divelab/Sys2Bench huggingface dataset:
Question: If q and y are positive integer and q/y is an even integer, which of the following can be an odd integer?
Options:
A)x
B)xy
C)x−y
D)x+2y
E)q/3
Rationale: C q-Y
Let says q =12 Y=3 iT BECOMES q-Y =9 This is odd True
q = 12 Y = 6 THEN q-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: E
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)15
B)30
C)38
D)42
E)48
Rationale: For deciding such task we should calculate all parts 4 + 5 + 11 = 20 parts
and we should calculate how many sandwiches holds 1 part:
120 / 20 = 6 sandwiches in one part
For bologna we have 7 parts so:
5* 6 = 30
Answer is B
Answer: B
Question: P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Options:
A)5 days
B)9 days
C)30 days
D)20 days
E)10 days
Rationale: Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10
ANSWER:E
Answer: E
Question: For some integer m, m^2 - 5 is divisible by all of the following EXCEPT
Options:
A)38
B)41
C)30
D)31
E)29
Rationale: Hint: m^2-5 (m is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: C
Answer: C
Question: John deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
Options:
A)$10,100
B)$10,101
C)$10,200
D)$10,201
E)$10,404
Rationale: 8 percent annual interest compounded quarterly --> 2% in 3 moths.
For the first 3 moths interest was 2% of $10,000, so $200;
For the next 3 moths interest was 2% of $10,000,plus 4 earned on previous interest of $100, so $200+$4=$204;
Total interest for 6 months was $200+$204=$404, hence balance after 6 months was $10,000+ $404=$10,404.
Answer:E.
Answer: E
Question: The number of the members of a club is more than 50 and less than 80. When 4 people sit at a table, other people exactly divided to 8-people groups (8 people sit at a table) or 7-people groups (7 people sit at a table). If the members are divided to 9-people groups, how many people will be left?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: The number of members is 7k+4 = 8j+4
The only number in this range which satisfies this is 60.
60/9 = 6(9) + 6
The answer is D.
Answer: D
Question: A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum.
Options:
A)Rs. 600
B)Rs. 60
C)Rs. 60000
D)Rs. 600000
E)Rs. 6000
Rationale: Let sum = P and original rate = R.
Then, [ (P*(R+2)*3)/100] – [ (P*R*3)/100] = 360.
3PR + 6P - 3PR = 36000
6P=36000
P=6000
Hence, sum = Rs. 6000
Answer is E.
Answer: E
Question: The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?
Options:
A)432 sq m
B)363 sq m
C)452 sq m
D)428 sq m
E)525 sq m
Rationale: 2(3x + x) = 88
l = 33 b = 11
lb = 33 * 11 = 363
ANSWER:B
Answer: B
Question: A rectangular tiled patio is composed of 80 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 80 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
Options:
A)5
B)6
C)10
D)12
E)28
Rationale: r*c=80 and (12+4)(c-2)=80 --> r=12 and c=7.
Answer: D.
Answer: D
Question: The distance from Steve's house to work is 35 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
Options:
A)5.
B)10.
C)14.
D)15.
E)17.5
Rationale: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 35km => Speed = 17.5kmph
E
Answer: E
Question: During a certain two-week period, 60 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 3 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
Options:
A)5 A
B)6 A
C)8 A
D)14 A
E)20 A
Rationale: Movies: 60 % comedies. 40 % remaining genre.
Now in this 40 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 3x. Total 4x.
4x = 40; x = 10
Action movies: 10 %
Drama movies: 30 %
we can say that out of 100z,:
comedies: 60z
action: 10z
drama: 30 z
Now action movies wereA
This means:
A = 10z.
z = (A/10)
Comedies: 60z = 60 * (A/10)
6 A
B is the answer.
Answer: B
Question: For any natural number n, F(n) is the least common multiple of all natural numbers upto. For how many values of n less than 100, F(n+1) - F(n) = 0?
Options:
A)33
B)64
C)29
D)27
E)01
Rationale: F(n) is the LCM of al natural numbers upto n.
For example,
F(3) = 6
F(5) = 60
F(6) = 60 etc.
F(n + 1) - F(n) = 0
⇒⇒ F(n + 1) = F(n)
It would hapen only when factors of (n + 1) are already present in the LCM of first n natural numbers. In other words, Whenever (n + 1) is Prime number or is any Integral power of any prime number, F(n + 1) ≠≠ F(n)
for example, F(31) ≠≠ F(32) as 32 = 2525 which is, 2 raised to power 5. or F(4) ≠≠ F(5) as 5 is prime so the power of 5 does not contain in F(4).
Between 1 and 100, there are 25 prime numbers. So if (n+1) is one of these number then F(n + 1) ≠≠ F(n).
Also {4, 8, 16, 32, 64, 9, 27, 81, 25, 49} are prime numbers raised to some exponent.
Hence, none of these 35 numbers from 1 to 99 cannot be the possible values of n. So for 99 - 35 = 64 numbers F(n)
= F(n+1)
Answer:B
Answer: B
Question: How many integers between 263,205and 658,805 have tens digit 1 and units digit 3?
Options:
A)3,955
B)3,925
C)3,956
D)3,926
E)3,915
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...
The difference between 263,205 and is 658,805 -263205=395,600 - one number per each hundred gives 133,900/100=3,956
Answer:C.
Answer: C
Question: What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 145° each?
Options:
A)96 cm
B)108 cm
C)120 cm
D)132 cm
E)154.28 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 145*n
from here
n = 10.28
So perimeter becomes 15*10.28= 154.28
Answer: E
Answer: E
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 20 kmph, then the speed in downstream is?
Options:
A)27
B)27
C)20
D)99
E)35
Rationale: M = 15
S = 25
DS = 15 + 25 = 35
Answer:E
Answer: E
Question: Every person in a certain group is either a Cowboys fan or a Saints fan, but not both. The ratio of Cowboys fans to Saints fans is 6 to 4. If 54 Cowboys fans change teams to become Saints fans, the ratio of Saints fans to Cowboys fans will be 1 to 1. How many people are in the group?
Options:
A)90
B)64
C)30
D)360
E)240
Rationale: By checking the answer choices:
Since we have a initial ratio of 6:4, the total count should be divisible by 10.
A. 90/10=9, Cowboys Fan = 54, Saints Fan = 27, Since 54-54 is not equal to 27+54 this can not be the answer.
B. Out, since not divisible by 10.
C. 30/10=3, Cowboys Fan = 36, Saints Fan = 9, Since 36-54 is not equal to 9+54 this as well can not be the answer.
D. 360/10=36, Cowboys Fan = 216, Saints Fan = 108, Since 216-54 equal to 108+54 this is the correct answer.
E. 240/10=24, Cowboys Fan = 144, Saints Fan = 72, Since 144-54 is not equal to 72+54 this as well can not be the answer.
D is the correct answer.
Answer: D
Question: In what time a sum of money double itself at 4% per annum simple interest?
Options:
A)25%
B)33 1/3%
C)83 1/3%
D)33 4/3%
E)73 1/3%
Rationale: P = (P*4*R)/100
R = 25%
Answer:A
Answer: A
Question: Cara and Dan will throw three dice each. The score is the sum of points on all three dice. If Cara scores 16 in her attempt, what is the probability that Dan will outscore Cara in his attempt?
Options:
A)1/36
B)1/54
C)5/54
D)1/216
E)5/216
Rationale: The total number of ways the dice can land is 6*6*6=216.
Dan can get a score of 18=6+6+6
There is only 1 way to do this.
Dan can get a score of 17=6+6+5
There are 3 ways to do this.
P(Dan wins)=4/216=1/54
The answer is B.
Answer: B
Question: Each of the three people individually can complete a certain job in 4, 5, and 6 hours, respectively. What is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates?
Options:
A)4/15
B)7/30
C)11/30
D)5/18
E)7/18
Rationale: The two slowest people work at rates of 1/5 and 1/6 of the job per hour.
The sum of these rates is 1/5 + 1/6 = 11/30 of the job per hour.
The answer is C.
Answer: C
Question: A car traveled 40% of the way from Town X to Town Y at an average speed of 40 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph?
Options:
A)50
B)45
C)55
D)60
E)65
Rationale: Assume total distance = 100miles
Time taken for 40 miles = 40/40 = 1 hour
Time taken for the rest of the 60 miles = 60/v hours.
Average speed = 50
Therefore the total time needed = 2 hours.
2 = 1 + 60/v
Hence v = 60 mph
Answer : D
Answer: D
Question: The ratio of the volumes of two cubes is 343 : 512. What is the ratio of their total surface areas?
Options:
A)12:24
B)8:16
C)45:25
D)18:56
E)49:64
Rationale: Ratio of the sides = Â³âˆš343 : Â³âˆš512
= 7 : 8
Ratio of surface areas =49:64
Answer: E
Answer: E
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 40% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
Options:
A)1.8 lakh
B)1.0 lakh
C)1.9 lakh
D)8.1 lakh
E)6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.4 = 4.2 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 4.2 - 1.2 = 3 lakh
Average SP of all the 3 cars = 1 lakh
Answer: B) 1 lakh
Answer: B
Question: 3 persons started placementpapers with a capital of Rs.3000 . B invest Rs.600 less than A, C invest Rs.300 less than B. Then what is the share amount of B in a profit of Rs.886 ?
Options:
A)Rs.245.8
B)Rs.265.8
C)Rs.285.8
D)Rs.365.8
E)Rs.165.8
Rationale: a+(a-600)+(a-900)=3000
sove then a=1500 (50%)
b=900 (30%)
c=600 (20%)
Hence share for B = 886*30/100 => B share = Rs.265.8
ANSWER:B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 210 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)89
B)20
C)36
D)41
E)34
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 200 + 210 = 410 m.
Time taken = 410/10 = 41 sec.
Answer: Option D
Answer: D
Question: Two equilateral triangle of side 12cm are placed one on top another, such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the Star?
Options:
A)21
B)88937
C)269
D)279
E)2701
Rationale: Answer:A
Answer: A
Question: Rectangular tile each of size 70cm by 30cm must be laid horizontally on a rectangular floor of size 110cm by 130cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Area of tile = 70*30 = 2100
Area of floor = 130*110 = 14300
No of tiles = 14300/2100 = 6.8
So, the no of tile = 6
ANSWER:B
Answer: B
Question: If x is positive integer,y is negative integer, and 5x+2y=4, which of the following could be the value of x ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Use answer options to solve this problem -
Put x = 2
So, 5x+2y=4
Or, 5(2)+2y=4
Or, 10+2y=4
Or, 2y=4-10;2y=-6
Or, y=-3(y is negative integer)
Answer will be (C)
Answer: C
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?
Options:
A)2
B)50
C)92
D)96
E)98
Rationale: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After some water evaporates the cucumbers become 98% water and 2% of non-water, so now 1 pound of non-water composes 2% of cucucmbers, which means that the new weight of cucumbers is 1/0.02=50 pounds.
Answer: B.
Answer: B
Question: Working alone, John finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. John alone cleans the entire house in 6 hours. How many hours will it take Nick and John to clean the entire house if they work together?
Options:
A)1.5
B)2
C)2.4
D)3
E)3.6
Rationale: Answer is 3.6 hours.
John does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6
answer is E
Answer: E
Question: Line J has a y-intercept of 7 and passes through point (a,b). What is the slope of Line J in terms of a and b?
Options:
A)(b-7)/a
B)(a−b)/6
C)(6−a)/b
D)(6−b)/a
E)(b−6)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 7 tells you that the line also goes through point (0,7).
slope m = (y-y1)/(x-x1) = (b-7)/(a-0)
A
Answer: A
Question: A candy company sells premium chocolate at $3 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?
Options:
A)[A] 1
B)[B] 2
C)[C] 3
D)[D] 4
E)[E] 5
Rationale: This question is a bit of Special equations with a single set of unique values.
the Equation stands : 3X + 4Y = 31
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 5 / 5 = 1
Correct Option : A
Answer: A
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)26 km/hr
B)17 km/hr
C)60 km/hr
D)42 km/hr
E)46 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/5 = 3x => x = 20/3.
So, speed of the faster train = 40/3 = 40/3 * 18/5
= 42 km/hr.
Answer:D
Answer: D
Question: If a certain number is divisible by 22 and 40, it is NOT necessarily divisible by which of the following?
Options:
A)4
B)11
C)20
D)42
E)44
Rationale: If a certain number is divisible by 22 and 40, it is NOT necessarily divisible by which of the following?
let the certain number be 440, which is both divisible by 22 and 40.
440/42 = 220/21
D. 42
Answer: D
Question: Which of the following options is an appropriate approximate value in the following equation’? 3 4/3 of 155.83+22% of 1547= ? - 504.7
Options:
A)1855.94
B)1557.94
C)1257.94
D)1837.94
E)1857.94
Rationale: 3 4/3 of 155.83+22% of 1547= ? - 504.7
1012.9+340.34= ? - 504.7
1012.9+340.34 +504.7= ?
≈ 1857.94
Answer E
Answer: E
Question: Mario and Nina each have a bag of marbles, each of which contains 12 blue marbles, 10 red marbles, and 18 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
Options:
A)3/4
B)2/4
C)1/4
D)1/8
E)1/16
Rationale: Mario and Nina each select one marble from their respective bags.
Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble
Probability that either Mario or Nina select a red marble = (10/40)*(10/40) + (10/40)*(10/40) = 2*(1/16)
Probability that either Mario or Nina select a red marble = 1/8
Answer would be D.
Answer: D
Question: The average weight of 10 person's increases by 5 kg when a new person comes in place of one of them weighing 60 kg. What is the weight of the new person?
Options:
A)85.5
B)86.5
C)87.5
D)110
E)89.5
Rationale: Total increase in weight =10 ×5 = 50
If x is the weight of the new person, total increase in weight = x−60
=> 50= x - 60
=> x = 50 + 60= 110
ANSWER:D
Answer: D
Question: Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.580?
Options:
A)Rs.500
B)Rs.5100
C)Rs.530
D)Rs.540
E)None of these
Rationale: Explanation:
580 = P [1 + (5*16/5)/100]
P= 500
Answer: Option A
Answer: A
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
Options:
A)9% decrease
B)8% decrease
C)6% decrease
D)1% decrease
E)2% decrease
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Answer: B
Question: In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 1 metres then what will be the area of the square so formed?
Options:
A)144 cm2
B)260 cm2
C)2500 cm2
D)302 cm2
E)None of these
Rationale: Let the side of the square be x m.
∴ Perimeter of the square = 48 × 1 = 4x ∴ x = 12 m
∴ Area = (12)2 = 144 cm2
Answer A
Answer: A
Question: Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $70?
Options:
A)4
B)12
C)15
D)20
E)24
Rationale: you could set-up a quick table and brute force the answer.
A	4	*	50	200 1800	-200 1600	26 61.54
B	12	*	50	600 1800	-600 1200	18 66.67
C	15	*	50	750 1800	-750 1050	15 70.00
D	20	*	50	1000 1800	-1000 800	10 80.00
E	24	*	50	1200 1800	-1200 600	6 100.00
Answer is C
Answer: C
Question: The number of sequences in which 3 players can throw a ball, so that the youngest player may not be the last is ?
Options:
A)3
B)8
C)5
D)4
E)10
Rationale: x Not younger
The last ball can be thrown by any of the remaining 3 players. The first 6 players can throw the ball in 2P2 ways.
The required number of ways = 2(2!)
= 4
Answer:D
Answer: D
Question: There are 12 balls in a jar: 6 red, 2 blue and 4 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
Options:
A)1/12
B)1/4
C)1/2
D)2/3
E)3/4
Rationale: Blue + Red =8
Total number of balls is 6+2+4=12
So the answer is 8/12=2/3
Answer D
Answer: D
Question: How many pairs of letters in the word 'CHAIRS' have as many letters between them in the word as in the alphabet?
Options:
A)2
B)5
C)6
D)8
E)3
Rationale: Explanation:
Letters in the word Letters in the alphabet
Answer: A) 2
Answer: A
Question: A bag contains 25 paise, 50 paise and 1 rupee coins in the ratio 7:4:3 . total no. of coins is 360. sum of total coins is Rs. 99 so how many 25 paise coins?
Options:
A)160
B)170
C)180
D)190
E)200
Rationale: total coins=360
25 p coins =(7/14)*360=180
ANSWER:C
Answer: C
Question: Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 20, 28 and 35, what is the minimum possible range in scores of the three test-takers?
Options:
A)30
B)35
C)25
D)15
E)28
Rationale: I simply looked at the 3 different possible scores for each individual test: 20,35,28
We have to find the minimum range:
35-20=15
35-28=7
28-20=8
The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.
7*5 = 35
Answer:B
Answer: B
Question: Which of the following numbers is between 1⁄5 and 1⁄6?
Options:
A).45
B).35
C).29
D).22
E).18
Rationale: 1/5 = .2
1/6 = .1666...
The only number between these two is 0.18.
The answer is E.
Answer: E
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 90 km/hr. What is the length of the platform?
Options:
A)229
B)240
C)400
D)277
E)221
Rationale: Speed = 90 * 5/18 = 25 m/sec.
Length of the train = 25 * 20 = 500 m.
Let the length of the platform be x m . Then,
(x + 500)/36 = 25 => x = 400 m.
Answer: C
Answer: C
Question: Which is smallest prime number?
Options:
A)5
B)3
C)7
D)19
E)4
Rationale: Answer :B
Answer: B
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 126 grams of water?
Options:
A)110
B)112
C)114
D)116
E)118
Rationale: (16/18)*126 = 112 grams
The answer is B.
Answer: B
Question: P and Q started a business investing Rs 85000 and Rs 10000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Options:
A)17:5
B)17:3
C)17:6
D)17:2
E)17:8
Rationale: Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 85000:10000
= 85:10
= 17:2
Option D
Answer: D
Question: The area of a circle is increased by 300%. By what percent has the radius of the circle increased?
Options:
A) 400%
B) 200%
C) 100%
D) 600%
E) 800%
Rationale: The area of the circle is increased by 300%, thus the area is increased 4 times.
The area of a circle it proportional to the square of the radius (area=πr^2), therefore the radius must increase 2 times (diameter increase 2 times = area increase 4 times), which is increase by 100%.
Answer: C
Answer: C
Question: If the number 54773*4 is completely divisible by 8, then the smallest whole number in place of * will be?
Options:
A)1
B)2
C)3
D)4
E)None of these
Rationale: The number 3x4must be divisible by 8.
x=4 as 344 is divisible by 8.
Correct Option : D
Answer: D
Question: On multiplying a number F by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
Options:
A)104345
B)107375
C)108385
D)109395
E)105355
Rationale: The only thing you actually know about the correct number F is that it is divisible by 153 and has 5 as a factor.
You should immediately try to find the factors of 153 and look for them in the options.
153 = 9*17
Divisibility by 9 is easy to check. Only (D) satisfies.
Answer: D
Question: The number of livestock in a farm at the beginning of year 2000 was 110,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 110,000. Which of the following expressions is correct?
Options:
A)q>p
B)p > q
C)p = q
D)With the exception of 1 instance, p will be equal to q
E)There is no relation between p and q
Rationale: Number plugging in will be best strategy for this question.
Let p = 5%,
Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence B is the correct answer.
Answer: B