divelab/Sys2Bench huggingface dataset:
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 182 votes. Find the total number of valid votes?
Options:
A)455
B)570
C)480
D)520
E)550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 182 => 4x/10 = 182
=> 4x = 1820 => x = 455.
ANSWER:A
Answer: A
Question: Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ?
Options:
A)28
B)20
C)27
D)29
E)21
Rationale: Average price per book
= (1000+ 800) / (50 + 40)
= 1800 / 90
= Rs.20
Answer:B
Answer: B
Question: By selling a house for Rs.55000, it was found that 1/10 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)38020
B)38000
C)38028
D)38019
E)47500
Rationale: CP + CP/10 = 55000
CP = 50000
SP = 50000*(95/100)
=47500
Answer: E
Answer: E
Question: Ratio of the ages of Mahesh and Nilesh is 5 : x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
Options:
A)13.9
B)16.5
C)14.7
D)12.5
E)14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be m, n and r respectively.
m/n = 5/x ------ (1)
m = r - 18 ------ (2)
r + 9 = 47 ------ (3)
m - n = r ----- (4)
(3) => r = 47 - 9 = 38 years
(2) => m = 38 -18 = 20 years
(1) => 20/n = 5/x => n = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: E
Question: If [x] is the greatest integer less than or equal to x, what is the value of [-11.6]+[13.4]+[12.7]?
Options:
A) 3
B) 10
C) 13
D) 16
E) 17
Rationale: You are asked what the closest lesser integer value to [x] is.
[-11.6] = -12.0
[13.4] = 13.0
[12.7] = 12.0
Therefore , answer is: -12.0 + 13.0 + 12.0 = 13.0
Option A.
Answer: C
Question: A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
Options:
A)28
B)21
C)29
D)27
E)13
Rationale: 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer:B
Answer: B
Question: A question paper has 2 parts, A & B, each containing 5 questions. If a student has to choose 3 from part A & 4 from part B, in how many ways can he choose the questions?
Options:
A)50
B)100
C)152
D)150
E)55
Rationale: There 3 questions in part A out of which 4 question can be chosen as = 5C3.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 5C4.
Hence, total number of ways,
=5C3*5C4
=[5!/(2!3!)]*[5!/(4!*1)]
= {10}*{5*4!/(4!)}
= 10*5=50.
A
Answer: A
Question: The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 14.56 years. What was the average age of five new men?
Options:
A)15.5
B)15.4
C)15.25
D)10.4
E)15.6
Rationale: Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 364.
Total age of five men added later = 364 - 312 = 52.
Hence, the total average of five men = 52/5 = 10.4
ANSWER:D
Answer: D
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.865 per pound?
Options:
A)1:3
B)1:2
C)1:1
D)2:1
E)3:1
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.865
0.9 – 0.1x = 0.865
x = 0.35
Thus ratio of both flours is 1:2
B
Answer: B
Question: The average number of printing error per page in a book of 512 pages is 4. If the total number of printing error in the first 302 pages is 1,208, the average number of printing errors per page in the remaining pages is
Options:
A)0
B)4
C)840
D)90
E)80
Rationale: Remaining pages = 512 – 302 = 210
Let average printing error in remaining pages = x
Then, 1208+210×x /512=4
⇒ 210x = 840 ⇒ x = 4
Answer B
Answer: B
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 36 Km/hr. His average speed during the whole journey in km/hr. is :
Options:
A)45
B)43
C)40
D)38
E)29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*60*36 / 60+36
= 45
Answer : A
Answer: A
Question: If c and d are unique prime integers, which of the following must be odd?
Options:
A)a−b
B)a−2b
C)2c−2d
D)2c/2d
E)c-d
Rationale: The answer is C. Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Answer C
Answer: C
Question: When the positive integer C is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer Dis divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of C-D?
Options:
A) 12
B) 24
C) 35
D) 16
E) 30
Rationale: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5c + 3
n = 7d + 4
I will need to check for the smallest such number.
I put d= 1. n = 11. Is it of the form 5c + 3? No.
Put d= 2. n = 18. Is it of the form 5c + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so
your answer is C
Answer: C
Question: What is the difference between the compound interests on $5000 for 1 years at 4% per annum compounded yearly and half-yearly?
Options:
A)$2.04
B)$3.06
C)$4.80
D)$8.30
E)$9.30
Rationale: A.
$. 2.04
B.
$. 3.06
C.
$. 4.80
D.
$. 8.30
Answer: Option A
Explanation:
C.I. when interest
compounded yearly = $ 5000 x 1 +	4 x 1 + x 4
100 100
= $. 5000 x	26	x	51
25 50
= $. 5304.
C.I. when interest is
compounded half-yearly	= $ 5000 x 1 +	2 3
100
= $ 5000 x	51	x	51	x	51
50 50 50
= $5306.04
Difference = $. (5306.04 - 5304) =$. 2.04
ANSWER : A $2.04
Answer: A
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
Options:
A)18
B)19
C)27
D)29
E)31
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: C
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 147 km downstream.
Options:
A)4 hours
B)5 hours
C)6 hours
D)7 hours
E)8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 147/21 = 7 hours
Option D
Answer: D
Question: Find the number of ways of arranging the host and 5 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)5!
B)8!
C)11!
D)12!
E)14!
Rationale: Ans.(A)
Sol. Total number of persons = 6 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 5 places => 5! Ways ... The number of required arrangements = 5! x 1= 5! = 5! ways
Answer: A
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
Options:
A)3
B)5
C)9
D)11
E)None of these
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
ANSWER : D
Answer: D
Question: The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 7:5:3. Someone removes 5 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The weights of the items in the suitcase are 7k, 5k, and 3k.
If removing 5 pounds of clothes doubles the ratio of books to clothes, then 5 pounds represents half the weight of the clothes.
2.5k = 5 pounds and then k = 2 pounds.
The electronics weigh 3(2) = 6 pounds.
The answer is D.
Answer: D
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)22
B)88
C)48
D)99
E)12
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Answer: C
Question: One half of a two digit number exceeds its one third by 5. What is the sum of the digits of the number?
Options:
A)A)3
B)B)5
C)C)7
D)D)9
E)E)11
Rationale: x/2 – x/3 = 5 => x =30
3 + 0 = 3
ANSWER:A
Answer: A
Question: If the price of sugar rises from Rs. 10 per kg to Rs. 13 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
Options:
A)15%
B)20%
C)23%
D)30%
E)none
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 13 = x = 77 kg.
∴ Reduction in consumption = 23%.
Answer C
Answer: C
Question: If x > y^5 > z^6, which of the following statements could be true? I.x=y II. x>y III.x>y>z
Options:
A)I only
B)II only
C)II,III only
D)III only
E)I,III only
Rationale: Answer : C
Answer: C
Question: Ram, who is half as efficient as Krish, will take 30 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?
Options:
A)16 days
B)10 days
C)8 days
D)6 days
E)18 days
Rationale: Number of days taken by Ram to complete task = 30
Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days
If total work done by Ram in 30 days is 30w
Amount of work done by Ram in 1 day = w
Amount of work done by Krish in 1 day = 2w
Total amount of work done by Krish and Ram in a day = 3w
Total amount of time needed by Krish and Ram to complete task = 30w/3w = 10 days
Answer B
Answer: B
Question: trisha bakes 6 cookies for 6 friends. 4 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?
Options:
A)6
B)0
C)4
D)3
E)1
Rationale: trisha made 6*6 cookies = 36 cookies. 4 friends eat 3 cookies, leaving 24 remaining for 2 friends.
24 is divisible by 2. The 2 friends ate a cumulative number of cookies divisible by 2, because the number is the same.
24-24=0;
B is the correct answer
Answer: B
Question: A can do a piece of work in 12 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
Options:
A)5days
B)6days
C)7.5days
D)8.5days
E)9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =12∗1/2= 6 days
Option B
Answer: B
Question: From the given equation find the value of x: x² − 3x + 2
Options:
A)0
B)2
C)4
D)5
E)6
Rationale: (x − 1)(x − 2)
x = 1 or 2.
B
Answer: B
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 4 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
Options:
A)1 ≤ n ≤23
B)7 ≤ n ≤17
C)5 ≤ n ≤19
D)6 ≤ n ≤18
E)9 ≤ n ≤15
Rationale: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-4+3=17 for the maximum, and 12-6+4-3=7 for the minimum, so B is the answer
Answer: B
Question: The average of five numbers is 18. The average of first two numbers is 14 and the average of last two numbers is 19. What is the middle number?
Options:
A)24
B)27
C)29
D)32
E)34
Rationale: The total of seven numbers = 5X18 = 90
The total of first 2 and last 2 numbers is = 2 X 14+2 X 19 = 66
So, the middle number is (90 - 66 ) = 24
A
Answer: A
Question: About the number of pairs which have 16 as their HCF and 125 as their LCM, the conclusion can be
Options:
A)only one such pair exists
B)no paid is exists
C)many such pairs exist
D)pair exists
E)None of these
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option:B
Answer: B
Question: Ram, who is half as efficient as Krish, will take 24 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?
Options:
A)16 days
B)12 days
C)8 days
D)6 days
E)18 days
Rationale: Answer
Ram takes 24 days to complete the task, if he works alone.
Krish is twice as efficient as Ram is. So, working alone, Krish will take half the time to complete the task.i.e., 12 days.
Ram will complete 1/24th of the task in a day.
Krish will complete 1/12th of the task in a day.
When they work together, they will complete 1/24+1/12=1/8th of the task in a day.
Therefore, when they work together they will complete the task in 8 days.
Choice C
Answer: C
Question: Find the fraction which has the same ratio to 1/13 that 5/34 has to 7/48.
Options:
A)110/1547
B)120/1547
C)140/1547
D)160/1547
E)220/1547
Rationale: P : 1/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 1/13 * 5/34
P*7/48 = 5/442
P = 240/3094 => P = 120/1547
ANSWER:B
Answer: B
Question: The measurements obtained for the interior dimensions of a rectangular box are 100 cm by 100 cm by 150cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
Options:
A)50,000
B)40,000
C)45,000
D)50,000
E)60,000
Rationale: The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 100*100*1 = 10,000 cubic centimeters.
So, approximate maximum possible difference is 15,000 + 15,000 + 10,000 = 40,000 cubic centimeters.
Answer: B.
Answer: B
Question: At Company X senior sales representatives visit the home office once every 30 days, and junior sales representatives visit the home office once every 20 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
Options:
A)10%
B)25%
C)33%
D)50%
E)67%
Rationale: When you say Senior is 1/30, what do you mean by it? It is the rate of visit. The time of visit is 30 days. The rate is 1/30. Similarly, the rate of visit for junior is 1/20.
The 2 yrs has no significance in this case. The rate stays the same for every time interval.
{1/20} - {1/30}/ {1/30} * 100 = 50%
ANSWER:D
Answer: D
Question: In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
Options:
A)12
B)14
C)36
D)38
E)40
Rationale: There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3 = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3 = 3! = 6.
Total number of ways = (6 x 6) = 36.
ANSWER C
Answer: C
Question: A rectangular grass field is 65 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)1350
B)1971
C)9676
D)1679
E)1250
Rationale: Area = (l + b +2d) 2d
= (65 + 55 +2.5 * 2) 2*2.5 => 625
625 * 2 = Rs.1250
Answer:E
Answer: E
Question: A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 60 percent.
Options:
A)145
B)150
C)175
D)180
E)130
Rationale: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 60 percent 180 min.Answer:D
Answer: D
Question: How long does a train 250 meters long running at the rate of 72km/hr take to cross a bridge 150 meters in length?
Options:
A)10sec
B)20sec
C)25sec
D)30sec
E)35sec
Rationale: Distance = length of train + length of bridge = 250+150 = 400
speed = 72km/hr = 72*5/18 = 20m/s
Required time = 400/20 = 20 seconds
Answer is B
Answer: B
Question: The average length of 6 strings is 80 cm. If the average length of one third of the strings is 70 cm, what is the average of the other strings?
Options:
A)75.
B)85.
C)90.
D)94.
E)100.
Rationale: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third strings is 70. That means out 6 / 3 = 2 strings.
let the avg length of two strings be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining strings.
IMO correct option is B.
Answer: B
Question: A sum of money is distributed among w,x,y,z in the proportion of 1:6:2:4. If X gets $1500 more than Y, what is the W's share?
Options:
A)$1500
B)$150
C)$375
D)$200
E)$450
Rationale: Let the shares of w,x,y,z are 1a,6a,2a,4a
6a-2a = 1500
4a = $1500, A=375
W's share = 1a = $375
Answer is C
Answer: C
Question: A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 10,000 units?
Options:
A) Between $15,000 and $25,000
B) Between $30,000 and $50,000
C) Between $75,000 and $125,000
D) Between $150,000 and $250,000
E) Between $300,000 and $500,000
Rationale: Number of defective units is between = .3 % of 10000 and .5% of 10000
= 30 and 50
Retail Price per unit = 2500 $
Expected price of refund is between = 2500 x 30 and 2500 x 50
=75,000 and 125,000 dollars
Answer C
Answer: C
Question: On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 2) II. (2, 5) III. (3, 2)
Options:
A)I only
B)II only
C)III only
D)I and III
E)I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 3 lies on the parabola, so (1, 2) will be enclosed by the parabola and x axis.
When x = 2, y = 4 lies on the parabola, so (2, 5) will not be enclosed by the parabola and x axis.
When x = 3, y = 3 lies on the parabola, so (3, 2) will be enclosed by the parabola and x axis.
The answer is D.
Answer: D
Question: If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n?
.
Options:
A)10
B)12
C)15
D)18
E)20
Rationale: 20! = 1*2*3*4*5...*19*20 (This is 20 factorial written as 20!)
n = 1*2*3*4*5*6*7.....*19*20
How many 2s are there in n?
One 2 from 2
Two 2s from 4
One two from 6
Three 2s from 8
and so on...
When you count them all, you get 18.
ANSWER:D
Answer: D
Question: The sum of the ages of 4 children is 52 years. The age of the youngest child is 4. If the intervals of years each born is same find the interval?
Options:
A)4
B)8
C)10
D)6
E)Cannot be determined
Rationale: Explanation:
Let the interval is x .The youngest child's age is 4. Each of the other 3 children will then be 4+x, 4+2x, 4+3x
We know that the sum of their ages is 52 .
so, 4+(4+x)+(4+2x)+(4+3x) = 52
x= 6
Answer: D
Answer: D
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Options:
A)20 m
B)10 m
C)40 m
D)30 m
E)40 m
Rationale: To reach the winning point , A will have to cover a distance of 500 - 140= 360 metre
ratio of the speeds of two contestants A and B is 3 : 4
i.e., when A covers 3 metre, B covers 4 metre.
When A covers 360 metre, B covers 4/3×360 = 480 metre.
Remaining distance B have to cover = 500-480= 20 metre
A wins by 20 metre
Answer isA
Answer: A
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 72 km/hr
Options:
A)5 seconds
B)2.8 seconds
C)3.5 seconds
D)2.5 seconds
E)2.6 seconds
Rationale: First convert speed into m/sec
Speed = 72*(5/18) = 20 m/sec
Time = Distance/speed
= 100/20 = 5 seconds
Answer: A
Answer: A
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)20000
B)22000
C)23090
D)24000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: Find the value of y 9^y = 3^12, what is y?
Options:
A)2
B)4
C)5
D)7
E)6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: E
Question: The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?
Options:
A)7 kg
B)6 kg
C)5 kg
D)8 kg
E)18 kg
Rationale: Say Iron = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
ANSWER:C
Answer: C
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 61.5. When one student dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?
Options:
A)a) 10
B)b) 24
C)c) 40
D)d) 55
E)e) 70
Rationale: Total Score of 16 students is 16*61.50 = 984
Total Score of 15 students is 15*64 = 960
So, the score of the person who left is 24 ( 984 - 960 )
Answer will be (B)
Answer: B
Question: 18! is equal to which of the following?
Options:
A)6,402,373,705,728,125
B)6,402,373,705,728,216
C)6,402,373,705,728,624
D)6,402,373,705,728,000
E)6,402,373,705,728,989
Rationale: After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is D.
Answer: D
Question: A straight pipe 1 meter in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?
Options:
A) 1/6 and 1/3 only
B) 1/4 and 1/3 only
C) 1/6, 1/4, and 1/3
D) 1/12, 1/6 and 1/4
E) 1/12, 1/6, and 1/3
Rationale: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3
Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 2th : 0/2, 1/2, 2/2
and 3rd : 0/3, 1/3, 2/3, 3/3
Now with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6
Now comine : 0,2,3,4,6
Now find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates.
answer : A
Answer: A