mathewhe/aqua_rat huggingface dataset:
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 388
(B) 476
(C) 557
(D) 2885
(E) 271
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476
Answer: B
Answer: (B) 476
Question: It takes 5 tons of copper ore and 9 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?
(A)  18
(B)  18 3/4
(C)  16
(D)  12
(E)  10
Rationale: Yes, you need copper ore:iron ore in the ratio 5:9. Total 14 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/5 = 12 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/9 = 10 tons of alloy A.
Since iron ore is available for only 10 tons of alloy A, you can make only 10 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 10.
(E)
Answer: (E)  10
Question: 4 guys buy same cellphones cost them 250 each. Two guy have 25% of for his first cellphone. What is the total cost all of them pay to seller.
(A) 1000
(B) 850
(C) 875
(D) 775
(E) 750
Rationale: Solution: C.250*2=500 for 2 guy without discount, for other 2 (250*2) with 25% is 375. total cost 500+375=875
Answer: (C) 875
Question: In a public show 45 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
(A) 330
(B) 110
(C) 120
(D) 140
(E) 150
Rationale: 75 % of 600
= 45/100 × 600
= 270
Therefore, the number of vacant seats = 600 - 270 = 330.
Answer:A
Answer: (A) 330
Question: How many three digit numbers B greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
(A) 72
(B) 48
(C) 120
(D) 96
(E) 76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=B
Answer: A.
Answer: (A) 72
Question: Let the sides of a rectangular prism are consecutive multiples of 5. Which among the following could be the base area
(A) 360
(B) 450
(C) 560
(D) 670
(E) 780
Rationale: Length=5*a
breadth=5*(a+1) or 5*(a+2)
Base area -> multiple of 25
450=25*18
Answer:B
Answer: (B) 450
Question: Two trains, 250 metres and 150 metres long respectively, are running on parallel lines. If they are running in the same directions, the faster train crosses the slower train in 40 seconds. If they are moving in the opposite direction they pass each other in eight seconds. What is the speed of the slower train?
(A) 108kmph
(B) 82kmph
(C) 92 kmph
(D) 72 kmph
(E) 87 kmph
Rationale: Let the speed of faster train be f and slower train be y.
Time taken to cross each other traveling in the same direction = 250 +150/ (x-y) = 40………(1)
Time taken to cross each other traveling in the opposite direction = 250+150 /(x+y) = 8 …….(2)
From (1) and (2) f= 30 m/s and s = 20 m/s
Speed of slower train = 20 * 18/5 = 72 kmph
Answer : D
Answer: (D) 72 kmph
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 502 to 598, inclusive?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: 502 x 504 x 506 x 508 => unit digit 4
512 x 514 x 516 x 518 => unit digit 4
592 x 594 x 596 x 598 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer: B.
Answer: (B) 6
Question: Today is Brian's birthday. In two years from today he will be twice as old as he was 11 years ago. How old is Brian today ?
(A) 24 years
(B) 22 years
(C) 19 years
(D) 26 years
(E) 28 years
Rationale: Let Brian's age=xx+2=2(x-11)x=24ANSWER:A
Answer: (A) 24 years
Question: The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?
I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180.
II. When B is divided by 60, the remainder is 30.
III. The value of the decimal digits is greater in the number A/90 than in the number B/90.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: A = 180n + 30 (n is any non negative integer)
A is 30/210/390...
If the total sum is reduced by 300, with 5 numbers, the average will go down by 60.
B = A - 60
I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180.
B = 180n + 30 - 60 = 180n - 30 = 180(n-1) + 150
Not True. Remainder is 150
II. When B is divided by 60, the remainder is 30.
B = 180(n-1) + 150 = 180(n-1) + 120 + 30
True. B leaves remainder 30 on division by 60.
III. The value of the decimal digits is greater in the number A/90 than in the number B/90.
The decimal part of A is 30/90 = .333
The decimal part of B will be obtained by 150/90 = (90 + 60)/90 => 60/90 = .666
Not True.
Answer (B)
Answer: (B) II only
Question: A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?
(A) 143
(B) 145
(C) 156
(D) 134
(E) 100
Rationale: Final number = Initial number + 30%(original number) = 110 + 30%(110) = 110 + 33 = 143.
Answer A
Answer: (A) 143
Question: In what time will a train 135 m long cross an electric pole, it its speed be 140 km/hr?
(A) 3.5
(B) 2.7
(C) 2.9
(D) 2.3
(E) 2.1
Rationale: Speed = 140 * 5/18 = 38.8 m/sec
Time taken = 135/38.8
= 3.5 sec.
Answer: A
Answer: (A) 3.5
Question: A committee of four is to be chosen from seven employees for a special project at ACME Corporation. Two of the seven employees are unwilling to work with each other. How many committees are possible if the two employees do not work together?
(A) 15
(B) 20
(C) 25
(D) 35
(E) 50
Rationale: total combinations =7C4
total combinations if 2 persons who dont like each other are selected together= 5C3
Ans= 7C4-5C3
=25
ANSWER:C
Answer: (C) 25
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 Years
(B) 20 Years
(C) 25 Years
(D) 22 Years
(E) 28 Years
Rationale: A
23 Years
Let the average age of the whole team by x years.
11x - (26 + 29) = 9(x -1)
11x - 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years
Answer: (A) 23 Years
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 30
(B) 31
(C) 32
(D) 34
(E) 35
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer: Option E
Answer: (E) 35
Question: IF 1+3=10 ; 3+5=52 ; 5+7=174 Then 7+11=?
(A) 354
(B) 225
(C) 654
(D) 741
(E) 464
Rationale: 1^3 + 3^2= 1 + 9 = 10
3^3 + 5^2= 27 + 25 = 52
5^3 + 7^2= 125 + 49 = 174
and
7^3 + 11^2= 343 + 121 = 464
ANSWER:E
Answer: (E) 464
Question: CONVERT 1.3 hectares in ares
(A) 130 ares.
(B) 160 ares.
(C) 180 ares.
(D) 230 ares.
(E) 250 ares.
Rationale: 1.3 hectares in ares
1 hectare = 100 ares
Therefore, 1.3 hectares = 1.3 × 100 ares
= 130 ares.
ANSWER- A
Answer: (A) 130 ares.
Question: Lorna invests $8000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
(A) $160
(B) $1,700
(C) $2,200
(D) $4,400
(E) $5,840
Rationale: We have that 'x' invested at 6%
We also have that '8000-x' invested at 11%
Now then 580/8000 is approx 10%
Therefore, -4x+8000-x=0
5x=8000
x=1600 approximately. Probably higher
Only B matches
Answer: (B) $1,700
Question: It would take one machine 8 hours to complete a large production order and another machine 7 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) A 15/56
(B) B 14/45
(C) C 24/56
(D) D 45/56
(E) E 56/15
Rationale: The rate of the first machine is 1/8 job per hour;
The rate of the second machine is 1/7 job per hour;
Thus, the combined rate of the machines is 1/8+1/7=15/56 job per hour, which means that it takes 1/(15/56)=56/15 hours both machines to do the job.
Answer: E.
Answer: (E) E 56/15
Question: An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. what is the rate of the wind?
(A) 60km/hr
(B) 70km/hr
(C) 80km/hr
(D) 90km/hr
(E) 100km/hr
Rationale: Let the speed of the air plane in still air be x km/hr
And the speed of the wind be y km/hr.
Then speed of the airplane going with the wind = (x + y) km/hr
and speed of the airplane going against the wind = (x - y) km/hr.
We know that,
Distance = Speed ? Time
or, Speed = Distance
Time
According to the problem,
An airplane travels 4362 km against the wind in 6 hours
x - y = 4362/6
or, x - y = 727 ----------- (1)
Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours
x + y = 5322/6
or, x + y = 887 ----------- (2)
Now add (1) and (2) we get,
x - y = 727
x + y = 887
2x = 1614
or, 2x/2 = 1614/2, (Divide both sides by 2)
or, x = 807
Now substitute the value of value of x = 807 in equation (2) we get,
807 + y = 887
-807 -807, (Subtract 407 from both sides)
y = 80
Answer:Rate of the wind = 80km/hr
correct answer C
Answer: (C) 80km/hr
Question: 5^2010
what will be the sum of digits?
(A) 6028
(B) 6029
(C) 6031
(D) 3021
(E) 6032
Rationale: 5^2=25 sum of digits =2+5=7
now if we take the power of 5 and do 2*3+1=7
similarly for 5^4=625 and sum=6+2+5=13
now do 4*3+1=13
similarly, 5^2010 sum of the digits would be 2010*3+1=6031
ANSWER:C
Answer: (C) 6031
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 210, the sum due is:
(A) s. 768
(B) s. 960
(C) s. 1960
(D) s. 2400
(E) s. 2800
Rationale: td=pw*r*t/100 so 210=pw*14*2/100 so pw=750
sum=pw+td..
sum=750+210=960
ANSWER:B
Answer: (B) s. 960
Question: From given equation find the value of x: 2x² + 9x − 5
(A) 1/2
(B) 1
(C) 3
(D) 4
(E) 5
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
A
Answer: (A) 1/2
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
(A) 3312
(B) 2888
(C) 4312
(D) 2881
(E) 1221
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: C
Answer: (C) 4312
Question: An design manager has 10patterns of chairs & 6patterns of tables. In how many ways can he make a pair of table & chair?
(A) 20
(B) 60
(C) 80
(D) 90
(E) 100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 6 ways
Hence one chair and one table can be arranged in 10 x 6 ways = 60 ways
B
Answer: (B) 60
Question: A driver just filled the car's gas tank with 18 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance?
(A) 1
(B) 1.5
(C) 1.8
(D) 2.4
(E) 3
Rationale: Let x be the number of liters of ethanol added to the gas tank.
0.05(18) + x = 0.1(18+x)
0.9x = 1.8 - 0.9
x = 1 liter
The answer is A.
Answer: (A) 1
Question: The denominator of a fraction is 5 greater than the numerator. If the numerator and the denominator are increased by 1, the resulting fraction is equal to 7â„12. What is the value of the original fraction?
(A) 6/11
(B) 8/13
(C) 11/16
(D) 12/17
(E) 14/19
Rationale: Let the numerator be x.
Then the denominator is x+5.
x+1 / x+6 = 7/12.
12x+12=7x+42.
5x=30.
x=6.
The original fraction is 6/11.
The answer is A.
Answer: (A) 6/11
Question: The interest on a certain deposit at 5% per annum is Rs. 101.20 in one year. How much will the additional interest in one year be on the same deposit at 6% per annum?
(A) Rs.20.8
(B) Rs.19.74
(C) Rs.20.24
(D) Rs.19.5
(E) Rs.19.00
Rationale: Explanation :
Principal, P = 100×SI/RT=100×101.20/5×1=20×101.20=Rs. 2024
Simple Interest for Rs.2024 at 6% per annum for 1 year, SI = 2024×6×1100=121.44
Additional Interest = Rs.121.44 - Rs.101.20 = Rs.20.24
Answer : Option C
Answer: (C) Rs.20.24
Question: 0.0004?=0.01
(A) 4
(B) 0.4
(C) 0.04
(D) 40
(E) None of these
Rationale: Explanation :
Required Answer = 0.0004/0.01 = 0.04/1 = 0.04. Answer : Option C
Answer: (C) 0.04
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 2887
(B) 444
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer: B
Answer: (B) 444
Question: What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12 p.c.p.a?
(A) Rs.10111.00
(B) Rs.10123.20
(C) Rs.10123.00
(D) Rs.10100.00
(E) Rs.10110.00
Rationale: = Rs.(25000x(1+12/100)³
= Rs.(25000x28/25x28/25x28/25)
= Rs. 35123.20.
C.I = Rs(35123.20 -25000)
= Rs.10123.20
answer :B
Answer: (B) Rs.10123.20
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:3 be mixed with another Mixture Q of milk and water in the ratio 1:3 so that the resultant mixture contains equal quantities of milk and water?
(A) 5:2
(B) 4:3
(C) 3:2
(D) 2:1
(E) 4:1
Rationale: (5/8)*P +(1/4)*Q = (3/8)*P+(3/4)*Q
2P=4Q
P/Q = 2/1
The answer is D.
Answer: (D) 2:1
Question: The difference of two numbers is 2 and the difference of their squares is 12. The sum of the number is
(A) 6
(B) 8
(C) 10
(D) 22
(E) 24
Rationale: Explanation:
Let the numbers be a, b; ⇒ a-b=2 and
a2−b2=12
a+b=a2−b2/a−b=12/2=6
Correct Option: A
Answer: (A) 6
Question: For the positive integers x, x + 2, x + 4, x + 7, and x + 22, the mean is how much greater than the median?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 7
Rationale: Mean = (x + x+2 + x+4 + x+7 + x+22)/5
=(5x+35)/5
=x+7
Median = x+4
Thus Mean - Median = x+7 - (x+4)
=3
Answer = D
Answer: (D) 3
Question: There are cats got together and decided to kill the mice of 999951. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
(A) 941,1009
(B) 993,1007
(C) 991,1009
(D) 791,1009
(E) 931,1009
Rationale: 999951 can be written as 1000000 â€“ 49
= 10002 â€“ 72 ie of the form a2-b2=(a+b)(a-b)
=(1000+7)*(1000-7)
= (1007)*(993)
Given that number of cats is less than number if mice.
So number of cats is 993 and number of mice were 1007
Answer B
Answer: (B) 993,1007
Question: A’s speed is 25/18 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/18
(B) 7/18
(C) 7/25
(D) 3/25
(E) 1/25
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 25 meters, B covers 18 meters in that time. So if the race is 25 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 25 meters) would be the same as the time required by B (to cover 18 meters) to reach the finish line.
So B should get a head start of 7/25th of the race.
Answer (C)
Answer: (C) 7/25
Question: The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?
(A) 4x–3
(B) 16x–15
(C) (x+3)/4
(D) (x+3)/16
(E) (x+15)/16
Rationale: Since we know a(3) we can find a(2),
if we can find a(2) we can find a(1).
a(3)=4a(2)-3 ---> x=4a(2)-3 ---> a(2)=(x+3)/4
a(2)=4a(1)-3 ---> (x+3)/4=4a(1)-3 ---> 4a(1)=(x+15)/4 ---> a(1)=(x+15)/16
The answer is E.
Answer: (E) (x+15)/16
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11-sided polygon)?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/8
(E) 1/11
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/8 = 1/4.
The answer is C.
Answer: (C) 1/4
Question: The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number?
(A) A)318
(B) B)65
(C) C)58
(D) D)62
(E) E)48
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*98+6*65-11*60 = 318
Answer is A
Answer: (A) A)318
Question: Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:7
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4=C
Answer: (C) 4:4
Question: In a group of 90 students, 30 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
(A) 9
(B) 19
(C) 33
(D) 27
(E) 31
Rationale: Number of students taking history =H=30
Number of students taking statistics =S= 32
Total number of students =T= 90
Number of students taking History or Statistics or both =B= 59
Number of students taking neither history nor statistics =N= 90-59=31
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 90 = 30+ 32 +31 - X
or X = 3
Now,
Number of students taking only history will be
H-X
or 36-3 = 33
Answer:- C
Answer: (C) 33
Question: Two bullet train s are running in opposite directions with the same speed. If the length of each bullet train is 120 metres and they cross each other in 12 seconds, then the speed of each bullet train (in km/hr) is:
(A) 46 km/hr.
(B) 36 km/hr.
(C) 56 km/hr.
(D) 76 km/hr.
(E) 66 km/hr.
Rationale: B
36 km/hr.
Let the speed of each bullet train be x m/sec.
Then, relative speed of the two bullet train s = 2x m/sec.
So, 2x = (120 + 120)/12
--> 2x = 20
--> x = 10.
--> Speed of each bullet train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
Answer: (B) 36 km/hr.
Question: A nickel is placed flat on a table. What is the maximum number of nickels that can be placed
around it, flat on the table, with each one tangent to it?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Connect the midpoints of the given nickel and two others placed around it so that
all three touch. This creates an equilateral triangle with 60 degree angles. Since 360=60 = 6,
six nickels can be placed around the given nickel.
correct answer C
Answer: (C) 6
Question: What is the remainder when 750*810*830*790 is divided by 13?
(A) 4
(B) 9
(C) 10
(D) 8
(E) 6
Rationale: OA is 'C'.
OE:
take the remainder from each of 750/15, 810/15 and so on..
750/13 gives remainder = 9
810/13 gives remainder = 4
830/13 gives remainder = 11
790/13 gives remainder = 10
the net remainder is the product of above individual remainders. i.e = 9*4*11*10
break them into pairs 9*4/13 gives remainder 10
and 11*10/13 gives remainder 6
so 10*6/13 gives remainder 8.
Answer: C
Answer: (C) 10
Question: If a and b are the two values of t that satisfy
the equation t^2 â€“ 10t + 16 = 0, with a > b, what is the value of a â€“ b?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Factor the left side of the equation:
t^2 â€“ 10t + 16 = 0
(t â€“ 2)(t â€“ 8) = 0
t = 2, t = 8
Thus, a = 8 and b = 2. So a â€“ b = 8 â€“ 2 = 6.
The answer is C.
Answer: (C) 6
Question: k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
(A) 2^n - 8
(B) 2^n - 4
(C) 2^n
(D) 2^n + 4
(E) 2^n + 5
Rationale: Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 5
We also know that 9 is a divisor of9.
So, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4
B
Answer: (B) 2^n - 4
Question: A certain distance is covered by a cyclist at a certain speed. I a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is:
(A) 1:2
(B) 2:1
(C) 1:4
(D) 4:1
(E) None of these
Rationale: let the distance covered by the cyclist be x and the time taken be y. Then, Required ratio=1/2x/2y:x/y=1/4:1=1:4.
Correct Option: C
Answer: (C) 1:4
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
(A) 5:18
(B) 5:12
(C) 5:10
(D) 5:11
(E) 5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5:16
Answer:E
Answer: (E) 5:16
Question: A and B start a business, with A investing the total capital of Rs.100000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.10000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) A)2520000
(B) B)2620000
(C) C)2820000
(D) D)2920000
(E) E)2420000
Rationale: Interest received by A from B = 10% of half of Rs.100000 = 10% * 50000 = 5000.
Amount received by A per annum for being a working partner = 10000 * 12 = Rs.120000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (5000+ 120000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(5000 + 120000 + P) = 2(P)
P = 125000
Total profit = 2P + 120000
= 2*125000 + 120000 = 2620000
Answer:B
Answer: (B) B)2620000