divelab/Sys2Bench huggingface dataset:
Question: Prove that if a and b are different integers, then there exist infinitely many positive integers n such that a+n and b+n are relatively prime.
Options:
A)(a+n, b+n) = 50
B)4
C)3
D)2
E)(a+n, b+n) = 1
Rationale: Let a ,and b be two different integers. Assume for instance a < b, and let n = (b-a)k+ I-a. For k sufficiently large, n will be positive integer. We have a+n = (b-a)k+l, b+n = (b-a) (k+l)+l, hence a+n and b+n will be positive integers. If we had d|a+n and d|b+n, we would have d|a-b, and, in view of d|a+n, also d|1, which implies that d = 1. Thus, (a+n, b+n) = 1.
So Answer is E (a+n, b+n) = 1
Answer: E
Question: While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%)
Options:
A)4.09
B)4.0
C)4.04
D)4.02
E)4.01
Rationale: Explanation:
Given Error = 2% while measuring the side of a square.
If the correct value of the side of square is 100, the measured value:
=> 100 + 2% *100
= 100+2=102
The area of square with edge 100 = side*side
=> 100*100
=> 10000
The area of square with side 102 = 102*102= 10404
Error in area calculation = 10404-1000 = 404
% error= (404/10000)*100
= 4.04%
ANSWER: C
Answer: C
Question: 3, 22, 7, 45, 15, ?, 31 Complete the series
Options:
A)91
B)92
C)93
D)94
E)95
Rationale: 3+4*1=7
7+4*2=15
15+4*4=16
Similarly
22+23*1=45
45+23*2=91
ANSWER:A
Answer: A
Question: Find the value of y from (12)^2 x 6^4 ÷ 432 = y?
Options:
A)2134
B)2234
C)2540
D)2560
E)432
Rationale: 432
E
Answer: E
Question: A train 120 m long running at 60 kmph crosses a platform in 20 sec. What is the length of the platform?
Options:
A)213
B)298
C)350
D)726
E)267
Rationale: D = 60 * 5/18 = 20
= 333 â€“ 120
= 213
Answer: A
Answer: A
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)2177
B)2876
C)4500
D)2981
E)2711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500.Answer: C
Answer: C
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 150 kilometers?
Options:
A)3.5 gallons
B)2.7 gallons
C)5.75 gallons
D)3.75 gallons
E)7.50 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 150 kilometers?
150 Ã· 40 = 3.75 Ã— 1 gallon = 3.75 gallons
correct answer is D) 3.75 gallons
Answer: D
Question: The schedule of G first year students was inspected. It was found that M were taking a Mathematics course, L were taking a Language course and B were taking both a Mathematics course and a Language course. Which of the following expression gives the percentage of the students whose schedule was inspected who were taking neither a mathematics course nor a language course?
Options:
A)100 x G/B+L+M)
B)100 x (B+L+M)/G
C)100 x (G-L-M)/G
D)100 x (G-B-L-M)/G
E)100 x (G+B-L-M)/G
Rationale: Explanatory Answer
M students are taking a math course.
L students are taking a language course.
B students are taking both a math and a language course.
Number of students taking at least one of the two courses = M U L
M U L = M + L - B
Hence, number of students taking neither of the two courses = G - (M + L - B) = G + B - M - L
Expressed as a percent of the total number of students, we get 100 x (G+B-L-M)/G
Answer E
Answer: E
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 12 minutes earlier than usual. How much time did the man spend walking?
Options:
A)45 minutes
B)50 minutes
C)40 minutes
D)54 minutes
E)35 minutes
Rationale: As they arrived 12 minutes earlier than usual, they saved 12 minutes on round trip from home to station (home-station-home) --> 6 minutes in each direction (home-station) --> wife meets husband 6 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-6 minutes=54 minutes.
Answer: D
Answer: D
Question: There are 5 different letters and 5 letter boxes of same size shape and colors. How many method are possible to post the letters?
Options:
A)50
B)51
C)52
D)53
E)54
Rationale: 50000 ->1
41000 ->5
31100 ->10
32000 ->10
21110 ->10
22100 ->15
11111 ->1
1+5+10+10+10+30+1=52
ANSWER:C
Answer: C
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4.
Options:
A)50p coins = 400 20p coins = 600 10p coins = 800
B)50p coins = 480 20p coins = 600 10p coins = 800
C)50p coins = 400 20p coins = 600 10p coins = 780
D)50p coins = 400 20p coins = 608 10p coins = 800
E)50p coins = 400 20p coins = 600 10p coins = 820
Rationale: 50*2k + 20*3k + 10*4k = 40000
200k = 40000 => k = 200
50p coins = 2k = 2*200 = 400
20p coins = 3k = 3*200 = 600
10p coins = 4k = 4*200 = 800
Answer:A
Answer: A
Question: The difference of two numbers is 1360. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Options:
A)240
B)270
C)295
D)360
E)269
Rationale: Let the smaller number be x. Then larger number = (x + 1360).
x + 1360 = 6x + 15
5x = 1345
x = 269
Smaller number = 270.
ANSWER E
Answer: E
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 50 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
Options:
A)100 % decrease
B)30% decrease
C)40% decrease
D)50% increase
E)60% increase
Rationale: Let's say here is the formula of how A and B affects the reaction speed:
rate = B/A
After the concentration A is increased by 50%, the percentage of A
become 1.5A, to keep 'rate' the same, need to have 1.5B.
Which means B increased by 50%
Answer : D
Answer: D
Question: Ace Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?
Options:
A)87,500 miles
B)100,000 miles
C)107,750 miles
D)112,500 miles
E)The residual values will never be equal.
Rationale: Truck 1 : 70,000 = m1 * 165,000 + 4,000 , where m1 is the depreciation $ per mile
Solve for m1 = 0.4
So the depreciation line for Truck 1 is y = 0.4 x + 4,000 , where y is in dollars and x is in mileage.
Similarly for Truck 2 : 52,000 = m2 * 200,000 + 4,000
and this gives m2 = 0.24
and similar line for Truck 2 is y = 0.24 x + 4,000.
The question is where values are same, and in terms of the equation, it's where the two depreciation lines meet.
so solve for x, 0.4 x + 4,000 = 72,000
0.24x + 4,000 = 52,000
gives x = 112,500,
ANSWER:D
Answer: D
Question: An association of mathematics teachers has 1,260 members. Only 560 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
Options:
A)75%
B)26.67%
C)42%
D)34%
E)25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 560
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*560 = 336
Percent of total membership that voted for winning candidate = (336/1260)*100 = 26.67%
Answer B
Answer: B
Question: Out of 450 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
Options:
A)75
B)100
C)125
D)150
E)None of these
Rationale: Explanation:
Students who play cricket, n(A) = 325
Students who play football, n(B) = 175
Total students who play either or both games,
=n(A∪B)=450−50=400Required Number,n(A∩B)=n(A)+n(B)−n(A∪B)=325+175−400=100
Option B
Answer: B
Question: ?% of 360 = 129.6
Options:
A)277
B)36
C)64
D)72
E)None of these
Rationale: ?% of 360 = 129.6
or, ? = 129.6×100/360=36
Answer B
Answer: B
Question: Factory X's bulbs work for over 5000 hours in 79% of cases, whereas factory Y's bulbs work for over 5000 hours in 85% of cases. It is known that factory X supplies 80% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
Options:
A)80.2%
B)88%
C)87.4%
D)85%
E)83.9%
Rationale: For X, 80% of 79% will work.
For Y, 20% of 85% will work. *20% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.80(0.79) = .632
0.20(0.85) = 0.17
The combined probability then is 63.2 + 17 = 80.2%
ANS A
Answer: A
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
Options:
A)4050
B)3500
C)4000
D)4500
E)5000
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
Subtracting (ii) from (iv), we get P = 4000.
P's monthly income = Rs. 4000.
Answer: C
Answer: C
Question: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 6
Options:
A) I only
B) II only
C) None
D) I and III
E) II and III
Rationale: I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5.
Therefore C is the answer.
Answer: C
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
Options:
A)Tuesday
B)Monday
C)Sunday
D)Friday
E)Wednesday
Rationale: The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday.
answer : C
Answer: C
Question: The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 5) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
Options:
A)80
B)82.5
C)78.5
D)75.5
E)74
Rationale: 1/2bh=1/2(2a+1)(2a+5)
Now 4a-5=2a+5
2a=10 ,a=5
Therefore,
A(0,0); B(0,15); C(10,15)
1/2*11*15=82.5
Answer: B
Answer: B
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 15%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)32.5
B)35
C)48
D)56.8
E)67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 10%, therefore bringing down the price to $63.75.
4) Now 63.75 has to be added byX %in order to equal the original price.
63.75 + ( X% ) 63.75 = 100.
Solving this eq for X, we get X = 56.8
Ans is D.
Answer: D
Question: A lady has fine gloves and hats in her closet- 25 blue, 7 red, and 9 yellow. The lights are
out and it is totally dark. In spite of the darkness, she can make out the difference between
a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a
glove. How many gloves must she take out to make sure she has a pair of each color?
Options:
A)36
B)37
C)38
D)39
E)40
Rationale: since it is not given hw many hats so he has hance to take any so 25+7+depends on given answer if 36 is answer round off to 25+7+4=36
ANSWER:A
Answer: A
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following:
I. 3
II. 4
III. 6
Options:
A)I only
B)II only
C)III only
D)I and III
E)I, II, and III
Rationale: let the six numbers be k-2, k-1, k, k+1, k+2, k+3
then, there sum will be 6k+3
3(2k+1),which is clearly a multiple of 3. Also, 2k+1 will always be odd. thus the sum will never be divisible by 2.
hence option A
Answer: A
Question: he average of 5 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)0
B)4
C)10
D)19
E)8
Rationale: Average of 5 numbers = 0.
Sum of 5 numbers (0 x 5) = 0.
It is quite possible that 4 of these numbers may be positive and if their sum is a the 5th number is (-a).
Answer: Option C
Answer: C
Question: if a@b = a * b^(1/2) then 3@9 = ?
self made
Options:
A)2
B)6
C)3
D)8
E)9
Rationale: a@b = a * b^(1/2)
3@9 = 3*9^(1/2) = 3*3 = 9
Correct Option: E
Answer: E
Question: If we want to choose out of 6 consonants and 4 vowels, how many words of 3 consonants and 3 vowels can be formed?
Options:
A)12200
B)720
C)9002
D)57600
E)12130
Rationale: Required selection = select 3 consonants from 6 and 3 vowels frm 4
= 6C3 * 4C3
= 80
As we have to form 6 letter word the above combination of consonants and vowels can be done in 6! = 720 different ways
Required no. of ways = 80 * 720
= 57600
Ans - D
Answer: D
Question: A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed
at which the train must run to reduce the time of journey to 40 minutes
Options:
A)50 km/hr
B)60 km/hr
C)65 km/hr
D)70 km/hr
E)None of these
Rationale: Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed
for given time and distance.
Lets solve it.
Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km
New Ɵme will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph
Answer: B
Answer: B
Question: If A:B=4:7 AND B:C=5:9,THEN A:C=?
Options:
A)28:37
B)18:37
C)16:53
D)20:63
E)15:48
Rationale: A/B=4/7 AND B/c=5/9
A/B*B/C=4/7*5/9=20/63
SO A/C=20/63
20:63
ANSWER D
Answer: D
Question: A car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
Options:
A)37 km
B)76 km
C)25 km
D)15 km
E)30 km
Rationale: A
37 km
The total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in AP whose first term is 28 and last term is 46 = 10/2 [28 + 46] = 370 km.
Answer: A
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 153, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Options:
A)22
B)33
C)55
D)27
E)88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 153 => .1x + 3/4x = 153=> x = 180
180 - 153 = pure gala = 27.
D
Answer: D
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 19 more than the first integer. Find the three integers?
Options:
A)7, 9, 29
B)7, 2, 10
C)7, 9, 10
D)7, 9, 11
E)13,15,17
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 19 => x = 13
Hence three consecutive odd integers are 13, 15 and 17.
Answer:E
Answer: E
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 46. What is a possible value for the mean of the distribution?
Options:
A)46
B)52
C)48
D)49
E)50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 46:
{Mean} - 3*{SD} > 46;
{Mean} - 6 > 46;
{Mean} > 52.
Answer: B.
Answer: B
Question: Health insurance Plan P requires the insured person to pay $500 but then the insurance pays 80% of the cost over $500. Plan Q requires the insured to pay the initial $300, but then pays 60% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$1100
B)$1600
C)$2200
D)$2800
E)$3300
Rationale: 0.8(x-500)=0.6(x-300)
0.2x=400-180
x=1100
The answer is A.
Answer: A
Question: The contents of a certain box consist of 14 apples and 25 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
Options:
A)3
B)6
C)14
D)19
E)20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 25 oranges, so to get to 6 oranges, we should remove 25 - 6 = 19 oranges.
Answer D
Answer: D
Question: What is the tens digit of 7^545?
Options:
A)0
B)1
C)2
D)3
E)0
Rationale: 7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
7^6 = 117649
We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )
0 , 4 , 4 , 0 .
546= 4*136 + 1
The ten's digit will be 0 .
Answer E
Answer: E
Question: Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 6 pages a minute more than printer A ?
Options:
A)600
B)800
C)1000
D)720
E)1500
Rationale: Answer: D.
Answer: D
Question: The sector of a circle has radius of 20 cm and central angle 135o. Find its perimeter?
Options:
A)91.5
B)87.1
C)91.7
D)91.3
E)91.1
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 20) + 2(20)
= 47.1 + 40 = 87.1 cm
Answer:B
Answer: B
Question: If books bought at prices ranging from Rs. 250 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
Options:
A)23267
B)1400
C)1800
D)2778
E)76611
Rationale: Explanation:
Least Cost Price = Rs. (250 * 8) = Rs. 2000.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400 - 2000) = Rs. 1400.
Answer: B) 1400
Answer: B
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 12% per annum then the gain of B in a period of 3 years is?
Options:
A)200
B)210
C)220
D)225
E)230
Rationale: (3500*2*3)/100 => 210
Answer: B
Answer: B
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
Options:
A)35
B)34
C)45
D)25
E)65
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Option A
Answer: A
Question: There are 40 doors marked with numbers 1 to 40. And there are 40 individuals marked 1 to 40.
An operation on a door is defined as changing the status of the door from open to closed or vice versa. All doors are closed to start with.
Now one at a time one randomly picked individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For e.g. individual marked with number 5 operates the doors marked with the following numbers: 5, 10, 15,... and 40.
If every individual in the group get one turn then how many doors are open at the end?
Options:
A)0
B)1
C)2
D)4
E)6
Rationale: Let us start with 1.
When 1 goes, all the doors are open since every number is a multiple of 1.
Also 1 will remain opened since 1 is not a multiple of any number.
Prime numbers can only be operated by people with prime numbers.
So 2,3,5,7,11,13,17,19,23,29,31,37 will be closed when people with respective numbers perform operations on them.
Our numbers left are 4,6,8,9,10,12,14,15,16,18,20,21,22,24,...28 and
From these numbers, only those numbers will remain opened on which even number of operations are performed including the operation performed by number 1.
This is possible only for perfect squares which are 4,9,16,25 and 36.
So our numbers are 1,4,9, 16,25 and 36.
Answer:- E
Answer: E
Question: If x/y =1/4, then (x-y)/x?
Options:
A)-1/2
B)-1
C)-3
D)1/2
E)4
Rationale: we have this law of fraction:
a/b=c/d= (a-c)/(b-d)
x/y=1/4 ---> x/1=y/4= (x-y)/(1-4)=(x-y)/(-3) ---> (x-y)/x= -3
Answer: C
Answer: C
Question: A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?
Options:
A)1/4
B)56/27
C)2
D)3
E)4
Rationale: Soln:
28 = 1*28
2*14
4*7
sum of reciprocals = 1+1/28+1/2+1/14+1/4+1/7=56/28=2
ANSWER:C
Answer: C
Question: what is the least number. which should be added to 0.0282 to make it a perfect square?
Options:
A)0.0007
B)0.0042
C)0.0002
D)0.0003
E)0.0004
Rationale: 0.0282+0.0007=0.0289
(0.17)^2
ANSWER:A
Answer: A
Question: Given that 2x + 17 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
Options:
A)-4 and -1
B)-1 and 4
C)-4 and 1
D)-6 and 4
E)2 and 5
Rationale: 2x + 17 > 5
i.e 2x >5-17
i.e. 2x > -12
i.e. x > -6
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -6 < x < 4
Answer: Option D
Answer: D
Question: For the positive numbers, n, n + 2, n + 4, n + 6, and n + 8, the mean is how much greater than the median?
Options:
A)n+l
B)1
C)0
D)n+2
E)n+3
Rationale: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + n + 2 + n + 4 + n + 6 + n + 8)/5
mean = (5n + 20)/5
mean = n + 4
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n, n + 2, n + 4, n + 6, n + 8
The median is n + 4.
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 4 – (n + 4) = n + 4 – n – 4 = 0
The answer is C
Answer: C
Question: if 7v passes to that wire and a current of 260mA then find the resistance
Options:
A)26.9
B)27.9
C)28.9
D)29.9
E)30.9
Rationale: V=IR
=> R=V/I = 7 V / 260 mA = 7 V / 260*10^(-3) A = 26.92 ohm
ANSWER:A
Answer: A
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?
Options:
A)10
B)11
C)101
D)1011
E)10001
Rationale: Starting from right count the positions of 1 s
100010000=(1*2^8) + (1*2^4)=(2^8 + 2^4)
similarly,
1000100000=(1*2^9)+(1*2^5)=(2^9 + 2^5)
Lets simplify them further,
(2^8 + 2^4)=2^4(2^4 +1)=2^4(16+1)=2^4(17)
(2^9 + 2^5)=2^5(2^4 +1)=2^5(16+1)=2^5(17)
The prime numbers common in both are 2 and 17, and the largest one is 17.
from the options, (E) 10001=1*2^4+1*2^0=16+1=17
Hence answer (E).
Answer: E