mathewhe/aqua_rat huggingface dataset:
Question: If p is the sum of x consecutive positive integers. q is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that p = q?
(A) x = 2 and y = 6
(B) x = 3 and y = 6
(C) x = 7 and y = 9
(D) x = 10 and y = 7
(E) x = 10 and y = 4
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that p = q if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integers which are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and D (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with E to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus E is the right answer.
Answer: (E) x = 10 and y = 4
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is
(A) 3 hr.
(B) 5 hr.
(C) 2 hr.
(D) 7 hr.
(E) 1 hr.
Rationale: E
1 hr.
Let the duration of the flight be x hours.
Then, 600/x - 600/0.5x = 200
--> 600/x - 1200/(2x+1) = 200
--> x(2x + 1) = 3
--> 2x^2 + x - 3 = 0
--> (2x + 3)(x - 1) = 0
--> x = 1 hr.
Answer: (E) 1 hr.
Question: Two numbers are such that the ratio between them is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. The larger number is
(A) 36
(B) 46
(C) 56
(D) 64
(E) None
Rationale: Sol.
Let the numbers be 4x and 7x.
Then, 4x+4 / 7x+4 = 3/5
⇔ 5(4x+4) = 3(7x+4)
⇔ x = 8.
∴ Larger number = 7x = 56.
Answer C
Answer: (C) 56
Question: If the charge of staying in a student youth hostel $18.00/day for the first week, and $11.00/day for each additional week, How much does it cost to stay for 23 days?
(A) $160
(B) $176
(C) $282
(D) $302
(E) $286
Rationale: Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*11 = 16*11 = 176 $
Total charge =126 +176 = 302$
Answer D
Answer: (D) $302
Question: Which fraction will come next, 1/2,3/4,5/8,7/16,?
(A) 9/30
(B) 11/32
(C) 9/28
(D) 9/32
(E) 9/28
Rationale: Numerators are getting increased by 2. i.e., numerators goes like 1,3,5,7,...
Hence, next numerator = 7+2 = 9
Denominators are getting multiplied by 2. i.e., denominators goes like 2,4,8,16,...
Hence, next denominator = 16×2 = 32
So, the next fraction is 9/32
Answer: (D) 9/32
Question: Cindy is thinking of a number which is 4 less than the square of a positive integer. The number
has the property that it has two 2-digit prime factors. What is the smallest possible value of
Cindy's number?
(A) 221
(B) 231
(C) 241
(D) 251
(E) 261
Rationale: Let x be Cindy's number. Then x = n2-4 = (n-2)(n+2) for some positive integer
n. Since n + 2 and n - 2 differ by 4, our goal is hence to find two 2-digit prime numbers which
dier by 4. By writing the first few prime numbers, we find that the pair (13,17) is the smallest
pair possible, which gives us a value of 13 * 17 = 221 .
correct answer A
Answer: (A) 221
Question: If x, y, and z are consecutive odd integers, with x < y < z, then which of the following must be true?
I. x + y + z is even
II. (x+y)/z is an integer
III. xz is even
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None of the above
Rationale: consecutive odds are:
2x+1, 2x+3, 2x+5
I. 2x+1+2x+3 +2x+5 =6x+9=3(2x+3), 2x+3 is not divisible by 2 - NOT TRUE
II. 2x+1+2x+3=4x+4/2x+5=2(2x+2)/(2x+5)=Not an integer, so NOT TRUE
III. (2x+1)*(2x+5)=4x^2+10x+2x+5=4x^2+12x+5=(2x(x+6)+5)/2 is not integer, so NOT TRUE
ANSWER:E
Answer: (E) None of the above
Question: Find the area of circle whose radius is 28m?
(A) 2464
(B) 1543
(C) 7675
(D) 1683
(E) 1784
Rationale: 22/7 * 28 * 28
= 2464
Answer: A
Answer: (A) 2464
Question: The difference between the ages of two persons is 30 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the younger person is?
(A) 30yr
(B) 25yr
(C) 45yr
(D) 40yr
(E) 50yr
Rationale: Let their ages be x years and (x+30) years
Then, (x+30) - 15 = 2(x-15)
x +15 = 2x-30
x = 45
Answer is C
Answer: (C) 45yr
Question: The sum of ages of 5 children born 3 years different each is 75 yrs. What is the age of the Elder child?
(A) 7
(B) 9
(C) 16
(D) 18
(E) 21
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 75
5x = 45
x = 9.
x+12= 9+12= 21
E
Answer: (E) 21
Question: One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?
(A) 18/25
(B) 17/20
(C) 11/15
(D) 7/10
(E) 3/5
Rationale: The cars with CD players which were not rented is (2/5)(3/5) = 6/25 of all the cars.
The cars which were not rented is 1/3 of all the cars.
The percent of non-rented cars which had CD players is (6/25) / (1/3) = 18/25
The answer is A.
Answer: (A) 18/25
Question: When n is divided by 9, the remainder is 2. When n is divided by 13, the remainder is 8. If 1 < n < 200, what is the greatest possible value of n?
(A) 47
(B) 65
(C) 103
(D) 164
(E) 117
Rationale: Looking at the choices, options B E can be eliminated as they are divisible by 13
Starting from the highest number 164;
164 = 162 + 2 (162 divisible by 9)
164 = 156 + 8 (156 divisible by 13)
it fits the result
Answer = D
Answer: (D) 164
Question: Two cars cover the same distance at the speed of 50 and 65 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 212 km
(B) 214 km
(C) 224 km
(D) 200 km
(E) 204 km
Rationale: 50(x + 1) = 65x
X = 3.33
60 * 3.33 = 200 km
ANSWER:D
Answer: (D) 200 km
Question: shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) Rs. 25000
(B) Rs. 20000
(C) Rs. 15000
(D) Rs. 22000
(E) None of these
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
ANSWER:B
Answer: (B) Rs. 20000
Question: Water is poured into a cylindrical well at the rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the diameter of the tank in meters?
(A) √10/2
(B) √10
(C) 2√10
(D) 5
(E) 10
Rationale: Here's my re-worked solution:
volume = 22 = pi (r^2)(0.7)
22 = 22/7 (7/10)(r^2)
10 = r^2
r = sqrt(10)
Diameter=2*sqrt(10)
Ans: C
Answer: (C) 2√10
Question: A shopping mall charges 70 cents for the first hour of parking and $5 for each additional hour until the customer reaches 4 hours, after that the parking fee is $2 per hour. If a certain customer parked his in the mall for 7 hours and 30 minutes, how much is he going to pay?
(A) $36.4
(B) $12.
(C) $13.
(D) $14.5.
(E) $15.
Rationale: 0.70+5*5+2*5+0.70= $36.4
Answer: $36.4
Answer: (A) $36.4
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
(A) 1/5
(B) 2/5
(C) 3/10
(D) 3/7
(E) 1/7
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Answer: (C) 3/10
Question: A bakery currently has 6 pies and 5 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
(A) 100/231
(B) 25/77
(C) 5/11
(D) 93/116
(E) 50/147
Rationale: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 6C3*5C2 = 20*10 = 200
P(exactly 3 pies) = 200/462 = 100/231
The answer is A.
Answer: (A) 100/231
Question: A thief is noticed by a policeman from a distance of 300 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100
(B) 277
(C) 2987
(D) 278
(E) 200
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 300 - 100 = 200 m.
Answer: E
Answer: (E) 200
Question: What is the value of 3x^2 − 1.8x + 0.3 for x = 0.9?
(A) −0.3
(B) 0
(C) 0.3
(D) 1.11
(E) 2.46
Rationale: 3x^2-1.8x+0.3 for x=0.5
=3(0.9*0.9)-2*0.9*(0.9)+0.3
=0.9*0.9+0.3
=0.81+0.3
=1.11
Correct Option : D
Answer: (D) 1.11
Question: 21, 9, 21, 11, 21, 13, 21, ?
(A) 11
(B) 17
(C) 19
(D) 15
(E) 20
Rationale: D
15
In this alternating repetition series, the number 21 is interpolated. If you exclude 21, the series increases by 2, beginning with the number 9.
Answer: (D) 15
Question: At Tom's party, there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?
(A) 384
(B) 258
(C) 216
(D) 120
(E) 72
Rationale: we have to work on the info and understand what that info takes us to...
1) there were five times as many females as males At Tom's party..
this means F=5M.. so total number=6M..
2) There were three times as many adults as children..
A=3C...
or total = 4C..
so the total is 4C or 6M..
since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6..
or Total is multiple of LCM of 4,6..
LCM of 4,6= 12..
lets see which number is not multiple of 12..
A. 384...12*32
B. 258... no
C. 216....12*18
D. 120....12*10
E. 72......12*6..
so B is our answer..
Answer: (B) 258
Question: The first, second and third terms of the proportion are 56, 16, 49. Find the fourth term.
(A) 10
(B) 14
(C) 40
(D) 50
(E) 60
Rationale: Explanation :
Let the fourth term be x.
Thus 56, 16, 49, x are in proportion.
Product of extreme terms = 56 x
Product of mean terms = 16 X 49
Since, the numbers make up a proportion
Therefore, 56 x = 16 49
or, x = (16 49)/56
or, x = 14
Therefore, the fourth term of the proportion is 14.
Answer : B
Answer: (B) 14
Question: If each year the population of the country grows by 50%, how many years will elapse before the population of the country doubles?
(A) 3
(B) 4
(C) 2
(D) 6
(E) 7
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 150 ............. 1 Year elapsed
Year 2002: Population > 200 ............. 2 Year elapsed
Answer:C
Answer: (C) 2
Question: A two-digit number exceeds the sum of the digits of that number by 18. if the digit at the unit’s place is double that digits in the ten’s place, what is the number ?
(A) 24
(B) 42
(C) 48
(D) data inadequate
(E) None
Rationale: Solution
Let the ten's digit be x. then, unit's digit = 2 x.
Number = 10 x + 2 x = 12 x, sum of digits = x + 2 x = 3 x.
∴ 12 x - 3 x = 18 ⇔ 9 x = 18 ⇔ x = 2.
Hence, required number = 12 x = 24
Answer A
Answer: (A) 24
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 10 sec. What is the length of the platform?
(A) 187 m
(B) 350 m
(C) 267 m
(D) 287 m
(E) 870 m
Rationale: Speed = 300/10 = 30 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 =30
=> x = 870m.
Answer:E
Answer: (E) 870 m
Question: The average of 10 result is 42. Average of the first 7 of them is 30 and that of the last 7 is 80. Find the 8th result?
(A) 35
(B) 37
(C) 70
(D) 75
(E) 50
Rationale: Sum of all the 10 results = 10 * 42 = 420
Sum of the first 7 of them = 7 * 30 = 210
Sum of the last 7 of them = 7 * 80 = 560
So, the 8th number = 420+ 210 - 560= 70.
C
Answer: (C) 70
Question: Mother,her daughter and her grand child weighs 120 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: mother + daughter + child = 120kg
daughter + child = 60kg
mother = 120 - 60 = 60kg
child = 1/5th of mother = (1/5)*60 = 12kg
So now daughter = 120 -(mother + child) = 120 - (60+12) = 48kg
ANSWER:C
Answer: (C) 48
Question: Plane leaves from Chelsea every 35 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
(A) 5:35 p.m
(B) 6:50 p.m
(C) 7:35 p.m
(D) 8:35 p.m
(E) 9:35 p.m
Rationale: Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 35 min = 6:25 p.m
As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:25 p.m + 25 min = 6:50 p.m
Answer B
Answer: (B) 6:50 p.m
Question: Rohit spent 30 percent of his earning last month on rent and 20 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Rohit have left over?
(A) 29%
(B) 35%
(C) 46%
(D) 47%
(E) 52%
Rationale: SayRohit's earning last month was $100.
Rohit spent 30 percent of his earning last month on rent --> $30 on rent;
20 percent less than what he spent on rent to purchase a new dishwasher --> $30*0.8=$24 on the dishwasher.
Left over amount 100 - (30 + 24) = $46
Answer: C
Answer: (C) 46%
Question: A fruit seller had some oranges. He sells 40% oranges and still has 480 oranges. How many oranges he had originally?
(A) 800
(B) 710
(C) 720
(D) 730
(E) 740
Rationale: 60% of oranges = 480
100% of oranges =(480×100)/6=800
total oranges = 700
ANSWER : A
Answer: (A) 800
Question: If 2^5, 3^3, and 10^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?
(A) 26
(B) 39
(C) 120
(D) 65
(E) 156
Rationale: Here 156 has three two's
two three's
and one 10
rest of them must be in w
so w= 10*3*4 = 120
Smash C
Answer: (C) 120
Question: A sum of Rs. 350 made up of 110 coins, which are of either Re.1 or Re.5 denomination. How many coins are of Re.1?
(A) 50
(B) 60
(C) 65
(D) 54
(E) 47
Rationale: Rs.1 coins= 50 ;50*1=50
Rs.5 coins=60 ; 60*5=300
Total=50+300=350
So total Rs.1 coins are 50
ANSWER:A
Answer: (A) 50
Question: A car takes 4.5 hours to travel from A to B, which is 360 miles apart. What is the average speed of the car?
(A) 40
(B) 50
(C) 60
(D) 80
(E) 85
Rationale: Average speed= 360/4.5 hours
= 360/270
=1.33 miles per min
=80 miles per hour
Answer: D
Answer: (D) 80
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
(A) 19828.29
(B) 19828.2
(C) 19828.8
(D) 19828.88
(E) 19828.21
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P
= 2828.80 / (0.08)(2.08)
= 1360/0.08 = 17000 Principal + Interest
= Rs.19828.80
Answer:C
Answer: (C) 19828.8
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
(A) 200
(B) 300
(C) 400
(D) Cannot be determined
(E) 600
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: Option D
Answer: (D) Cannot be determined
Question: How many numbers from 10 to 10000 are exactly divisible by 9?
(A) 900
(B) 1000
(C) 1110
(D) 1200
(E) 1400
Rationale: 10/9 = 1 and 10000/9 = 1111 ==> 1111 - 1 = 1110. Therefore 1110
Answer : C
Answer: (C) 1110
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
(A) x(x+1)(x+2)
(B) 3x^3
(C) 9x^2
(D) x-1
(E) 9x/3
Rationale: *any number multiplied by 3, will be divided by 3
for option D if we put value x=8, 8-1=7 is not divisible by 3
Answer : E
Answer: (E) 9x/3
Question: If two numbers are in the ratio 7:2. If 5 is subtracted to both of the numbers then the ratio becomes 2:3then find the largest number?
(A) 26/17
(B) 37/17
(C) 35/17
(D) 25/17
(E) 24/17
Rationale: 7:2
7x - 5: 2x - 5 =2 : 3
3[7x - 5] =2[2x- 5]
21x - 15= 4x - 10
21x - 4x = 15 - 10
17x = 5, then x=5/17
Then the first number is = 7
7x = 35/17
Option C
Answer: (C) 35/17
Question: Panya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
(A) 1/24
(B) 1/8
(C) 1/4
(D) 1/3
(E) 3/8
Rationale: Total Panya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.?
Answer: (D) 1/3
Question: saran professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
(A) 67 6/9%
(B) 54 1/2%
(C) 33 3/8%
(D) 11 1/9%
(E) 87 7/9%
Rationale: D
900 --- 100
100 --- ? => 11 1/9%
Answer: (D) 11 1/9%
Question: 47% of the students in a class of 44 students has glasses or contacts. How many students in the class have either glasses or contacts?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 21
Rationale: a=r⋅b
47%=0.47a
=0.47⋅34
a≈21
Option E is correct.
Answer: (E) 21
Question: There are 324,437 chicks in a farm. Jack wants to distribute these evenly across 9 different retail shops, how many chicks would remain with him.
(A) 1 chicks
(B) 2 chicks
(C) 3 chicks
(D) 4 chicks
(E) 5 chicks
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 324,437.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 324,437 = 23 and 18 is divisible by 9.
Hence, we need to remove 5 to this number for it to be divisible by 9
Correct Option: E
Answer: (E) 5 chicks
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/16 hours
(B) 80/13 hours
(C) 30/73 hours
(D) 30/13 hours
(E) 50/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream
= d/s = 60/26
= 30/13 hours.
Answer:D
Answer: (D) 30/13 hours
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 28 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
(A) 6 2/3
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Here is how I did it:
The cyclist travels 28 miles in 60 mins, so in 5 mins he will travel [(28*5)/60] miles, which equals 7/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 7/3 miles, he will take [(60*7/3)/4] = 35 mins.
hence 35-5 =30 mins
E
Answer: (E) 30
Question: Ella and Frank race around a running track. Ella runs at a constant rate of one lap every 3 minutes and Frank runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Ella to get exactly one lap ahead of Frank?
(A) 5.5
(B) 6.5
(C) 7.5
(D) 8.5
(E) 9.5
Rationale: Let x be the number of minutes it takes for Ella to get one lap ahead.
Then Ella ran x/3 laps and Frank ran x/5 laps.
x/3 = 1+x/5
5x=15+3x
2x=15
x=7.5
The answer is C.
Answer: (C) 7.5
Question: A person spent Rs. 6,040 from his salary on food and 5,000 on house rent. After that he was left with 80% of his monthly salary. What is his monthly salary ?
(A) 55,200
(B) 65,200
(C) 75,200
(D) 85,200
(E) 95,200
Rationale: Total money spent on food and house rent = 6,040+5,000 = 11,040
Which is 100 - 80 = 20% of his monthly salary
∴ His salary = 11040x100/20 = 55200
Answer : A
Answer: (A) 55,200
Question: What is the smallest no. which must be added to 25268 so as to obtain a sum which is divisible by 11?
(A) 5
(B) 10
(C) 11
(D) 20
(E) 30
Rationale: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 25268, Difference =(2+2+8) -(5+6)=12-11=1.
The units digit is at odd place. So we add 10 to the number
=> 25268 +10= 25278
Now , (2+2+8) -(5+7)=12-12=0=>25268 is also divisible by 11
B
Answer: (B) 10
Question: 15 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 190
(B) 200
(C) 210
(D) 220
(E) 225
Rationale: Though 2*(15C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 14, so he'll play 28 matches.
Similarly, second guy has to play with the rest of 13 as his 2 games with the first guy are already played. So he plays 26 matches.
This continues like this and the total matches are 28+26+24...+2
28+26+...+2 = 2(14+13+...+1) = 2((14*15)/2) = 14*15 = 210.
ANSWER:C
Answer: (C) 210
Question: In measuring the sides of a rectangle, one side is taken 10% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
(A) 3.5%
(B) 2.4%
(C) 3%
(D) 4.5%
(E) 2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 110*95=10,450, which is 4.5% greater than the actual area.
Answer: D.
Answer: (D) 4.5%
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3240, how much was it in the beginning?
(A) A)3800
(B) B)4200
(C) C)4400
(D) D)4500
(E) E)4600
Rationale: X * (90/100) * (80/100) = 3240
X = 4500
ANSWER:D
Answer: (D) D)4500
Question: The ratio between the speeds of two Bullet trains is 7: 8. If the second Bullet train runs 460 kms in 4 hours, then the speed of the first train is:
(A) 100.6 km/hr.
(B) 37.25 km/hr.
(C) 90.25 km/hr.
(D) 94.25 km/hr.
(E) 96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 8x km/hr.
Then, 8x = (460/4) = 115
x = (115/8) = 14.375
Hence, speed of first bullet train = (7 x 14.375) km/hr = 100.6 km/hr.
A
Answer: (A) 100.6 km/hr.
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively. If they cross each other in 23 seconds, what is the ratio of their speeds?
(A) 1:2
(B) 3:2
(C) 3:1
(D) 1:3
(E) 1:4
Rationale: Speed =x and y resp
length of first = 27x
length of second train = 17y
related speed = x + y
time taken to cross each other = 23 s
27x+17y/x+y = 23
27x+17y = 23(x+y)
4x=6y
x/y=6/4=3/2
ANSWER B
Answer: (B) 3:2