divelab/Sys2Bench huggingface dataset:
Question: There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?
Options:
A)4
B)8
C)12
D)16
E)20
Rationale: 4 pairs = 4*2 = 8 people total
8C4 = 8!/4!4! = 70 total outcomes
Total – unfavorable = favorable
Unfavorable outcomes
Assuming one pair of twins in the committee, we have two spaces left. Since we plugged a pair of twins in the committee, we have 8-2= 6 people to fill 2 spaces.
6C2 = 6!/2!4! = 15 ways to fill the two remaining slots
We only filled the slots with one pair, and we have to account for arrangements of the pairs. Now, we have 4 pairs. 4*15= 60 total arrangements
When we place members into the remaining slots, there may be an additional set of twins. There are 2 remaining slots to which we can fit a pair of twins. If it were one remaining slot, we cannot fit a pair of twins, so we wouldn’t have to account for duplicates.
Now we account for the number of duplicates.
# of duplicates = Total arrangements - # of unique combinations
To find the # of duplicates of twins, we need treat a pair of twins as one unit.
This means the 4 slots are really 2 slots.
Total ways of arranging four pairs of twins in two slots
4P2 = 4*3 = 12 total ways
Total # of unique combinations
Choosing two pairs out of 4 pairs
= 4C2
= 6
Therefore, # of duplicates = 12 - 6 = 6 duplicates
70 – 60 + 6 = 16
ANS:D
Answer: D
Question: A train is moving at 6/7 of its usual speed. The train is 30 minutes too late. What is the usual time for the train to complete the journey?
Options:
A)1 hour
B)30 minutes
C)3 hours
D)2 hours 30 min
E)2 hours
Rationale: new time = d / (6v/7) = 7/6 * usual time
30 minutes represents 1/6 of the usual time.
The usual time is 3 hours.
The answer is C.
Answer: C
Question: A box has 12 shapes; 3 circles, 5 squares, and 4 triangles. How many groups of 3 shapes can be made with at least 1 triangle?
Options:
A)46
B)64
C)164
D)146
E)56
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 12
r = 3
So, total groups is 12C3 = 12!/(3!(12 - 3)!) = 220, and
n = 12 - 4 = 8
r = 3
for groups without a triangle is 8C3 = 8!/(3!(8 - 3)!) = 56,
so, groups with at least 1 triangle = 220 - 56 = 164
Answer: C
Answer: C
Question: Helen went to the stationers and bought things worth Euro 50, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Euro 15
B)Euro 15.7
C)Euro 19.7
D)Euro 44.7
E)None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [50 - (5 + 0.30)] = Euro 44.70
Answer: Option D
Answer: D
Question: A student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
.
Options:
A)50
B)80
C)110
D)220
E)360
Rationale: 1) preferred one
as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
ANSWER:C
Answer: C
Question: The cricket team of 11members is 25yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
Options:
A)21
B)22
C)23
D)25
E)28
Rationale: Let the average age of the whole team be x years.
11x - (25 + 28) = 9 (x - 1)
=> 11x - 9x = 44
=> 2x = 44
=> x = 22.
So, average age of the team is 22 years.
B
Answer: B
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 6 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Options:
A)48%
B)80%
C)100%
D)120%
E)125%
Rationale: For A, r=8/2pi. Its capacity = (4pi)^2 * 6= 96pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 96pi/200pi = 0.48
A
Answer: A
Question: What is the chance that a leap year selected at random contains 53 fridays?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)5/7
Rationale: normal year =365 days
leap year = 366 days
now there are 52 weeks i.e. 364 days+2 odd days
the 2 odd may have Friday over a week has 7 days
so probability = 2/7
ANSWER:B
Answer: B
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 4 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 2 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
Options:
A)16:00.
B)18:00
C)20:00
D)22:00.
E)24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 4 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 2 hours
Time taken by both buses to meet again in St. Louis will be LCM of 4 and 2 = 4
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 16:00 hours
Answer A
Answer: A
Question: If a trader sold two cars each at $ 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)3.44%
B)2.44%
C)6.44%
D)1.44%
E)7.44%
Rationale: D
1.44%
SP of each car is $ 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer: D
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)40%
B)45%
C)50%
D)60%
E)70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: If U is an odd number and V and W are different integers, which of the following must be even?
Options:
A)UV+UW
B)U+VW
C)UVW
D)U+V+W
E)None of these
Rationale: Let U = 3.
a. UV + UW
If V = 1 and W = 2 -> UV + UW = 3*1 + 3*2 = 9 (Odd)
b. U + VW
If V = 1 and W = 2 -> U+VW = 3 + 1*2 = 5 (Odd)
c. UVW
If V = 1 and W = 5 -> UVW = 1*3*5 = 15 (Odd)
d. U + V + W
If V = 1 and W = 5 -> U + V + W = 1 + 3 + 5 = 9 (Odd)
Answer is E.
Answer: E
Question: What is the probability that the sum of two dice will yield a 5, and then when both are thrown again, their sum will again yield a 5? assume that each die has 4 sides with faces numbered 1 to 4.
Options:
A)1/144
B)1/36
C)1/12
D)1/16
E)1/3
Rationale: Solution -
Rolling dices is an independent event.
The combinations to get 5 are (1,4), (4,1), (2,3), (3,2), and total combinations of both dices is 16.
The probability of getting 5 in first attempt is 4/16=1/4.
Probability of getting 5 again in second attempt = (1/4)*(1/4) = 1/16. ANS D
Answer: D
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)16 sec
B)12 sec
C)17 sec
D)21 sec
E)23 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: B
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Options:
A)18
B)24
C)42
D)81
E)28
Rationale: Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
ANSWER:B
Answer: B
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?
Options:
A)1/5
B)1/1
C)1/6
D)1/3
E)1/7
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.
Answer: C
Answer: C
Question: In the first week of the Year, Pancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Pancy saved during the 52 weeks?
Options:
A)$1,326
B)$1,352
C)$1,378
D)$2,652
E)$2,756
Rationale: In the first week of the Year, Pancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: C
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 5 people play both cricket and football. How many people play only cricket?
Options:
A)11
B)2
C)5
D)3
E)9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-5 = 2
Answer is B
Answer: B
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)477
B)420
C)279
D)276
E)291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 14 + 21 = 35
T = 12
D = 35 * 12 = 420.Answer: B
Answer: B
Question: A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?
Options:
A)43%
B)50%
C)52%
D)54%
E)56%
Rationale: The tank of 24 gallons is filled to a quarter so it had 6 gallons of water with 40% sodium chloride. In 2 hrs, .5*2 = 1 gallon of pure water (0% sodium chloride) will evaporate.
In essence, the initial mix of 6 gallons (40% sodium chloride) was a mix of 5 gallons of x% sodium chloride and 1 gallon of pure water.
Working with sodium chloride concentrations:
w1/w2 = (A2 - Avg)/(Avg - A1)
5/1 = (0 - 40)/(40 - x)
x = 48
So concentration of water is 100 - 48 = 52%
ANSWER:C
Answer: C
Question: Find the roots of the quadratic equation: x2 + 2x - 15 = 0?
Options:
A)-5,3
B)6,5
C)8,9
D)7,6
E)3,5
Rationale: Explanation:
x2 + 5x - 3x - 15 = 0
x(x + 5) - 3(x + 5) = 0
(x - 3)(x + 5) = 0
=> x = 3 or x = -5.
Answer A
Answer: A
Question: Pipe A can fill a tank in 24 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?
Options:
A)4 minutes
B)32/7 minutes
C)192/7 minutes
D)3 minutes
E)28 minutes
Rationale: Pipe A can fill a tank in 24 minutes --> the rate of A = 1/24 tank/minute;
Pipe B can fill the same tank6 times fasterthan pipe A --> the rate of B = 1/24 + 6/24 = 7/24 tank/minute.
Their combined rate = 1/24 + 7/24 = 1/3tank/minute;
Therefore, A and B can fill the tank in 3 minutes.
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)12899
B)12800
C)27891
D)18992
E)78812
Rationale: 16*8: x*4 = 5:2
x = 12.8
=> Rs.12800
Answer: B
Answer: B
Question: A and B started a business investing Rs. 75,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Options:
A)9:2
B)3:2
C)18:20
D)18:4
E)13:4
Rationale: A: B = 75000 : 20000
= 75 : 20
= 13 : 4
ANSWER:E
Answer: E
Question: A boatman can row 3 km against the stream in 30 minutes and return in 18 minutes. Find the rate of current ?
Options:
A)2 kmph
B)8/2 kmph
C)5/2 kmph
D)1/2 kmph
E)2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/30 = 6 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-6)/2 = 2 km/hr.
Answer: A
Answer: A
Question: If a(a + 4) = 21 and b(b + 4) = 21, where a ≠ b, then a + b =
Options:
A)−4
B)−5
C)2
D)46
E)48
Rationale: i.e. if a = 3 then b = -7
or if a = -7 then b = 3
But in each case a+b = -7+3 = -4
Answer: option A
Answer: A
Question: Two representatives must be selected from each of two groups of students. One group consists of two men and one woman, and the other group consists of two women and one man. What is the probability that 2 men and 2 women will be selected ?
Options:
A)1/6
B)1/4
C)5/9
D)1/3
E)1/2
Rationale: Group 1: 2 Men and 1 Woman
Group 2: 1 Men and 2 Woman
Need: 2 Men and 2 women
Case 1: 2 Men from Group 1 and 2 women from group 2 - 2C2*2C2 = 1 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 2*1*1*2 = 4 ways
Total Favorable cases = 1+4 = 5
Total Possible ways of selecting students 2 from each group = 3C2*3C2 = 3*3 = 9
Probability = 5/9
Answer : Option C
Answer: C
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 5 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 5 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 8 a.m.
Answer: C
Answer: C
Question: At a company, the average wage of male employees is $4 per hour, and the average wage of female employees is $8 per hour. If the average wage of all employees is $7.5 per hour, what is the ratio of the number of male employees to the number of female employees?
Options:
A)1 to 7
B)2 to 3
C)3 to 2
D)5 to 3
E)2 to 1
Rationale: Average hourly wage of male employees = 4 $
Average hourly wage of female employees = 8 $
Average hourly wage of all employees = 7.5 $
Let number of male employees = m
number of female employees = f
7.5 = (4m + 8f ) / m+f
=>7.5m + 7.5f = 4m + 8f
=> 3.5m = .5f
=> m/f = .5/.15 = 1/7
Answer A
Answer: A
Question: A sum of Rs. 12500 amounts to Rs. 16500 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)4%
B)5%
C)6%
D)8%
E)14%
Rationale: S.I. = (16500 - 12500) = Rs. 4000/-
Rate = (100 * 4000) / (12500 * 4) = 8%
ANSWER:D
Answer: D
Question: what is the probability of getting 53 mondays in a leap year?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)5/7
Rationale: in a leap year contains 52 monday's since 52 weeks are present and 2 days extra
it may be sunday and monday
2.monday and tuesday
3.tuesday and thursday
4.thursday and friday
similary 7 alternatives are possible .among this only 2 are possible cases so 2/7
ANSWER:B
Answer: B
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 18 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)20/8 sec
B)20/4 sec
C)20/7 sec
D)4 sec
E)60/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (18 + 72)*5/18 = 5*5 = 25 mps.
The time required = d/s = 100/25 = 4 sec.Answer:D
Answer: D
Question: The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
Options:
A)89.8 cm³
B)92.5 cm³
C)132.8 cm³
D)144.5 cm³
E)none
Rationale: Sol.
Volume of the block = (10 * 5 * 2) cm³.
Volume of the cone carved out = [1/3 * 22/7 * 3 * 3 * 7] cm³ = 66 cm³
∴ Wood wasted = (100 - 66)% = 34%.
Answer A
Answer: A
Question: A factory produces 6400 toys per week. If the workers at this factory work 3 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)1375 toys
B)2133 toys
C)3375 toys
D)4375 toys
E)5375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 3 days) by 3.
6400 / 3= 2133 toys
correct answer B
Answer: B
Question: There are three different hoses used to fill a pool: hose x, hose y, and hose W. Hose x can fill the pool in a days, hose y in b days, and hose W in c days, where a > b > c. When all three hoses are used together to fill a pool, it takes d days to fill the pool. Which of the following must be true?
I. d<c
II. d>b
III. c/3<d<a/3
Options:
A)I
B)III
C)II&III
D)II
E)I&II
Rationale: Name T = full pool
X fills a pool in a days ==> 1 day X fills: T/a
Y fills a pool in b days ==> 1 day Y fills: T/b
W fills a pool in c days ==> 1 day W fills: T/c
1 day (X+Y+W) together fill: T(1/a + 1/b + 1/c)
d days (X+Y+W) together fill: T
==> d = Tx1 / T(1/a+1/b+1/c) = abc/(ab+bc+ca)
==>d = abc/(ab+bc+ca)
d cannot be greater than c ; d is greater than b ; d is greater than c/3 but not less than a/3
D
Answer: D
Question: A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points Q that an individual player might have scored?
Options:
A)7
B)13
C)16
D)21
E)23
Rationale: General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.
Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11=77.
Therefore, the maximum number of points Q for 12th player is 100-77=23.
Answer: E.
Answer: E
Question: A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 9 years. What is the average age (in years) of the family?
Options:
A)27
B)29
C)31
D)33
E)35
Rationale: Total age of the grandparents = 66 Ã— 2 = 132
Total age of the parents = 40 Ã— 2 = 80
Total age of the grandchildren = 9 Ã— 4 = 36
Average age of the family = (132+80+36)/8 = 248/8 = 31 years
The answer is C.
Answer: C
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 2 years is
Options:
A)s.9621
B)s.6921
C)s.8820
D)s.6261
E)s.6361
Rationale: c.i=p(1+r/100)^n
=8000(1+5/100)^2
=Rs8820
ANSWER:C
Answer: C
Question: A baseball game is played at Wickley Field. The Blues vs. The Grays. 25% of all players hit a home-run (hit the ball out of the park). Some players on The Grays team were injured, so they didn't play. If the ratio of players of the teams is 5:4, respectively, and the percentage of players who hit a home-run for The Blues is 15%, what percentage of players for The Grays hit a home-run?
Options:
A)40%
B)45%
C)35%
D)45.5%
E)35.5%
Rationale: Let B and G be number players Blues and Grays, respectively, and h represent hit a home-run.
B + G = total players.
B:G = 5:4
Bh/B = 15%
Gh/G = ?
[(5)(Bh/B) + (4)(Gh/G)]/(5 + 4) = 25%
[(5)(15%) + (4)(Gh/G)]/9 = 25%
Gh/G = 45%
Answer: B
Answer: B
Question: John can eat a quarter of a pizza in one minute. How long does it take John to eat one pizza and a half?
Options:
A)1 min
B)3 min
C)7 min
D)6 min
E)9 min
Rationale: The above problem could also be solved by dividing the mixed number 1 and 1/2 by 1/4
1 (1/2) * 1 / 4 = 3 / 2 * 4 / 1 = 6 minutes.
correct answer D
Answer: D
Question: If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, the cost of the article is
Options:
A)289
B)400
C)200
D)288
E)111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 360 - 340 = 20
x/20 = 20 => x = 400
Answer: B
Answer: B
Question: At golds gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?
Options:
A) 20
B) 24
C) 36
D) 48
E) 96
Rationale: We are given that golds gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of both 8 and 12.
We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.
Starting with 8, we have: 8, 16, 24, 32
For 12, we have: 12, 24
For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.
Answer B.
Answer: B
Question: Reena and Shaloo are partners in a business. Reena invests Rs. 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months. Out of a profit of Rs. 31,570, Reena's share is :
Options:
A)Rs. 9471
B)Rs. 12,628
C)Rs. 18,040
D)Rs. 18,942
E)Rs. 18,000
Rationale: Explanation:
Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.
Reena's share = Rs.
(31570âˆ—2/5)
= Rs. 12628.
ANSWER IS B
Answer: B
Question: What will be the LCM of 8, 24, 36 and 54
Options:
A)54
B)108
C)216
D)432
E)None of these
Rationale: Explanation:
LCM of 8-24-36-54 will be
2*2*2*3*3*3 = 216
Answer: Option C
Answer: C
Question: 6x − 24 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
Options:
A)Exactly one
B)Exactly three
C)Exactly two
D)More than three
E)None
Rationale: 6x − 24 = 6y
=> 6x - 6y = 24
=> x- y =4 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 7
=> x=3.5
y=.5
Therefore , the given system will have Exactly one solution
Answer : A
Answer: A
Question: Each of 435 bags contains at least one of the following three items: coconut, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only coconut and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
Options:
A)256
B)260
C)316
D)320
E)350
Rationale: Fill the diagram step by step:
coconut, almonds, and peanuts.PNGAlso given that there are total of 435 bags and 210 bags contain almonds.
From the diagram 20y=5x --> y=x/4. Now, Total=435={Almonds}+10x+y+x --> 435=210+10x+x/4+x --> x=20 --> # of bags that contain only one kind of item is the sum of yellow segments: 10x+x+5x=16x=320.
Answer: D.
Answer: D
Question: A train running at the speed of 70 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)227 m
B)150 m
C)167 m
D)175 m
E)187 m
Rationale: Speed = 70 * 5/18 = 175/9 m/sec
Length of the train = speed * time = 175/9 * 9
= 175 m
Answer: D
Answer: D
Question: A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train?
Options:
A)82 kmph
B)76 kmph
C)44 kmph
D)58 kmph
E)56 kmph
Rationale: Explanation:
Total distance = 108+112 = 220 m
Time = 6s
Relative speed = distance/time = 220/6 m/s = 110/3 m/s
= (110/3) × (18/5) km/hr = 132 km/hr
=> 50 + speed of second train = 132 km/hr
=> Speed of second train = 132-50 = 82 km/hr
Answer: Option A
Answer: A