divelab/Sys2Bench huggingface dataset:
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)10
B)15
C)12
D)14
E)13
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	30:39 :: 12 : x
Working hours/day	6:5
:. 30 x 6 * x = 39 * 5 * 12
x =	(39 * 5 * 12)/(30 * 6)
x = 13.
Answer is E
Answer: E
Question: How many multiples of 4 are there between 8 and 160 ?
Options:
A)28
B)37
C)32
D)35
E)39
Rationale: It should be mentioned whether 8 and 160 are inclusive.
If 8 and 160 are inclusive, then the answer is (160-8)/4+1=39.
If 8 and 160 are NOT inclusive, then the answer is (156-12)/4+1=37.
Since OA is B, then we have NOT inclusive case.
Answer: B
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options:
A)190
B)200
C)225
D)230
E)none
Rationale: Sol.
Relative speed = (120 + 80) km/hr [200 * 5/18] m/sec = [500/9] m/sec.
Let the length of the other tain be x metres.
Then, x + 270 / 9 = 500/9 ⇔ x + 270 = 500 ⇔ x = 230.
Answer D
Answer: D
Question: If 4 men can colour 48 m long cloth in 2 days, then 8 men can colour 36 m long cloth in
Options:
A)0.75 day
B)2 days
C)1.2 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 8 = 0.75 day.
A
Answer: A
Question: 377 ÷ 13 ÷ 29 × 1/4 ÷ 2 = ?
Options:
A)1/6
B)1/8
C)1/10
D)1/12
E)1/15
Rationale: Explanation:
377 ÷ 13 ÷ 29 × 1/4 ÷ 2 = ?
=> ? = (337/(13 × 29 × 4 × 2)) = 1/8
Answer: Option B
Answer: B
Question: Two numbers are less than third number by 20% and 37% respectively. How much percent is the second number less than by the first
Options:
A)5%
B)10%
C)9%
D)11%
E)12%
Rationale: Let the third number is x.
then first number = (100-20)% of x
= 80% of x = 80x/100
Second number is (63x/100)
Difference = 80x/100 - 63x/100 = 17x/100
So required percentage is, difference is what percent of first number
(17x/100 * 100/80x * 100 )% = 5% ANSWER :A
Answer: A
Question: What is the smallest positive integer x such that 180-x is the cube of a positive integer
Options:
A)50
B)52
C)60
D)55
E)12
Rationale: Given 180-x is a perfect cube
so we will take 125= 5*5*5
180-x = 125
x =180-125 = 55
correct option is D
Answer: D
Question: A dealer offers a cash discount of 15% and still makes a profit of 36% when he further allows 25 articles to be sold at the cost price of 20 articles to a particular sticky bargainer. How much percent above the cost price were his articles listed?
Options:
A)60%
B)80%
C)100%
D)120%
E)150%
Rationale: Given
Cash Discount - 15%
Profit - 36%
Items Sold - 25
Price Sold at = List Price of 20
Assume List price = $10
Total Invoice = $200
-15% Cash Discount = $170
Let cost price of 25 items be x
So total cost = 25*x
Given the shopkeeper had a profit of 36%
25 * x * 136/100 = 170
or x = $5
Which means his products were listed at $10 which is a 100% markup over $5
Answer C
Answer: C
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
Options:
A)31/111
B)36/145
C)21/115
D)11/153
E)None
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: B
Question: What will come in place of the x in the following Number series? 5,28,57,88,125, x
Options:
A)120
B)143
C)166
D)170
E)180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: C
Question: Praveen starts business with Rs.3640 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
Options:
A)s.7500
B)s.8000
C)s.8500
D)s.9000
E)s.9360
Rationale: Let Hari’s capital be Rs. x. Then, 3640 * 12/7x = 2/3
=> 14x = 131040
=> x = 9360.
ANSWER:E
Answer: E
Question: A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the string place is
Options:
A)11 km
B)71 km
C)21 km
D)41 km
E)91 km
Rationale: Explanation:
Let the distance covered be D km.
\inline \frac{D}{10+4}+\frac{D}{10-4}=5
\Rightarrow \frac{D}{14}+\frac{D}{6}=5
\inline \Rightarrow 10D= 42\times 5=210
\inline \Rightarrow D= 21 km
Answer: C
Answer: C
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 226 m, what is its area?
Options:
A)2510
B)2535
C)3060
D)2515
E)2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=226 m
⇒ breadth =45 m
length =45+23=68 m
Area =68×45=3060 m2
Answer is C.
Answer: C
Question: The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
Options:
A)12%
B)40/3%
C)15%
D)14%
E)24%
Rationale: si of 4 month ie of 1/3 years=122
so p=2562-122=2440
now R=(si*100)/p*time
so R=122*100*3/2440*1=15
ANSWER:C
Answer: C
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Options:
A)720
B)420
C)None of these
D)5040
E)Cannot be determined
Rationale: Explanation :
The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 10P3
= 10 x 9 x 8
= 720. Answer : Option A
Answer: A
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs.40,000. the amount invested by Y is
Options:
A)Rs.45,000
B)Rs.50,000
C)Rs.60,000
D)Rs.80,000
E)None
Rationale: Solution
Suppose Y invested Rs.y
Then,	40000 /y = 2 / 3
‹=› y=(40000×3 / 2).
‹=› y=60000.
Answer C
Answer: C
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)11
B)12
C)18
D)17
E)19
Rationale: Explanation:
Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
Answer:C
Answer: C
Question: What is the sum of the first 25 natural numbers (starting from 1)?
Options:
A)325
B)350
C)375
D)400
E)425
Rationale: The sum of n natural numbers = n*(n+1) / 2 = 25*26/2 = 325
The answer is A.
Answer: A
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 42 kmph. For how many minutes does the bus stop per hour?
Options:
A)10 min
B)7 min
C)8.2 min
D)9.6 min
E)40 min
Rationale: D
9.6 min
Due to stoppages, it covers 8 km less.
Time taken to cover 9 km = (8/50 x 60) min = 9.6 min
Answer: D
Question: (1.00001)(0.99999) - (1.00003)(0.99997) =
Options:
A)0
B)10^-10
C)8(10^-10)
D)10^-5
E)3(10^-5)
Rationale: (1.00001*0.99999)-(1.00003*0.99997)
= (1+0.00001)(1-0.00001) - (1+0.00003)(1-0.00003)
= 1 - (0.00001)^2 - 1 + (0.00003)^2
= -(0.0000000001) + (0.0000000009)
= 0.0000000008=8(10^-10)
Answer C
Answer: C
Question: If (m-8) is a factor of m^2-km-24, then k=
Options:
A)3
B)5
C)6
D)11
E)16
Rationale: (m-8)(m-a)=m^2-km-24
A=-3
k=8+a=5=B
Answer: B
Question: The number of diagonals of a polygon of n sides is given by the formula f=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
Options:
A) 3
B) 5
C) 6
D) 7
E) 8
Rationale: f=n(n-3)
f=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: B
Question: The area of a triangle will be when a = 1m, b = 1m, c = 2m, a, b, c being lengths of respective sides?
Options:
A)2
B)7
C)5
D)3
E)4
Rationale: S = (1 + 1 + 2)/2
= 2
Answer: A
Answer: A
Question: Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1234
B)1596
C)1350
D)1467
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1345).
x + 1345 = 6x + 15
5x = 1330
x = 266
Large number = 266+1330 = 1596
B
Answer: B
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 9 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)11
B)10
C)8
D)12
E)15
Rationale: Suppose they meet x hours after 9 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 12 a.m.
Answer: D
Answer: D
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students W in the class?
Options:
A)A)10
B)B)12
C)C)15
D)D)20
E)E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: C
Question: A man is 24 years older than his son. In six years, his age will be twice the age of his son. The present age of the son is
Options:
A)14 years
B)28 years
C)20 years
D)22 years
E)None
Rationale: Solution
Let the son's present age be x years .Then, man's present age	= (x+24)years.
Then	â€¹=â€º(x+24)+6= 2(x+6)
â€¹=â€ºx+30=2x+12
x= 18.
Answer E
Answer: E
Question: There are 20 girls inhostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
Options:
A)1 year
B)2 years
C)3 years
D)4 years
E)None
Rationale: Total decrease = 20 * 2 = 40 month
= 3 years 4 month
E)None
Answer: E
Question: If P = 2Q+1 where P is an Integer then which of the following is true?
Options:
A)P is always Odd
B)P is even if Q is a non integer and a multiple of 0.5
C)P is a non multiple of 2
D)P= 1
E)P IS ALWAYS EVEN
Rationale: B
Answer: B
Question: Four athletes, Wendy, Michelle, Brenda, and Jamal, scored in a soccer (football) game. If Michelle scored 1 more goal than Brenda did, Jamal scored 3 less than Wendy did, and Wendy scored 3 more than Michelle did, how many fewer goals did Brenda score than Jamal?
Options:
A)-8
B)-6
C)-2
D)-1
E)-3
Rationale: In this word problem, the first key is to turn the story into equations:
Michelle scored 1 more than Brenda did: M = 1 + B
Jamal scored 3 less than Wendy did: J = W - 3
Wendy scored 3 more than Michelle did: W = 3 + M
Then, in classic GMAT style, the problem doesn't ask you to solve for a single variable, but instead to solve for the difference between B and J (how many more goals did Brenda score than Jamal did?). This means that your goal is to get the equations in terms of B and J so that you can solve for the expression B - J.
Taking the first equation and solving for B, you have B = M - 1.
Taking the second equation and solving for J you have J = W - 3, and then with the third equation you can replace W with 3 + M so that both B and J are in terms of M: J = (3 + M) - 3.
So if B = M - 1 and J = M, then:
B - J = (M - 1) - (M)
B - J = M - 1 - M (remove the parentheses by distributing the multiplication)
B - J = -1, so the answer is D.
Answer: D
Question: Five years ago, John’s age was half of the age he will be in 4 years. How old is he now?
Options:
A)14years
B)15years
C)16years
D)17years
E)18years
Rationale: Let John=j,j-5=(j+4)/2,then j=14years
ANSWER:A
Answer: A
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)358m
B)850m
C)350m
D)150m
E)340m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
Answer: C
Question: A train 440 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)80
B)26
C)24
D)54
E)15
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 440 * 3/55 = 24 sec.
Answer: C
Answer: C
Question: The mean of 50 observations was 36. It was found later that an observation 60 was wrongly taken as 23. The corrected new mean is?
Options:
A)36.7
B)36.1
C)36.5
D)36.9
E)36.3
Rationale: Correct sum
= (36 * 50 + 60 - 23)
= 1837.
Correct mean = 1837/50
= 36.7
Answer:A
Answer: A
Question: A bag contains 5 red & 3 black balls and the second one 4 red and 5 black balls. One of is selected at random and a draw of two balls is made from it. What is the chances that one of them is red and the other is black?
Options:
A).5456
B)1.5456
C)2.5456
D)3.5456
E)4.5456
Rationale: secet 1 bag from two=1/2
from 1 st bag=5c1*3c1/8c2=15/28
from 2nd bag=4c1*5c1/9c2=20/36
toatl p(s)=1/2(15/28 + 20/36)=.5456
ANSWER:A
Answer: A
Question: n a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)127.6
B)127.5
C)127.0
D)127.2
E)127.3
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.Answer: OB
Answer: B
Question: The average of fifteen numbers is 0. In those 15, at the most, how many may be greater than zero?
Options:
A)0
B)1
C)10
D)14
E)17
Rationale: Explanation :
Average of 15 numbers = 0
Sum of 15 numbers =(0 x 15) =0.
It is quite possible that 14 of these numbers may be positive and if there sum is a, then 15th number is (-a).
Answer : D
Answer: D
Question: If n is a natural number, then (6n^2+6n) is always divisible by?
Options:
A)6 only
B)6 and 12
C)12 only
D)by 18 only
E)None of these
Rationale: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B
Answer: B
Question: Jonathan can type a 40 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Options:
A)5 minutes
B)10 minutes
C)15 minutes
D)18 minutes
E)20 minutes
Rationale: You may set up common equation like this:
job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.
and find x from this equation
In this specific case, the equation will look like this:
40/40+40/30+40/24=40/x
If you solve this equation, you get the same answer B (10)
Answer: B
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 9 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
Options:
A) 18/79
B) 1/6
C) 1/25
D) 19/900
E) 1/900
Rationale: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/9 = 19
P = 19/900
Ans:D
Answer: D
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)2
B)6
C)8
D)4
E)10
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/54x 60) min= 10 min.
ANSWER E
Answer: E
Question: A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options:
A)12
B)18
C)25
D)74
E)88
Rationale: Number of runs scored more to increase the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
Answer D
Answer: D
Question: How many different three-digit multiples of 5 can be composed of digits 1, 3, 4, and 5 if none of the digits is repeated?
Options:
A)3
B)6
C)10
D)12
E)18
Rationale: = 3c2 x 2 = 6
can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Answer: B
Question: If n is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)N(N+1)(N-4)
B)N(N+2)(N-1)
C)N(N+3)(N-5)
D)N(N+4)(N-2)
E)N(N+5)(N-6)
Rationale: The product of 3 numbers to be divisible by 3 at least one of them must be divisible by 3. So, to ensure that the product of 3 integers shown is divisible by 3 all 3 numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3. We should have something like n(n+1)(n+2) (for example: if n divided by 3 yields remainder of 1, then n+1 yields remainder of 2 and n+2 yields remainder of 0, thus it's divisible by 3 OR if n divided by 3 yields remainder of 2, then n+2 yields remainder of 1 and n+1 yields remainder of 0, thus it's divisible by 3).
Only option A satisfies this, because n(n+1)(n−4)=n(n+1)(n−6+2) and n−6has the same remainder as nn upon division by 3 thus we can replace it by n.
Answer: A.
Answer: A
Question: When x is divided by 3, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
Options:
A)4z/7 + 5
B)(7z + 5) / 6
C)(6z + 7) / 4
D)(5z + 5) / 3
E)(4z + 6) / 7
Rationale: When x is divided by 3, the quotient is y and the remainder is 1: x = 3y + 1.
When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.
Equate those two:
3y + 1 = 5z + 6;
y = (5z + 5)/3.
Answer: D.
Answer: D
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 20 mangoes. Find the gain percent?
Options:
A)27%
B)25%
C)21%
D)15%
E)24%
Rationale: SP = CP + g
150 SP = 150 CP + 20 SP
130 SP = 150 CP
130 --- 20 CP
100 --- ? => 15%
Answer:D
Answer: D
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 63?
Options:
A)68
B)69
C)128
D)68^2
E)68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 64 and the next number as its multiple.
So, I can take 64 and 128 as two distinct numbers, such that Lowest LCM = 128.
Answer should be C.
Answer: C
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Options:
A)100
B)50
C)26
D)1000
E)None of these
Rationale: Solution:
1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be 'n'.
Therefore, using 'n' alphabets we can form n *n *n = n3 distinct 3 digit initials.
NOTE:
Distinct initials are different from initials where the digits are different. For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million.
i.e. n3 = 106 (1 million =106).
n3 = 1023.
=> n = 102 = 100.
Hence, the language needs to have a minimum of 100 alphabets
Answer: Option A
Answer: A
Question: If Finn was 17 months old one year ago, how old was he, in months, x months ago?
Options:
A)x − 30
B)x − 12
C)18 − x
D)29 − x
E)30 − x
Rationale: Age Today = 17 months + 12 months (1year) = 29 months
X months ago- Today's Age - X = 29 - X
Ans- D
Answer: D
Question: What should come in place of the question mark (?) in the following equation?
9568 – 6548 – 1024 = ?
Options:
A)2086
B)1996
C)2293
D)1896
E)None of these
Rationale: ? = 9568 – 6548 – 1024 = 1996.
Answer B
Answer: B
Question: A cyclist bikes x distance at 8 miles per hour and returns over the same path at 812miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
Options:
A)8.1
B)8.3
C)8.6
D)9.6
E)9.0
Rationale: Distance = d1 = x miles
Speed = s1 = 8 miles per hour
Time = t1 = Distance/ Speed = x/8
2. Going from B to A
Distance = d2 = x miles
Speed = s2 = 12 miles per hour
Time = t2 = Distance/ Speed = x/12
3. Average Speed = Total Distance/Total Time
Total Distance = x + x = 2x
Total Time = x/12 + x/8 = x (1/12 + 1/8) = =5x/24
Speed = 2x/(5x/24) = 48/5
= 9.6
Answer : D
Answer: D
Question: If x = -6 and y = -3, what is the value of 4(x-y)^2 - xy ?
Options:
A)20
B)18
C)17
D)22
E)23
Rationale: x = -6 and y = -3
x-y = -6 - (-3) = -6+3 = -3
x*y = -6 * -3 = 18
Now we apply it in the equation 4(x-y)^2 - xy =4 (-3)^2-18
==>4*9 -18 = 36-18 =18
Answer : B
Answer: B
Question: Eleven men and eleven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Options:
A)5!*6!
B)7!*8!
C)10!*11!
D)10!*12!
E)11!*12!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 11 men in a circle can be arranged in (11-1)! ways and if we place 11 women in empty slots between them then no two women will be together. The # of arrangement of these 11 women will be 11! and not 10! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 10!*11!.
C
Answer: C