divelab/Sys2Bench huggingface dataset:
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 130 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)15 kmph
C)19 kmph
D)17 kmph
E)29 kmph
Rationale: Speed of the boat in still water
= (100+130)/2
= 115 kmph. Speed of the stream
= (130-100)/2
=15 kmph.
Answer: B
Answer: B
Question: Sarah, Fatima, Salma, and Lina all got scholarship packages to the college they applied to. The average of Sarah, Fatima, and Salma's scholarships was $20000. The average of Fatima, Salma, and Lina's tips was $17000. If Lina earned $15000, what was Sarah awarded?
Options:
A)$24000
B)$25000
C)$27000
D)$30000
E)$32000
Rationale: Solution: Average scholarships for Sarah, Fatima and Sarah = $20000
Total scholarship = 3*20000 = $60000
Average scholarship for Fatima, Salma, and Lina = $17000
Total scholarship = 3*17000 = $51000
Lina's scholarship award = $15000
Now,
(Sarah+Fatima+Salma) - (Fatima+Salma+Lina) = $60000-$51000 = $9000
Sarah-Lina = $9000
Sarah = Lina +$9000 = $24000
Answer: Option A
Answer: A
Question: Company Z has 53 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
Options:
A)6
B)7
C)8
D)11
E)12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 53.
Now, plug options for x. D x > y as needed.
Answer: D.
Answer: D
Question: Out of 11 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
A)5/17
B)26/13
C)26/31
D)26/33
E)5/33
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 7C₃/11C₃ = 1 - (7 * 6 * 5 )/(11* 10 * 9 )
= 26/33
Answer: D
Answer: D
Question: Priya covers journey from kavali to nellore by car at average speed of 60 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
Options:
A)20Km/hr
B)48Km/hr
C)50Km/hr
D)52Km/hr
E)53km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*60*40/100
= 48 Km/hr
Answer: Option B
Answer: B
Question: Find the 10th and 12th term of the series 1, 3.5, 6, 8.5,...? And their ratio is?
Options:
A).98
B)2.5
C)1.21
D)3.4
E)2
Rationale: common difference = d = 3.5 - 1 = 2.5 ,, n = 10, a = first term = 1-----
By using arithmetic progression , t10 = a + (n-1)*d = 1 + (10-1)*2.5 = 1+22.5 = 23.5 Also 12th term , t12 = a + (n-1)*d = 1 + (12-1) * 2.5 = 28.5
Ratio = t12/t10 = 28.5/23.5 = 1.21..... Ans - C
Answer: C
Question: 10 3/4 + 7 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)8 817/1020
E)None of them
Rationale: Given sum=10+3/4+7+2/17-(9+1/15)
=(10+7-9)+(3/4+2/17-1/15)
=8+(765+120-68/1020
=8 817/1020
Answer is D
Answer: D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)2/215
B)3/155
C)1/216
D)2/213
E)3/212
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: Some persons can do a piece of work in 32 days. Two times the number of these people will do half of that work in?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: 32/ (2 * 2) = 8 days
Answer:E
Answer: E
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a gamma raised to the seventh power?
Options:
A)alpha
B)beta
C)gamma
D)delta
E)epsilon
Rationale: Let the alpha be 5k and let the gamma be 5j+2.
(5k)^7 + (5j+2)^7 which has the form 5k+3, which is a gamma.
The answer is C.
Answer: C
Question: How many words, meaningful or meaningless, can be formed by shuffling the letters of the word INFORMATION?
Options:
A)11!
B)11!/2!
C)11!/(2!^3)
D)11!/{(3!)(2!^3)}
E)6!
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
In the given problem, we have 11 letters out of which 2 are I's (identical), 2 are N's (identical), 2 are F's (identical) and rest all are different.
Hence the number of words that can be formed is 11!/{2!2!2!}
Ans C
Answer: C
Question: A right triangle AQC has to be constructed in the xy-plane so that the right angle is at A and AQ is parallel to x axis. The coordinates of A, Q and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Options:
A)63
B)336
C)567
D)3024
E)5040
Rationale: All the cordinates are integer hence,
possible AQ values are
{-1,0}, {-1,1} ....{-1,7}: 8 ways
....
{7,-1}, {7,0} ......{7,6}: 8 ways
9*8 ways = 72
for AC values can be
{1,2}, {1,3} .... {1,7} : 6ways
......
{7,1}, {7,2} ..... {7,6} : 6 ways
7*6 = 42
Total = 72 * 42 = 3024 hence D
Answer: D
Question: A club wants to mix 20 pounds of candy worth $10.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (20*10 + 5*w)/(20 +w)
=>120 + 6w = 200 + 5w
=> w = 80
Answer E
Answer: E
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 5, and 6, what is the greatest number of four-digit extensions that the company can have?
Options:
A)4
B)6
C)11
D)12
E)24
Rationale: Since the phone number must be even, the unit's digit can be either 2 or 6.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 6 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:D
Answer: D
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 70 km more than the other. What is the distance between the two stations?
Options:
A)630 km
B)540 km
C)276 km
D)178 km
E)176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 70 km more than the other,
25x â€“ 20x = 70
5x = 70
x = 14 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*14= 630 km.
ANSWER: A
Answer: A
Question: If the sides of a triangle are 28 cm, 26 cm and 10 cm, what is its area?
Options:
A)120 cm2
B)112 cm2
C)776 cm2
D)130 cm2
E)886 cm2
Rationale: The triangle with sides 28 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 28 cm.
Area of the triangle = 1/2 * 26 * 10 = 130 cm2
Answer: D
Answer: D
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 180 resolutions?
Options:
A)724 m
B)704 m
C)287 m
D)278 m
E)253.4 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 180 resolutions.
= 180 * 2 * 22/7 * 22.4 = 25344 cm
= 253.4 m
Answer:E
Answer: E
Question: What is the next number of the following sequence
123, 444, 888, 1776, 8547, . . . .
Options:
A)38799
B)16005
C)27887
D)27072
E)27081
Rationale: Explanation:
1) 123 + 321 = 444
2) 444 + 444 = 888
3) 888 + 888 = 1776
4) 1776 + 6771 = 8547
5) 8547 + 7458 = 16005
Answer: B
Answer: B
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
A)3/5
B)1/2
C)1/5
D)1/8
E)1/32
Rationale: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32
Answer: E
Answer: E
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
Options:
A)5000
B)25000
C)7500
D)8500
E)9000
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 â€“ 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
ANSWER A
Answer: A
Question: A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 5 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options:
A)17.5%
B)26%
C)30%
D)35%
E)38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 120
And enrollment in 1993 will be 120*1.05=126
Increase in 1993 from 1991 = 126-100= 26
Answer : B
Answer: B
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
Options:
A)9800
B)100020
C)120960
D)140020
E)150000
Rationale: Explanation:
The word 'MATHEMATICS' has 11 letters. It has the vowels 'A','E','A','I' in it and these 4 vowels must always come together. Hence these 4 vowels can be grouped and considered as a single letter. That is, MTHMTCS(AEAI).
Hence we can assume total letters as 8. But in these 8 letters, 'M' occurs 2 times, 'T' occurs 2 times but rest of the letters are different.
Hence,number of ways to arrange these letters
=8!(2!)(2!)=8!(2!)(2!) =8Ã—7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—1(2Ã—1)(2Ã—1)=10080=8Ã—7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—1(2Ã—1)(2Ã—1)=10080
In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.
Number of ways to arrange these vowels among themselves =4!2!=4Ã—3Ã—2Ã—12Ã—1=12=4!2!=4Ã—3Ã—2Ã—12Ã—1=12
Hence, required number of ways
=10080Ã—12=120960
ANSWER IS C
Answer: C
Question: The sum of ages of 5 girls born at the intervals of 3 years each is 60 years. What is the age of the youngest girl?
Options:
A)years
B)years
C)years
D)years
E)years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60
5x = 30
x = 6.
Age of the youngest child = x = 6years.
A)
Answer: A
Question: Laura took out a charge account at the General Store and agreed to pay 4% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
Options:
A)$36.4
B)$37.10
C)$37.16
D)$38.10
E)$38.80
Rationale: Principal that is amount taken by Laura at year beginning = 35$
Rate of interest = 4%
Interest = (4/100)*35 = 1.4$
Total amount that Laura owes a year later = 35+1.4 = 36.4 $
Answer A
Answer: A
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)2
B)6
C)7
D)8
E)2
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer:C
Answer: C
Question: In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
Options:
A)515
B)545
C)618.
D)644.
E)666
Rationale: Solution : Total number of students studying both are 423 + 226 - 134 = 515 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 515, so 100% is approx. 644.
Answer is D :644
Answer: D
Question: In a caravan, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, the number of keepers is
Options:
A)5
B)8
C)10
D)15
E)20
Rationale: Explanation:
Let number of keepers be x. Then,
Total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2x = 2x + 312.
Total number of heads = 50 + 45 + 8 + x= 103 + x.
Therefore (2x + 312) = (103 + x) + 224 or x = 15.
Answer: D
Answer: D
Question: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
Options:
A)23
B)21
C)25
D)26
E)24
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 20.
So, a+b+c3a+b+c3 = 20 or a + b + c = 60
a ≤ b ≤ c
Median = (a + 11)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 11
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)
Or 3a = 38 or a = 12.66
So, b = c = 12.66 + 11 = 23.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 11) + (a + 12) = 60
Or 3a = 37. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 11) + (a + 13) = 60
Or 3a = 36 or a = 12.
If a = 12, b = 23 and c = 25.
The least value for c that satisfies all these conditions is 25.
Correct answer is choice C.
Answer: C
Question: Find the Missing Number 6, 24, 60,120, 210, ?
Options:
A)331
B)336
C)333
D)339
E)332
Rationale: 1*2*3=6
2*3*4=24
3*4*5=60
4*5*6=120
5*6*7=210
6*7*8=336
ANSWER:B
Answer: B
Question: 39! is divided by 41. Then what is the remainder?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: A
Question: A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?
Options:
A)Rs. 3050
B)Rs. 3150
C)Rs. 3450
D)Rs. 4000
E)Rs. 3500
Rationale: SI on Rs. 5760 for 1 year = 6912 – 5760 = Rs. 1152
Therefore, Rate of interest for 1 year = 100*1152/5760*1 = 20%
Let the principal be p.
Then, Principal = p[1+ 20/100]2 = 5760
Solving which gives Principal = Rs. 4000 ANSWER : D
Answer: D
Question: X and Y start a business with Rs.2000 and Rs.12000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)1:6
B)6:1
C)1:5
D)5:1
E)1:4
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by X and Y =
2000 : 12000 => 1:6 .
Answer: A
Answer: A
Question: In a office work is distribute between p persons. If 1/4 members are absent then work increased for each person is?
Options:
A)33.33%
B)24.33%
C)15.33%
D)16.33%
E)17.33%
Rationale: let total % of work is 100%
total person=p
1/4 person are absent of total person . so absent person is 1/4p ie p/4.
left person is, p-p/4=3p/4.
p person do the work 100%
1 person do the work 100*p%
3p/4 person do the work (100*p*4)/3p%=133.33%
work increased for each person is=(133.33-100)%=33.33%
ANSWER:A
Answer: A
Question: A jogger running at 9 km/hr along side a railway track is 270 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)67 sec
B)89 sec
C)39 sec
D)87 sec
E)45 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 270 + 120 = 390 m.
Time taken = 390/10
=39 sec.
Answer: C
Answer: C
Question: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, and yellow. This pattern continues (red, green, blue, and yellow) until it ends with a red shirt. If there are more than 4 people in line, which of the following cannot be the number of people in the line?
Options:
A)17
B)37
C)49
D)61
E)72
Rationale: The correct answer should not take the form: 4x + 1. Hence, it is E
Answer: E
Question: At the end of the month, a certain ocean desalination plant’s reservoir contained 26 million gallons of water. This amount is eighth the normal level. If this amount represents 65% of the reservoir’s total capacity, how many million gallons short of total capacity is the normal level?
Options:
A)15
B)25
C)35
D)45
E)55
Rationale: the Q talks of total capacity, normal level, present level, shortage etc..
so it is all about not going wrong in these terms
26 MG= 65% of Total..
total = 26/.65=40 MG..
Normal level= 1/8 of 40=5MG..
shortage of normal level=40-5=35MG..
C
Answer: C
Question: The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 3: 13. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
Options:
A)10.5 kg
B)6.625 kg
C)6.25 kg
D)6.35 kg
E)6.55 kg
Rationale: sodium chloride in 100 kg = 3/16 x 100 = 18.75 kg
ammonium in 100 kg = 13/16 x 100 = 81.25 kg
Now 81.25 is 25 parts out of (25 + 9) = 34 parts.
Hence 9 parts = 9/25 x 81.25 = 29.25
Amount to be added = 29.25 - 18.75= 10.5 Kg
ANSWER:A
Answer: A
Question: If taxi fares were $2.00 for the first 1/5 mile and $0.40 for each 1/5 mile there after, then the taxi fare for a 4-mile ride was
Options:
A)$4.60
B)$9.80
C)$19.60
D)$9.60
E)$29.60
Rationale: In 4 miles , initial 1/5 mile charge is $2
rest of the distance = 4 - (1/5) = 19/5
rest of the distance charge = 19(0.4) = $7.6 (as the charge is 0.4 for every 1/5 mile)
=> total charge for 4 miles = 2+7.6 = 9.6
Answer is D
Answer: D
Question: If a = 1, what is the value of –(a^2 + a^3 + a^4 + a^5)?
Options:
A)-14
B)-4
C)0
D)4
E)14
Rationale: if a = 1, then putting values in equation
= -[ (1)^2 + (1)^3 + (1^4) + (1^5) ]
= -[ 1 + 1 + 1 + 1 ]
= -4
Answer = B = -4
Answer: B
Question: The greatest number which can divide 1356,1868 and 2764 leaving the same remainder 12 in each case, is :
Options:
A)64
B)124
C)156
D)260
E)None of these
Rationale: Solution
Required number = H.C.F. of (1356-12), (1868-12) and (2764-12)
= H.C.F of 1344,1856 and 2752 = 64. Answer A
Answer: A
Question: If X+Y = 2X-2Z, X+2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
Options:
A)-4.5.
B)0.667.
C)1.7.
D)3.
E)2.5.
Rationale: X+Y = 2X-2Z
Y= X-2Z---------- 1
X+2Y = 4Z
-X+4Z= 2Y--------- 2
Adding equation 1 from equation 2
2Z = 3Y
Y/Z = 0.667
B is the answer
Answer: B
Question: Two children want to walk together to visit their aunt, who lives exactly 6 blocks north and 5 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 11 blocks. How many different 11-block routes may they take to travel the shortest possible distance to their aunt’s house?
Options:
A)11!/(6!*5!)
B)11!/(6*5)
C)11!*6!*5!
D)6!*5!
E)11*6*5
Rationale: If they need to walk 6 blocks north and 5 blocks east, we can express this route as NNNNNNEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 11 things is 11!
We then divide by the repetitions of N's and E's, which are 6! and 5! respectively.
The number of walking routes is 11!/(6!*5!).
The answer is A.
Answer: A
Question: 65% of x = 20% of 487.50. Find the value of x?
Options:
A)100
B)150
C)160
D)180
E)199
Rationale: 65% of x = 20% of 487.50
Then, 65/100 * x = 20/100 * 4875/10
x= 150
Answer is B
Answer: B
Question: On seven consecutive flips of a coin, what is the probability that all seven produce the same result?
Options:
A)1/64
B)1/8
C)1/4
D)3/8
E)1/2
Rationale: TTTTTTT case --> P = (1/2)^7 = 1/128
HHHHHHH case --> P = (1/2)^7 = 1/128
P(TTTTTTT or HHHHHHH) = 1/8 + 1/8 = 1/64
Answer: A
Answer: A
Question: find The last digit in the product 287 x 287 + 269 x 269 - 2 x 287 x 269?
Options:
A)5
B)6
C)8
D)9
E)4
Rationale: Explanation:
Given Exp.	= a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Answer is E
Answer: E
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations G are possible?
Options:
A)3
B)4
C)5
D)6
E)G=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10 ,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8..E
Answer: E
Question: An arithemetic sequence of numbers begins p, 2p + 3, 4p + 4... What is the 13th member of this sequence?
Options:
A)A)37
B)B)40
C)+ 13
D)D)62
E)+ 13
Rationale: Common difference of an arithmetic series is constant.
2p+3-p=4p+4-2p-3
p=2
1, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62
Ans:D
Answer: D
Question: Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first seven positive multiples of six, what is the ratio of a to b?
Options:
A)5:4
B)10:13
C)5:6
D)13:10
E)4:3
Rationale: The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42, 48, 54}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42 }
Both sets are evenly spaced, thus their median=mean:
a=30 and b=24 --> a/b=30/24=5/4.
Answer: A.
Answer: A
Question: In how many W ways can 5 people from a group of 6 people be seated around a circular table
Options:
A)56
B)80
C)100
D)120
E)144
Rationale: W=6C5 * (5-1)! (Select 5 out of 6 and arrange them in circular manner)
= 6 * 4!
= 6 * 24
= 144
Answer - E
Answer: E
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 5 boys when a boy gets any no. of prizes?
Options:
A)125
B)150
C)130
D)167
E)190
Rationale: Ans.(A)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 5 ways, i.e. (5 x 5 x 5) ways = 53 ways = 125 ways Or nr ways = 43 ways = 125 ways
Answer: A
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?
Options:
A)31( 5/7
B)31( 5/9
C)31( 5/6
D)31( 5/3
E)31( 5/1
Rationale: Explanation:
Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)
= (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.
Answer: A) 31( 5/7)
Answer: A