divelab/Sys2Bench huggingface dataset:
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 25 men in 3 days?
Options:
A)65mtr.
B)52mtr
C)70mtr.
D)78mtr.
E)17mtr.
Rationale: 20 men is 6 days can build 112 metres
25 men in 3 days can build = 112*(25/20)x(3/6)
= 70 meters
Answer: C.
Answer: C
Question: A cyclist rides a bicycle 9 km at an average speed of 11 km/hr and again travels 11 km at an average speed of 9 km/hr. What is the average speed for the entire trip?
Options:
A)9.3
B)9.6
C)9.8
D)10.1
E)10.3
Rationale: distance = 20 km
time = 9/11 + 11/9 = (81 + 121) / 99 = 202 / 99 hours
average speed = (20 * 99) / 202 = 9.8 km/h
The answer is C.
Answer: C
Question: If M and N are positive integers that have remainders of 2 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
Options:
A)89
B)53
C)34
D)29
E)11
Rationale: M=6p+2
N=6q+3
We need M+N=6p+3+6q+3=6(p+q)+5
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 6 so
p+q=0 ; M+n = 5
p+q=1 ; M+N = 11
P+q=2 ; M+N = 17
and so on, so basically you get something like - 5,11,17,23,29,35,41,..... all the other options were turning up.
Then I directly tried p+q=5 because it was closer to 34 , i got 35,
So Answer C.
Answer: C
Question: If the sum of two positive integers is 18 and the difference of their squares is 36, what is the product of the two integers?
Options:
A)108
B)80
C)128
D)135
E)143
Rationale: Let the 2 positive numbers x and y
x+ y = 18 -- 1
x^2 - y^2 = 36
=> (x+y)(x-y)=36 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 10
y= 8
Product = 10*8 = 80
Answer B
Answer: B
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be C's share of the earnings?
Options:
A)$1100
B)$520
C)$1080
D)$1170
E)$630
Rationale: Explanatory Answer
A, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.
Hence, C's share will be 2*2340/9 = 520.
correct choice is (B)
Answer: B
Question: A man can row three-quarters of a kilometre against the stream in 11 1/4 minutes. The speed (in km/hr) of the man in still water is:
Options:
A)4 1/4 km/hr
B)5 km/hr
C)6 km/hr
D)7 km/hr
E)None
Rationale: Sol.
Rate upstream = [750 / 675] m/sec = 10/9 m/sec.
Rate downstream = [750 / 450] m/sec = 5/3 m/sec.
∴ Rate in still water = 1/2 [10/9 + 5/3] m/sec = 25/18 m/sec = [25/18 * 18/5] km/hr
= 5 km/hr
Answer B
Answer: B
Question: we have 6 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 0.5 kg one of 0.25 kg by using only two weight how many wight u can weight
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: select 2 weight out of 6, 6C2=15
ANSWER:E
Answer: E
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 14 such machines produce in 4 minutes ?
Options:
A)2520
B)1800
C)2700
D)10800
E)None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 14 Ã— 4 Ã— 270 â‡” x = 14x4x270/6= 2520 . Answer A
Answer: A
Question: If a 2-digit integer is selected at random from the integers 60 through 99, inclusive, what is the probability that the first digit is equal to two less than the second digit?
Options:
A) 4/40
B) 4/90
C) 60/100
D) 1/99
E) 4/60
Rationale: The tens digit may be 6, 7, 8, or 9
The units digit may be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
The tens digit has to be 2 less than the value of the units digit so we will add 2 to possible tens digits
6+2 = 8
7+2 = 9
8+2 = 10
9+2 = 11
Of these values, 8 and 9 are possible units digits which means that 6 and 7 are possible tens digits
Possible numbers are 68, 69, 78, and 79
We have 4 possible numbers
Total numbers between 60 and 99 = (99-60)+1 = 40
Probability = 4/40
Answer A
Answer: A
Question: In an examination, a student scores 6 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 280 marks, the no of questions he attempts correctly is :
Options:
A)A)20
B)B)38
C)C)90
D)D)88
E)E)37
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
6x – (60 – x) = 280
=> 7x = 340
=> x = 20
Answer:A
Answer: A
Question: If 11 ml of water is mixed with 1 ml of a chemical, a magical perfume is manufactured. The manufacturer initially wanted to have 500 ml of one box of the magical perfume. How much extra ml is to be added with the proposed box size to comply with the formula?
Options:
A)3
B)4
C)5
D)7
E)8
Rationale: The magical perfume should have 11/12 of water and 1/12 of chemical. With 500 ml, there will be a need to add 4 ml more such that the final solution is divisible by 12; that is , 42x12=504. Answer B.
Answer: B
Question: A book seller marks his books 50% more than the real price and allows 30% discount. His profit is:
Options:
A)3%
B)4%
C)5%
D)6%
E)None of these
Rationale: Let the CP = 100 Rs.
Mark Price = 150
Discount = 30%
Selling price 70/100 Ã— 150
Hence profit = 5%
Answer: C.
Answer: C
Question: There are 20 balls of green color,20 balls of red color,20 balls of blue color,20 of balck,20 of yellow. how many u have to pick to guarantee 2pairs of same color?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Here we have five different colours.(Red, Green, Black, Blue and Yellow)
Consider If we pick 1st ball as red. After that, there may be a chance to pick FOUR different colours of ball.
But, if we pick the 6th ball, it must be match any one of the colour ball.
So for guarntee the same pair of colur balls, we pick 6 balls.
ANSWER:E
Answer: E
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
Options:
A)8200
B)7500
C)7000
D)8000
E)None of these
Rationale: Explanation :
State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer : Option D
Answer: D
Question: John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 : 1/4 : 1/5 . What is the minimum no. of pencils that the person should have?
Options:
A)65
B)68
C)70
D)77
E)80
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D)
Answer: D
Question: Jim’s only source of income comes from his job as a question writer. In this capacity, Jim earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Jim takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Jim wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Jim’s median annual income over the past 5 years?
Options:
A)$22,474
B)$25,673
C)$27,318
D)$28,441
E)$31,227
Rationale: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, D and E and u will find that only option D is divisible by 9 (once 10,000 is subtracted from 28441)
so its the right choice.D
Answer: D
Question: 270 Ã· ? Ã— 15 + 270 = 405
Options:
A)24
B)25
C)30
D)39
E)43
Rationale: Explanation:
270 Ã· ? Ã— 15 = 405 - 270 = 135
(270 Ã— 15)/? = 135
? = (270 Ã— 15)/135 = 30
Answer: Option C
Answer: C
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. one years from today, the difference between the age of the boy and the combined ages of the girls will be
Options:
A)0
B)2
C)3
D)–2
E)–1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
Difference = 4 - (2+2) = 0
Answer = A
Answer: A
Question: Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/7 of an ounce and one to measure exactly 1/8 of an ounce. You can pour precisely measured amounts into a beaker, which initially is empty. You can use either pipette to remove distilled water from the vat or from the beaker and use either pipette to dispense water into either of those receptacles, but you cannot use either pipette to take any quantity of distilled water other than the amount for which it is designed. Which of the following represents, in ounces, a precise amount of distilled water you can transfer from the vat to the beaker?
I. 1/6
II. 1/7
III. 1/12
Options:
A)I only
B)III only
C)I and III only
D)II and III only
E)1/56 and 1556
Rationale: Looking at the potential answer choices, 1/7 is immediately out as 7 is a prime that cannot be created from either 4 or 3.
1/7-1/8=1/56
1/7+1/8=15/56
Answer: E
Answer: E
Question: A van takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)40 Kmph
B)50 Kmph
C)60 Kmph
D)75 Kmph
E)860 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
C)
Answer: C
Question: Find the value of 3 + 3 â€¢ (8 â€“ 3)
Options:
A)25
B)18
C)17
D)24
E)15
Rationale: 3 + 3 â€¢ (8 â€“ 3)
= 3 + 3 (5)
= 3 + 3 *5
= 3 + 15
= 18
correct answer B
Answer: B
Question: Find the smallest no divisible by 5 ,3,7 and leave a remainder of 2 in each case and is divisible by 11 ?
Options:
A)737
B)735
C)105
D)107
E)108
Rationale: the smallest no divisible by 5,3 and 7 and leaving reminder 2
and which is divisible by 11 is 737..
737/11=67
and when divided by 5,3 & 7 leave the reminder 2.....
so ans is 737
ANSWER:B
Answer: B
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?
Options:
A)70 kmph
B)50 kmph
C)57 kmph
D)54 kmph
E)70 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60
= (6x + 6x)/120 = 12x/120
= x/10 Average speed
= (2x + 3x)/(x/10) = 50 kmph.
Answer: B
Answer: B
Question: Question: What is the remainder when W=(1!)!^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144?
Options:
A) 0
B) 25
C) 49
D) 81
E) 100
Rationale: 144 =12 *12
(1!)^3=1
2!=2, therefore (2!)^3=2*2*2=8
3!=6, therefore (3!)^3=6*6*6=216
4!=24 therefore (4!)^3= 24*24*24 which is completely divisible by 144
thus from 4! onwards each term will be divisible by 144 and will leave the remainder of 0
now the remainder when W=(1!)^3 + (2!)^3 + (3!)^3 + … + (432!)^3 is divided by 144 is same as, when 1+8+216 =225 is divided by 144
now remainder when 225 is divided by 144 is 81. hence answer should be D
Answer: D
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many E women are currently in the room?
Options:
A)12
B)14
C)15
D)24
E)36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number=5*3-3=12, then doubled=24..
ans D
Answer: D
Question: Find the odd man out
2880, 480, 92, 24, 8, 4, 4
Options:
A)480
B)92
C)24
D)8
E)4
Rationale: divide by 6, 5, 4, 3, 2, 1 respectively to obtain the next number.
92 is wrong.
ANSWER:B
Answer: B
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer:A
Answer: A
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 120 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)384
B)320
C)960
D)192
E)640
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 120hrs. hence, possible scenarios, if
(1)2x =120 => 16x = 960 (2) 3x =120 => 16x = 640 (3) 5x =120 => 16x = 384 (4) 6x =120 => 16x = 320
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: A train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
Options:
A)5 hrs 22 min
B)6 hrs 21 min
C)7 hrs 14 min
D)6 hrs
E)None of these
Rationale: Explanation:
Time taken to travel 600 km = Distance/Speed =600/100 = 6 hour
Now we need to find out the number of stops in the 600 km travel.
Given that train stops after every 75 km.
600/75 = 8
It means train stops 7 times before 600 km and 1 time just after 600 km. Hence we need
to take only 7 stops into consideration for the 600 km travel.
Hence, total stopping time in the 600 km travel = 7 x 3 = 21 minutes
Total time needed to reach the destination = 6 hours + 21 minutes = 6 hrs 21 min
Answer: Option B
Answer: B
Question: One hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.20 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
Options:
A)400
B)450
C)500
D)550
E)600
Rationale: The fuel is consumed at this rate: $0.20/$0.80 = 0.25 gallons per hour.
The time it takes to consume 100 gallons is: 100 / 0.25 = 400 hours.
The answer is A.
Answer: A
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Options:
A)Rs. 1550
B)Rs. 1650
C)Rs. 1750
D)Rs. 2000
E)Rs. 2500
Rationale: Explanation:
C.I.
= Rs.[4000x(1+10/100)2-4000]
=Rs.(4000x11/10x11/10-4000)
=Rs.840.
Sum = Rs.(420 x 100/ 3x8)=Rs. 1750.
ANSWER IS C
Answer: C
Question: There are 10person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Options:
A)7!*1!
B)7!*2!
C)6!*2!
D)8!*2!
E)6!*2!
Rationale: Total number of ways = 7!*2!.
B
Answer: B
Question: Charlene's annual bonus is calculated in the following manner: Charlene receives 40 percent of her first $11,000 in sales and 30 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales?
Options:
A)$ 20,666
B)$ 22,000
C)$ 24,000
D)$ 26,000
E)$ 28,000
Rationale: Let x be the total sales in $.
For the 1st 11,000 you get 40% ---> 0.4*11000 = 4400$
For the remaining (x-11000) $, you get 30% ---> 0.3*(x-11000)
Thus, 0.3*(x-11000) + 4400 = 7300 ----> x= 20,666 $
A is thus the correct answer.
Answer: A
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $210, what were her original savings?
Options:
A)$840
B)$800
C)$1000
D)$700
E)$1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $210. So 1 / 4 of her savings is $210. So her original savings are 4 times $210 = $840
correct answer A
Answer: A
Question: How much more would Rs.30000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
A)482
B)725
C)992
D)837
E)723
Rationale: 30000(11/10)4 - 30000(6/5)2 = 723
Answer:E
Answer: E
Question: It was 7:00 when Bill looked at the clock, he looks at the clock again 30 minutes later. What time is it now?
Options:
A)7:30
B)7:00
C)8:00
D)1:28
E)2:40
Rationale: If it's 7:00 and 30 minutes pass buy, it will be 7:30
A
Answer: A
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)8 kmph
B)4 kmph
C)2 kmph
D)10 kmph
E)12 kmph
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
ANSWER:B
Answer: B
Question: A statue is being carved by a sculptor. The original piece of marble weighed 250 kg. In the first week 30 per cent is cut away. In the second week 20 per cent of the remainder is cut away. In the third week the statue is completed when 25 percent of the remainder is cut away. What is the weight of the final statue?
Options:
A)105 kg
B)145 kg
C)165 kg
D)115 kg
E)100 kg
Rationale: A
105 kg
= 250 Ã— 0.7 Ã— 0.8 Ã— 0.75.
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 25, 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)19.7
B)20
C)22
D)21.4
E)21.5
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A
Answer: A
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)8
B)9
C)10
D)13
E)14
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: The ratio of 2 seconds to 4 hours
Options:
A)1:80
B)1:6000
C)1:7200
D)1:400
E)1:500
Rationale: 1 hour =3600 sec
then 4 hours =4*3600=14400
so ,2:36000=1:7200
ANSWER:C
Answer: C
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 40%, then the cost price of the article is:
Options:
A)500
B)277
C)222
D)297
E)400
Rationale: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/140 = Rs. 400
Answer:E
Answer: E
Question: For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 171?
Options:
A)4420
B)4860
C)5250
D)5780
E)6340
Rationale: 100 + 102 +...+ 170 = 36*100 + (2+4...+70) = 36*100 + 2(1+2+...+35) =
36*100 + 2(35)(36)/2 = 135*36 = 4860
The answer is B.
Answer: B
Question: A dealer buys dry fruits at Rs. 100, Rs. 80, and Rs. 60 per kilogram. He mixes them in the ratio 3:4:5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruits?
Options:
A)Rs. 80
B)Rs. 100
C)Rs. 95
D)None of these
E)Cannot be determined
Rationale: Solution: Let the dealer buys 3 kg, 4 kg and 5 kg.
Price of total dry fruits = 3*100+4*80+5*60 = Rs. 920.
SP = 920 + 50% of 920 = 1380.
Hence,
Price of mix dry fruits per kg = 1380/12 = Rs. 115.
Answer: Option D
Answer: D
Question: Evaluate permutation
6P6
Options:
A)710
B)720
C)730
D)740
E)None of these
Rationale: Explanation:
nPn=n!
6P6=6*5∗4∗3∗2∗1=720
Option B
Answer: B
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 37 what is the value of a1 ?
Options:
A)1
B)6
C)17
D)16
E)21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 37
a4 = 32
a3 = 27
a2 = 22
a1 = 17 <<<< Ans C
Answer: C
Question: A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction U of the sum of the 21 numbers in the list?
Options:
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21
Rationale: This is how I used to calculate which I think works pretty well:
if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)
n + 20a = S
the question tells us that
n = 4a
plug this back into the first equation and you get that the sum is 24a
4a + 20a = 24a
therefore fraction U of n to the total would be
4a/24a or 1/6
answer B
Answer: B
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
Options:
A)3:6
B)3:1
C)3:4
D)3:9
E)3:2
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80
=3:4
Answer:C
Answer: C
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 625 meters in length?
Options:
A)62
B)72
C)55
D)82
E)52.7
Rationale: Explanation:
T = (625 + 165)/54 * 18/5
T = 52.7
Answer: Option E
Answer: E
Question: The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
Options:
A)w=25/L=36
B)w=15/L=20
C)w=35/L=27
D)w=14/L=35
E)w=19/L=39
Rationale: L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
Answer: B
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 459?
Options:
A)18%
B)21%
C)20%
D)26.1%
E)None of these
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 459, Discount = 621 - 459 = 162
Discount % = 162/621 * 100 = 26.1%
ANSWER:D
Answer: D