divelab/Sys2Bench huggingface dataset:
Question: A women walking at 3 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
Options:
A)1 3/5 Km
B)3 1/5 Km
C)4 1/3 Km
D)5 Km
E)5 1/3 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 3*6/3 * 16/60
= 18/3 * 16/60
= 6 * 4/15
= 1 3/5 Km
A
Answer: A
Question: Which of the following is not a prime number ?
Options:
A)98
B)101
C)103
D)107
E)109
Rationale: Clearly, 98 is not a prime number.
Answer : A
Answer: A
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.5
B)635.87
C)635.51
D)635.19
E)635.29
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: A
Question: The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is :
Options:
A)11.0
B)11.5
C)11.1
D)11.9
E)11.3
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.
Answer: B) 11.5
Answer: B
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 5 points if you must draw exactly 2 “low” cards?
Options:
A)1
B)2
C)3
D)4
E)12
Rationale: Great question Ravih. This is a permutations problem (order matters) with repeating elements. Given thatlowcards are worth 1 pt andhigh cards2 pts, and you must draw 3 low cards, we know that you must also draw 1 high card. The formula for permutations problems with repeating elements isN!/A!B!...where N represents the number of elements in the group and A, B, etc. represent the number of times that repeating elements are repeated. Here there are 4 elements and thelowcard is repeated 2 times. As a result, the formula is:
4!/2! which represents (4*3*2*1)/(2*1) which simplifies to just 4, giving you answer E.
Answer: E
Question: A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 90% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
Options:
A)5%
B)4%
C)3%
D)2%
E)1%
Rationale: Let x be the amount of money paid for the first purchase.
The second time, the customer paid 0.9(1.1x)=0.99x.
The difference is 1%.
The answer is E.
Answer: E
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 80 metres?
Options:
A)18
B)17
C)17
D)12
E)16
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 80 m = 80/5 = 16 seconds.
Answer: E
Answer: E
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/25
B)2/27
C)5/26
D)3/19
E)2/19
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: C
Question: Five years hence, father’s age will be three times the age of his son. Five years ago, father was enven times as old as his son. Find their present ages.
Options:
A)40 years and 10 years
B)42 years and 12 years
C)35 years and 5 years
D)41 years and 11 years
E)None of these
Rationale: Let the present age of father be x years and the present age of son be y years.
five year’s hence
x + 5 = 3(y + 5)
=>x - 3y -10 = 0 -----(1)
Five year’s ago
x - 5 = 7(y - 5)
=>x - 7y + 30 = 0 -----(2)
Solving Equations (1) and (2), we get
x = 40 and y = 10
Hence, present age of father is 40 years and present age of son is 10 years.
ANSWER:A
Answer: A
Question: Ms. Morris invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A?
Options:
A)$32,000
B)$36,000
C)$40,000
D)$42,000
E)$45,000
Rationale: solution
This one could be solved with a good deal of hairy algebra, but backsolving is an incredibly efficient alternative. Let’s start with (C) — we’ll say Ms. Morris invested $40,000 in Fund A, which means she invested $60,0000 in fund B. In Fund A, she earned 23%, which was (0.23)*40000 = $9200. In Fund B, she earned 17%, which was (0.17)*60000 = $10200. Here, the interest earned in Fund B was $1000 more than the interest earned in Fund A, a bigger difference than we want. To make the difference smaller, we need less money in Fund B and more money in Fund A. Eliminate answers (A) & (B) & (C). Try D: We’ll say Ms. Morris invested $42,000 in Fund A, which means she invested $58,000 in Fund B. In Fund A, she earned 23%, which was (0.23)*42000 = $9660. In Fund B, she earned 17%, which was (0.17)*58000 = $9860. The difference is exactly $200, so answer D
Answer: D
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
Options:
A)0 sq m
B)7 sq m
C)2 sq m
D)3 sq m
E)6 sq m
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer:A
Answer: A
Question: How many four-digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ?
Options:
A)400
B)1728
C)108
D)216
E)432
Rationale: The number of ways u can chose two digits from 9 digits is 9C2=(9*8)/2.
And the no of ways u can arrange two digits like asked is 4C2=(4*3)/2.
total ways is 36*6=216.
Answer : D
Answer: D
Question: Find the one which does not belong to that group?
Options:
A)16
B)36
C)23
D)64
E)4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 23.
Answer:C
Answer: C
Question: The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
Options:
A)720
B)180
C)75
D)65
E)None of these
Rationale: Explanation:
The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.
Answer: C
Answer: C
Question: 72519 x 9999 = ?
Options:
A)725117481
B)674217481
C)685126481
D)696217481
E)None of them
Rationale: =7259 x 9999
=7259 x (10000 - 1)
=72519 x 10000 - 72519 x 1
=725190000 - 72519
=725117481
Answer is A
Answer: A
Question: Three business people wish to invest in a new company. Each person is willing to pay one third of the total investment. After careful calculations, they realize that each of them would pay $3,500 less if they could find two more equal investors. How much is the total investment in the new business?
Options:
A)$64,000
B)$4,800
C)$21,000
D)$ 19,400
E)$ 26,250
Rationale: Total Investment between 5: (x/5)
Total investment including 3500 less between 3 people(x-(3500*3))/3
Set both eq. equal to eachother.
26,250
The answer is E)
Answer: E
Question: In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
Options:
A)150
B)200
C)250
D)350
E)None
Rationale: Sol.
Let the number of grils be x.
Then, number of boys = (600 - x).
Then, (11 3/4 × 600)
⇔ 11x + 12(600 - x) ⇔ x = 7200 - 7050 ⇔ 150.
Answer A
Answer: A
Question: If the probability that Green Bay wins the Super Bowl is 1/10 and the probability that Milwaukee wins the World Series is 1/15, what is the probability that either Green Bay wins the Super Bowl or Milwaukee wins the World Series (but not both)?
Options:
A)23/150
B)19/120
C)17/100
D)11/80
E)7/50
Rationale: 9/10*1/15 + 1/10*14/15 = 23/150
The answer is A.
Answer: A
Question: The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 10, then their difference is:
Options:
A)10
B)46
C)70
D)90
E)100
Rationale: Let the numbers be x and (100 - x).
Then, x(100 - x) = 5 * 495
x2 - 100x + 2475 = 0
(x - 55)(x - 45) = 0
x = 55 or 45
The numbers are 45 and 55.
Required difference = 55 - 45 = 10.
ANSWER:A
Answer: A
Question: Richie made a part payment of $325 toward buying a brand new scooter, which represents 8% of the total cost of the scooter, how much remains to be paid?
Options:
A)$2275
B)$3275
C)$1275
D)$1175
E)$5275
Rationale: Explanation:
Let's start with what the total price of the scooter would be. If 8% is equal to $325 then 100% equals $x. We just have to multiply $325 by 8% to get total amount=$2600. Out of this amount we then need to deduct the amount already paid which was $325 so we have $2600-$325=$2275
Answer: Option A
Answer: A
Question: 317 x 317 + 283 x 283=?
Options:
A)79698
B)80578
C)80698
D)180578
E)None of them
Rationale: =(317)^2 + (283)^2
=(300+17)^2 + (300-17)^2
=2[(300)^2+(17)^2]
=2[90000+289]
=2 x 90289 = 180578
Answer is D
Answer: D
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 5h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 6
B)52 : 35
C)13 : 7
D)15 : 6
E)13 : 6
Rationale: Sol. Distance travelled by Car A = 65 Ã— 8 = 520 km
Distance travelled by Car B = 70 Ã— 5 = 350 km
Ratio = 520/350 = 52 : 35
B
Answer: B
Question: Q and F represent two distinct digits. If the number 457Q89F is divisible by 36, what is the value of (Q+F)?
Options:
A)a) 9
B)b) 3
C)c) 12
D)d) 6
E)e) 10
Rationale: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find Q could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then Q have to be 6 but as per condition QF are distinct) So
Q=1
F=2
Ans:- 3.B
Answer: B
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)1000
B)2000
C)3000
D)4000
E)5000
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
ANSWER:A
Answer: A
Question: What is the largest 4 digit number exactly divisible by 72?
Options:
A)4676
B)4678
C)8888
D)9504
E)9936
Rationale: Largest 4 digit number = 9999
9999 ÷ 72 = 138, remainder = 63
Hence largest 4 digit number exactly divisible by 88
= 9999 - 63 = 9936
answer :E
Answer: E
Question: If John covers a certain distance in 1 hr. 24 min. by covering two third of the distance at 4 kmph and the rest at 5 kmph, then find the total distance.
Options:
A)9 km
B)2 km
C)1 km
D)6 km
E)7 km
Rationale: Explanation:
Let the total distance be y km. Then,
(2/3)y/4 +(1/3)y/5 =7/5
y/6 + y/15 = 7/5
7y =42
y = 6 km
ANSWER:D
Answer: D
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 120?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 120
5x -20 = 120
5x = 140
x = 28
The answer is D.
Answer: D
Question: A man buys a cycle for Rs.1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs.1090
B)Rs.1160
C)Rs.1190
D)Rs.1202
E)NONE
Rationale: Solution
S.P	= 85% of Rs.1400
= Rs.(85/100×1400)
Rs.1190.
Answer C
Answer: C
Question: When 28 is divided by the positive integer e, the remainder is 1. What is the sum of all the possible values of e for which this is true?
Options:
A)2
B)3
C)9
D)30
E)39
Rationale: The only possible values of the form 28=ep+1 are 3,9 or 27
The sum = 3+9+27 =39. E is the correct answer. We dont need to look for values >28 as all these values will leave a remainder of 28 and not 1.
Answer: E
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly 8 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
Options:
A)28/3
B)32/3
C)35/3
D)40/3
E)44/3
Rationale: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.
(x+1.5x) = 2.5x = 1/8 of the capacity of the whole pool per hour.
The rate of the fast pump is (1.5/2.5)*1/8 = 3/40 of the whole pool per hour.
The time it takes the faster pump to fill the pool would be 40/3 hours.
The answer is D.
Answer: D
Question: Select the correct combi nat ion of mathematical signs to replace * signs and to balance the given equation. 8 * 5 * 2 * 72 * 4
Options:
A)= × + ÷
B)× = + ÷
C)+ × = ÷
D)× + = ÷
E)+ + = ÷
Rationale: C
8 + 5 × 2 = 72 ÷ 4
8 + 10 = 18
18 = 18
Answer: C
Question: The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle?
Options:
A)22
B)37
C)87
D)84
E)82
Rationale: Let inner radius be r metres. Then, 2
r = 440 ; r = = 70 m.
Radius of outer circle = (70 + 14) m = 84 m.
Answer: D
Answer: D
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 162 km/hr
Options:
A)8.5 seconds
B)2.22 seconds
C)3.5 seconds
D)2.5 seconds
E)2.6 seconds
Rationale: First convert speed into m/sec
Speed = 162*(5/18) = 45 m/sec
Time = Distance/speed
= 100/45 = 2.22 seconds
Answer: B
Answer: B
Question: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams T?
Options:
A)T=16
B)T=32
C)T=64
D)128
E)512
Rationale: Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B)
Answer: B
Question: A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 3% higher then what would the sum amount in the same time period?
Options:
A)Rs. 4465
B)Rs. 3683
C)Rs. 3596
D)Data inadequate
E)None of these
Rationale: 3422=2900+(2900*R*3/100)
R=6
If R is 3 more.
Then R=9
Sum=2900+(2900*9*3/100)
Sum=3683
ANSWER:B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 square feet, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)3932
C)3929
D)3926
E)3902
Rationale: Let the side of the square plot be a foot
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 foot
Cost of building the fence = 68 * 58
= Rs.3944.
Answer:A
Answer: A
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)26%
C)80%
D)10%
E)50%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: A
Question: X is the largest prime number less than positive integer N. P is an integer such that P = X – 16. Also, Z = 1*2*…*P√P. If N is the first non-zero perfect square whose tens digit and units digit are same, How many different prime factors does Z have?
Options:
A)4
B)5
C)6
D)160
E)320
Rationale: If N is the first perfect square whose tens digit and units digit are same, then N=100.
X is the largest prime number less than positive integer N , then X is
97.
P is an integer such that P = X – 16.
So P=81
Z=(P^1/2)! = 9!
How many different prime factors does Z have?
Answer 4 (2,3,5,7)
ANSWER:A
Answer: A
Question: If x^2 + y^2 = 15 and xy = 3, then (x − y)^2 =
Options:
A)8
B)9
C)14
D)17
E)20
Rationale: but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 15-2*3=9..
Answer B
Answer: B
Question: Magnabulk Corp sells boxes holding n magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
Options:
A)100bn/m
B)100m/bn
C)bn/(100m)
D)m/(bn)
E)bn/m
Rationale: We're given some facts to work with:
1) Magnabulk Corp sells boxes holding N magnets each.
2) The boxes are shipped in crates, each holding B boxes.
3) Magnabulk charges M DOLLARS for each crate
We're asked for the price charged per magnet, in CENTS....
IF....
N = 2
B = 3
M = 12
(2 magnets per crate)(3 crates) = 6 magnets
$12 for 6 magnets = $2 per magnet = 200 cents per magnet
So we're looking for an answer that equals 200 when N=2, B=3 and M=12.
There's only one answer that matches...
Answer: B
Question: Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is :
Options:
A)81
B)82
C)85
D)90
E)95
Rationale: Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F of 551 and 1073 = 29;
First number = 551/29 = 19
Third number = 1073/29 = 37.
Required sum = 19 + 29 + 37 = 85.
ANSWER:C
Answer: C
Question: There is a equilateral triangle whose area is A. Another triangle is formed by joining the mid points. This process is continued. Find the sum of these areas.
Options:
A)43A
B)45A
C)47A
D)49A
E)41A
Rationale: Let ABC is an equilateral triangle with area = A
Remember: The area of the triangle formed when mid points of the triangle is joined is exactly one-fourth of the bigger triangle. So Area of DEF = A/4. Similarly Area of GHI = A/16 and so on ...
So Sum of the areas of all triangles = A+A4+A16+...A+A4+A16+...
⇒A(1+14+116+...)⇒A(1+14+116+...)
The series in the bracket is G.P. and S∞=a1−rS∞=a1−r
⇒A⎛⎝11−14⎞⎠⇒A(11−14) ⇒43A
Answer:A
Answer: A
Question: Some amount is lent at 6% per annum simple interest.After 1 year rupees 6800 is repaid and the rest of the amount is repaid at 5% per annum.If the second year's interest is 11/20 of the first years interest,find what amount of money was lent out.
Options:
A)17000
B)16800
C)16500
D)17500
E)18500
Rationale: Let the amount=x
Interest after 1st year= x*6/100=3x/50
Lent sum remained after repaying 6800 Rs= x+(3x/50) - 6800= (53x/50)- 6800
Interest after 2nd year=[(53x/50)- 6800]*5/100
Given, second year's interest is 11/20 of the first years interest,so [(53x/50)- 6800]*5/100=(11/20)*3x/50
=> (53x/50)- 6800 = 33x/50
=> 20x= 340000
=> x= 17000
ANSWER:A
Answer: A
Question: A cyclist covers a distance of 820 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)17 km/hr
C)18 km/hr
D)19.8 km/hr
E)20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=820meter
Time=2 min 30sec=150sec
Speed=820/150=5.5m/sec
=>5.5âˆ—18/5km/hr=19.8km/hr
Option D
Answer: D
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)18
B)16
C)21
D)26
E)28
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18.
Answer: A
Answer: A
Question: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)6 sec
B)7 sec
C)8 sec
D)9 sec
E)2 sec
Rationale: T = 70/36 * 18/5
= 7 sec
Answer:B
Answer: B
Question: In a 1000 m race, A beats B by 50 m and B beats C by 50 m. In the same race, by how many meters does A beat C?
Options:
A)A)98m
B)B)829m
C)C)822m
D)D)929m
E)E)132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 50) = 950 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/950 = 1000/902 So, by the time A covers 1000 m, C covers 902 m.
So in 1000 m race A beats C by 1000 - 902 = 98 m.
Answer:A
Answer: A
Question: If the President and Vice President must sit next to each other in a row with 5 other members of the Board, how many different seating arrangements are possible?
Options:
A)120
B)1440
C)300
D)360
E)720
Rationale: We need to take President and VP as one unit. Therefore we have 6 people to arrange=6! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=6!*2!=1440 ways
Answer B
Answer: B
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
Options:
A)16mtr.
B)52mtr
C)70mtr.
D)78mtr.
E)98mtr.
Rationale: 20 men is 6 days can build 112 metres
35 men in 3 days can build = 112*(35/20)x(3/6)
= 98 meters
Answer: E.
Answer: E
Question: The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
Options:
A)10m
B)20m
C)50m
D)40m
E)30m
Rationale: lb = 460 m power2...(Equation 1)
Let the breadth = b
Then length, l = b × (100+15)/100 = 115b/100 ...(Equation 2)
From Equation 1 and Equation 2,
115b/100 × b = 460
b2 = 46000/115 = 400
⇒ b = √400 = 20 m
Answer is B.
Answer: B
Question: If x = 4^16 and x^x = 4^k, what is k?
Options:
A)4^14
B)4^16
C)4^18
D)4^20
E)4^22
Rationale: Solution:
We know that x=4^16
which implies x^x = (4^16)^(4^16) = 4^(16 * 4^16) [because (x^y)^z = x^(y*z))]
so 4^(4^2 * 4^16) = 4^(4^(2+16)) [because x^a * x^b = x^(a+b)]
therefore x^x = 4^(4^18)
Given that x^x=4^k
so 4^(4^18) = 4^k
Since the base is same the exponent will also be same
therefore k = 4^18
Answer:C
Answer: C
Question: If x=1/8, which expression has the greatest value?
Options:
A)x^(1/3)
B)x^(1/2)
C)1/(2x)
D)x/.03
E)x^(-3)
Rationale: Options A and B are both less than 1.
Option C: 1/(2(1/8)) = 8/2 = 4
Option D: (1/8) / 0.03 = 1/0.24 = 4.16666....
Option E: (1/8)^(-3) = 8^3 = 512
The answer is E.
Answer: E
Question: Find the greatest number that exactly divides 35, 91 and 840?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: The greatest number that exactly divides 35, 91 and 840 is the HCF of the three numbers. So, calculating HCF we get the answer 7.
ANSWER:C
Answer: C
Question: A man buys a cycle for Rs. 1900 and sells it at a loss of 18%. What is the selling price of the cycle?
Options:
A)s. 1590
B)s. 1560
C)s. 1558
D)s. 1252
E)s. 1062
Rationale: S.P. = 82% of Rs. 1900 = Rs.	82	x 1900/100 = Rs. 1558
Answer: Option C
Answer: C
Question: The average of the marks of 12 girls in a class is 36. If the marks of each girl are doubled, find the new average?
Options:
A)68
B)70
C)72
D)74
E)75
Rationale: Sum of the marks for the 12 girls= 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72
C
Answer: C
Question: A hollow spherical metallic ball has an external diameter 6 cm and is 1/2 cm thick. The volume of metal used in the metal is:
Options:
A)47 1/5cm3
B)47 3/5cm3
C)47 7/5cm3
D)47 9/5cm3
E)None of these
Rationale: Explanation:
Please note we are talking about "Hollow" ball. Do not ignore this word in this type of question in a hurry to solve this question.
If we are given with external radius and thickness, we can get the internal radius by subtracting them. Then the volume of metal can be obtained by its formula as,
External radius = 3 cm,
Internal radius = (3-0.5) cm = 2.5 cm
Volume of sphere =4/3πr3
=4/3∗22/7∗[3(2)−2.52]cm3
=4/3∗22/7∗91/8cm3
=143/3cm3=47 2/3cm3
Option B
Answer: B