divelab/Sys2Bench huggingface dataset:
Question: In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
Options:
A)55.5 kg
B)66.5 kg
C)77.5 kg
D)88.5 kg
E)None of these
Rationale: Explanation:
Let Arun's weight be X kg.
According to Arun, 65 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg Answer: B
Answer: B
Question: A palindrome is a number that reads the same forward and backward, such as 124. How many odd, 4-digit numbers are palindromes?
Options:
A)40
B)45
C)50
D)60
E)2500
Rationale: A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.
In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*12 = 60 ways
D
Answer: D
Question: . A boy has four trousers and 7 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)18
B)20
C)26
D)28
E)30
Rationale: Explanation:
The boy can select one trouser in four ways.
The boy can select one shirt in 7 ways.
The number of ways in which he can select one trouser and one shirt is 4 * 7 = 28 ways.
Answer: Option E
Answer: E
Question: A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)160
B)180
C)200
D)220
E)240
Rationale: The speed of the train is 54 * 5/18 m/s = 15 m/s
The length of the train is 15 x 20 = 300 m
platform + 300 = 15 * 32
platform = 480 - 300 = 180
The answer is B.
Answer: B
Question: Every day Daniel drives 100 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
Options:
A)10%
B)28%
C)33%
D)42%
E)52%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 100 miles at 4 miles/hour.
D = (R)(T)
100 = (4)(T)
100/4 = 25 = T
It takes 25 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (68 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
68 = (2)(T)
68/2 = 34 = T
It takes 34 hours for the second part
Total time to drive home on Monday = 4+34 = 38 hours
We're asked by what percent 38 hours is greater than 25 hours.
38/25 = 1.52, so it is 52% greater.
E
Answer: E
Question: a percent of b is c and c percent of d is e, then a is what percent of e?
(a, b, c, d, e > 0)
Options:
A)bd/1000
B)10000/bd
C)10000 bd
D)bd/1000
E)1000000/bd
Rationale: Given:
a/100∗b=c
c/100∗d=e
substitute c in 2nd equation with LHS of the first
a∗b/100∗d/100=e
abd/100=100e
a=100e∗100/bda
convert this into a percent
1000000/bd of e.
Answer- E
Answer: E
Question: 9 people decided to split the restaurant bill evenly. If the bill was $314.16 dollars, how much money did they 1 cent is the smallest unit?
Options:
A)$314.16
B)$314.17
C)$314.18
D)$314.19
E)$314.20
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs after 31416.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 31416 = 15 and 18 is divisible by 9.
Hence, we need to add 3 to this number for it to be divisible by 9
Correct Option: D
Answer: D
Question: How many 3 digit even numbers do not use any digit more than once
Options:
A)280
B)216
C)2240
D)246
E)2520
Rationale: The Way i solved it is
A B C ( hundreds, tens, units)
C can be 0 2 4 6 8 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 7 * 8 * 5 = 280
Ans :A
Answer: A
Question: What day of the week was 31st July, 1993?
Options:
A)Monday
B)Sunday
C)Saturday
D)Tuesday
E)Friday
Rationale: SOLUTION :
31st July, 1993 = (1992 years + period from 1st January, 1993 to 31st July, 1993)
1600 years have 0 odd days and 300 years have 1 odd day.
Now, the period from 1900 to 1992 have 69 ordinary years and 23 leap years
= (69*1 + 23*2) = 115 odd days = (16 weeks + 3 days) = 3 odd days.
January	February	March	April	May	June	July
31 28 31 30 31 30 31
= 212 days = (30 weeks + 2 days) = 2 odd days
Therefore, total number of odd days = 1 + 3 + 2 = 6 odd days.
Therefore, the required day was Saturday.
ANSWER IS C
Answer: C
Question: 12KM is how many miles?
Options:
A)6 Miles
B)7Miles
C)7.5Miles
D)8Miles
E)9miles
Rationale: 7.5 Miles
12/1.6=7.5
Answer:C
Answer: C
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Options:
A)286 m
B)150 m
C)177 m
D)287 m
E)267 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: B
Question: In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?
Options:
A)2.5 sec
B)2.9 sec
C)3.5 sec
D)4 sec
E)2.4 sec
Rationale: Speed = 90 * 5/18 = 25 m/sec
Time taken = 100/25
= 4 sec.
Answer: D
Answer: D
Question: A work as fast as B. If B can complete a work in 20days independently,the number of days in which A and B can together finish the work in?
Options:
A)20/3days
B)10/3days
C)15days
D)10days
E)20days
Rationale: Ratio of rates of working of A and B = 2:1
ratio of times taken = 1:2
A's 1day work = 1/10
B's 1day work = 1/20
A+B 1day work = 1/10 + 1/20 = 3/20 =3/20
A and B can finish the work in 20/3days
Answer is A
Answer: A
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length E of the fence including the fence posts on each end?
Options:
A)mn
B)m(n + x)
C)E=m(n + x) + x
D)m(n + x) + 2x
E)2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: C
Question: Sum of Rs.36.90 is created by 180 coins which are possibly 10 paise coins or 25 paise coins. The count of 10 paise coins are
Options:
A)54
B)55
C)56
D)57
E)58
Rationale: Explanation :
-> Total count of coins = 180
If “a” is count of 10paise coins and “b” be count of 25paise coins
A + b = 180 —Eqn (i)
-> Given 10 paise coins and 25 paise coins create the addition = Rs. 36.90
[ (10a/100) + (25b/100) ]= 36.90
=> 10a + 25b = 3690 ———(ii)
-> Solving (i) and (ii)
a10 => 10 a + 10b = 1800 (-)
=> 10a + 25b = 3690
- 15b = -1890
B = 1890 / 15 = 126
Substitute b value in eqn (i) , A = 180 – 126 = 54
Therefore Count of 10 paise coins = 54
Answer : A
Answer: A
Question: The length, the breadth and the height of a rectangular solid are in the ratio 1:2:3. If the length, breadth and height are increased by 100%, 200% and 200% respectively , then the increase in the volume of the rectangular solid is
Options:
A)5 times
B)6 times
C)12 times
D)17 times
E)20 times
Rationale: Here, we're told that the dimensions of a rectangular solid (re: cuboid) - the length, width and height - are in the ratio of 1:2:3.
Let's TEST VALUES and say that...
Length = 1
Width = 2
Height = 3
Next, we're told that the length, width and height are increased 100%, 200% and 200% respectively. Thus, they would now be..
Length = 1+1 = 2
Width = 2 + 2(2) = 6
Height 3 + 2(3) = 9
We're asked for the increase in the VOLUME of the shape (and the answers hint that we should use the Percentage Change Formula).
Initial Volume = (L)(W)(H) = (1)(2)(3) = 6
New Volume = (L)(W)(H) = (2)(6)(9) = 108
Percentage Change = (New-Old)/Old = (108-6)/6 = 102/6 = 17
Thus, the new volume is 17 times greater than the old volume.
D
Answer: D
Question: Mr. X, a mathematician, defines a number as 'connected with 6 if it is divisible by 6 or if the sum of its digits is 6, or if 6 is one of the digits of the number. Other numbers are all 'not connected with 6'. As per this definition, the number of integers from 1 to 60 (both inclusive) which are not connected with 6 is
Options:
A)18
B)22
C)42
D)43
E)45
Rationale: Explanation:
Numbers from 1 to 60, which are divisible by 6 are : 6,12,18, 24, 30, 36,42, 48, 54, 60.
There are 10 such numbers.
Numbers from 1 to 60, the sum of whose digits is 6 are : 6, 15, 24, 33, 42, 51, 60.
There are 7 such numbers of which 4 are common to the above ones. So, there are 3such uncommon numbers.
Numbers from 1 to 60, which have 6 as one of the digits are 6, 16, 26, 36, 46, 56, 60.
Clearly, there are 4 such uncommon numbers.
So, numbers 'not connected with 6' = 60 - (10 + 3 + 4) = 43.
Answer: D
Answer: D
Question: Three people (1 couple and 1 single) are seated at random in a row of 9 chairs. What is the probability that the couple does not sit together?
Options:
A)3/4
B)4/7
C)5/8
D)5/9
E)7/9
Rationale: The total number of arrangements of 3 people is 9*8*7 = 504
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 8*7*2 = 112.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 504 - 112 = 392
P(couple won't sit together) = 392/504 = 7/9
The answer is E.
Answer: E
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is:
Options:
A)18 years.
B)11 years.
C)21 years.
D)36 years.
E)58 years.
Rationale: Age of the 15th student=
[15 * 15 - (14 * 5 + 16 * 9)] = (225 - 214) = 11 years.
Answer: B
Answer: B
Question: Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
.
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: 150 employees
80 are full-time
100 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
150-80=70 employees not full time
70-20= 50 employees not full time who worked over a year
100 employees have worked at company X for at least a year-50 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year
ANSWER:C
Answer: C
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)75
B)72
C)30
D)80
E)50
Rationale: Explanation:
speed= Distance/ Time
S = (90 + 60)/2 = 75 kmph
Answer: A
Answer: A
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 25% alcohol, is?
Options:
A)3
B)4
C)5
D)6
E)9
Rationale: 4.5 4.5
25% 75%
25% ----- 4.5
75% ------? => 13.5 - 4.5 = 9 ml
ANSWER:E
Answer: E
Question: Ana is 5 years more than Jack. The sum of their ages is 29. Find the ages of Jack.
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Let Jack's age = x
And Ana's age, y = x+5---->(1)
Sum of their ages, x+y = 29----->(2)
substitute equation 1 in 2,
x+(x+5)=29
2x+5=29
2x=29-5
2x=24 ==>x=12(Jack's age)
ANSWER:C
Answer: C
Question: If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
Options:
A)100π
B)7π
C)60π
D)50π
E)70π
Rationale: 4/3 π * 10 * 10 * 10 = 8 * 4/3 πr3
r = 5
4π * 5 * 5 = 100π
ANSWER:A
Answer: A
Question: Find the odd man out. 7,13,19,25,29,37,43
Options:
A)19
B)29
C)25
D)43
E)53
Rationale: Explanation :
All given numbers except 25 are prime numbers. Answer : Option C
Answer: C
Question: The radius of a wheel is 22.5 cm. What is the distance covered by the wheel in making 500 resolutions?
Options:
A)708 m
B)707.14 m
C)774 m
D)714 m
E)744 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.5 = 70714 cm
= 707.14 m
Answer:B
Answer: B
Question: Solution A is 20% ammonia and Solution B is 80% ammonia. 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% ammonia 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: 10 distinct integers are arranged in ascending order. The range of the first 7 is 25 and that of last 7 is 30. What is the maximum range W of the 10 numbers?
Options:
A)25
B)27
C)30
D)52
E)55
Rationale: Positions: 1 2 3 4 5 6 7 8 9 10
Given: 1st position = x; 4th position = a; 7th position = y; 10th position = b
y - x = 25
Let x be 0 and y = 25. We are asked to maximize the range and the integers are distinct.
b - a = 30 --> b = 30 + a
In order to increase the range, we have to maximize the value of 'b'.
'b' can be maximized by taking the max value of 'a'.
From the assumed values, maximum value of 'a' can be 22.
Therefore, b = 30 + 22 = 52
Range W= 52 - 0 = 52
Answer: D
Answer: D
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 4 years the amount to be paid is?
Options:
A)8118
B)8127
C)8618
D)8774
E)8128
Rationale: A = 7500(26/25)4
= 8774
Answer: D
Answer: D
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
Options:
A)10000
B)30000
C)50000
D)60000
E)20000
Rationale: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000
Option C
Answer: C
Question: The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 75 black cars in the lot, how many red cars are there in the lot?
Options:
A)11
B)28
C)24
D)29
E)32
Rationale: B is correct
R/B = 3/8 and B =75
R = 75*3/8 = 28
Answer: B
Question: Mr. Donald has $900 in ten, twenty, fifty and one hundred dollar bills. He has an equal number of each denomination of bill. How many total bills does Mr. Donald have?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Let the number of each type of bill = bThen 10b + 20b + 50b + 100b = 900180b = 900b = 5So: The total number of bills that Mr. Donald has = 4b = 20Answer: B
Answer: B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)42 6/9%
B)42 5/7%
C)42 6/8%
D)42 6/7%
E)43 6/7%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: D
Question: Find the next term in the given series -
47, 94, 71, 142, 119, 238, . ?
Options:
A)331
B)360
C)320
D)340
E)215
Rationale: 47+47=94 & 94-23=71
71+71=142 & 142-23=119
119+119=238, So 238-23=215
ANSWER:E
Answer: E
Question: Let a,b,c and d be the result of rounding off 7382.196 to the nearest thousand, hundred, ten and one, respectively. Which of the following statements is true?
Options:
A)d<c<b<a
B)d<c<a<b
C)a<d<c<b
D)c<d<b<a
E)a<c<d<b
Rationale: Soln:
7382.196..
Nearest thousand 7000..a
Nearest hundred 7400..b
Nearest ten 7380..c
Nearest one 7382...D
a<c<c<b
ANSWER:E
Answer: E
Question: How many pairs (w, w+1) have one or more prime factors common, where w is an integer and 2 ≤ w ≤9 ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: w and w+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: A
Question: How many odd numbers between 10 and 1,200 are the squares of integers?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
16 numbers.
Answer: E.
Answer: E
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Options:
A)1000
B)2777
C)2688
D)2772
E)2991
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: A
Answer: A
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)Rs.4528
B)Rs.4520
C)Rs.4527
D)Rs.4530
E)Rs.4521
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 5
= Rs.4530
Answer:D
Answer: D
Question: If m, n, and o are three different positive integers whose sum is prime, which of the following statements could be true?
Options:
A)Each of m + n, m + o, and n + o is prime.
B)Each of m + 3, n + 3, and o + 3 is prime.
C)Each of m, n, and o is prime.
D)The average (arithmetic mean) of m, n, and o is prime.
E)m + n = o
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that C is the answer.
Answer: C
Question: A basketball is dropped from a height of 30 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 2 full bounces.
Options:
A)50
B)55
C)60
D)75
E)80
Rationale: Initial distance = 30 feet
first bounce = 15 feet up + 15 feet down = 30 feet
second bouche = 7.5 feet up + 7.5 feet down = 15 feet
total distance covered = 30+30+15=75
Answer : D
Answer: D
Question: The difference between a number and its two fifth is 510. What is 10% of that number?
Options:
A)12.75
B)50
C)85
D)204
E)None
Rationale: Solution
Let the number be x.
Then, x - 2 / 5 x = 510.
‹=›3 / 5 x = 510
‹=›x = [510 x 5 / 3] = 850.
Therefore 10% of 850 = 85.
Answer C
Answer: C
Question: A and B can complete a job in 30 and 20 days respectively. They start working together and B leaves 5 days before the work is finished. In how many days is the total work finished?
Options:
A)20 days
B)30 days
C)12 days
D)14 days
E)15 days
Rationale: explanation:
A and B can do the job in 30 and 20 days individually, so together they will take 30*20/(30 + 20) = 600/50 = 12 days.
The work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after (5/6)*12 = 10 days
Total time taken = 10 + 5 = 15 days.
Answer E
Answer: E
Question: Four of the following five are alike in a certain way and so form a group. which one does not belong to that group?
Options:
A)Tooth
B)Chin
C)Nose
D)Eye
E)Hand
Rationale: All others have two vowels each
Answer :B
Answer: B
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, what is the average for the last four matches?
Options:
A)34.25
B)36.4
C)40.2
D)32.25
E)32
Rationale: Explanation:
Total runs scored in 10 matches = 10 × 38.9
Total runs scored in first 6 matches = 6 × 42
Total runs scored in the last 4 matches = 10 × 38.9 - 6 × 42
Average of the runs scored in the last 4 matches = 10×38.9−6×42/4
=389−252/4=137/4=34.25
Answer: Option A
Answer: A
Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $11.00?
Options:
A) 40
B) 60
C) 90
D) 132
E) 240
Rationale: Cost price of 1 pound of bananas = 0.5/3 = 1/6
Selling price of 1 pound of bananas = 1/4
Profit per pound = (1/4 - 1/6) = (1/12)
Total profit is given as 11
(1/12)*x = 11
x = 132
Answer: D
Answer: D
Question: Pipe A can fill a tank in 6 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)1.5
B)2
C)2.5
D)3
E)3.5
Rationale: The part filled by A + B + C in 1 hour
= 1/6 + 1/4 + 1/12
= 12/24 = 1/2
All the three pipes together will fill the tank in 2 hours.
The answer is B.
Answer: B
Question: We have 7770 balls available, and there is 1 ball on d top of rack and then 3 balls on d 1st floor behind the top rack (horizontal rack) and then 6 balls on 2nd floor then 10 balls on 3rd floor,
How many floors can be accomdated with the given no of balls...???
Options:
A)36
B)35
C)34
D)33
E)32
Rationale: 1+3+6+10+........=7770 sum of triangular number
n*(n+1)*(n+2)/6 gives 35
ANSWER:B
Answer: B
Question: A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.
Options:
A)18 days
B)22 ½ days
C)24 days
D)26 days
E)28 days
Rationale: Explanation :
If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
ANSWER IS B
Answer: B
Question: If 3a – 2b – 2c = 32 and √3a-√(2b+2c)=5, what is the value of a + b + c?
Options:
A)3
B)9
C)10
D)12
E)14
Rationale: when we look at the two equations, we can relize some similarity, so lets work on it..
3a – 2b – 2c = 32 can be written as √3a^2-√(2b+2c)^2=32
{√3a-√(2b+2c)}{√3a+√(2b+2c)}=32..
or 4*√3a+√(2b+2c)=32..
or √3a+√(2b+2c)=8..
now lets work on these two equations
1)√3a-√(2b+2c)=4..
2)√3a+√(2b+2c)=8..
A) add the two eq..
√3a+√(2b+2c)+√3a-√(2b+2c)=12..
2√3a=12..
or √3a=6..
3a=36..
a=12.
B) subtract 1 from 2..
√3a+√(2b+2c)-√3a+√(2b+2c)=4..
2√(2b+2c)=4..
√(2b+2c)=2..
2b+2c=4..
or b+c=2..
from A and B a+b+c=12+2=14..
B
Answer: B
Question: A group of men decided to do a work in 12days, but 6 of them became absent. If the rest of the group did the work in 14days, Find the original number of men?
Options:
A)15
B)42
C)44
D)45
E)18
Rationale: Original number of men = 6*14 / (14-12) = 42
Answer is B
Answer: B
Question: Two numbers are in the ratio 5:8 and thier H.C.F is 4. Find the numbers.
Options:
A)25 and 40
B)20 and 32
C)30 and 48
D)15 and 24
E)16 and 25
Rationale: Explanation:
Let two numbers 5x, 8x their H.C.F = 4
Therefore H.C.F is 4
i.e, x in this case.
Therefore The numbers are 5 x 4 = 20
8 x 4 = 32
Answer: Option B
Answer: B