divelab/Sys2Bench huggingface dataset:
Question: Palindromes are words or phrases that read the same in both directions, e.g. EYE
Now consider the word LEVEL, such a word is known as palindromes.
Find the maximum possible number of five letter palindromes.
Options:
A)17515
B)17566
C)17576
D)None
E)Cannot be determined
Rationale: Explanation :
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26*26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676*26=17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer : C
Answer: C
Question: -2, 5, 24, 61, ?
Options:
A)228
B)278
C)299
D)122
E)271
Rationale: ANSWER: D
Answer: D
Question: what is the next term of this series6,10,9,15,12,20,15,25...?
Options:
A)9
B)10
C)11
D)12
E)18
Rationale: 3&2=6;
5*2=10;
3*3=9
3*5=15
3*4=12
5*4=20
3*5=15
5*5=25
3*6=18
ANSWER:E
Answer: E
Question: Helen went to the stationers and bought things worth Euro 22, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)uro 19.70
B)uro 15.70
C)uro 13.70
D)uro 18.70
E)uro 16.70
Rationale: E
Euro 16.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [22 - (5 + 0.30)] = Euro 16.70
Answer: E
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
Options:
A)140
B)120
C)125
D)130
E)190
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
ANSWER A
Answer: A
Question: What is the are of an equilateral triangle of side 16 cm?
Options:
A)64√8 cm2
B)64√1 cm2
C)68√3 cm2
D)64√3 cm2
E)24√3 cm2
Rationale: Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
Answer: D
Question: A marketing company devised a methodology of spreading its message through one another. One person can tell it to 3 persons in 4 minutes and these three persons tell the other three persons each in further 4 minutes and the process continues so on. How many minutes will it take to spread the message to 2187 persons.
Options:
A)48 minutes
B)24 minutes
C)32 minutes
D)28 minutes
E)29 minutes
Rationale: according to the given condition 3^1 + 3^2 + 3^3 + ........ = 2187
or 3(3^x - 1)/(3-1) = 2187
or 3(3^x - 1)/2 = 2187
or 3^x - 1 = 2187*2/3 = 4374/3 = 1458
or 3^x = 1459 so x = 6 to 7
so total time taken = (6to7)*4 = 24 to 28 min
but if we take only the last step persons then 3^x = 2187 so x = 7
so time = 7*4 = 28 min
ANSWER:D
Answer: D
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 7000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
Options:
A)100000
B)100500
C)147000
D)Data inadequate
E)None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 7000) From the question,
(x - 7000) × 126⁄100 = 6⁄5x ⇒ x = 147000
Answer C
Answer: C
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
Options:
A)13
B)15
C)17
D)19
E)21
Rationale: A. 13 (cannot be weighed)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 11(can be weighed by keeping weights of 10 and 1 kg)
E. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
A
Answer: A
Question: The average monthly salary of 10 employees in an organisation is Rs. 1600. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
Options:
A)Rs.3601
B)Rs.3618
C)Rs.2700
D)Rs.3619
E)Rs.3610
Rationale: Manager's monthly salary
= Rs. (1700 * 11 - 1600 * 10)
= Rs. 2700 Answer:C
Answer: C
Question: The angle between the minute hand and the hour hand of a clock when the time is 10.30, is
Options:
A)35°
B)65°
C)45°
D)135°
E)95°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 10, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(10−30/5)+30/2
=30(10−6)+15
=30×4+15 =135°
Answer is D.
Answer: D
Question: When x is multiplied by 3, the result is 26 more than the result of subtracting x from 26. What is the value of x?
Options:
A)-4
B)-2
C)11
D)13
E)22
Rationale: The equation that can be formed is:
3x-26=26-x
or, 4x=52
or, x=13.
D answer.
Answer: D
Question: All the following EXCEPT one are correct values for a in the equation: a = x/5 + y/5^2 + z/4^3, where x, y, and z are each equal to 1 or 0.
Options:
A)15/32
B)7/64
C)13/32
D)1/64
E)5/32
Rationale: a = x/5 + y/5^2 + z/4^3
= x/5 + y/25 + z/64
= (25x + 5y + z ) /64
Depending on whether x, y and z take 0 or 1.
Answer E
Answer: E
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
Options:
A)20,20
B)20,10
C)25,15
D)30,10
E)None of these
Rationale: Explanation:
Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Option D
Answer: D
Question: The Brookfield girl scouts sold 90 boxes of cookies on their first day which averaged 30% more than the other local area teams. Increasing their effort, by the end of the second day their sales increased their average to be 50% more than the other teams. How many boxes of cookies must the girls have out sold by to have attained this average?
Options:
A)12
B)50
C)20
D)36
E)15
Rationale: Explanation: First, set the information into algebraic phrases, set that information into an equation, then solve.
Number of boxes sold the first day @ 30% more: 30% * 90=27
Increasing their effort on the second day average increased to 50%. (Let x represent the unknown amount of additional cookies sold to solve the equation.) Therefore, the total boxes sold by the girls is 90+x, and the total number of boxes increased in 27+x. This gives the equation as: 50%*(90+x)=27+x
Solve: Let's get rid of the percent sign
50/100*(90+x)=27+x
1/2 *(90+x)=27+x
Get rid of the fraction:
2[1/2 * (90+x)]=2(27+x)
1 * (90+x) =54+2x
90+x =54+2x
(90-54)+x = (54-54)+2x
36+x/x = 2x/x
36 = x
Answer: D
Answer: D
Question: In a class of 25 students in an examination in maths 5 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
Options:
A)A)47
B)B)45.6
C)C)44
D)D)48
E)E)49.6
Rationale: Explanation:
Total marks obtained by a class of 25 students
= 5*95 + 3*0 + 17 * 45 =1240
Average marks of whole class = 1240/25 =49.6
Answer: Option E
Answer: E
Question: If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per person. If there were 4 other contributions made before john's, what is the size of his donation?
Options:
A)$100
B)$175
C)$200
D)$250
E)$450
Rationale: Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John.
If he needs to increase the average contribution by $25, he must put in $25 for each of the 4 people.
so $100.
But, he also has to put in the average for himself (the fiveth person), so add $75.
So $175 is your answer.
Answer B
Answer: B
Question: If the length of the longest chord of a certain circle is 14, what is the radius of that certain circle?
Options:
A)2.5
B)5
C)10
D)7
E)9
Rationale: Longest chord of a circle is the diameter of the circle
diameter = 2 * radius
If diameter of the circle is given as 14 = 2 * 7
so radius of the circle = 7
correct answer - D
Answer: D
Question: 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is :
Options:
A)62 *2/0
B)62 *2/3
C)62 *2/6
D)62 *2/2
E)62 *2/1
Rationale: Explanation:
Total number of students = 1100 + 700 = 1800.
Number of students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.
Number of failues = 1800-672 = 1128.
Percentage failure = (1128/1800 * 100 )% = 62 * 2/3 %.
Answer: B) 62 *2/3
Answer: B
Question: A clock is set at 5 am. If the clock loses 16 minutes in 24 hours, what will be the true time when the clock indicates 10 pm on 4th day?
Options:
A)7 pm
B)8 pm
C)12 pm
D)11 pm
E)10 pm
Rationale: Time from 5 am to 10 pm on the 4th day
= 3 days 17 hours
= 3 Ã— 24 + 17
= 89 hours.
Given that clock loses 16 minutes in 24 hours.
=> 23 hour 44 minutes of the given clock = 24 hours in a correct clock
23 44/60 hours of the given clock = 24 hours in a correct clock
=> 23 11/15 hours of the given clock = 24 hours in a correct clock
=> 356/15 hours of the given clock = 24 hours in a correct clock
89 hours of the given clock =24Ã—15/356Ã—89 hours in a correct clock
24Ã—15/4= 6Ã—15= 90 hours in a correct clock.
So the correct time is 90 hours after 5 am
= 3 days 18 hours after 5 am
= 11 pm on the 4th day.
Answer: D
Answer: D
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
Options:
A)Rs.1529
B)Rs.1510
C)Rs.1500
D)Rs.1329
E)Rs.1181
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer:C
Answer: C
Question: The speed of a train is 90 kmph. What is the distance covered by it in 5 minutes?
Options:
A)7.5
B)66
C)77
D)52
E)42
Rationale: 90 * 5/60 = 7.5 kmph
Answer:A
Answer: A
Question: Mangala completes a piece of work in 60 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)12 days
C)14 days
D)16 days
E)24 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 60 × 40/100 = 24 days
E
Answer: E
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)50
B)88
C)77
D)55
E)23
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
Options:
A)2:3
B)4:3
C)6:7
D)9:16
E)5:2
Rationale: Answer: Option B
Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš16 : âˆš9 = 4:3
Answer: B
Question: How many different pairs of numbers (s, t) such that s = 3t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: s = 3t.
So, s/3 = t
That means s is divisible by 3.
Only 0, 3, 6, 9 are divisible by 3.
Hence option (D).
Answer: D
Question: The division of a whole number N by 13 gives a quotient of 34 and a remainder of 2. Find N.
Options:
A)797
B)197
C)597
D)412
E)444
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 34* 13 + 2 = 444 correc answer E
Answer: E
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/100 that a person who randomly guesses the answer to each question will be a winner?
Options:
A)5
B)10
C)50
D)100
E)1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/100
n = 50 satisfies this.
C
Answer: C
Question: 5000 - 4500 ÷ 10.00 = ?
Options:
A)4550
B)5000
C)0.5
D)4000
E)None
Rationale: Answer
Given expression =5000 - 4500 ÷ 10.00
= 5000 - 450
= 4550
Correct Option: A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Options:
A)5/6
B)5/9
C)5/3
D)5/0
E)5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: B
Question: Find the no.of ways of arranging the boy and 6 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)3!
B)6!
C)7!
D)9!
E)11!
Rationale: Ans.(B)
Sol. Total number of persons = 7 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 6 places in 6P6 = 6! Ways ... The number of required arrangements = 6! x 1= 6! = 6! ways
Answer: B
Question: one machine 10 hours to complete a production order and another machine 20 hours to complete the same order. How many hours would it take both machines working simultaneously at their respective rates to complete the order?
Options:
A)12/7hrs
B)20/3hrs
C)15/6hrs
D)8/9hrs
E)15/2hrs
Rationale: Machine A = 10 hours to complete an order
Machine B = 20hours to complete the same order
We're asked how long it would take the two machines, WORKING TOGETHER, to complete the order.
Using the Work Formula: (A)(B)/(A+B).....
(10)(20)/(10+20) = 20/3 hours to complete the job; Answer is B
Answer: B
Question: What is the greatest integer m for which the number 50!/10^m is an integer?
Options:
A)5
B)8
C)10
D)11
E)12
Rationale: As for 50!/10^m, the greatest value of m will be obtained by finding the maximum number of 5s in 50!
The quick process for that (discussed in the link above) is
50/5 = 10
10/5 = 2
Total number of 5s is 12. So maximum value of m will also be 12.
Answer (E)
Answer: E
Question: If f(x) = 2x^2 + y, and f(2) = 20, what is the value of f(5)?
Options:
A)104
B)60
C)62
D)50
E)25
Rationale: f(x) = 2x^2 + y
f(2) = 20
=> 2*(2)^2 + y = 20
=> 8 + y = 20
=> y = 12
f(5)= 2*(5)^2 + 12
= 62
Answer C
Answer: C
Question: John makes $30 a week from his job. He earns a raise and now makes $40 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)18%
D)21%
E)33.33%
Rationale: Increase = (10/30)*100 = 33.33%.
E
Answer: E
Question: If a and b are positive integers and (5^a)^b = 5^2, what is the value of 2^a*2^b?
Options:
A)3125
B)625
C)5
D)25
E)125
Rationale: 5^ab =5^2 therefore ab=2 either a=1 or 2 or b=2 or 1
therefore 5^a* 5^b = 5^(a+b)= 5^3 =125
E
Answer: E
Question: A motor car starts with a speed of 70km/hr with its speed increasing every 2hours by 10kmph. In how many hours will it cover 345kms?
Options:
A)3hours
B)2hours 30mnts
C)4hours
D)4hours 30mnts
E)5hours
Rationale: Distance covered in first 2hours = 70*2 = 140km
Distance covered in next 2hours = 80*2 = 160km
remaining distance = 345- (140+160) = 45km
speed in the fifth hour = 90km/hr
total time to cover 45km = 45/90 = 1/2 hr
total time taken = 4+(1/2) = 4hours 30minutes.
correct option is D
Answer: D
Question: How many positive integers less than 256 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)31
C)42
D)43
E)64
Rationale: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice D is correct here.
Answer: D
Question: A runs 1 ¾ times as fast as B. if A gives B a start of 84 m, bow far must
winning post be so that A and B might reach it at the same time?
Options:
A)196 m
B)194 m
C)186 m
D)296 m
E)106 m
Rationale: . Ratio of the rates of A and B = 7/4 : 1 = 7 : 4.
So, in a race of 7 m, A gains 3m over B.
:. 3 m are gained by A in a race of 7 m.
:. 84 m are gained by A in a race of (7/3 x 84) m = 196 m.
:. Winning post must be 196 m away from the starting point.
Answer is A.
Answer: A
Question: |x+3| – |4-x| = |7+x| How many solutions will this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, số x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, số ít becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) =1
C
Answer: C
Question: In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability W this college graduate has a graduate degree?
Options:
A)1/11
B)1/12
C)1/13
D)3/19
E)3/43
Rationale: In believe the answer is D. Please see below for explanation.
0) we are told the following ratios
CGD - College Graduate with Degree
NCG - Non College Graduate
CGN - College Graduate no Degree
CGD NCG CGN
1 8
3 2
In order to make CGD and CGN comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get
CGD NCG CGN
3 24 16
If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?
Nr of CGD = 3
Nr of CG = 3+ 16 = 19
Probability W of CGD / (CG) -> 3/19
Answer D
Answer: D
Question: Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)2500
B)2550
C)5050
D)6275
E)11325
Rationale: Set A contains 2,4 , 6 ... 50
Set B contains 102 , 104 , 106 ... 150
Number of terms in each set = 25
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*25 = 2500
Answer A
Answer: A
Question: Aarti can do a piece of work in 8 days. In how many days will she complete three time of work of same type?
Options:
A)6 days
B)19 days
C)24 days
D)3 days
E)13 days
Rationale: We have the important relation, More work, More time (days)
A piece of work can be done in 8 days.
Three times of work of same type can be done in 8 x 3
= 24 days
Answer C
Answer: C
Question: There were 9 lottery ticket winners for payout of 4 million dollars. If the all winners get the same amount and none of them have bills smaller than $1, how much money would they have to pay?
Options:
A)4,000,000
B)4,000,001
C)4,000,005
D)4,000,008
E)4,000,010
Rationale: Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 4,000,000 = 4 and 9 is divisible by 9.
Hence, we need to add 5 to this number for it to be divisible by 9
Correct Option : C
Answer: C
Question: A salesperson receives a base salary of $700 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
Options:
A)$1,500
B)$1,800
C)$2,100
D)$2,500
E)$2,800
Rationale: Ans : 700+ 7.5 % * 150 * (210-50) = $ 2500
Answer D
Answer: D
Question: Of the 120 passengers on Flight 750, 30% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?
Options:
A)44
B)28
C)50
D)52
E)56
Rationale: Number of passengers on flight = 120
Number of female passengers= .3*120 = 36
Number of passengers in first class = (10/100)* 120 = 12
Number of passengers in coach class = (90/100)* 120 = 108
Number of male passengers in first class = 1/3 * 12 = 4
Number of female passengers in first class = 12-4 = 8
Number of female passengers in coach class = 36 - 8 = 28
Answer B
Answer: B
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 35 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Options:
A)30%
B)40%
C)50%
D)60%
E)70%
Rationale: Expensive item = $100;
Cheap item = $ 65;
We must increase $65 to $100, so by $35, which is approximately 50% increase: (100-65)/65 = ~0.53.
Answer: C.
Answer: C
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <3>*<1>?
Options:
A) 60
B) 116
C) 63
D) 263
E) 478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <3> is the sum of all integers from 1 to 2*3=6 and <1> is the sum of all integers from 1 to 2*1=2 --> <3>=21 and <2>=3 --> <3>*<2>=21*3=63
Answer: C.
Answer: C
Question: A pump can fill a tank with water in 5 hours. Because of a leak, it took 10 hours to fill the tank. The leak can drain all the water in ?
Options:
A)12hr
B)11hr
C)13hr
D)10hr
E)16hr
Rationale: Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10
Leak will empty the tank in 10 hours
Answer is D
Answer: D
Question: College T has 1000 students. Of the 260 students majoring in one or more of the sciences,160 are majoring in Chemistry and 120 are majoring in Biology. If at least 50 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
Options:
A)60 to 110
B)70 to 130
C)80 to 130
D)70 to 120
E)80 to 120
Rationale: Total = Chemistry + Biology - Both + Neither
260 = 160 + 120 - Both + N
We know that N (Neither) must be at least 30, so set N=30 and solve:
260 = 160 + 120 - Both + 50
260 = 330 - Both
Both = 70
Even if you're not sure whether 70 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,
Both can not be greater than 120, because even if every biology major was also a chemistry major, there are only 120 biology majors total. D the solution.
Answer: D