divelab/Sys2Bench huggingface dataset:
Question: A’s speed is 25/18 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)1/18
B)7/18
C)7/25
D)3/25
E)1/25
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 25 meters, B covers 18 meters in that time. So if the race is 25 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 25 meters) would be the same as the time required by B (to cover 18 meters) to reach the finish line.
So B should get a head start of 7/25th of the race.
Answer (C)
Answer: C
Question: The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?
Options:
A)4x–3
B)16x–15
C)(x+3)/4
D)(x+3)/16
E)(x+15)/16
Rationale: Since we know a(3) we can find a(2),
if we can find a(2) we can find a(1).
a(3)=4a(2)-3 ---> x=4a(2)-3 ---> a(2)=(x+3)/4
a(2)=4a(1)-3 ---> (x+3)/4=4a(1)-3 ---> 4a(1)=(x+15)/4 ---> a(1)=(x+15)/16
The answer is E.
Answer: E
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11-sided polygon)?
Options:
A)1/2
B)1/3
C)1/4
D)1/8
E)1/11
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/8 = 1/4.
The answer is C.
Answer: C
Question: The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number?
Options:
A)A)318
B)B)65
C)C)58
D)D)62
E)E)48
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*98+6*65-11*60 = 318
Answer is A
Answer: A
Question: Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution?
Options:
A)6:4
B)6:14
C)4:4
D)4:6
E)3:7
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4=C
Answer: C
Question: In a group of 90 students, 30 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
Options:
A)9
B)19
C)33
D)27
E)31
Rationale: Number of students taking history =H=30
Number of students taking statistics =S= 32
Total number of students =T= 90
Number of students taking History or Statistics or both =B= 59
Number of students taking neither history nor statistics =N= 90-59=31
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 90 = 30+ 32 +31 - X
or X = 3
Now,
Number of students taking only history will be
H-X
or 36-3 = 33
Answer:- C
Answer: C
Question: Two bullet train s are running in opposite directions with the same speed. If the length of each bullet train is 120 metres and they cross each other in 12 seconds, then the speed of each bullet train (in km/hr) is:
Options:
A)46 km/hr.
B)36 km/hr.
C)56 km/hr.
D)76 km/hr.
E)66 km/hr.
Rationale: B
36 km/hr.
Let the speed of each bullet train be x m/sec.
Then, relative speed of the two bullet train s = 2x m/sec.
So, 2x = (120 + 120)/12
--> 2x = 20
--> x = 10.
--> Speed of each bullet train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
Answer: B
Question: A nickel is placed flat on a table. What is the maximum number of nickels that can be placed
around it, flat on the table, with each one tangent to it?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Connect the midpoints of the given nickel and two others placed around it so that
all three touch. This creates an equilateral triangle with 60 degree angles. Since 360=60 = 6,
six nickels can be placed around the given nickel.
correct answer C
Answer: C
Question: What is the remainder when 750*810*830*790 is divided by 13?
Options:
A)4
B)9
C)10
D)8
E)6
Rationale: OA is 'C'.
OE:
take the remainder from each of 750/15, 810/15 and so on..
750/13 gives remainder = 9
810/13 gives remainder = 4
830/13 gives remainder = 11
790/13 gives remainder = 10
the net remainder is the product of above individual remainders. i.e = 9*4*11*10
break them into pairs 9*4/13 gives remainder 10
and 11*10/13 gives remainder 6
so 10*6/13 gives remainder 8.
Answer: C
Answer: C
Question: If a and b are the two values of t that satisfy
the equation t^2 â€“ 10t + 16 = 0, with a > b, what is the value of a â€“ b?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Factor the left side of the equation:
t^2 â€“ 10t + 16 = 0
(t â€“ 2)(t â€“ 8) = 0
t = 2, t = 8
Thus, a = 8 and b = 2. So a â€“ b = 8 â€“ 2 = 6.
The answer is C.
Answer: C
Question: k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Options:
A)2^n - 8
B)2^n - 4
C)2^n
D)2^n + 4
E)2^n + 5
Rationale: Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 5
We also know that 9 is a divisor of9.
So, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4
B
Answer: B
Question: A certain distance is covered by a cyclist at a certain speed. I a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is:
Options:
A)1:2
B)2:1
C)1:4
D)4:1
E)None of these
Rationale: let the distance covered by the cyclist be x and the time taken be y. Then, Required ratio=1/2x/2y:x/y=1/4:1=1:4.
Correct Option: C
Answer: C
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
Options:
A)5:18
B)5:12
C)5:10
D)5:11
E)5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128 = 5:16
Answer:E
Answer: E
Question: A and B start a business, with A investing the total capital of Rs.100000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.10000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options:
A)A)2520000
B)B)2620000
C)C)2820000
D)D)2920000
E)E)2420000
Rationale: Interest received by A from B = 10% of half of Rs.100000 = 10% * 50000 = 5000.
Amount received by A per annum for being a working partner = 10000 * 12 = Rs.120000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (5000+ 120000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(5000 + 120000 + P) = 2(P)
P = 125000
Total profit = 2P + 120000
= 2*125000 + 120000 = 2620000
Answer:B
Answer: B
Question: An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of B?
Options:
A)360
B)358
C)356
D)514
E)504
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of B = 4/13 * 1638 = Rs. 504
Answer: E
Answer: E
Question: A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Options:
A)$200
B)$333.33
C)$100.25
D)$277.78
E)$377.00
Rationale: Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 )
$25000 is 60% of total amount.
So total amount = 25000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 25000 * (100/60) * (40/100) = 50000/3
This amount has to be divided by 50( remaining people are 50 )
So per head amount is 50000/3 / 50 = 32000/180 = 333.33;
ANSWER:B
Answer: B
Question: In a company of 11 employees, 5 employees earn $32,000, 4 employees earn $45,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 11 employees is $48,000, what is the annual salary for each of the highest-paid employees?
Options:
A)$90,000
B)$94,000
C)$98,000
D)$102,000
E)$106,000
Rationale: 5*32,000+4*45,000+2x=11*48,000
2x=528,000-160,000-180,000
2x=188,000
x=94,000
The answer is B.
Answer: B
Question: (1000)7÷(10)16=?
Options:
A)10
B)100
C)1000
D)100000
E)None of these
Rationale: Explanation:
=(103)7/(10)16
=(10)21/(10)16=10(5)=100000
Option D
Answer: D
Question: Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)54
B)59
C)63
D)71
E)62
Rationale: Total = 70
Thrower = 46
Rest = 70 - 46 = 24
Left Handed = 24/3 = 8
Right handed = 16
If all Thrower are right handed then total right handed is 46 + 16 = 62
so E. 62 is the right answer
Answer: E
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
Options:
A)70 km/hr
B)75 km/hr
C)84 km/hr
D)87.5 km/hr
E)77.5 km/hr
Rationale: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours,
then the speed of the first train = 400/4= 100 kms/hr
then the speed of the first train is:100*7/8 = 700/8 = 87.5 km/hr
ANSWER:D
Answer: D
Question: One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
Options:
A)11 km
B)13 km
C)16 km
D)18 km
E)19 km
Rationale: Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
So, x + (61 -x) = 9
4 9
9x + 4(61 -x) = 9 x 36
5x = 80
x = 16 km.
C
Answer: C
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
Options:
A)9
B)12
C)14
D)15
E)60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
=3*20=60
E. 60
Answer: E
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?
Options:
A)R=7/10
B)R=3/5
C)R=2/5
D)R=3/10
E)1/10
Rationale: Method 1
Probability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: A
Question: Which of the following options is an arithmetic sequence?
I. m-9, n-5, o-9,p-9, q-9, r-9
II. m^5, n^5, o^5, p^5, q^5
III. 4m,4n,4o,4p,4q
Options:
A)I only
B)I and II
C)I and III
D)II and III
E)III only
Rationale: lets look at the three choices...
I. m-9, n-5, o-9,p-9, q-9, r-9
since the difference is not constant, it is not an arithmetic sequence...
II. m^5, n^5, o^5, p^5, q^5
since the difference is not constant, it is not an arithmetic sequence
III. 4m,4n,4o,4p,4q
since the difference is constant it is an arithmetic sequence...
The answer is E)
Answer: E
Question: Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
Options:
A)Rs. 692.80
B)Rs. 905
C)Rs. 990
D)Rs. 1385
E)None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 3 - 650 x 2 Rs.
= 905 Rs.
Correct Option: B
Answer: B
Question: In how many ways the word "RITUAL" can be arranged?
Options:
A)120
B)240
C)720
D)None
E)Cannot be determined
Rationale: Explanation :
The required number of ways = 6!
= 720
Answer : C
Answer: C
Question: 210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Options:
A)25
B)40
C)50
D)60
E)75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: B
Question: 5 identical snow plows can clear an iced parking lot in 24 hours. How long would it take 6 such snow plows to clear the same parking lot?
Options:
A)1 hour, 15 minutes
B)2 hours, 30 minutes
C)3 hours
D)7 hours, 30 minutes
E)20 hourss
Rationale: 6/5 as many plows will take 5/6 as many hours --> 24*5/6=20 hours.
Answer: E.
Answer: E
Question: If |q|=−q, which of the following must be true?
Options:
A)q≥0
B)q≤0
C)q2>x
D)x3<0
E)2x<x
Rationale: |q| =-q means absolute value of q is equal to negative of q. Since absolute value cannot be negative hence negative of q should result in a non negative number. It means q is a non positive number i.e. q<0. Answer is B
Answer: B
Question: If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: Explanation:
Let n ÷ 4 = p , remainder = 3
=> n = 4p + 3
2n = 2(4p + 3)
= 8p + 6
= 8p + 4 + 2
= 4(2p + 1) + 2
Hence, if 2n is divided by 4, we will get 2 as remainder.
Answer: C
Answer: C
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
Options:
A)27 sec
B)87 sec
C)67 sec
D)47 sec
E)37 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds.
Answer: A
Answer: A
Question: How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.
Options:
A)648
B)720
C)890
D)980
E)None of these
Rationale: Explanation :
Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number.
We will go through this step by step.
Divisible by 1 and 1 at the unit place:
_ _ _ _ _ 1
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 2 and 2 at the unit place:
_ _ _ _ _ 2
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 3 and 3 at the unit place:
_ _ _ _ _ 3
Since, any number will have all the digits from 1 to 6 and the sum 1 + 2 + 3 + 4 + 5 + 6 = 21 is divisible by 3
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 4 and 4 at the unit place:
_ _ _ _ _ 4
Here, there are two cases
_ _ _ _ 2 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
_ _ _ _ 6 4
This gives 4 x 3 x 2 x 1 = 24 numbers.
This gives us total of 24 + 24 = 48 numbers.
Divisible by 5 and 5 at the unit place:
_ _ _ _ _ 5
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
Divisible by 6 and 6 at the unit place:
_ _ _ _ _ 6
As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even.
This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.
None of these cases will have numbers overlapping with each other.
So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120 = 648
Answer : A
Answer: A
Question: One year ago, Priya was four times as old as her daughter Sneha. Six years hence, Priya’s age will exeed her daughter’s age by 9 years. The ratio of the present ages of Priya and her daughter is :
Options:
A)9 : 2
B)11 : 3
C)12 : 5
D)13 : 4
E)13 : 6
Rationale: Let the ages of Priya and Sneha 1 year ago be 4x and x years respectively.
Then, [(4x + 1) + 6] - [(x + 1) + 6] = 9
3x = 9
x = 3
Required ratio = (4x + 1) : (x + 1) = 13 : 4
ANSWER:D
Answer: D
Question: A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: Let T be the total time of the trip.
35*4 + 44(T-4) = 38T
6T = 176-140
T = 6
The answer is A.
Answer: A
Question: A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p v pv = 300
p-5 v+2n (p-5)(v+2n) = 300
p+5 v-n (p+5)(v-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So v = 20 satisfies all equations!!
Answer: C
Question: It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
Options:
A)72/17
B)17/72
C)14/24
D)24/56
E)34/56
Rationale: The rate of the first machine is 1/9 job per hour;
The rate of the second machine is 1/8 job per hour;
Thus, the combined rate of the machines is 1/9+1/8=17/72 job per hour, which means that it takes 1/(17/72)=72/17 hours both machines to do the job.
Answer: A.
Answer: A
Question: find the average of first 20 multiples of 7?
Options:
A)73.5
B)70.5
C)63.5
D)54.5
E)40.5
Rationale: Required average =7(1+2+3+…….+20)/20
(7*20*21)/(20*2)
(147/2)=73.5.
ANSWER A 73.5
Answer: A
Question: Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?
Options:
A)7/8
B)9/10
C)11/12
D)13/14
E)15/16
Rationale: P(no graduates) = 4C3 / 8C3 = 4/56 = 1/14
P(at least one graduate) = 1- 1/14 = 13/14
The answer is D.
Answer: D
Question: John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.51 more than Jane, what was the original price of the dish?
Options:
A) 24
B) 34
C) 37.8
D) 42
E) 84
Rationale: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.51--> 15p - 13.5p = 51 --> p = 34.
Answer: B.
Answer: B
Question: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
Options:
A)y + 3z
B)(y +z) / 4
C)5y + 3z
D)3y + z
E)3y + 4.5z
Rationale: Soln:
The resulting equation is
=> (.01x + .05y + .03z)/(x+y+z) = 1.5/100
=> x + 5y + 3z = 1.5x + 1.5y + 1.5z
taking x to one side and y and z to other side we get
=> x = 5y + 3z
Ans is C
Answer: C
Question: If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x?
Options:
A)308
B)210
C)200
D)120
E)100
Rationale: If x is divisible by 3, 14, and 15, then x must be a multiple of 3,14 and 5.
Hence,the least multiple of x will be 3*14*5=210.
ANSWER:B
Answer: B
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450?
Options:
A)Rs.1000
B)Rs.1250
C)Rs.1010
D)Rs.10000
E)None of these
Rationale: Explanation:
1450 = P [1 + (5*16/5)/100]
P= 1250
Answer: Option B
Answer: B
Question: How many different section of 4 books can be made from 10 different books if two particular books are always selected?
Options:
A)36
B)38/
C)26
D)28
E)24
Rationale: This means two books are seclected out of the remaining 8 books. Required number of ways = 8C2= 8!/6!x2!=28. Ans: D.
Answer: D
Question: 4 couples are seating at a round tables how many ways can the 4 women sit together
Options:
A)4!*4!
B)3!*4!
C)4!*3!
D)5!*4!
E)6!*4!
Rationale: 4 men can be arranged around a table in (4-1)!=3! ways;
Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.
So, total # of ways is 3!*4*4!=4!*4!
ANS:A
Answer: A
Question: 417 + 4.017 + 0.417 + 4.0017 = ?
Options:
A)425.4357
B)423.7563
C)629.6357
D)425.5637
E)629.6753
Rationale: 417
4.017
0.417
+ 4.0017
--------
425.4357
---------
Answer is A
Answer: A
Question: If the radius of a circle is increased by 60% then the area is increased by:
Options:
A)44%
B)120%
C)156%
D)40%
E)None of the above
Rationale: initially A=pi*r2
now R2=160/100r
then area=Pi*(160R/100)2
area=256R/100
that is area increases from 100 to 256=increase in area=156%
ANSWER:C
Answer: C
Question: A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?
Options:
A)(5y-1)/(755-y)
B)5/(755+y)
C)5y/(755+y)-1
D)5y/(755+y)
E)5y
Rationale: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).
Answer: B.
Answer: B