divelab/Sys2Bench huggingface dataset:
Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Options:
A)9
B)7
C)4
D)8
E)6
Rationale: E
6
Explanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 9 (X)
2343 12 (/)
3474 18 (X)
4131 9 (X)
5286 21 (/)
5340 12 (/)
6336 18 (X)
7347 21 (/)
8115 15 (/)
9276 24 (/)
Required number of numbers = 6
Answer: E
Question: A store is having a store-wide sale of 10% off all merchandise. If a discontinued item is an additional 25% off, what is the sale price of an item whose original non-sale price was $50?
Options:
A) $33.50
B) $33.75
C) $34.00
D) $34.25
E) $34.50
Rationale: sale price = (original price - 10% decrease) - 25% decrease
price = [50 * (90/100)] * (75/100) = 50 * (.90) * (.750) = 45 * .75 = 33.75
The answer is B.
Answer: B
Question: An amount of money is to be divided between Priya, Mani and Rani in the ratio of 2:4:8. If the difference between the shares of Priya and Mani is Rs.200, what will be the difference between Mani and Rani's share?
Options:
A)1266
B)3000
C)2866
D)2999
E)400
Rationale: 4 -2 = 2 --- 200
8-4 = 4 --- > 200/2*4= 400
Answer: E
Answer: E
Question: A person crosses a 600 metre long street in 5 minutes. What is his speed in km per hour?
Options:
A)8.2
B)4.2
C)6.1
D)7.2
E)6.5
Rationale: Distance = 600 m = 0.6 km
time = 5 min = 1/12 hr
speed = dist/time = 06./(1/12) = 7.2 km/hr
ANSWER D
Answer: D
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $36400, how many months will it take Joan to pay back her mortgage?
Options:
A)6
B)8
C)10
D)11
E)13
Rationale: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 36400
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 364
So we have 1 , 3 , 9 , 27 ..... 36400 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
364 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
364 x -2 = 1- 3^n
- 728 = 1 - 3^n
- 729 = - 3 ^n
729 = 3 ^n (negatives cancel out)
729 can also be re written as 3 ^ 6
Therefore ; 3 ^6 = 3 ^n
Thus n = 6 (A)
Answer: A
Question: How many ways could three boxes can be arranged in a shelf with five boxes space in which two places in the shelf will remain empty?
Options:
A)118
B)60
C)8
D)12
E)120
Rationale: ways in which 3 places out 5 can be selected = 5C3
ways in which 3 boxes can be arranged in 3 places = 3!
Total ways of arrangement = 5C3*3!
=5*4/2*6
=10*6
=60
Ans = B
Answer: B
Question: Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
Options:
A)2%
B)2.15%
C)2.25%
D)2.50%
E)3%
Rationale: Generally in such cases, there is always loss.
So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.
Loss% = Common loss and gain% 2 = x 2
10 10
Therefore, here common loss and gain % = 15%
Hence,
Loss% = 15 2 = 2.25%
C
Answer: C
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 2?
Options:
A)0.4
B)1
C)π/4
D)4
E)π
Rationale: Maximum distance straight line is diameter
d = 2r = 4..
ANS option D.
Answer: D
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -12 (t-3)^2 + 120. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
Options:
A)48
B)54
C)60
D)66
E)72
Rationale: We see that h will be a maximum h=120 when t-3=0, that is when t=3.
At t=5, h = -12*(5-3)^2 + 120 = -12(4) + 120 = 72
The answer is E.
Answer: E
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.19
B)7.18
C)7.16
D)7.15
E)7.12
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer: D
Answer: D
Question: A train passes a man standing on the platform. If the train is 125 meters long and its speed is 90 kmph, how much time it took in doing so?
Options:
A)6 sec
B)2 sec
C)9 sec
D)5 sec
E)1 sec
Rationale: D = 125
S = 90 * 5/18 = 25 mps
T = 125/25 = 5 sec
Answer:D
Answer: D
Question: Addison High School’s senior class has 300 boys and 240 girls. If 60% of the boys attended the college then 60% of the total class attended college, what percentage of the girls class attended college?
Options:
A)60
B)50
C)46
D)55.56
E)65
Rationale: Number of boys attending the party : 0.60*300 = 180
Total students = 300+240 = 540
number of students attending the party: 0.60*540 = 324
number of girls attending = 324-180 = 144
% of girls attending = 144/240 = 60%. A is the correct answer
Answer: A
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.9 sec
C)2.7 sec
D)8.7 sec
E)8.5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: A
Answer: A
Question: In a certain country, 60 percent of the population likes basketball, and 32 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
Options:
A)20%
B)33%
C)40%
D)53%
E)67%
Rationale: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 32 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 32/60 = 53%, or choice D.
Answer: D
Question: The C.P of 15 books is equal to the S.P of 19 books. Find his gain% or loss%?
Options:
A)16 2/3%
B)16 2/8%
C)16 2/5%
D)21 1/19%
E)16 1/3%
Rationale: 15 CP = 19 SP
19 --- 4 CP loss
100 --- ? => 21 1/19% loss.Answer: D
Answer: D
Question: In the rectangular coordinate system, if the line x = 5y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
Options:
A)1/2
B)2/3
C)1/4
D)2/5
E)3/7
Rationale: x = 5y+5, and thus y = x/5 - 1
The slope is 1/5.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/5 and thus p = 2/5
The answer is D.
Answer: D
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/37
C)31/29
D)31/28
E)31/08
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T)
= 1 - 1/32
= 31/32
Answer: A
Answer: A
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)9:37
B)9:31
C)9:27
D)9:19
E)9:17
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: B
Question: A man persuaded Weary Willie, with some difficulty, to try to work on a job for thirty days at eight dollars a day, on the condition that he would forfeit ten dollars a day for every day that he idled. At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labor. Can you tell just how many days' work he put in and on how many days he idled?
Options:
A)1673 &13 1/3 days
B)1633 &13 1/2 days
C)1433 &13 1/6 days
D)2173 &13 1/5 days
E)2273 &13 1/7 days
Rationale: A
1673 &13 1/3 days
Weary Willie must have worked 1673 days and idled 13 1/3 days. Thus the former time, at $8.00 a day, amounts to exactly the same as the latter at $10.00 a day
Answer: A
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
Options:
A)11
B)18
C)99
D)77
E)51
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Answer: B
Question: If f(b)=b^2, what is the value of (f(a+b)−f(a))/b ?
Options:
A)a
B)b
C)2a + b
D)2a +-b
E)2b - a
Rationale: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - a^2/b = (simplify a^2)
2ab+b^2/b = (cancel b's)
= 2a+b
Ans : C
Answer: C
Question: Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
Options:
A)1
B)4
C)3
D)8
E)6
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1
Answer: A
Answer: A
Question: A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water.
Options:
A)15,20
B)30,20
C)1,20
D)20,20
E)10,20
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(30-10) = 10 kmph
=> Rate in still water = 1/2(30+10) = 20 kmph
Option E
Answer: E
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 6 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
Options:
A)64
B)32
C)36
D)48
E)61
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
17 + 6 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 52
b = 39
Number of freshmen who take Art = 39 + 20 + 5 = 64
Answer A
Answer: A
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)287 m
B)287 m
C)288 m
D)150 m
E)287 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: D
Question: If The GCD of two numbers (not equal, both integers, greater than 1) is 2, then which of the following can be true?
A. They are prime.
B. They are even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 2.
Options:
A)Only A
B)Only B
C)Only C
D)Only D
E)Only B and D
Rationale: The GCD of two numbers (not equal, both integers, greater than 1) is 2 means that they don't share factors other than 1 and 2.
This also means that both numbers are even ( divisible by 2.)
A. They are not prime. 2 is the only even number that is prime, so one number can be prime but the other number cannot be.
B. They are even. Since they are divisible by 2, they are even..
C. They have a common prime factor. The question defines the numbers as having a GCD of 2, which is prime.
D. They have a common factor other than 2. Both numbers have common factors of 2 and 1. For example:
The factors of 4 are 1 and 2, the factors of 6 are 1, 2, and 3.
Therefore, (B) is the only correct answer.
Answer: B
Question: X can do a piece of work in 15 days. If he is joined by Y who is 50% more efficient, in what time will X and Y together finish the work?
Options:
A)10 days
B)6 days
C)18 days
D)Data insufficient
E)None of these
Rationale: X’s one day’s work = 1⁄15 th work.
Y’s one day’s work = 1⁄15 + 50% of 1⁄15 = 1⁄10 th work.
∴ (X + Y)’s one day’s work = 1⁄15 + 1⁄10 = 1⁄6 th work.
Hence, they together finish the work in 6 days.
Answer B
Answer: B
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Options:
A)25
B)35
C)75
D)80
E)79
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 7 = 75
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 75 + 4 = 79
E
Answer: E
Question: A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 6 persons for the position of sales manager, 4 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hiring of these three people are possible?
Options:
A)6 + 4 + 10
B)6 × 4 × 10
C)21 × 20 × 19
D)6! + 4! + 10!
E)6! × 4! × 10!
Rationale: 1 sales manager can be selected out of 6 in 6 ways
1 clerk can be selected out of 4 in 4 ways
1 receptionist can be selected out of 10 in 10 ways
total no. of ways these 3 can be selected = 6 *4 * 10
Ans. B) 6 × 4 × 10
Answer: B
Question: In the first 10 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.25
B)6.5
C)6.75
D)7
E)6
Rationale: 10 overs - run rate = 4.2
runs scored in first 10 overs = 42
remaining overs 40
total runs to be scored= 282
42 runs already scored 282-42=240
240 runs to be scored in 40 overs
let required runrate be x
40*x=240
x=240/40
x=6.0
the required runrate is 6.0
ANSWER:E
Answer: E
Question: A father left a will of 68,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attains the age of 18 years If the money is reckoned at 10% p.a., find how much each gets at the time of the will.
Options:
A)30,000, 38,000
B)28,000, 40,000
C)32,000, 36,000
D)Cannot be determined.
E)None of these
Rationale: Let one gets = x
then, second gets = (68,000 – x)
Given : A1 = A2
x+x×10×8/100=(68,000−x)+(68,000−x)×10×6/100
⇒ x[100 + 80] = (68,000 - x)[100 + 60]
⇒ 180⁄160x = 68,000 - x
⇒ 34x = 68000 × 16 ⇒ x = 32000
∴ second gets = 36,000
Answer C
Answer: C
Question: The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What is the weight of the new person?
Options:
A)75 kg
B)85 kg
C)95 kg
D)65 kg
E)55 kg
Rationale: The total weight increase = (8 x 2.5) kg = 20 kg
weight of new person = (55 + 20) kg = 75 kg
The answer is A.
Answer: A
Question: If a - b = 3 and a^2 + b^2 = 35, find the value of ab.
Options:
A)12
B)13
C)10
D)18
E)13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 35 - 9 = 26
ab = 13.
Answer is B.
Answer: B
Question: Jack spent 1/6 of his lifetime in adolescence. His facial hair started growing after 1/12 more of his life. He successfully married his girlfriend Diana after 1/7 more of his life. Their son was born after 5 years from then. The son lived just 1/2 of what Jack lived. Jack dies four years after his son died.
How long did Jack live ?
Options:
A)75
B)90
C)45
D)80
E)84
Rationale: E
84
Explanation:
Let us assume that jack lived for p years.
p/6 + p/12 + p/7 + 5 + p/2 + 4 = x
=> p = 84.
Therefore, Jack lived for 84 years.
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)227
B)277
C)272
D)150
E)221
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: D
Answer: D
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)5/7
E)None of these
Rationale: Explanation:
P (getting a prize) =	10/(10 + 25)	=	10/35	= 2/7.
ANSWER : C
Answer: C
Question: Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability Q, that a book selected at random is either a hard cover book or a chemistry book?
Options:
A)1/10
B)3/20
C)1/5
D)1/4
E)9/20
Rationale: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, Q=9 provide the desired outcome, making the answer E.
Answer: E
Question: Two trains A and B are 125 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Options:
A)10 s
B)11 s
C)4 s
D)8 s
E)12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 125 + 150 = 275 m. Time taken = 275/25 = 11 s.
CORRECT ANSWER B.
Answer: B
Question: The length of the bridge, which a train 170 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)245
B)777
C)282
D)266
E)205
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (170 + x)/30 = 25/2 => 2(170 + x) = 750 => x = 205 m.
Answer: E
Answer: E
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Options:
A)230
B)277
C)299
D)267
E)221
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.Answer:A
Answer: A
Question: If the side length of Square B is five times that of Square A, the area of Square B is how many times the area of Square A?
Options:
A)5
B)15
C)25
D)35
E)45
Rationale: Let x be the side length of Square A.
Then the area of Square A is x^2.
The area of Square B is (5x)^2=25x^2.
The answer is C.
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/95
B)33/91
C)33/99
D)33/96
E)33/92
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= 12C4/15C4
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
Answer: B
Answer: B
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)44
B)11
C)12
D)98
E)58
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: C
Question: Sum of 3 consecutive even no.'s is 30 more than the 1st no. of the series. Find the middle no.?
Options:
A)8
B)12
C)14
D)16
E)18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+30
3x + 6 = x + 30
2x = 24
\inline \therefore x = 12
\inline \therefore Middle number = x + 2 = 12+2 = 14
C
Answer: C
Question: How many words can be formed by using all letters of the word “BIHAR”
Options:
A)452
B)320
C)365
D)456
E)120
Rationale: The word BIHAR contains 5 different letters.
Required number of words = 5p5 = 5! = (5x4x3x2x1) = 120
Ans: E
Answer: E
Question: An investment yields an interest payment of $228 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
Options:
A)$28,300
B)$30,400
C)$31,300
D)$32,500
E)$35,100
Rationale: Let the principal amount = P
Simple annual interest = 9%
Simple monthly interest = (9/12) = (3/4)%
(3/4)*(P/100) = 228
=>P = (228 *4 * 10^2 )/3
= 76*4*10^2
= 304 * 10^2
Answer B
Answer: B
Question: The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is
Options:
A)18
B)67
C)02
D)Data inadequate
E)23
Rationale: Explanation:
Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.
So, the data provided is inadequate.
Answer: D
Answer: D
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates W apply to what fraction of a week?
Options:
A) 1/2
B) 5/8
C) 9/14
D) 16/21
E) 9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates W/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: C
Question: If 10 toys cost Rs, 234, what do 35 toys cost?
Options:
A)645
B)564
C)546
D)819
E)None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
x=(35 X 234)/10 =819
Answer is D
Answer: D
Question: What is the greatest positive integer n such that 3^n is a factor of 54^100?
Options:
A)100
B)200
C)300
D)600
E)900
Rationale: 54 = 3^3 * 2.
54^100 = 3^300 * 2^100
The answer is C.
Answer: C
Question: How many odd integers F between 200 and 600 are there such that their tens digit is even?
Options:
A)20
B)25
C)100
D)150
E)200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total F: 4*5*5=100.
Answer: C.
Answer: C
Question: In the presidential election, 55% of the people who voted, voted for the democratic candidate and 35% voted for the republican candidate. If 8% of the number of people eligible to vote, voted for neither the republican nor the democrat, what percent of people eligible to vote actually voted in the elections?
Options:
A)40
B)60
C)80
D)88
E)90
Rationale: let people eligible to vote = y
people actually voted = x
Democratic = 0.55x
Republican = 0.35 x
total voters = 0.90 x
hence 0.10x voters who voted didnt voted for D and R.
now, 0.10 x = 0.08 y
=> x/y = 8/10
hence 80%
Hence C
Answer: C
Question: If Sharon's weekly salary increased by 15 percent, she would earn $460 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?
Options:
A)Rs.400
B)Rs.440
C)Rs.150
D)Rs.460
E)Rs.520
Rationale: Soln:-
460/115)110 =385
In this case long division does not take much time.
(4/1)110=Rs.440
ANSWER:B
Answer: B
Question: In a certain village, n litres of water are required per household per month. At this rate, if there are m households in the village, how long (in months) will p litres of water last?
Options:
A)p /m
B)P/mn
C)mp / n
D)np / m
E)npm
Rationale: I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p:
(p/m*n)
Answer (B)
Answer: B