mathewhe/aqua_rat huggingface dataset:
Question: The present population of a town is 60,000. The population increases annually at 10%. Find the population after 3 years.
(A) 86000
(B) 79860
(C) 76300
(D) 82900
(E) None of these
Rationale: Explanation :
Solution: The required population is 60000(1 + 10/100)^3 = 60000 * 110/100 * 110/100 * 110/100 = 79,860
Answer : B
Answer: (B) 79860
Question: Of the 4 distinguishable wires that lead into an apartment, 2 are for cable television service, and 4 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y = 6
Answer is Option A
Answer: (A) 6
Question: Oak trees line both sides of a street for a length of 4/10 of a kilometer. If there is 15 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
(A) a)	26
(B) b)	23
(C) c)	24
(D) d)	44
(E) e)	46
Rationale: There is a gap of 15 m between every 2 trees , each tree is 1 m wide.
4/10 of 1 km = 400 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*15 = 400
Solve for x and we get x = 26, answer is A
Answer: (A) a)	26
Question: The average age of a committee of 8 members is 42 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
(A) 39 years
(B) 38 years
(C) 36 years
(D) 35 years
(E) 40 years
Rationale: Exp. Total age of the committee = 42*8 = 336,
Total age when a member is retired
and a new one was joined = 336-55 +39, =320
Average age of present committee = 320/8 = 40.
Answer: E
Answer: (E) 40 years
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 8
(C) 9
(D) 4
(E) 1
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer:A
Answer: (A) 6
Question: David mixed 10 kg of ghee at Rs. 200 per kg with 30 kg ghee at the rate of Rs. 100 per kg. At what price per kg should he sell the mixture to make a profit of 50% in the transaction?
(A) Rs. 180.50
(B) Rs. 187.50
(C) Rs. 107.50
(D) Rs. 188.50
(E) Rs. 187.00
Rationale: Cost of Ghee = 10*200+ 30*100 /40 =5000/40 = 125
50% of 125 = 62.50
S.P. should be = 125+62.50= Rs. 187.50/ kg
Answer : B
Answer: (B) Rs. 187.50
Question: In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 90% of the total?
(A) 515.
(B) 572.
(C) 618.
(D) 644.
(E) 666.
Rationale: Answer is B :572
Solution : Total number of students studying both are 423 + 226 - 134 = 515 (Subtracting the 134 since they were included in the both the other numbers already).
So 90% of total is 515, so 100% is approx. 572.
Answer: (B) 572.
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/26
(B) 17/25
(C) 17/22
(D) 17/20
(E) 17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.
Answer: D
Answer: (D) 17/20
Question: the cost if hiring a bus is shared equally by all passengers.the bus has seats for 40 passengers and the total bill comes to rs.70.37.How many seats went unoccupied?
(A) 13
(B) 11
(C) 10
(D) 9
(E) 7
Rationale: 70.37/31=2.27
so 31 passengers give 2.27/- each..so 9 seats unoccupied
ANSWER:D
Answer: (D) 9
Question: A Classroom contains 20 students. Eleven of the students are girls, nine are boys. If two students are randomly selected from the classroom, one after the other, what is the probability that both will be girls?
(A) 1/11
(B) 11/38
(C) 1/3
(D) 21/47
(E) 8/9
Rationale: Probability of getting the first girl student - 11/20
Probability of getting the second girl student - 10/19
total probability = 11/20*10/19 = 11/38
correct option B
Answer: (B) 11/38
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 45 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 40 km/h. If the distance between City P and City Q is 300 km, at what time will the truck and the car meet each other?
(A) 4:30
(B) 5:00
(C) 5:30
(D) 6:00
(E) 6:30
Rationale: At 2:00 pm, the truck and the car are 255 km apart.
The truck and the car complete a distance of 85 km each hour.
The time it takes to meet is 255/85 = 3 hours.
They will meet at 5:00 pm.
The answer is B.
Answer: (B) 5:00
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 5/9
(C) 5/2
(D) 5/1
(E) 5/6
Rationale: Two balls can be picked from nine balls in ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ₁ ways.
The required probability = (5 * 4)/ = 20/36 = 5/9
Answer:B
Answer: (B) 5/9
Question: Of the 100 athletes at a soccer club, 40 play defense and 64 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
(A) 10 to 20
(B) 10 to 40
(C) 24 to 40
(D) 30 to 70
(E) 40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 64 - {both} + {neither}
{both} = {neither} + 4.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+4=24.Eliminate A and B.
Answer: C.
Answer: (C) 24 to 40
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playing-card deck, and success would be picking a diamond card. If any of these task are successful, then you win the game. What is the probability of winning?
(A) 1/48
(B) 5/16
(C) 11/12
(D) 11/18
(E) 11/16
Rationale: First lets get the overview
Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2)
Event 2(B) = Rolling a dice( Probability of winning = 1/6 ;Probability of loosing= 1 - 1\6 =5\6)
Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ;Probability of loosing= 1 - 3/4 =1/4)
So now as above we have three events A,BC.
1st method(This is lengthy method)
Possible cases in which it's a win( the highlighted green event is a win and red is loose.
1.ABC= 1/2*5/6*3/4
OR
2.ABC= 1/2*1/6*3/4
OR
3.ABC= 1/2*5/6*1/4
OR
4.ABC= 1/2*1/6*3/4
OR
5.ABC= 1/2*5/6*1/4
OR
6.ABC= 1/2*5/6*1/4
OR
7.ABC= 1/2*1/6*1/4
As we now OR means add
Adding up all of them we'll get the probability of winning ie 11/16
Answer : E
Answer: (E) 11/16
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) 8:6
(B) 8:7
(C) 8:9
(D) 8:1
(E) 8:2
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: 2 students gave an examination. One of them scored 9 marks more than other and his marks were 56% of the sum of total of both their marks. What are their individual marks?
(A) 42,38
(B) 42,31
(C) 42,32
(D) 42,33
(E) 42,34
Rationale: Explanation:
Let marks of one of the students be X.
The marks of the other will be X+9
According to question, X+9 = 56% of X+ (X+9)
Solving, X + 9 = 56/100* (2X + 9)
=> 25X + 225 = 28X + 126
=> 3X = 99
=> X = 33
Marks of one are 33, while of the other are 33+9 = 42.
ANSWER: D
Answer: (D) 42,33
Question: If the weight of 12 meters long rod is 13.4 kg. What is the weight of 6 meters long rod ?
(A) 6.7 kg.
(B) 10.8 kg.
(C) 12.4 kg.
(D) 18.0 kg
(E) None
Rationale: Answer
∵Weight of 12 m long rod = 13.4 kg
∴ Weight of 1 m long rod = 13.4 / 12 kg
∴ Weight of 6 m long rod = 13.4 x 6 / 12
= 6.7 kg
Option: A
Answer: (A) 6.7 kg.
Question: If two numbers are in the ratio 2:3. If 15 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)10
(B) B)20
(C) C)25
(D) D)30
(E) E)35
Rationale: 2:3
2x + 15 : 3x + 15 = 3 : 4
4[2x + 15] = 3[3x + 15]
8x + 60 = 9x + 45
9x - 8x = 60 - 45
x = 15
Then smallest number is = 2
2x = 30
Correct Option D
Answer: (D) D)30
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34 sq m
(B) 4.98 sq m
(C) 2.88 sq m
(D) 2.98 sq m
(E) 2.56 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4)
= 53.38/16
= 3.34 sq m
Answer:A
Answer: (A) 3.34 sq m
Question: If a trader sold two cars each at Rs. 325475 and gains 11% on the first and loses 11% on the second, then his profit or loss percent on the whole is?
(A) 1.21%
(B) 1.74%
(C) 1.84%
(D) 1.47%
(E) 1.24%
Rationale: SP of each car is Rs. 325475, he gains 11% on first car and losses 11% on second car.
In this case, there will be loss and percentage of loss is given by
= [(profit%)(loss%)]/100
= (11)(11)/100 % = 1.21%
Answer:A
Answer: (A) 1.21%
Question: If a and b are both odd prime numbers and a < b, then how many different positive integer factors does 2ab have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: a and b are both odd prime numbers- It means either a or b is not 2
and since prime numbers have only two factors - 1 and the number itself
a and b each will have (1+1)= 2 factors
Hence 2ab will have (1+1)(1+1)(1+1)= 8 factors
D is the answer
Answer: (D) 8
Question: A tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 30% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.4 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 6 hours?
(A) 30%
(B) 35%
(C) 40%
(D) 45%
(E) 50%
Rationale: The number of gallons in the tank is (1/4)24 = 6 gallons
The amount of sodium chloride is 0.3(6) = 1.8 gallons
At the start, the amount of water is 0.7(6) = 4.2 gallons
After 6 hours, the amount of water is 4.2 - 0.4(6) = 1.8 gallons
The concentration of water is 1.8 / (1.8+1.8) = 1.8/3.6 = 50%
The answer is E.
Answer: (E) 50%
Question: A corporation triples its annual bonus to 50 of its employees. What percent R of the employees’ new bonus is the increase?
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Rationale: R of the employees’ new bonus is the increase Hence B.
Answer: (B) 662⁄3%
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 348
(B) 177
(C) 342
(D) 165
(E) 189
Rationale: 400*(90/100)*(95/100)
= 342
Answer:C
Answer: (C) 342
Question: A tradesman by means of his false balance defrauds to the extent of 28%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 37
(B) 27
(C) 68.84
(D) 78.45
(E) 62.89
Rationale: Explanation:
g% = 28 + 28 + (28*28)/100
= 63.84%
Answer: C
Answer: (C) 68.84
Question: There are 5person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
(A) 4!*2!
(B) 2!*2!
(C) 6!*1!
(D) 2!*1!
(E) 5!*1!
Rationale: Total number of ways = 2!*2!.
B
Answer: (B) 2!*2!
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 1/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) 7/16
(B) 7/15
(C) 10/21
(D) 14/17
(E) 1/2
Rationale: Let the total # of cups be 10.
# of small cups sold 1/5*10=2;
# of large cups sold 10-2=8;
Let the price of small cup be $6, then the price of larges cup would be 7/6*6=$7;
Revenue from small cups: 2*$6=$12;
Revenue from large cups cups: 8*$7=$56;
Fraction of total revenue from large cups: 56/(56+12)=14/17.
Answer: D.
Answer: (D) 14/17
Question: If a and b are the roots of the equation x2 - 8x + 8 = 0, then the value of a2 + b2 is:
(A) 36
(B) 48
(C) 17
(D) 6
(E) 5
Rationale: Sol.(b) The sum of roots = a+ b = 8
Product of roots = ab = 8
Now, a2 + b2 = (a + b)2 - 2ab = 64 - 16 = 48
Answer B
Answer: (B) 48
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 7th shift?
(A) 1/27
(B) 1/54
(C) 1/81
(D) 1/162
(E) 1/1458
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after SIXTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after SIXTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after SEVENTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=1458
Answer: option E
Answer: (E) 1/1458
Question: A train running at a speed of 60 kmph crosses a pole in 9 seconds.What is the length of the train?
(A) 120 m
(B) 180 m
(C) 190 m
(D) 150 m
(E) 160 m
Rationale: 60 kmph=50/3 m/sec
50/3*9=150 m
ANSWER:D
Answer: (D) 150 m
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 138 hats in this group, how many of these hats are not blue?
(A) 96
(B) 42
(C) 48
(D) 64
(E) 76
Rationale: B:G:P = 7:4:12 --> total of 23 parts.
Not blue = (G + P)/(total)*92 = 16/23*138 = 96.
Answer: A.
Answer: (A) 96
Question: 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
(A) 4
(B) 8
(C) 16
(D) 24
(E) 32
Rationale: To find the number of vans, we divide 123 by 8.
123 *8 = 15 and remainder = 3
So 15 vans are needed to transport 15 ? 8 = 120 girls, and 1 van is needed to transport the 3 remaining girls. A total of 16 vans are needed.
correct answer C
Answer: (C) 16
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 11
(B) 10
(C) 21
(D) 20
(E) 25
Rationale: B
10
1/6 – 1/15 = 1/10 => 10
Answer: (B) 10
Question: A boat can move upstream at 22 kmph and downstream at 42 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 10
(E) 3
Rationale: US = 22
DS = 42
M = (42 - 22)/2 = 10.Answer:D
Answer: (D) 10
Question: A sum of money at simple interest amounts to Rs. 2240 in 2 years and to Rs. 2600 in 5 years. What is the principal amount
(A) 1000
(B) 1500
(C) 2000
(D) 2500
(E) None of these
Rationale: Explanation:
SI for 3 year = 2600-2240 = 360
SI for 2 year 360/3 * 2 = 240
principal = 2240 - 240 = 2000
Option C
Answer: (C) 2000
Question: If M and N are non-zero integers, and M/N > 1, then which of the following must be true?
(A) M > N
(B) 2M > N
(C) MN > N
(D) M^2< N^2
(E) M^3 < N^3
Rationale: C
Answer: (C) MN > N
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 10%, he is only able to save Rs. 500 per month. What is his monthly salary?
(A) Rs.4500
(B) Rs.4000
(C) Rs.4167
(D) Rs.4200
(E) Rs.3000
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80+80*(10/100) = Rs.88
Present Savings = 100 – 88 =Rs. 12
If savings is Rs. 12, salary = Rs. 100
If savings is Rs.500, salary = 100/12*500 = 4167
Answer : C
Answer: (C) Rs.4167
Question: What should be added to 4750 so that it may become a perfect square?
(A) 11
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 69x69=4761
4761-4750 = 11
If added to 11 get perfect square
answer =A
Answer: (A) 11
Question: Ayesha's father was 29 years of age when she was born while her mother was 23 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Mother's age when Ayesha's brother was born = 23 years.
Father's age when Ayesha's brother was born = (29 + 3) years = 32 years.
Required difference = (32 - 23) years = 9 years. Answer: Option E
Answer: (E) 9 years
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability Q that all three secretary are assigned at least one report?
(A) 8/9
(B) 64/81
(C) 4/9
(D) 16/81
(E) 5/9
Rationale: I got the same answer: Here's my reasoning
First Report you have 3 choices
Second Report you have 2 choices
Third Report you have 1 choice
Fourth report 3 choices again
Then total number of ways is: 3*2*1*3=3^2*2
This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.
The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36
Required probability Q = 36/81.C
Answer: (C) 4/9
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 16 m wide at the top and 4 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is?
(A) 76
(B) 28
(C) 27
(D) 80
(E) 70
Rationale: 1/2 * d (16 + 4) = 700
d = 70
Answer: E
Answer: (E) 70
Question: A train passes a station platform in 31 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) 165 m
(B) 240 m
(C) 300 m
(D) 365 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)/31	= 15
x + 300 = 465
x = 165 m.Answer: Option A
Answer: (A) 165 m
Question: A store raised the price of an item by exactly 50 percent. Which of the following could NOT be the resulting price of the item?
(A) 150
(B) 300
(C) 275
(D) 600
(E) 225
Rationale: If it raised the value by 50% then the resulting price is 1.5 times the original price. So the final answer has to be a multiple of 1.5. Check the answers.
150 - Yes
300 - Yes
275 - No
600 - Yes
225 - Yes
Answer : C
Answer: (C) 275
Question: The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of the closet is 4 feet. What is the area of the closet in square feet?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 32
Rationale: Other side =
15 2 - 9 2
2 2
ft
=
225 - 81
4 4
ft
=
144
4
ft
= 6 ft.
Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.
B)
Answer: (B) 27
Question: The ages of two persons differ by 16 years. 5 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
(A) 29
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 5) = 3 (x-16-5)
=> x � 5 = 3x � 63
=> 2x = 58
=> x = 58/2 = 29
Answer: Option A
Answer: (A) 29
Question: a printer number the page of a book starting with 1 and uses 3189 digits in all How many pages dose the book have ?
(A) 1000
(B) 1074
(C) 1075
(D) 1080
(E) None of these
Rationale: Solution
No of digits in 1-digit page nos. = 1 * 9 = 9 .
No of digits in 2-digit page nos. = 2 * 90 = 180.
No of digits in 3-digit page nos. = 3 * 900 = 2700 .
No of digits in 4-digit page nos. = 3189 - (9 + 180 + 2700) = 3189 - 2889 = 300.
∴ N0. of pages with 4-digit page nos. = (300/4) =75
Hence, total number of pages = (999 + 75) = 1074 .
Answer B
Answer: (B) 1074
Question: A sum of money deposited at compound interest (compounded yearly) amounts to $6200 in 2 years and to $6324 in 3 years. What is the interest rate?
(A) 2%
(B) 3%
(C) 4%
(D) 5%
(E) 6%
Rationale: 6324 - 6200 = 124
124 / 6200 = 0.02 = 2%
The answer is A.
Answer: (A) 2%