divelab/Sys2Bench huggingface dataset:
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)100
B)110
C)120
D)125
E)130
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER C
Answer: C
Question: Joe drives 600 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
Options:
A)42
B)55
C)50
D)54
E)56
Rationale: t1= 600/60=10 hours
t2=120/40=3 hours
T=t1+t2=13 hours
Avg speed = Total Distance/T
= 720/13 = 55mph=B
Answer: B
Question: Two pipes A and B can fill a cistern in 12 and 20 minutes respectively, and a third pipe C can empty it in 30 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)15 min
B)13 min
C)12 min
D)10 min
E)17 min
Rationale: 1/12 + 1/20 - 1/30
= 1/10
10/1 = 10
Answer:D
Answer: D
Question: What number should replace the question mark?
24, 30, ?, 60, 84, 114
Options:
A)45
B)44
C)48
D)42
E)49
Rationale: D
42
The sequence progresses +6, +12, +18, +24, +30.
Answer: D
Question: 4 pipes can fill a reservoir in 15, 20, 30 and 60 hrs the first was opened at 6 am and 2nd at 7 am and thirds at 8 am and 4th at 9 am when will the reservoir be full?
Options:
A)6 hrs
B)7 hrs
C)8 hrs
D)9 hrs
E)10 hrs
Rationale: Explanation:
let time be t hrs after 6 am
t/15 + (t-1)/30 + (t-2)/30 + (t-3)/60 =1
t = 7 hrs
Answer: Option B
Answer: B
Question: A man took loan from a bank at the rate of 8% p.a. simple interest. After 4 years he had to pay $250 interest only for the period. The principal amount borrowed by him was:
Options:
A)$881.25
B)$781.25
C)$761.35
D)$661.25
E)$681.55
Rationale: Principal(P) = ?
Time(T) = 4 years
Simple Interest(SI) = $250
R = 8%
P = 100×SI / RT=100×250 / 8×4 = $781.25
ANSWER:B
Answer: B
Question: A train is approaching a tunnel which is AB in length.Ther is a cat inside the tunnel which is 3/8 distance from the starting point of the tunnel.When the train whistes the cat starts to run.The train catches the cat exactly at the entry point of the tunnel.If the cat runs towards the exit,the train catches tha cat exactly at the exit point.The speed of the train is greater than the speed of the cat in what order?
Options:
A)1:4
B)4:1
C)1:3
D)3:1
E)1:2
Rationale: D / v1 = (3/8) x / v2 ... ( 1 )
( D + x ) / v1 = (5/8) x / v2
=> D / v1 = (5/8) x / v2 - x / v1 ... ( 2 )
From equns. ( 1 ) and ( 2 ),
(3/8) x /v2 = (5/8) x / v2 - x / v1
=> 3 / (8v2) = 5 (8v2) - 1/ v1
=> 1 / v1 = ( 5/8 - 3/8) / v2
=> 4v2 = v1
ANSWER:B
Answer: B
Question: If M and N are positive integers that have remainders of 2 and 3, respectively, when divided by 5, which of the following could NOT be a possible value of M+N?
Options:
A)80
B)52
C)35
D)25
E)10
Rationale: M=5p+2
N=5q+3
We need M+N=5p+2+5q+3=5(p+q)+5
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 5 so
p+q=0 ; M+n = 5
p+q=1 ; M+N = 10
P+q=2 ; M+N = 15
and so on, so basically you get something like - 5,,10,15,20,25,30,..... all are multiples of 5 except 52
So Answer B.
Answer: B
Question: What are the last two digits of 63*35*37*82?
Options:
A) 10
B) 30
C) 40
D) 70
E) 80
Rationale: We know that to find the last two digits, we need to find the remainder we get when we divide the product by 100.
Remainder of (63*35*37*82*71*41)/ 100
Note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator. But before we do that, here is an important note:
Note: We cannot just cancel off the common terms in the numerator and denominator to get the remainder. But, if we want to cancel off to simplify the question, we can do it, provided we remember to multiply it back again.
So say, we want to find the remainder when 14 is divided by 10 i.e. 14/10 (remainder 4). But we cancel off the common 2 to get 7/5. The remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10. But if we multiply 2 back by 2 (the number we canceled off), the remainder will become 2*2 = 4 which is correct.
Take another example to reinforce this – what is the remainder when 85 is divided by 20? It is 5.
We might rephrase it as – what is the remainder when 17 is divided by 4 (cancel off 5 from the numerator and the denominator). The remainder in this case is 1. We multiply the 5 back to 1 to get the remainder as 5 which is correct.
So keeping this very important point in mind, let’s go ahead and cancel the common 5 and 2.
We need the
Remainder of (63*7*37*41*71*41*5*2)/10*5*2
Remainder of (63*7*37*41*71*41)/10
Now using concept 2, let’s write the numbers in form of multiples of 10
Remainder of (60+3)*7*(30+7)*(40+1)*(70+1)*(40+1)/10
Remainder of 3*7*7*1*1*1/10
Remainder of 147/10 = 7
Now remember, we had canceled off 10 so to get the actual remainder so we need to multiply by 10: 7*10 = 70.
When 63*35*37*82*71*41 is divided by 100, the remainder is 70. So the last two digits of 63*35*37*82*71*41 must be 30.
Answer (B)
Answer: B
Question: Samantha is driving from City A to City B. The distance between the two cities is 88 miles. She is driving at a constant speed of 22 miles per hour, and has been travelling for half an hour after starting from City A. What percent of the total distance she is yet to cover?
Options:
A)87
B)87.5
C)88
D)90
E)97.5
Rationale: She is driving at the rate of 22 miles per hour for half an hour.
Means the distance she has covered so far is = speed x time = 22 miles per hour x 0.5 hour = 11 miles.
Therefore, the distance she is yet to cover is 88 - 11 = 77 miles.
We want to know 77 miles is what percent of the total distance (88 miles). Let it be x % of the total distance.
This means x % of 88 = 77
Solving we get, x = 87.5
Ans B
Answer: B
Question: Laura took out a charge account at the General Store and agreed to pay 8% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
Options:
A)$2.10
B)$37.10
C)$37.16
D)$37.8
E)$38.80
Rationale: Principal that is amount taken by Laura at year beginning = 35$
Rate of interest = 8%
Interest = (8/100)*35 = 2.8$
Total amount that Laura owes a year later = 35+2.8 = 37.8 $
Answer D
Answer: D
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
Options:
A)897
B)164,850
C)164,749
D)149,700
E)156,720
Rationale: Explanatory Answer
Step 1: Identify the series
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
It is evident that any number in the sequence will be a 3 digit positive integer of the form (3n + 2).
So, the given numbers are in an Arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3.
Step 2: Compute the sum
Sum of an Arithmetic Progression (AP) = [first term + last term/2]n
We know the first term: 101
We know the last term: 998.
The only unknown is the number of terms, n.
In an A.P., the nth term an = a1 + (n - 1)*d
In this case, therefore, 998 = 101 + (n - 1)* 3
Or 897 = (n - 1) * 3
(n - 1) = 299 or n = 300.
Sum of the AP will therefore, be [101+998/2]∗300 = 164,850
Choice B is the correct answer.
Answer: B
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, 17, (....)
Options:
A)27
B)20
C)22
D)24
E)26
Rationale: There are two series (8, 11, 14, 17) and (7, 12, 17, 22) increasing by 3 and 5 respectively.
answer : C
Answer: C
Question: Car E and Car Y traveled the same 80-mile route. If Car E took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car E, how many hours did it take Car Y to travel the route?
Options:
A) 2/3
B) 1
C) 4/3
D) 8/5
E) 3
Rationale: The speed of car E is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: C
Question: What is the product of all the prime factors of 22?
Options:
A)18
B)9
C)22
D)6
E)3
Rationale: 22 , factors are 2,11,1. Now again prime Numbers are Only Two i.e 2 and 11 , this time we would have 2*11=22
Answer : C
Answer: C
Question: One type of liquid contains 25% of Kerosene, the other contains 30% of Kerosene. P can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of the Kerosene in the new mixture.
Options:
A)28%
B)25%
C)30%
D)27 %
E)35%
Rationale: Let P be filled by 60 lts of 1st liquid and 40 lts. of 2nd liquid.
amount of kerosene = (25*60/100) + (30*40/100) = 27 lts.
% of kerosene = 27 %
ANSWER:D
Answer: D
Question: What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9. I.The number is multiple of 51. II.The sum of the digits a and b is 6.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: Explanation:
From statement I:
A two digit number, greater than 9 and multiple of 51 should be 51 itself.
Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.
From statement II:
A two digit number, greater than 9 and sum of the digit is 6.
It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.
Thus, I alone give the answer while II alone not sufficient to answer.
Option A
Answer: A
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
Options:
A)2/9
B)2/2
C)2/5
D)2/1
E)2/7
Rationale: Explanation:
A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
Answer: C
Answer: C
Question: A candidate who gets 20% of the marks fails by 40 marks. But another candidate who gets 30% marks gets 20 marks more than necessary for passing. Find the number of marks for passing?
Options:
A)160 Marks
B)200 Marks
C)280 Marks
D)371 Marks
E)827 Marks
Rationale: 20% ------------ 40
30% ------------ 20
----------------------
10% ------------- 60
20% -------------- ?
120 + 40 = 160 Marks
Answer:A
Answer: A
Question: Given positive even integer y, which of the following CANNOT be evenly divisible by y?
Options:
A)y + 2
B)y + 8
C)2y + 4
D)3y − 1
E)2y - 2
Rationale: This can be easily solved by substituting values:
Assume y to be 2
A. y + 2: 4 is evenly divisible by 2
B. y + 8: 10 is evenly divisible by 2
C. 2y + 4: 8 is evenly divisible by 2
D. 3y − 1: 5 is not evenly divisible by 2
E. 2y + 2: 2 is evenly divisible by 2
Option D
Answer: D
Question: The probability of Sam passing the exam is 1/4. The probability of Sam passing the exam and Michael passing the driving test is 1/3. What is the probability of Michael passing his driving test?
Options:
A)1/24.
B)1/2.
C)1/3.
D)2/3.
E)2/5
Rationale: 1/3 *1/m= 1/6 , 1/m = 1/2
Answer B
Answer: B
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 30 degrees?
Options:
A)π
B)3π/2
C)2π/3
D)5π/2
E)8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 30 degrees. 30/360 = 1/12.
Therefore length of arc = 1/12 * 8π = 2π/3 - Answer choice C.
Answer: C
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?
Options:
A)150
B)140
C)160
D)170
E)180
Rationale: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 – 65x/100 = 21
5 x = 2100
x = 140.
so the answer is option B) 140.
Answer: B
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 340 m long platform?
Options:
A)37 min
B)46 min
C)47 min
D)67 min
E)45 min
Rationale: B
46 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +340)/ 36 * 5/18 = 46 min.
Answer: B
Question: The average age of applicants for a new job is 31, with a standard deviation of 9. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Options:
A)8
B)14
C)15
D)18
E)19
Rationale: within one standard deviation of the average age means 31 +/- 7
24--31--38
number of dif.ages -22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
total=19
E
Answer: E
Question: A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)17 km/hr
C)18 km/hr
D)19 km/hr
E)20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 30sec=150sec
Speed=750/150=5m/sec
=>5∗18/5km/hr=18km/hr
Option C
Answer: C
Question: In the Clock Game, part of the game show The Price Is Right, a contestant must
guess the price (rounded to the nearest dollar) of a prize which is worth less than $2,000. After
each guess, the contestant is told whether her guess was correct, too low, or too high. Assume
that the contestant is mathematically savvy but has no idea how much the prize is worth.
With how many guesses is she guaranteed to win the prize?
Options:
A)10
B)11
C)12
D)13
E)1997
Rationale: At each stage, the contestant has narrowed the range of possible prices to an interval,
and she should guess exactly in the middle this interval. For example, for the first guess she
should guess either $1,000 or $1,001. (On the actual show, your time is limited rather than
the number of guesses, so you should start with $1,000 because it is quicker to say.)
At every step the contestant can at least halve the number of remaining possibilities.
Suppose that the interval has n possible prices and that the contestant's guess does not win
immediately. If n is odd there will be n􀀀1
2 prices on either side of her guess, and she will be
told which of these contains the correct price. If n is even then there will be n
2 prices on one
side n
2 *1 prices on the other, and we assume the worst case of n
2 .
Since 210 = 1024 and 2000
1024 < 2, after ten guesses she will be down to one remaining
possibility, which she guesses with her eleventh guess.
Conversely, ten guesses is not enough. After each the remaining number of possibilities
could be as high as: 1000,500,250,125,62,31,15,7,3. She is guaranteed only a 1-in-3 shot in
the tenth guess.
correct answer B
Answer: B
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 1 : 5 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)Rs. 500
B)Rs. 1000
C)Rs. 1500
D)Rs. 2000
E)NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. x, Rs. 5x and Rs. 3x respectively.
Then, 5x - 3x = 1000 ⇔ 2x = 1000 ⇔ x = 500.
∴ B's share = Rs. x= Rs. 500.
Answer A
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A. 20% B. 45%
Options:
A)77
B)66
C)44
D)99
E)11
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer:C
Answer: C
Question: John invested some money at the rate of 6% p.a. for the first three years, 9% p.a.for the next five years and 9% p.a.for the period beyond eight years. How much interest will he get after eleven years if he invested Rs 10000?
Options:
A)8,000
B)9,900
C)12,000
D)7,000
E)None of these
Rationale: Let the interest be i. Then,
(10000×3×6/100)+(10000×5×9/100)+(10000×3×12/100)=i
⇒ 1800 + 4500 + 3600 = i
⇒ i = 9900
Answer B
Answer: B
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3e/y is a prime integer greater than 2, which of the following must be true?
I. e = y
II. y = 1
III. e and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and III
Rationale: 3e/y and if e=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Answer: A
Question: A started a business with an investment of Rs. 10000 and after 7 months B joined him investing Rs. 12000. If the profit at the end of a year is Rs. 24000, then the share of B is?
Options:
A)10000
B)8000
C)12000
D)6000
E)14000
Rationale: Ratio of investments of A and B is (10000 * 12) : (12000 * 5) = 2 : 1
Total profit = Rs. 24000
Share of B = 1/3 (24000) = Rs. 8000
Answer: B
Answer: B
Question: A man walking at a constant rate of 12 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 24 miles per hour. The woman stops to wait for the man 10 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up?
Options:
A)13
B)10
C)15
D)11
E)9
Rationale: When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 10*24/60 =4 miles and the man walks the distance mM, which is 10*12/60 = 2 mile.
The difference of 4 - 2 = 2 miles (MW) will be covered by the man in (2)/9 = 2/9 of an hour, which is ~13 minutes.
Answer A.
Answer: A
Question: The sum of first five prime numbers is?
Options:
A)12
B)28
C)56
D)24
E)22
Rationale: Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
B
Answer: B
Question: If 8^x = 2^9, what is x?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 2^3x= 2^9
3x=9, therefore x=3
Answer B
Answer: B
Question: In what ratio must rice of Rs.16 per kg be mixed with rice of Rs.24 per kg so that cost of mixture is Rs.18 per kg?
Options:
A)4:1
B)2:1
C)3:1
D)4:3
E)4:5
Rationale: (18-24)/(16-18)=6/2=3:1
ANSWER:C
Answer: C
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.9
C)1.1
D)1.5
E)1.2
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: D
Question: The total car population in a Mumbai is 2,90,000 out of which 1,50,000 are made by Honda. Out of every 100 Honda cars, 90 are red in color, but only 60% of the total car population is red. Find the % of non-Honda cars that are red
Options:
A)5.24%
B)5.35%
C)6.125%
D)27.86%
E)8%
Rationale: Total Honda brand red cars = 90/100 *150000 = 135000
Total red cars = 60/100*290000 = 174000
No. of Non-Honda cars = 290000-150000 = 140000
No. of Non-Honda red cars = 174000 - 135000 = 39000
% of Non-Honda red cars = 39000/140000*100 = 27.86%
Answer : D
Answer: D
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.6
B)1.5
C)1.3
D)1.1
E)1.2
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:B
Answer: B
Question: How many numbers between 200 and 500 begin or end with 3?
Options:
A)20
B)60
C)100
D)110
E)120
Rationale: How many numbers between 200 and 500 begin or end with 3?
Just think that those numbers are:
i) The ones ending in 3: 203, 213, 223, ... , 493 --> 30 numbers
ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers
BUT 10 out of the first 30 numbers are repeated in the second set.
THEREFORE, the solution is 120 numbers.
Answer: E
Answer: E
Question: A certain computer manufacturing firm last year produced 82 percent of its computers using parts made by its subsidiary company. If the remaining 10,818 computers were produced using parts purchased from another parts manufacturer, how many computers were produced by the computer manufacturing firm altogether?
Options:
A)60000
B)60100
C)70000
D)75000
E)65000
Rationale: 82% parts used of subsidary company, so 18% parts used of other companies.
Now, 18% parts = 10,818 computers
So, 1% parts = 10,818/18
Or, 100% parts = 60,100 computers.
Hence answer is (B)
Answer: B
Question: A man's speed with the current is 25 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?
Options:
A)10
B)80
C)50
D)30
E)20
Rationale: Man's speed with the current = 25 km/hr
=> speed of the man + speed of the current = 25 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 25 - 2.5 = 22.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 22.5 - 2.5 = 20 km/hr
Answer is E.
Answer: E
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
Options:
A)kmph
B)kmph
C)kmph
D)kmph
E)kmph
Rationale: Speed downstream = 60 + 30 = 90 kmph
Speed upstream = 60 - 30 = 30 kmph
Answer:D
Answer: D
Question: Can you find the smallest non fractional number such that
If the number gets divided by 9 , we get the remainder of 1;
If the number gets divided by 10 , we get the remainder of 2
If the number gets divided by 11 , we get the remainder of 3;
If the number gets divided by 12 , we get the remainder of 4.
Options:
A)1450
B)1300
C)1205
D)2501
E)1978
Rationale: E.option E
As we know LCM of the numbers 9 10 11 & 12 is 1980.
So if i divide 1980 by any of the four number , it gives remainder as 0.
Now to get reminder as desired, is should be 2 short of 1978. (3-1,4-2,5-3,6-4 )
Ans:option E
Answer: E
Question: The sum of present age of Abe and the age before 7 years is 35. Find the present age of Abe. What will be his age after 7 years?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Present age = x
Before 7yrs, y=x-7
After 7yrs, z=x+7
By the qn,
x+(x-7)=35
2x-7=35
2x=35+7
x=42/2
x=21
z=x+7
=21+7
=28
ANSWER:D
Answer: D
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 5 characters in length. This year, it added the option of creating passwords having 6 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 62 unique alphanumeric case sensitive characters.
Options:
A)63^4
B)62^5
C)62(62^4)
D)63(62^5)
E)63(62^6)
Rationale: Total number of passwords = number of 5 character password +number of 6 character password
= 62^5 + 62^6 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=62^5(1+ 62)
=62^5 * 63
Answer D
Answer: D
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
Options:
A)77.9 litres
B)72.9 litres
C)72.8 litres
D)62.9 litres
E)72.5 litres
Rationale: Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Answer: B
Answer: B