divelab/Sys2Bench huggingface dataset:
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)
Options:
A) 1
B) 4
C) 5
D) 11
E) 10
Rationale: We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 3 ingredients...
3 ingredient blends:
ABC
ABD
ACD
BCD
4 ingredient blends:
ABCD
Total blends =4+1 = 5
C
Answer: C
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of four consecutive even integers starting with 10, respectively, what is the probability that b/a will not be an integer?
Options:
A)3/16
B)1/4
C)5/16
D)3/8
E)1/2
Rationale: a is from the following set {1,2,3,4}
b is from the following set {10,12,14,16}
The total number of ways of choosing 2 integers, one from each set is 4*4 = 16 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {10,3},{10,4},{14,3},{14,4},{16,3} = 5 ways
Thus the probability is 5/16
The answer is C.
Answer: C
Question: Lastly, jenny compared Canada’s CN Tower and Seattle’s Space
Needle. How tall is the Space Needle if the CN Tower stands at 553m
high and it is taller than the Space Needle by 369m?
Options:
A)127
B)184
C)170
D)113
E)099
Rationale: 553-369=184.Answer is B.
Answer: B
Question: A student chose a number, multiplied it by 6, then subtracted 250 from the result and got 122. What was the number he chose?
Options:
A)59
B)60
C)61
D)62
E)63
Rationale: Let x be the number he chose, then
6⋅x−250=122
6x=372
x=62
correct answer D
Answer: D
Question: Min (a, b, c)=min of a, b, c Max (a, b, c,)=max of a, b, c then what is the value of MAX {min (2,5,7), max (-7, -2, -3), 3}
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: MAX {min (2,5,7), max (-7, -2, -3), 3}
= MAX {2,-2,3}
=3
ANSWER:C
Answer: C
Question: A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
Options:
A)12
B)15
C)10
D)48
E)17
Rationale: Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Ans: B
Answer: B
Question: If x and y are positive integers such that x/y = 2.60, which of the following numbers could be y?
Options:
A)3
B)4
C)6
D)5
E)10
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 2.60 and because it's in the hundreds decimal place, put the given value (x/y = 2.60/1) and multiply it by 100.
Take the resulting fraction (x/y = 260/100) and reduce it to it's lowest form.
Both of the numbers are divisible by 20.
The result is x/y = 13/5.
Thus y = 5.
The correct answer is D.
Answer: D
Question: Initially two cups of same volume are present with milk filled upto 3/5th and 4/5th of their volumes.Water is then filled. Then two mixtures are mixed. Find the ratio of water to milk in the mixture
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)5/7
Rationale: water content can b in 1st and second is 2/5 and1/5 total:3/5.the total milk content is 7/5.the ratio is ((3/5)/(7/5))=3/7.
ANSWER:C
Answer: C
Question: What smallest number should be added to 8444 such that the sum is completely divisible by 7 ?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Explanation:
8444 ÷ 7 = 1206, remainder = 2
7 - 2 = 5
Hence, 5 should be added to 8444 such that the sum is completely divisible by 7.
Answer: B
Answer: B
Question: The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
Options:
A)13.5
B)14
C)15
D)12.5
E)None
Rationale: Solution:
At present the total age of the family = 5*20 =100.
The total age of the family at the time of the birth of the youngest member,
=[100−10−(10*4)]=50.
Therefore, average age of the family at the time of birth of the youngest member,
= 50/4 = 12.5.
Answer: Option D
Answer: D
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 27 seconds. What is the length of each train (in meters)?
Options:
A)50.5
B)88.5
C)37.5
D)55.5
E)23.5
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 27 seconds, the relative difference in distance traveled is 27 * 25/9 = 75 meters
This distance is twice the length of each train.
The length of each train is 75/2 = 37.5 meters
The answer is C.
Answer: C
Question: 180 metres long yard, 11 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
Options:
A)18
B)12
C)14
D)16
E)17
Rationale: 11 trees have 10 gaps between them,
Required distance (180/10) = 18
A
Answer: A
Question: If x and y are integers such that x^2+4x+2y+6=2x^2+5x+y-6, we can deduce that y is
Options:
A)not an even
B)an even
C)a perfect square
D)an odd
E)a prime
Rationale: x^2 + 4x + 2y + 6 = 2x^2 + 5x + y - 6
y = x^2 + x - 12
y = (x+4)(x-3) (Note that one factor is even and one factor is odd.)
Then y must be even.
The answer is B.
Answer: B
Question: A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got Rs.242. What is the share of C?
Options:
A)33
B)44
C)55
D)77
E)99
Rationale: The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.
Since, they work together, the share of C
= 2/11 * 242 = Rs.44
\Answer: B
Answer: B
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is q, what is the difference between the probability that q is even and the probability that q is odd?
Options:
A) 1/9
B) 1/6
C) 2/9
D) 1/4
E) 1/2
Rationale: Age of Boys q:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer: A
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 180,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
Options:
A)77,500
B)1,860,000
C)2,880,000
D)3,720,000
E)4,960,000
Rationale: 180,000 × 2 × 2×2×2 = 180,000 × 16 = C
Answer: C
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is this student’s weekly allowance?
Options:
A)$2.25
B)$2.75
C)$3.00
D)$3.50
E)$3.75
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 60 cents
(4/15)x = 60
x = $2.25
The answer is A.
Answer: A
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)5
B)4
C)7
D)9
E)None of these
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 954×60954×60 = 10 min.
Option(E) is correct
Answer: E
Question: Four bells commence tolling together and toll at intervals of 2, 3, 4 and 5 seconds respectively. In 10 minutes, how many times do they toll together ?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: LCM of 2, 3, 4, and 5 is 60.
So, after each 60 seconds, they would toll together.
Hence, in 10 minutes, they would toll 10*60 seconds / 60 seconds = 10 times
But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).
So, total tolls together = 10+1 = 11
Answer: B
Answer: B
Question: If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 100% of j ?
Options:
A)0.35
B)3.5
C)35
D)350
E)700
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
20% of 350, comes out to be 70....
100% of 10 is 10....
(70*100)/10=700....
Ans : E
Answer: E
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 120 metres?
Options:
A)22 seconds
B)65 seconds
C)24 seconds
D)12 seconds
E)21 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 120/5 = 24 seconds.
Answer:C
Answer: C
Question: A straight pipe 6 yard in length was marked off in fourths 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 yard?
Options:
A) 1/6 and 1/4 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: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 4-3=1=1/3 meters long pieces.
Answer: B.
Answer: B
Question: The average height of 20 students is 20 cm and the average height of 11 students is 20 cm . What is the average height of the 31 students?
Options:
A)40 cm
B)20 cm
C)30 cm
D)25 cm
E)35 cm
Rationale: The total height of the 31 students =(20 * 20) + (11 * 20) = 400 + 220 = 620 cm The required average height =620/31 = 20 cm Answer :B
Answer: B
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)187 m
B)287 m
C)279 m
D)270 m
E)197 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)Rs.10000
B)Rs.12800
C)Rs.6000
D)Rs.8000
E)Rs.9000
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
ANSWER:B
Answer: B
Question: What is K's position with respect to P?
Options:
A)Fifth to the LEFT
B)7
C)Fifth to the right
D)8
E)72
Rationale: Answer: Option C
Answer: C
Question: IF A'S INCOME IS 25%LESS THAN B'S.BY WHAT % B'S INCOME IS GREATER THAN A?
Options:
A)11
B)12
C)33
D)15
E)36
Rationale: If B 's income is rs 100,
A's income = Rs 75
% B'S INCOME IS GREATER THAN A = 100*25/75= 33.33 %
ANSWER:C
Answer: C
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)27 liters
B)18 liters
C)10 liters
D)11 liters
E)14 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer:C
Answer: C
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)11 m2
B)10 m2
C)54 m2
D)86 m2
E)42 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer:B
Answer: B
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (5/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
Options:
A) 3/8
B) 1/2
C) 9/16
D) 5/7
E) 3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 5/8*c:
(b+c)/2 = (5/8)*c
b = (1/4)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (1/4*c)/2 = (1/8)*c
Median = (a + c)/2 = (1/8*c + c)/2 = (9/8)*c/2 = (9/16)*c (ANSWER C)
Answer: C
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Options:
A)95
B)92
C)88
D)82
E)85
Rationale: Explanation:
Solution 1
Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34= 88 feet
Answer: Option C
Answer: C
Question: Of the mutual funds on a “select list,” 1/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 500 funds on the list have 3-star ratings, how many funds are on the list?
Options:
A)500
B)750
C)1,000
D)1,250
E)1,500
Rationale: D
Fraction of 5- and 4-star funds: 1/3 + (2/5)*(2/3) = 5/15 + 4/15 = 9/15
Fraction of 3-star funds = 1 - 9/15 = 6/15
(6/15)*Total = 500
Total = 1250
Answer: D
Question: The length of a rectangle is twice its breadth. If its length is decreased by 10 cm and breadth is increased by 10 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
Options:
A)25 cm
B)35 cm
C)30 cm
D)45 cm
E)55 cm
Rationale: Let breadth =x cm
Then, length =2x cm
Area =x×2x=2x^2 sq.cm.
New length =(2x−10) cm
New breadth =(x+10) cm
New area =(2x−10)(x+10) sq.cm.
Given that, new area = initial area +75 sq.cm.
⇒(2x−10)(x+10)=2x^2+75
⇒2x^2+20x−10x−100=2x^2+75
⇒10x−100=75
⇒10x=75+100=175
⇒x=175/10=17.5 cm
Length =2x=2×17.5=35 cm
ANSWER:B
Answer: B
Question: Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twuenty iron coins and thuenty copper coins, how many different sums from 1¢ to 140¢ can he make with a combination of his coins?
Options:
A)137
B)140
C)166
D)136
E)2
Rationale: The total sum is 20*2 + 20*5 = 140¢. If you can make each sum from 1 to 140 (1¢, 2¢, 3¢, ..., 140¢), then the answer would be 140 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 139¢ and 137¢ (since total sum is 140¢ we cannot remove 1¢ or 3¢ to get 139¢ or 137¢).
So, out of 140 sums 4 are for sure not possible, so the answer must be 140 - 4 = 136 sums or less. Only A fits.
Answer: D.
Answer: D
Question: A man sitting in a train which is traveling at 55 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 320 m long, find its speed
Options:
A)52 kmph
B)56 kmph
C)60 kmph
D)62 kmph
E)72 kmph
Rationale: Explanation:
Relative speed = 320/10 m / sec = ((320/10)×(18/5)) kmph = 115 kmph.
Speed of goods train = (115 - 55) kmph = 60 kmph
Answer: Option C
Answer: C
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 12 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Options:
A)54
B)66
C)80
D)36
E)96
Rationale: D
36
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 12 MPH = 36 miles
Answer: D
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,16
Options:
A)9906
B)9916
C)9936
D)9736
E)9746
Rationale: Explanation:
LCM of 27-18-12-16 is 432.
After dividing 9999 by 432 we get 63 remainder.
So answer will be 9999-63 = 9936
Option C
Answer: C
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 8 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)13
B)24
C)18
D)19
E)12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/8
=> 1/x = 1/6 - 1/8 = (4 - 3)/24 = 1/24
=> x = 24.
Answer: B
Answer: B
Question: A train 700 m long passes a man, running at 20 km/hr in the same direction in which the train is going, in 40 sec. The speed of the train is?
Options:
A)40 km/hr
B)41 km/hr
C)42 km/hr
D)43 km/hr
E)44 km/hr
Rationale: Speed of the train relative to man = 700/40 = 35/2 m/sec.
= 35/2 * 18/5 = 63 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 20) km/hr.
x - 20 = 63 => x = 43 km/hr.
Answer: D
Answer: D
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 20 on the fourth day, his average earning for the whole week is ?
Options:
A)Rs . 18.95
B)Rs 16
C)Rs. 20
D)Rs. 25.71
E)None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -20
= Rs. 140
∴ Average earning = 140 / 7
= Rs. 20
Correct Option: C
Answer: C
Question: If 15% of 40 is greater than 25% of a number by 2,then find the number is?
Options:
A)20
B)15
C)16
D)25
E)30
Rationale: 15/100 * 40 - 25/100 * x = 2 or x/4 = 4 so x = 16
ANSWER C
Answer: C
Question: Sandy is younger than Molly by 20 years. If the ratio of their ages is 7:9, how old is Sandy?
Options:
A)42
B)49
C)56
D)63
E)70
Rationale: Let Sandy's age be 7x and let Molly's age be 9x.
9x - 7x = 20
x = 10
Sandy is 70 years old.
The answer is E.
Answer: E
Question: A certain company charges $5 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $5 plus $1 per pound. If the company charged $30 to ship a certain package, which of the following was the weight of the package, in pounds?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: Let the weight of the package be X. Then the cost is 1*X + 5= 30 ---> X=25 ---> X=25
Answer : B
Answer: B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)247
B)249
C)245
D)882
E)279
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: C
Answer: C
Question: For a,q,d are the positive integers, and d|a means that “a is divisible by d”, if d|aq, which of the following must be true?
Options:
A)d|a
B)d|q
C)d|2aq
D)d|(a+q)
E)d|(a-q)
Rationale: d/a means a is divisible by d
d/aq means ab divisible by d.
all are integers so ,
if ab is divisible by d,
1 a can be divisible by d
or
2 q can be divisble by d.
so the question stem asks must true.
so option a and b are could but not must.
option c is 2aq divisible by d. if ab is divisible by d then 2aq is divisible by d.
option d and e we can't predict.
so option C is correct.
Answer: C
Question: A bus takes 4 hours to cover a distance of 480 Km. how much should the speed in Kmph be maintained to cover the same direction in 4/3th of the previous time?
Options:
A)50 Kmph
B)90 Kmph
C)95.9 Kmph
D)95.4 Kmph
E)90.5 Kmph
Rationale: Time = 4
Distance = 480
4/3 of 4 hours = 4 * 4/3 = 5.3 Hours
Required speed = 480/5.3 = 90.5 Kmph
E
Answer: E
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 8 months, find for how much time did Q invest the money?
Options:
A)11
B)10
C)18
D)16
E)12
Rationale: 7*5: 8*x = 7:10
x = 16
Answer:D
Answer: D
Question: When positive integer f is divided by 6, the remainder is 1. Which of the following must be true?
I. f is a prime number
II. f is odd
III. f is divisible by 7
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: f=6q+1
Examine II) put q=0,1,2,3....... we have f=1,7,13,...25 so f must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) f= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Answer: B
Question: A train 124 m long running at 68 kmph crosses a platform in 19 sec. What is the length of the platform?
Options:
A)338
B)234
C)240
D)881
E)271
Rationale: D = 68 * 5/18 = 19 = 358 – 124 = 234
Answer: B
Answer: B
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)60 kg
B)75 kg
C)80 kg
D)85 kg
E)90 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg
Option D
Answer: D
Question: My boss has $243,986 in the business account. What is the least amount of money (in whole number of dollars) that he must add to his account if she wants to split this money evenly among his nine employees?
Options:
A)$1
B)$2
C)$3
D)$4
E)$6
Rationale: To find the least amount he should add to his saving account to split the money evenly among his employees,
he needs to make the total divisible by 9
Simply add the individual digits of the total = 2+4+3+9+8+6 =
If you add 4 , the number is divisible by 9 (32+ 4)
Correct Option : D
Answer: D
Question: If 4,5qD + 8,737 = 13,qD3, where q and D are distinct digits, what is the value of D – q?
Options:
A)6
B)4
C)3
D)2
E)1
Rationale: 4500+10q+d+8737=13003+100q+10d
13237+10 q+d=13003+100q+10d
234=90q+9d
26=10 q+d
d=6 ^ q=2
==> d-q= 4
ANSWER B
Answer: B
Question: Two bags are randomly selected from a flight at the airport to be searched, one at a time, then sent through after being searched (this means: without return). Five smugglers are watching this and they each have three bags with contraband. There are 20 bags on the flight. What is the probability that they will get away? (Answer in lowest terms).
Options:
A)5/75
B)3/12
C)5/76
D)2/19
E)1/2
Rationale: The flight has 20 bags total. There are (5 smugglers)(3 bags) = 15 bags with contraband, and 20 - 15 = 5 with no contraband, so the probability of getting a bag with no contraband is P(N) = 5/20 on the first selected bag.
Because selection is (without return), the P(N) has changed for following selections. Now, there are 19 bags, but the number bags with contraband stay the same; since, we are only calculating for success as no bag with contraband... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:
Formula = P(A\B) = P(A and B)/P(B).
2 bags are selected; so,
P(A\B) = (5/20)(5/19) = 25/380 = 5/76
Answer: C
Answer: C
Question: A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 4, AB = 5 and AC = 11, what is the length of AE?
Options:
A)21
B)26
C)30
D)18
E)16
Rationale: A-----B----C--------D----E
Given: DE = 4 - (i)
AB = 5 - (ii)
AC = 11 - (iii)
BC = 2CD - (iv)
From (ii) and (iii), BC = 6
From (iv), CD = 3
Length of AE = AC + CD + DE = 11 + 3 + 4 = 18
Correct Option: D
Answer: D
Question: The top and bottom of a tower were seen
to be at angles of depression 30° and 60° from the top of a
hill of height 100 m. Find the height of the tower
Options:
A)64.67 m
B)66.67 m
C)68.67 m
D)56.67 m
E)46.67 m
Rationale: By making A diagram
AC represents the hill and DE represents the pole
Given that AC = 100 m
angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)
Let DE = h
Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE
tan 60°=ACCE=>3√=100CE=>CE = 1003√--- (1)
tan 30°=ABBD=>13√=100−hBD=>13√=100−h(1003√)
(∵ BD = CE and Substituted the value of CE from equation 1 )=>(100−h)=13√×1003√=1003=33.33=>h=100−33.33=66.67 m
i.e., the height of the pole = 66.67 m
ANSWER:B
Answer: B