divelab/Sys2Bench huggingface dataset:
Question: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man standing still. Find the length of the train and that of the platform.
Options:
A)83.3m41.7m
B)100m50m
C)50.8m45.7m
D)100/3 m200/3
E)none of these
Rationale: A train running at 25 km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
Distance = Speed*time
It's probably best to convert to meters so we can find the length of the platform.
Distance = 25000 meters/h * 18 seconds*(1/60*60)
Distance =(25000*18 / [3600] ) = 125m
I'm not sure how we take the length of the train into account (if we do at all) to solve this problem. For example, If we were measuring by the time the very front of the train passed one end of the platform to the time the very front of the train passed the other end, the result would be different than if we counted when the very front of the train passed one end of the platform to the time the back side of the train passed the end.
As for the problem involving the man, the man is standing still while the train is moving forward at a speed of 25km/h. Therefore, the train is moving past the man at a total speed of 25km/h.
distance = speed * time
distance = 25km/h * 12 seconds
distance (length of train) = 83.3 m
We know the length of the train is roughly 83.3m and the distance covered passing the platform was 125m. However, The platform isn't 125m long - it is 125m minus the length of the train long (or so I think) which is 125-83.3 or roughly 41.7m. Both of these answers are in A so I think that is the right answer. I am still having a bit of trouble conceptualizing why we have to subtract out the length of the train, however.
ANSWER: A) 83.3m41.7m
Answer: A
Question: A no. when divided by 35leaves a remainder 20, what is the remainder if the same no.be divided by 15?
Options:
A)2
B)4
C)7
D)8
E)9
Rationale: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
B
Answer: B
Question: x ÷ 4 × 5 + 10 – 12 = 48, then x =
Options:
A)60
B)40
C)100
D)28
E)50
Rationale: Follow reverse process
48 + 12 = 60 – 10 = 50 ÷ 5 = 10
×
× 4 = 40
Option B
Answer: B
Question: How many of the integers between 25 and 45 are even ?
Options:
A)21
B)20
C)11
D)10
E)9
Rationale: Number start between 25 to 45 is 20 numbers
half of them is even..which is 10
ANSWER:D
Answer: D
Question: How many numbers from 10 to 1000000 are exactly divisible by 9?
Options:
A)900
B)8000
C)1100
D)111110
E)14
Rationale: 10/9 = 1 and 1000000/9 = 111111 ==> 111111 - 1 = 111110.
Answer : D
Answer: D
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)45 Years
B)46 Years
C)49 Years
D)52 Years
E)54 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
C
Answer: C
Question: The number obtained by interchanging the two digits of a two digit number is lesser than the original number by 54. If the sum of the two digits of the number is 12, then what is the original number?
Options:
A)28
B)39
C)82
D)Can’t say
E)None of these
Rationale: Let with two digits x and y, original number= 10x+y
Number obtained by reversing the digits= 10y+x
Given the later number is less by 54 than the original, so 10x+y -(10y+x)=54 or x-y=6 ---(i)
Also Sum of the two digits is 12, so x+y= 12 ----(ii)
From (i) & (ii), x=9, y=3
So original number=10x+y= 10*9 +3= 93
ANSWER:E
Answer: E
Question: n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 5000m race?
Options:
A)300
B)400
C)500
D)600
E)750
Rationale: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40
and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40
solving equation A speed =8 and B=20/3
for 1000m b will take 5000/20/3= 750 sec
#
E
Answer: E
Question: A certain high school has 500 students. Of these students, 30 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
Options:
A)430
B)440
C)450
D)460
E)470
Rationale: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 30
Y = 20
Z = 10
So, we have 30 students taking music, 20 taking art and 10 taking BOTH music and art.
20 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 40 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 40 = 460.
D
Answer: D
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last
Options:
A)44
B)42
C)40
D)38
E)36
Rationale: Explanation :
Given that fort had provision of food for 150 men for 45 days
Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days
Remaining men after 10 days = 150 - 25 = 125
Assume that after 10 days,the remaining food is sufficient for 125 men for x days
More men, Less days (Indirect Proportion)
⇒Men150:125}::x:35
⇒ 150 × 35 = 125x
⇒ 6 × 35 = 5x
⇒ x =6 × 7 = 42
⇒The remaining food is sufficient for 125 men for 42 days. Answer : Option B
Answer: B
Question: If 100,000 microns = 1 decimeter, and 1,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)1.0e-05
B)0.0001
C)0.001
D)10
E)100,000
Rationale: Given that 100,000 microns = 1 decimeter
1,000,000 angstroms = 1 decimeter
So 100,000 microns =1,000,000 angstroms
1 micron = 1,000,000/100,000 = 10
Answer : D
Answer: D
Question: After giving a discount of rs.100the shopkeeper still gets a profit of 30%,if the cost price is rs.1000.find the markup %?
Options:
A).50
B).45
C).40
D).48
E).52
Rationale: cost price=1000
s.p=1000*130/100=1300
disc=100
so...mark price=1300+100=1400......
mark up%=1400-1000/1000=400/1000=.40 (OR) 40%
ANSWER:C
Answer: C
Question: The calendar of the year 2024 can be used again in the year?
Options:
A)2288
B)2052
C)2778
D)2719
E)1711
Rationale: Explanation:
Given year 2024 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2024 + 28 = 2052
Answer: B) 2052
Answer: B
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+20, what is the perimeter of the garden in feet?
Options:
A)32
B)36
C)40
D)44
E)48
Rationale: Let x be the length of one side of the square garden.
x^2 = 8x + 20
x^2 - 8x - 20 = 0
(x-10)(x+2) = 0
x = 10, -2
P = 4(10) = 40
The answer is C.
Answer: C
Question: The average of 65 numbers is 40. If two numbers, 50 and 60 are discarded, then the average of the remaining numbers is nearly
Options:
A)28.32
B)39.52
C)38.78
D)29
E)30
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (50+60) = 2600 - 110= 2490
Average = 2457/63 = 39.52
Answer : B
Answer: B
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)60 km
B)87 km
C)89 km
D)67 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x
= 20 km.
Answer:E
Answer: E
Question: A football field is 9600 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 5600 square yards?
Options:
A)450
B)600
C)700
D)2400
E)3200
Rationale: Answer C) 9600 yards need 1200 lbs
1 Yard will need 1200/9600 = 1/8 lbs
3600 Yards will need 1/8* 5600 Yards = 700lbs
Answer: C
Question: When a merchant imported a certain item, he paid a 9 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $85.50, what was the total value of the item?
Options:
A)$1,150
B)$1,350
C)$1,550
D)$1,750
E)$1,950
Rationale: Let x be the value in excess of $1,000.
0.09x = 85.5
x = $950
The total value was $950 + $1,000 = $1,950.
The answer is E.
Answer: E
Question: There are 7000 people in the particular village , among them 30% are educated and out of these 28% are doing agriculture and out of them 50% are woman's. Then find out the number of woman's who are educated and doing agriculture?
Options:
A)294
B)235
C)350
D)288
E)580
Rationale: Total number of people in the village = 7000; out of them 30% educated = 2100; out of them 28% doing agriculture = 588; out of them 50% are woman's = 294.
Answer: A
Question: What sum of money will produce Rs.80 as simple interest in 2 years at 16 percent?
Options:
A)400
B)250
C)300
D)350
E)200
Rationale: 80 = (P*2*16)/100
P = 250
Answer: B
Answer: B
Question: In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 3 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: The total number of books the students borrowed is 20*2=40.
The students who borrowed zero, one, or two books borrowed 8*1+3*2=14 books.
The 7 students who borrowed at least three books borrowed 40-14=26 books.
If 6 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 26-18= 8 books.
The answer is A.
Answer: A
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 15 percent, what was the annual interest rate last year?
Options:
A)1%
B)1.1%
C)9.1%
D)10%
E)13.63%
Rationale: 15=1.1*x
X=13.63%
Answer E)
Answer: E
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)10
B)12
C)14
D)16
E)17
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: B
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 5 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 5 more blue balls than white balls...
Equation #2: y = 5 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 5
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 5) = 100
5y - 5 = 100
5y = 105
y = 21
There are 21 blue balls. This is 5 more than the number of white balls, so z = 16. That's the answer. Just as a check, x = 63, and 63 + 21 + 16 = 100.
Answer = 16,(E)
Answer: E
Question: Which one of the following numbers is exactly divisible by 11?
Options:
A)11
B)13
C)14
D)15
E)16
Rationale: (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.
(2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.
(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
A
Answer: A
Question: P and Q started a business investing Rs. 54,000 and Rs. 36,000 respectively. Out of a total profit of Rs. 18,000, Q's share is :
Options:
A)5980
B)5990
C)6000
D)6010
E)6020
Rationale: Ratio of their shares = 54000 : 27000 = 6 : 3.
Q’s share = Rs. 18000 * 3/9
= Rs. 6000
ANSWER:C
Answer: C
Question: A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
A)150m
B)200m
C)250m
D)750m
E)300 m
Rationale: D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m
ANSWER:D
Answer: D
Question: The average salary/head of all the workers in a workshop is Rs.1100, if the average salary/head of 9 technician is Rs.1300 and the average salary/head of the rest is Rs.880, the total no. of workers in the work-shop is ?
Options:
A)18
B)20
C)22
D)17
E)26
Rationale: Let the total number of workers be y.So sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y -9 workers.9 x 1300 + 880(y -9) = 1100 y⇒ 11700 + 880y - 7920 = 1100y⇒ 220y = 3780∴ y = 17 So total number of workers = 17 D
Answer: D
Question: The perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)22.78
B)23.54
C)24.5
D)25.55
E)23.51
Rationale: Let the side of the square be a cm.
Perimeter of the rectangle = 2(15 + 14) = 58 cm
Perimeter of the square = 58 cm
i.e. 4a = 58
A = 14.5
Diameter of the semicircle = 14.5 cm
Circumference of the semicircle
= 1/2(∏)(14.5)
= 1/2(22/7)(14.5) = 22.78 cm to two decimal places
Answer: A
Answer: A
Question: In a consumer survey, 75% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: pick 100 and x= all set with exactly two items
75=30+50+20 -(X)-10
X=15
Answer D
Answer: D
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much W does she have in her account after two years?
Options:
A)$10079.44
B)W=$10815.83
C)$12652.61
D)$14232.14
E)$20598.11
Rationale: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Answer: B
Question: A man can row upstream at 15 kmph and down strem 30 kmph. He takes 9 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by him in 9 hours? He must return back to base point A in remaining time.
Options:
A)80
B)120
C)140
D)180
E)200
Rationale: Upward distance traveled per hour - 15 km,
distance traveled after 6 hours = 90 km.
He remained with 3 hours travel downward, i.e. distance traveled in remaining 3 hours downward = 90 km
so total distance traveled from A to B and Back to point A = 90 km upward + 90 km downhill = 180 km
(Answer : D)
Answer: D
Question: The calender for the year 2007 will be the same for the year :
Options:
A)2014
B)2016
C)2017
D)2018
E)None of these
Rationale: Answer D
Answer: D
Question: Calculate the circumference of a circular field whose radius is 6 centimeters.
Options:
A)12
B)4
C)6
D)8
E)10
Rationale: Circumference C is given by
C = 2Ï€r = 2Ï€*6 = 12 Ï€ cm
correct answer A
Answer: A
Question: How many real roots does the equation x^4y+16xy+64y=0 have if y < 0?
Options:
A)0
B)1
C)2
D)3
E)Infinite
Rationale: x^4y+16xy+64y=0
=> y ( x^2 + 16x + 64) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-6
So although there are 2 factors , they are the same x=-6 .
The equations has 3 distinct real root .
Answer D
Answer: D
Question: If the price of gasoline increases by 20% and a driver intends to spend only 8% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys?
Options:
A)4%
B)5%
C)6%
D)8%
E)10%
Rationale: Let x be the amount of gasoline the driver buys originally.
Let y be the new amount of gasoline the driver should buy.
Let P be the original price per liter.
(1.2*P)y = 1.08(P*x)
y = (1.08/1.2)x = 0.9x which is a reduction of 10%.
The answer is E.
Answer: E
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
Options:
A)52.7 m2
B)57.8 m2
C)52.8 metre sq
D)72.8 m2
E)52.8 m2
Rationale: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C
Answer: C
Question: Solution A is made up of alcohol and water mixed in the ratio of 21:4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2:3 by volume. If Solution A and Solution B are mixed in the ratio of 5:6 by volume, what percent of the resultant mixture is alcohol?
Options:
A)32.5%
B)40%
C)60%
D)65%
E)Cannot be determined
Rationale: let mixture after mixing A and B is 110 ml (number assumed for calculation because of 5:6)
now solution A is 50 ml and solu B is 60 ml
further in A 100 ml A contains 84 ml alch
so 50 ml contain 42 ml
in mix B 100 ml solution contain 40 ml alc , 60 ml of B , it will be 24 ml alcohol.
so 42+24 = 66 in 110 ml solution which is 60%
ANSWER:C
Answer: C
Question: How long will it take a sum of money invested at 5% p.a. S.I. to increase its value by 40%?
Options:
A)6 years
B)7 years
C)8 years
D)9 years
E)None
Rationale: Sol.
Let the sum be x. Then, S.I. = 40% of x = 2x/5; Rate = 5%.
∴ Time = [100 * 2x/5 * 1/x*5] = 8 yea
Answer C
Answer: C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)12:17:16
B)12:15:16
C)13:15:16
D)12:35:16
E)12:15:18
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer:B
Answer: B
Question: In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 250 runs?
Options:
A)6.25
B)6.28
C)6.11
D)5.53
E)6.21
Rationale: Required run rate
= [250 - (4.2 * 20)]/30
= 166/30
= 5.53
Answer:D
Answer: D
Question: Today is Sunday. After 65 days, it will be:
Options:
A)Tuesday
B)Saturday
C)Friday
D)Thursday
E)Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Sunday.
After 65 days, it will be Tuesday.
Answer :A
Answer: A
Question: If n = 6p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is E.
Answer: E
Question: Calculate the distance covered by 150 revolutions of a wheel of radius 20.5 cm.
Options:
A)293.3 m
B)197.3 m
C)193.3 m
D)143.3 m
E)198.3 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 150 * 2 * 22/7 * 20.5 = 19328.57 cm = 193.3 m
ANSWER:C
Answer: C
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] + 8 = f(3x – 6)
Options:
A)0
B)4
C)6
D)7
E)13
Rationale: Answer = D = 7
f(x) = 3x – 5
2*[f(x)] + 8 = f(3x – 6)
2(3x-5) + 8 = 3 (3x-6) - 5
6x - 2 = 9x - 23
x = 7
Answer: D
Question: In a renowned city, the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Options:
A)32,300
B)172,800
C)468,830
D)338,200
E)259,200
Rationale: Every 2 seconds, 6 persons are added (9-3). Every second 3 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 3 = 259200
Option E
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg, what is his percent?
Options:
A)2%
B)25%
C)5.26%
D)29%
E)45%
Rationale: 950 --- 50
100 --- ? => 5.26%
Answer:C
Answer: C
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
Options:
A)338
B)480
C)888
D)266
E)281
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer: B
Answer: B
Question: In how many ways can the letters of word INTELLIGENT be arranged such that all the vowels as well as all the Consonants always appear together?
Options:
A)9!
B)5!*4!
C)5!*5!
D)5!*4!*2!
E)4!*7!*2!
Rationale: Since all the vowels and consonants have to be together there can only be there are 4! way to order the vowels and 7! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 4!7!2! (E)
Answer: E
Question: What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x?
Options:
A)1
B)10
C)9
D)0
E)8
Rationale: Explanation :
E = (x-1)(x-6)(x-3)(x-4)+10
E = (x2-7x+6)(X2-7x+12)+10
Let x2-7x+6 = y
E = y2+6y+10
E = (y+3)2 + 1
Minimum value = 1 , when y = -3
Answer : A
Answer: A
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 805. How many houses are there?
Options:
A)125
B)111
C)101
D)121
E)131
Rationale: So it starts from 545 and goes like 547, 549,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([805-545][/2]+1 = 131
Ans E
Answer: E
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?
Options:
A)22
B)99
C)12
D)88
E)77
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12.Answer:C
Answer: C
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)177 m
B)786 m
C)272 m
D)100 m
E)127 m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300
= 100 m.
A can give B 100m start.
Answer:D
Answer: D
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options:
A)1:2
B)4:5
C)1:1
D)3:2
E)5:3
Rationale: Let c = revenue from car sales in 1996
Let t = revenue from truck sales in 1996
Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,
c(0.89) + t(1.07) = (c+t) (1.01)
Dividing throughout by t,
(c/t) (0.89) + 1.07 = (c/t + 1) (1.01)
=> (c/t) (0.12) = 0.06
=> (c/t) = 1/2
Option (A).
Answer: A
Question: Find the area of a parallelogram with base 36 cm and height 24 cm?
Options:
A)760
B)284
C)288
D)864
E)820
Rationale: Area of a parallelogram = base * height
= 36 * 24
= 864 cm2
Answer: D
Answer: D