divelab/Sys2Bench huggingface dataset:
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 180 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)1440
B)960
C)576
D)192
E)480
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =180 => 16x = 1440 (2) 3x =180 => 16x = 960 (3) 5x =180 => 16x = 576 (4) 6x =180 => 16x = 480
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: If the 1st of the month occurs on a Monday, on which day of the week does the 19th occur?
Options:
A)Friday
B)Saturday
C)Sunday
D)Monday
E)Tuesday
Rationale: Each weekday is repeated every 7 days. The 19th of the month is 18 days after the 1st. 18 divided by 7 is 2, with a remainder of 4. Therefore, the 19th occurs on whichever day of the week is four days after the day we started on, meaning it is a Friday. Answer: A
Answer: A
Question: A alone would take 8 days more to complete the job than if both A and B would together. If B worked alone, he took 4 1⁄2 days more to complete the job than A and B worked together. What time would they take if both A and B worked together?
Options:
A)7 days
B)5 days
C)4 days
D)6 days
E)None of these
Rationale: Let if both A and B work together, they take x days.
∴ (A + B)’s 1 days’s work = 1⁄x th work
A’s 1 day’s work = 1⁄(x + 8) th work.
B’s 1 day’s work = 1⁄(x + 9/2) th work.
Now, 1/x+8 + 2/2x+9==1/x
⇒ x(2x + 9 + 2x + 16) = (x + 8)(2x + 9)
⇒ 4x2 + 25x = 2x2 + 25x + 72
⇒ x2 = 36 ⇒ x = 6 days
Answer D
Answer: D
Question: In a T.V. factory, an average of 66 TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
Options:
A)18
B)39
C)48
D)50
E)52
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 66
= 90
âˆ´ Average for last 5 days = 90 / 5
= 18
A
Answer: A
Question: Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2 for x 2 (0, 1). Compute f(-3/2) + f(1).
Options:
A)-1
B)-1/2
C)-1/4
D)1/4
E)1/2
Rationale: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1=4. Because f
is odd, we know that f(1) = -f(/1), but because f is periodic, f(1) = f(-1). Therefore,
f(1) = 0 and the answer is 1=4.
correct answer D
Answer: D
Question: If W is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, W, 0, 1, 3, K, 7}?
I. -1.5
II. -2
III. 0
Options:
A) I only
B) II only
C) III only
D) I and III only
E) None
Rationale: If W is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E
Answer: E
Question: If you roll one fair six-sided die, what is the probability that the number is even or greater than 2?
Options:
A)1/2
B)2/3
C)4/5
D)5/6
E)7/12
Rationale: The numbers which satisfy the conditions are 2, 3, 4, 5, and 6.
The probability is 5/6
The answer is D.
Answer: D
Question: The speed of a railway engine is 96 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
Options:
A)19
B)18
C)16
D)17
E)14
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached
Doesreductionmean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.
Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.
In other words, if S = speed, and N = number of compartments, then
S = 42 - k*sqrt(N)
wherekis a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.
If N = 9, then S = 24
24 =96 - k*sqrt(9) = 96 - 3k
k = 24
Now, we need to know: what value of N makes S go to zero?
0 = 96 - 24*sqrt(N)
24*sqrt(N) = 96
sqrt(N) = 4
n = 4^2 = 16
Thus, 16 is the maximum number of cars the engine can pull and still move.
C
Answer: C
Question: Tough and Tricky questions: Work/Rate Problems.
If it takes 80 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?
Options:
A)40/3
B)11
C)7
D)8
E)9/7
Rationale: 80 Workers = 3 hours then,
1 Worker = 3*80 Hours
30 Workers = (3*80) /(30) = 8 Answer.D
Answer: D
Question: There are r members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of r?
Options:
A)11
B)12
C)15
D)18
E)22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, r = m + 1(Michael) = 12
option B
Answer: B
Question: 8 persons can build a wall 140m long in 42 days. In how many days can 30 persons complete a similar wall 100 m long?
Options:
A)12
B)10
C)8
D)6
E)4
Rationale: Explanation:
Work done by 8 persons working 42 days = 140
Work done by 1 person working 42 days =140/8
Work done by 1 person working 1 day =140/8×42
Work done by 30 persons working 1 day
=30×140/8×42=100/8
Assume that 30 persons working xx days complete a similar wall 100 m
=> Work done by 30 persons working x days = 100
Hence x=100/(100/8)=8
Answer: Option C
Answer: C
Question: A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 16 km, if the person completes half of the distance by walking and the other half by running?
Options:
A)2
B)2.5
C)3
D)3.5
E)4
Rationale: time = 8/4 + 8/8 = 3 hours
The answer is C.
Answer: C
Question: Salesperson A's compensation for any week is $360 plus 8 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?
Options:
A)$21,000
B)$18,000
C)$15,000
D)$ 7,750
E)$4,000
Rationale: sometime, setting up an equation is an easy way to go with:
350 + 0.04(x - 1000) = 0.08 x
x = 7,750
Ans : D
Answer: D
Question: A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in sƟll water and rate
of the stream.
Options:
A)0,5
B)5,5
C)15,5
D)10,5
E)None of these
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(20+10) = 15 kmph
=> Rate of current = 1/2(20-10) = 5 kmph
Answer: C
Answer: C
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 80 on the S scale?
Options:
A)26
B)28
C)32
D)36
E)40
Rationale: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(80)/5 - 12 = 48-12 = 36
The answer is D.
Answer: D
Question: 5358 x 71 = ?
Options:
A)273762
B)283758
C)383298
D)273258
E)380418
Rationale: E
5358 x 71 = 5358 x (70 + 1)
= 5358 x 50 + 5358 x 1
= 375060 + 5358
= 380418
Answer: E
Question: A class is given an exam. 87% of students pass with a C or greater, the remaining students fail. Of the passing students, 48% received a C, and those who received an A was 25% of those who received a B. What percent of students received an A?
Options:
A)9.05%
B)16.10%
C)36.19%
D)12.00%
E)13.00%
Rationale: Percent of students who pass the exam: 87%
Percent of students who received a C: 87% x 48% = 41.76%
Percent of students who received an A or B = 87% - 41.76% = 45.24%
A students = 25% B students
.25 B + B = 45.24%
B = 36.19%
25% of 36.19% = 9.05% of students received an A
9.05+36.19+41.76+13=100% of students
Answer is A
Answer: A
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
Options:
A)Rs.7506
B)Rs.7500
C)Rs.7572
D)Rs.7532
E)Rs.7555
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs.7500
Answer:B
Answer: B
Question: If a : b : : 3 : 5, b : c : : 4 : 3 and c : d : : 4 : 5, a : d = ?
Options:
A)4 :5
B)16 : 25
C)64 : 25
D)64 : 125
E)16 : 125
Rationale: Explanation:
a/b * b/c * c/d = 3/5 * 4/3 * 4/5 = 42/52 = 16/25
a : d = 16 : 25
ANSWER B
Answer: B
Question: Rahul went to a shop and bought things worth Rs. 25, 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)Rs 15
B)Rs 12.10
C)Rs 19.70
D)Rs 16.80
E)None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 25 - 5 - 0.30
=19.70
Answer : C
Answer: C
Question: There are five guys who have equal number of bullets. All of them shoot 4 bullets. The remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division. What was the original number of bullets each one had?
Options:
A)18
B)19
C)20
D)21
E)25
Rationale: let initially each was having x bullets
they shot 4 bullets
so 5x-20=x
x=5
so each was having 5 bullets.
total was 25.
ANSWER:E
Answer: E
Question: P, Q and R have $4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)2400
B)2403
C)3998
D)2539
E)1600
Rationale: E
1600
Let the amount with R be $ r
r = 2/3 (total amount with P and Q)
r = 2/3(4000 - r) => 3r = 8000 - 2r
=> 5r = 8000 => r = 1600.
Answer: E
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)200
B)255
C)260
D)265
E)290
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: B
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 24,000. What will be B's share in the total profit of Rs. 20,000 earned at the end of 2 years from the starting of the business?
Options:
A)A)6792.45
B)B)7389
C)C)7379
D)D)7453
E)E)7637
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (24000 * 18) = 20:15:18
B's share = 20000 * 18/53 = Rs.6792.45
Answer: A
Answer: A
Question: City A to city B, Andrew drove for 1hr at 48 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)57
B)57.5
C)61
D)61.5
E)62.5
Rationale: The total distance is 1×48+3×60=228
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=228/4=57
A
Answer: A
Question: A large tanker can be filled by two pipes A and B in 10 and 5 hours respectively. How many hours will it take to fill the tanker from empty state if A and B fill it together?
Options:
A)3hr 20min
B)3hr 50min
C)4hr
D)4hr 10min
E)4hr 15min
Rationale: Part filled by A in 1hr = 1/10
Part filled by B in 1hr = 1/5
part filled by A+B = 1/10 + 1/5 = 3/10
Both the pipes can fill the tank in = 10/3 hours = 3 hr 20min
Answer is A
Answer: A
Question: In a row of 30 seats, six team of 4 persons each will be seated. The members of any one team always sit together in four consecutive seats in the same order. Different teams may be adjacent or separated by empty seats. In how many ways can the six teams be seated in the 30 seats?
Options:
A)(6!)(6!)
B)12!/6!
C)12C6
D)30C12
E)30C6*6
Rationale: There are total 30 seats, but 4 members of 6 different groups always sit together and in same sequence...
So the group can be taken as one seat, making the total as 12 seats..
12 seats include 6 empty chairs as total 6*4 chairs are filled in 30 seats and these 6 seats will be identical while the other 6 would be different as each consists of different group..
Ans 12!/6!
B
Answer: B
Question: As part of a promotion designed to attract visitors, an amusement park gives out 24,600 free tickets per year. Usually, the number of tickets given away each month is constant. Due to an employee error, only 8500 tickets were given out in the first four months of the year. How many tickets should the amusement park give out in the fifth month so that it will begin the sixth month back on its regular giveaway schedule?
Options:
A)2054
B)2501
C)2200
D)1750
E)1000
Rationale: 24600/12=2050
2050*5=10250
10250-8500=1750
Answer D
Answer: D
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Options:
A)14420
B)14400
C)14600
D)14800
E)14700
Rationale: Ratio of the investment
=21000:17500=210:175 =42:35=6:5
Share of X in the profit
=26400×6/11=2400×6=14400
Answer is B.
Answer: B
Question: In a box of 16 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)1/6
B)2/9
C)6/20
D)13/20
E)3/4
Rationale: Method- 1
There are 9 fine pieces of pen and 3 defective in a lot of 16 pens
i.e. Probability of first pen NOT being defective = (13/16)
i.e. Probability of Second pen NOT being defective = (12/15) [15 pen remaining with 12 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (12/15)*(13/16) = 13/20
Answer: option D
Answer: D
Question: Find the average of first 4 multiples of 5?
Options:
A)10
B)15
C)12.5
D)13
E)21
Rationale: average = (5+10+15+20)/4 = 12.5
Answer is C
Answer: C
Question: If 36/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
Options:
A)I only
B)I, II, and III
C)I and II only
D)I only
E)III only
Rationale: The largest possible value of x is 36 (the greatest common factor of 36 and 108), and if x=36 then
E
Answer: E
Question: The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4332 sq cm. What is the ratio of the width and the area of the rectangle?
Options:
A)1:72
B)1:76
C)1:80
D)1:84
E)1:88
Rationale: Let the length and the width be 4x and 3x respectively.
Area = (4x)(3x) = 4332
12x^2 = 4332
x^2 = 361
x = 19
The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 76
The answer is B.
Answer: B
Question: What is the sum of all remainders obtained when the first 110 natural numbers are divided by 9?
Options:
A)397
B)401
C)403
D)405
E)399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=403.
Answer: C.
Answer: C
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
Options:
A)17 days
B)21 days
C)29 days
D)25 days
E)27 days
Rationale: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
ANSWER:B
Answer: B
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/10 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
Options:
A)20 greater
B)17 fewer
C)28 fewer
D)36 fewer
E)44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/10 * 480 =48
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 48-68 =20>>> therfore answer is 20 greater
A
Answer: A
Question: A train 455 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)22 sec
B)16 sec
C)17 sec
D)39 sec
E)12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 455 * 2/35 = 39 sec
Answer:D
Answer: D
Question: The ratio of the radius of two circles is 4: 3, and then the ratio of their areas is?
Options:
A)1: 8
B)1: 6
C)1: 9
D)16: 9
E)1: 2
Rationale: r1: r2 = 4: 3
Πr12: Πr22
r12: r22 = 16: 9
Answer:D
Answer: D
Question: {1,2,3,4,5,5,6,6}how many four digited numbers can be formed without repiting the numbers?
Options:
A)180
B)360
C)460
D)500
E)520
Rationale: n*(n-1)*(n-2)...
hence four digits with out repetition total 6 digits=n
6*5*4*3=360
ANSWER:B
Answer: B
Question: If k > 0, which of the following could be true?
I. k^3 > k^2
II. k^2 = k
III. k^2 > k^3
Options:
A)I only
B)III
C)IIIII
D)All of the above
E)None of the above
Rationale: 1. k^3 > k^2 Well this is true for all k > +1 (but not for values 0 < k < 1)
2. k^2 = k This is true for only one positive number, 1
3. k^2 > k^3 Again this is true only for values of k such that 0 < k < 1
So the answer is D, since there exists at least one value of k which satisfies the equation/ in equation(s)
Answer: D
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 12 more blue balls than white balls, and twice as many red balls as blue balls, how many white balls does The box has ?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 12 more blue balls than white balls...
Equation #2: y = 12 + z
...thrice as many red balls as blue balls...
Equation #3: x = 2y
Solve equation #2 for z: z = y - 12
Now, we can replace both x and z with y in Equation #1
2y + y + (y - 12) = 100
4y - 12 = 100
4y = 112
y = 28
There are 28 blue balls. This is 15 more than the number of white balls, so z = 16. That's the answer. Just as a check, x = 56, and 56 + 28 + 16 = 100.
Answer = 16,(E)
Answer: E
Question: Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 300 shoppers liked exactly 2 juices, and 100 shoppers liked all three juices, how many shoppers took the taste test?
Options:
A)1,300
B)1,000
C)900
D)700
E)500
Rationale: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(300) + 3*(100) = 1000
I = 100
Total number of shoppers who took the taste test = I + II + III = 100 + 300 + 100 = 500
Answer: E
Answer: E
Question: If m is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)m (m+2) (m-1)
B)m (m+1) (m-4)
C)m (m+3) (m-5)
D)m (m+4) (m-2)
E)m (m+5) (m-6)
Rationale: anything in the form of (m-1) (m) (m+1) is divisible by 3. in other word, a product of any 3 consecutive intevers is divisible by 3.
m (m+1) (m-4) = m (m+1) ((m-1)-3) is equivalant to (m-1) (m) (m+1)
m (m+2) (m-1) is equivalant to (m+1) missing.
m (m+3) (m-5) is equivalant to (m-1) missing and m repeating.
m (m+4) (m-2) is equivalant to odd/even consqcutive integers
m (m+5) (m-6) is equivalant to (m+1) missing and m repeating.
Answer : B
Answer: B
Question: A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)3
B)7.5
C)2.25
D)2
E)4
Rationale: M = 6
S = x
DS = 6 + x
US = 6 - x
6 + x = (6 - x)2
6 + x = 12 -2x
3x = 6
x = 2
ANSWER:D
Answer: D
Question: Mr. Kutty has only hens and sheep. If the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep?
Options:
A)2 : 1
B)1 : 2
C)6 : 13
D)13 : 6
E)None of these
Rationale: Let the total number of hens and sheep be x and y respectively.
i.e., x + y = 38 and 2x + 4y = 100
∴ Ratio = 13 : 6
Answer D
Answer: D
Question: If |4x+6| = 50, what is the sum of all the possible values of x?
Options:
A)2
B)-2
C)4
D)-3
E)6
Rationale: There will be two cases
4x+6= 50 or 4x+6 = -50
=> x =11 or x= -14
sum of both the values will be -14 +11 = -3
Answer is D
Answer: D
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
Options:
A)3/8
B)2/5
C)1/2
D)3/5
E)3/4
Rationale: Let "$x" be invested with the higher rate of 8%
Thus, "20000-x" must have been invested with lower rate of 6%
Simple Interest = Principal* Rate* Time
For the Amount invested at 8%
Principal = x
Rate = 0.08
Time = 1
Simple Interest = x* 0.08* 1= 0.08x
For the Amount invested at 6%
Principal = 20000-x
Rate = 0.06
Time = 1
Simple Interest = (20000-x)* 0.06* 1= 1200-0.06x
Total Interest = $1440
0.08x+1200-0.06x=1440
0.02x=240
x = 240/0.02=12000
Fraction of x per total amount = 12000/20000 = 12/20 = 3/5
Ans: "D"
Answer: D
Question: If ab = 3(a + 1) + b and a and b are integers, a could be any of the following values EXCEPT:
Options:
A)2
B)3
C)6
D)4
E)7
Rationale: ab = 3(a + 1) + b
ab - b = 3(a + 1)
b = 3(a + 1)/(a-1)
b won't be an integer only if a = 6 (from the options).
Answer: C
Answer: C
Question: If logX/(a2 + ab + b2) = log Y/(b2 + bc + c2) = logZ/(c2 + ca + a2), then Xa - b.Yb - c. Zc - a =?
Options:
A)0
B)-1
C)1
D)2
E)3
Rationale: Each ratio = k = log X = k(a2 + ab + b2)
=> (a - b)logX = k(a3 - b3)
Similarly, Yb - c = ek(b3 - c3), Zc - a= ek(c3 - a3)
Therefore, Xa - b.Yb - c.Zc - a = e0 = 1.
ANSWER:C
Answer: C
Question: If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following is false?
I.	a=0, b>0, c>0
II.	a>0, b=0, c>0
III.	a>0, b>0, c=0
Options:
A)I only
B)II only
C)III only
D)I, II and III
E)None of the above
Rationale: We could solve this easily.
I is false. If a=0 then ab=0, ac=0. But since ac<0, it is false.
II is false. If b=0 then ab=0, bc=0. But since bc>0, it is false.
III is false. If c=0 then ac=0, bc=0. But since ac<0, it is false.
So, the answer is D
Answer: D