 2/11
Probability of choosing 3rd card of the same type: 1/10
Multiply and you get 1/264
Answer D.
Answer: (D) 1/264
Question: A train crosses a platform of 180 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 30
(B) 887
(C) 167
(D) 197
(E) 161
Rationale: Length of the train be ‘X’
X + 180/15 = X + 250/20
20X + 3600 = 15X + 3750
5x=150
X = 30m
Answer: A
Answer: (A) 30
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 5 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 600
(D) 480
(E) 960
Rationale: Total # of outfits = 12 * 10 *5 = 600
Answer - C
Answer: (C) 600
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/28
(B) 2/27
(C) 2/21
(D) 2/89
(E) 2/11
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35)
= 2/21
Answer: C
Answer: (C) 2/21
Question: A bag contains 10 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 8/15
(B) 21/44
(C) 3/5
(D) 11/15
(E) 7/15
Rationale: Drawing two balls of same color from ten green balls can be done in 10C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 10C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 21/44
ANSWER:B
Answer: (B) 21/44
Question: Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.
B.
C.
D.
E.
(A) 8
(B) 13
(C) 16
(D) 24
(E) 27
Rationale: Each group has 8 = 8+8+8 = 24 max
4 people are in 2 groups, subtract 4 people twice as they are counted twice
Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group
Ans: 8+8+8-(2(4)) - 3 = 13
ANSWER:B
Answer: (B) 13
Question: What approximate value should come in place of the question mark (?) in each of the following equations ?
27.874 x 15.01 3 = ?
(A) 135
(B) 137
(C) 139
(D) 28
(E) 27
Rationale: Explanation :
27.9 x 15 3 = 27 - 9 x 5 = 139.5
Answer : Option C
Answer: (C) 139
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
(A) 8000
(B) 2787
(C) 27766
(D) 9976
(E) 21671
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160
18x + 45x + 39x = (8160 * 100)
102x = 816000 => x = 8000.
Answer: A
Answer: (A) 8000
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was?
(A) 9 years
(B) 10 years
(C) 11 years
(D) 14 years
(E) 16 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
D)
Answer: (D) 14 years
Question: If the sides of a triangle are 28 cm, 26 cm and 12 cm, what is its area?
(A) 120 cm2
(B) 156 cm2
(C) 178 cm2
(D) 189 cm2
(E) 176 cm2
Rationale: The triangle with sides 28 cm, 26 cm and 12 cm is right angled, where the hypotenuse is 28 cm.
Area of the triangle
= 1/2 * 26 * 12
= 156 cm2
Answer: B
Answer: (B) 156 cm2
Question: A pipe can fill the tank in 5 hours. Due to leakage at the bottom it is filled in 6 hours. When the tank is full, in how much time will it be empties by the leak?
(A) 30 hours
(B) 28 hours
(C) 27 hours
(D) 25 hours
(E) 24 hours
Rationale: When there is no leakage, the pipe can fill the cistern in 5 hours.
Therefore, The pipe fills 1/5 th part of the tank in one hour.
When there is a leakage, the pipe can fill the cistern in 6 hours.
In case of leakage, the pipe fills 1/6 th part of the tank in one hour.
So, in 1 hour due to leakage (1/5 – 1/6) th
= (6 – 5)/30 th
= 1/30 th
The part of the tank is emptied.
So, the tank will be emptied by leakage in 30 hours.
answer :A
Answer: (A) 30 hours
Question: There are 10 people and 7 chairs. In how many different ways people can occupy the chairs?
(A) 800
(B) 810
(C) 820
(D) 830
(E) 840
Rationale: number of ways = 10*9*8*7 = 5040
Answer is C
Answer: (C) 820
Question: A company decreased the price of its main product by 30%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
(A) 1.26
(B) 2.54
(C) 5.23
(D) 4.23
(E) 3.33
Rationale: For the total revenue to remain the same when the price is 3/10, the number of products sold must 3/10 times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/30% = 3.33
Answer : E
Answer: (E) 3.33
Question: What is the greatest positive integer R such that 3^R is a factor of 9^10?
(A) R=5
(B) R=9
(C) R=10
(D) R=20
(E) 30
Rationale: What is the greatest positive integer R such that 3^R is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: (D) R=20
Question: there are digits from 1 to 6 .from that 5 digit no are to be formed such that they are divisible by 4. find no of possible combinations?
(A) 1944 ways.
(B) 1844 ways.
(C) 1744 ways.
(D) 1644 ways.
(E) 1544 ways.
Rationale: A) w/o repeatations.
possible last two digits= 12, 16, 24, 32, 36, 52, 56, 64
so total of 8 ways to fill last two digit.
remaining 3 digits can be filled by (6-2)! =4! ways=24 ways
so total no of ways=24*8=192 ways.
B)with repeataions
possible last two digits= 12, 16, 24, 32, 36,44, 52, 56, 64
so total of 9 ways to fill last two digit.
remaining 3 digits can be filled by 6*6*6 ways=216 ways
so total no of ways=216*9=1944 ways.
ANSWER:A
Answer: (A) 1944 ways.
Question: Students are partnered in the class and are given stickers for their behavior. Green stickers are for good behavior, yellow stickers are for okay behavior, and red stickers for for behavior requiring discipline. The students' desks are labeled A, B, C, and D. If A:B = green/yellow, B:C = yellow/red, C:D = red/student absent no sticker, and then D:A are partnered. What will D:A sticker color be if behavior does not change?
(A) green only
(B) yellow only
(C) red only
(D) A & C
(E) none of the above
Rationale: Solution
A : B = green : yellow, B : C = yellow : red, C : D = red : student absent no sticker
âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= green : yellow : red : student absent no sticker.
Thus, A : D = green : student absent no sticker Or D : A = student absent no sticker: green
Correct Option A
Answer: (A) green only