divelab/Sys2Bench huggingface dataset:
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?
Options:
A)-2
B)5
C)-3
D)-4
E)-5
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+4 =5
Answer :B
Answer: B
Question: A train 240 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 240 m long?
Options:
A)28.8 sec
B)20.33 sec
C)60 sec
D)48 sec
E)49 sec
Rationale: total length= 240+240=480
speed=60 km/h=(60*5)/18= 50/3 m/s
time=(480*3)/50=28.8 sec.
ANSWER:A
Answer: A
Question: A sum amounts to Rs.4851 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
Options:
A)s.4000
B)s.5000
C)s.4400
D)s.4800
E)s.5800
Rationale: CI=4851,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
4851=P[21/20]^2
4851[20/21]^2
4400
ANSWER:C
Answer: C
Question: The sub-duplicate ratio of 16:36 is
Options:
A)4:6
B)1:2
C)1:3
D)1:4
E)2:3
Rationale: root(16):root(36)=4:6
ANSWER:A
Answer: A
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies?
Options:
A)50
B)48
C)54
D)55
E)60
Rationale: T = R
T - 20 ;R + 20
R + 20 = 5 ( T - 20 )
R + 20 =5T - 100
R - 5T = - 120
We knowR = T, so
R - 5T = - 120
Or, R - 5R = -120
Or, - 4R = - 120
Or, R = 30( This is the initital no of Candies Rebecca had)
Candles now she possesses is30+ 20 = 50
So , Rebecca now has 50 candies.
Answer will be (A) 50
Answer: A
Question: In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Options:
A)3 years
B)2 years
C)4 years
D)1 year
E)5 years
Rationale: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3
n = 3 years.
ANSWER A 3 years
Answer: A
Question: In given series 22, 33, 66, 99, 121, 279, 594 only one number is incorrect. Find out that wrong number
Options:
A)141
B)131
C)121
D)171
E)279
Rationale: Each of the number except 279 is a multiple of 11.
2 x 11=22
3 x 11=33
6 x 11=66
9 x 11=99
11 x 11=121
25 X 11= 275.... so 279 is wrong
54 x 11=594
ANSWER:E
Answer: E
Question: A committee is reviewing a total of 40x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?
Options:
A)20/11
B)16/11
C)17/11
D)10/11
E)19/11
Rationale: Say x=y=10. In this case we would have:
40x=200 black-and-white films;
4y=40 color films.
y/x%=10/10%=1% of the black-and-white films, so 4 black-and-white films and all 40 color films, thus total of 44 films were selected.
Color films thus compose 40/44=10/11 of the selected films.
Answer: D
Answer: D
Question: Car A is 16 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
Options:
A)1.5
B)2.0
C)2.5
D)3.0
E)3.5
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it'll need 24/8=3 hours.
Answer: D
Answer: D
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Options:
A)2
B)4
C)5
D)6
E)24
Rationale: C
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6. For re. 1.
Toffees sold = 6 * 5/6 = 5
Answer: C
Question: A certain list of 300 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d ?
Options:
A) 80 and 80
B) 85 and 85
C) 80 and 90
D) 85 and 80
E) 85 and 90
Rationale: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 85 and 85 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.
Answer: B
Answer: B
Question: If the price of a computer were reduced by 13 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
Options:
A)$844.10
B)$891.10
C)$1,051.90
D)$1,132.30
E)$1,259.60
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-16/100)------->X(67/77)=A(say)
means X=A*(77/67).....
so initial price to be integer(As per stem) final price must be multiple of 67
if we check options all were divisible by 67 except option (A)..which is Ans.
Ans A
Answer: A
Question: 19 people went to a hotel for combine dinner party 13 of them spent Rs. 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19. What was the total money spent by them.
Options:
A)1628.4
B)1534
C)1492
D)1496
E)None of these
Rationale: Solution: Let average expenditure of 19 people be x.
then,
19x = 13*79+6*(x+4);
Or, 19x = 13*79+6x+24;
Or, x = 80.84;
So, total money spent = 80.84*19 = Rs. 1536.07.
Answer: Option E
Answer: E
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, To gain 10%, at price he should sell?
Options:
A)Rs.400
B)Rs.450
C)Rs.550
D)Rs.600
E)Rs.650
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: C
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?
Options:
A)at 10:30 am
B)at 11:30 am
C)at 12:30 pm
D)at 1:30 pm
E)at 2:30 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (14-x)/20 = 1
5x + 14 - x = 20
4x = 6
x = 1.5
The answer is 10:30 am.
The answer is A.
Answer: A
Question: In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
4%*x = 20%*y
y/x = 1/5 = 20%
The answer is A.
Answer: A
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)17:9
B)17:76
C)17:9
D)17:2
E)17:3
Rationale: P:Q = 85000 : 15000 = 17:3.
Answer: E
Answer: E
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
Options:
A)20000
B)10000
C)25000
D)34000
E)30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: E
Question: A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ?
Options:
A)2.10 p.m on wednesday.
B)2.20 p.m on wednesday.
C)2.30 p.m on wednesday.
D)2.40 p.m on wednesday.
E)2.00 p.m on wednesday.
Rationale: Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours
\therefore The watch gains \inline \left ( 2+4\frac{4}{5} \right ) min. or \inline \frac{34}{5} min. in 170 hrs.
Now, \inline \frac{34}{5} min. are gained in 170 hrs.
\inline \therefore 2 min are gained in \inline \left ( 170\times \frac{5}{34}\times 2 \right ) hrs = 50 hrs
\inline \therefore Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at 2 p.m on wednesday.
Answer E
Answer: E
Question: A portion of the 85% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?
Options:
A)5/13
B)6/13
C)9/13
D)13/9
E)13/6
Rationale: Let the original amount of 85 percent solution = x and amount replaced be y
0.85(x - y)+ 0.2y = 0.4 x
0.85x -0.85y+0.2y = 0.4x
0.45x = 0.65y
9x = 13y
y = 9x/13
So, amount replaced = 9/13 of original amount
ANSWER:C
Answer: C
Question: Sujit incurred a loss of 45% on selling an article for Rs.3740/-. What was the cost price of the article?
Options:
A)Rs.5725/-
B)Rs.5080/-
C)Rs.6250/-
D)Rs.6750/-
E)None of these
Rationale: Explanation:
45% loss means SP of Rs.3740/- is 55% of CP
:. CP = 3740x100/55 = Rs.6800/-
Answer: Option E
Answer: E
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)8
B)9
C)12
D)16
E)18
Rationale: Explanation:
80% --- 12
120% --- ?
80/120 * 12 = 8
ANSWER IS A
Answer: A
Question: A can do a job in 18 days and B can do it in 24 days. A and B working together will finish twice the amount of work in days?
Options:
A)22 1/6
B)22 1/2
C)20 4/7
D)22 1/9
E)22 1/1
Rationale: 1/18 + 1/24 = 7/72
72/7 = 72/7 *2 = 20 4/7 days
Answer: C
Answer: C
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs 1920 less than the principal. What was the principal?
Options:
A)1500
B)2500
C)2507
D)3200
E)2400
Rationale: P - 1920 = (P*5*4)/100
P = 2400
Answer: E
Answer: E
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is:
Options:
A)22
B)50
C)99
D)35
E)12
Rationale: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: D
Answer: D
Question: 3/4th of a number exceeds its 2/3rd by 8. What is the number?
Options:
A)22
B)77
C)28
D)96
E)26
Rationale: Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 96
x = 96
ANSWER:D
Answer: D
Question: A and B start a business jointly. A invests Rs 16000 for 8 month and B remains in the business for 4 months. Out of total profit, B claims 2/7 of the profit . How much money was contributed by B?
Options:
A)12800
B)13000
C)11500
D)12500
E)12000
Rationale: B claims 2/7 of the profit
A claims remaining 5/7 of the profit
=> A : B =5/7:2/7=5:2
Let the money contributed by B =b
Then A:B =16000×8:b×4
Therefore,
16000×8:b×4=5:2
16000×8×2=b×4×5
16000×2×2=b×5
3200×2×2=b
b=12800
Answer is A.
Answer: A
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 502 to 600 inclusive?
Options:
A)23,550
B)27,550
C)31,550
D)35,550
E)39,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
502 + 504 + ... + 600 = 50(500) + (2+4+...+100) = 25,000 + 2550 = 27,550
The answer is B.
Answer: B
Question: 0.999999+0.111111=?
Options:
A)1
B)1.0001
C)1.0021
D)1.111
E)1.11111
Rationale: 0.999999 + 0.111111
= 0.999999 + 0.11111 + 0.000001
= (0.999999 + 0.000001) + 0.11111
= 1 + 0.11111
= 1.11111
E
Answer: E
Question: If a cyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent, what percent of the original speed is the total increase in speed?
Options:
A)10%
B)40%
C)43%
D)64%
E)140%
Rationale: let the sped be 100
an increase of 30%
the speed now is 130
a further increase of 10% on 130 =13
total increase =43 on 100 =43% C
Answer: C
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *5 + 3 and *5 + 5, inclusive?
Options:
A) None
B) One
C) Two
D) Three
E) Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *5 would be divisible by all numbers from 1 to 5.
=> *5+3 would give me a number which is a multiple of 3 and therefore divisible (since *5 is divisible by 3)
In fact adding anyprimenumber between 1 to 5 to *5 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *5 + 3 and *5 + 11 then the answer would be 1. For *5 +3 and *5 + 13, it is 2 and so on...
A
Answer: A
Question: If P and Q are positive integers, P - 2 is divisible by 4 and Q - 1 is divisible by 6, all of the following could be the value of P - Q Except?
Options:
A)3
B)1
C)15
D)4
E)29
Rationale: P-2 = 4Q
=> P = 4Q + 2 = 2,6,10,14,18,22,26,30,34,38,42,46,50
Q-1 = 6P
=> Q = 6P + 1 = 1,7,13,19,25,31,37,43,49,55,61,67,73
3=10-7
1=14-13
15=34-19
29=42-13
So , we can see that all the answer choices are possible here except D
Answer: D
Question: The length of a bridge in meters, which a train 120-meters long and traveling at 45 km/hr can cross in 30 seconds is?
Options:
A)255
B)285
C)315
D)345
E)375
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+120 = 375 meters
x = 255 meters
The answer is A.
Answer: A
Question: Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
Options:
A)2
B)3
C)4
D)5
E)7
Rationale: 2 + 3 + 5 + 7 + 11= 28 ( sum is even)
Least number = 2
A
Answer: A
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)30
C)35
D)45
E)50
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
Question: In a group of ducks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)10
B)12
C)13
D)15
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 36
=> 2x = 36 => x = 18
E
Answer: E
Question: Three coworkers P , T , R meet for Dinner. P had 5 sandwiches, T had 3 and R had none. Both PT share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PT, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
Options:
A)a) 5$
B)b) 3 $
C)c) 7 $
D)d) 4 $
E)e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
T:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: C
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
Options:
A)7/15
B)11/12
C)11/30
D)8/15
E)19/77
Rationale: 10/12 it is
8/15=(1/3) + (1/5)
Answer - D
Answer: D
Question: The average age of 6 persons living in a house is 23.5 years. Three of them are majors and their average age is 42 years. The difference in ages of the three minor children is same
Options:
A)6 years
B)5 years
C)3 years
D)8 years
E)9 years
Rationale: B
5 years
Total age of six persons = 23.5 × 6 = 141 years Total age of three major persons = 42 × 3 = 126 years
∴ Total age of three minor children = 141 – 126 = 15 years The difference in ages of the three minor children is same. Therefore, we take ages may be: 5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9 In all the cases, median will be 5 years
Mean age of minor children = 15/3 = 5 years
Answer: B
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)Rs.12829
B)Rs.12800
C)Rs.12293
D)Rs.12804
E)Rs.12830
Rationale: 16*8: x*4 = 5:2
x = 12.8 =>
Rs.12800
Answer: B
Answer: B
Question: Machine X takes 50 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
Options:
A)100
B)3.6
C)25
D)11
E)9
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 50
So, x = 50.
Hence 6x = 6*50 = 300 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/300
= 3.6
Hence option (B).
Answer: B
Question: A family with 1 mother, 1 father, and 4 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
Options:
A) 3
B) 4
C) 6
D) 8
E) 24
Rationale: Mother has a fixed place and father, so there are 4! ways to arrange the children, hence E
Answer: E
Question: The average salary of all the workers in a workshop is $8000. The average salary of 7 technicians is $12000 and the average salary of the rest is $6000. The total number of workers in the shop is?
Options:
A)15
B)18
C)21
D)25
E)31
Rationale: Let the total number of workers be x
8000x = 12000*7 + 6000(x-7)
x = 21
Answer is C
Answer: C
Question: Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9300, find the contribution made by David.
Options:
A)$540
B)$580
C)$600
D)$620
E)$650
Rationale: Given that A:(B+C+D)= 1:2.
Hence A contributed 1/3rd of the total price.
Given B:(A+C+D)=1:4
Hence B contributed 1/5th of the total price.
Given C:(A+B+D)=2:3
Hence C contributed 2/5th of the total price.
Thus the contribution made by A,B and C= 1/3+1/5+2/5=14/15
So, the remaining 1/15th of the price is contributed by David.
Hence David's contribution= 1/15×9300=$620.
The answer is D.
Answer: D
Question: The average weight of 8 person's increases by 1.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
Options:
A)81 kg
B)85 kg
C)90 kg
D)100 kg
E)110 kg
Rationale: Total weight increased = (8 x 1.5) kg = 6 kg.
Weight of new person = (75 +6) kg = 81 kg.
Answer : A
Answer: A
Question: What is the sum of all even numbers from 1 to 901?
Options:
A)122821
B)202950
C)281199
D)122850
E)128111
Rationale: Explanation:
900/2 = 450
450 * 451 = 202950
Answer: B
Answer: B
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1235
B)1456
C)1567
D)1624
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: if price of t.v set is reduced by 20%, then its sale increases by 80%, find net effect on sale value
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: - a + b + ((-a)(b)/100)
= -20+80+(-20*80)/100
= -20+80-16
=44
ANSWER:A
Answer: A
Question: 96% of the population of a village is 23040. The total population of the village is?
Options:
A)28882
B)28883
C)24000
D)29887
E)12991
Rationale: X * (96/100) = 23040
X = 240 * 100
X = 24000
Answer: C
Answer: C
Question: A woman sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)120
B)560
C)860
D)567
E)234
Rationale: Option C
Explanation:
CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: C
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Options:
A)273
B)800
C)277
D)251
E)121
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B:
Answer: B
Question: If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ?
Options:
A)4
B)7
C)5
D)3
E)6
Rationale: Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (5a + 4b) / (5a - 4b) = (5a/b + 4) / (5a/b - 4)
Since a/b = 6/5
this implies that
=[(5*6)/5 +4]/[(5*6)/5 -4)]
= (6 + 4) / (6 - 4)
= 5
Option: C
Answer: C
Question: Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 3 days?
Options:
A)24
B)18
C)16
D)12
E)8
Rationale: 4 machines do x units in 6 days
we have x/6 => rate of the 4 machines
we know that we need to have 2x units in 3 days
therefore, we need to get to 2x/3 rate of the machines.
rate of one machine is x/6*1/4 = x/24.
now, we need to know how many machines need to work simultaneously, to get 2x done in 3 days.
2x/3 work needs to be done by machines that work at x/24 rate.
let's assign a constant Y for the number of machines:
(x/24)*y = 2x/3
y = 2x/3 * 24/x
cancel 3 with 24, and x with x and get -> 16. Answer choice C
Answer: C
Question: If x > 7, which of the following is equal to (x^2 - 6x + 9)/(x^2 - 9) ?
Options:
A)(x + 4)/(4(x - 4))
B)(x - 4)/(x + 4)
C)(x - 3)/(x + 3)
D)(x + 4)/(x - 4)
E)(x - 8)/(x - 4)
Rationale: (x^2 - 6x + 9)/(x^2 - 9)
= (x - 3)(x - 3) / (x + 3)(x - 3)
=(x - 3)/(x + 3)
C. (x - 3)/(x + 3)
Answer: C
Question: Statement: Many people in city Y are suffering from flu.
Action:
I. The Municipal Corporation should take immediate steps to control the disease.
II. People in the city should be advised to take certain measures from their end to prevent the disease.
Options:
A)Only I follows
B)Only II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: Explanation: So here, both the options have a positive approach and objective of both the approaches is to treat and eradicate the disease.
ANSWER IS E
Answer: E
Question: At what price must an article costing Rs.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)69.44
B)62.0
C)62.6
D)62.1
E)62.2
Rationale: CP = 50
SP = 50*(125/100) = 62.50
MP*(90/100) = 62.50
MP = 69.44
Answer: A
Answer: A
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)350
B)289
C)208
D)270
E)287
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x
= 350m.
Answer: A
Answer: A
Question: What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?
Options:
A)814
B)266
C)287
D)999
E)661
Rationale: Explanation:
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile =
Required number of tiles = = 814
Answer: A) 814
Answer: A