MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x? Choose the correct answer.
A) 1	B) 10	C) 9	D) 0	E) 8

Solution: Explanation :   E = (x-1)(x-6)(x-3)(x-4)+10   E = (x2-7x+6)(X2-7x+12)+10   Let x2-7x+6 = y   E = y2+6y+10   E = (y+3)2 + 1   Minimum value = 1 , when y = -3   1nswer : 1
Answer: A
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 805. How many houses are there?	Pick one
A) 125
B) 111
C) 101
D) 121
E) 131

Solution: So it starts from 545 and goes like 547, 549,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.   i.e., ([805-545][/2]+1 = 131   Ans 131
Answer: E
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 42 years, was replaced by a new person. Find the age of the new person?	Choose the correct choice from the following
A) 22 B) 99 C) 12 D) 88 E) 77

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12.Answer:12
Answer: C
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?  Choices:
A) 177 m  B) 786 m  C) 272 m  D) 100 m  E) 127 m

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer:100 m
Answer: D
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?	Choose the correct choice from the following answers:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3

Solution: Let c = revenue from car sales in 1996   Let t = revenue from truck sales in 1996   Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,   c(0.89) + t(1.07) = (c+t) (1.01)   Dividing throughout by t,   (c/t) (0.89) + 1.07 = (c/t + 1) (1.01)   => (c/t) (0.12) = 0.06   => (c/t) = 1/2   Option (1:2).
Answer: A
Find the area of a parallelogram with base 36 cm and height 24 cm?	Choose the correct choice from the following.
A) 760	B) 284	C) 288	D) 864	E) 820

Solution: Area of a parallelogram = base * height   = 36 * 24= 
36 * 24 = 864
864 cm2   Answer: 864
Answer: D
Shreehari has 500 chocolates in his self. He eats 10% of the chocolates per month. How many chocolates will he have after 2 months?	Choose the correct choice from the following answers: A) 450 B) 400 C) 405 D) 410 E) 425

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   500 Ã— 90/100 Ã— 90/100 = 405   405
Answer: C
A, B and C started a business with capitals of Rs.6000, Rs.8000, and Rs.10000 respectively. At the end of the year, the profit share of B is Rs1000. The difference between the profit shares of A and C is
Choose the correct choice from the following
A) Rs. 400	B) Rs. 450	C) Rs. 500	D) Rs. 550	E) Rs. 650

Solution: Ratio of investments of A,B and C is 6000 : 8000 : 10000 = 3 : 4 : 5.   And also given that, Profit share of ‘B’ is Rs.1000.   Now required difference is 5 – 3 = 2 parts.   Therefore, Required difference = 2/4 (1000) = Rs.500.   ANSWER:Rs. 500
Answer: C
A shopkeeper labeled the price of his articles so as to earn a profit of 20% on the cost price. He then sold the articles by offering a discount of 5% on the labeled price. What is the actual percent profit earned in the deal?
Choose the correct choice:
A) 24% B) 20% C) 17% D) 18% E) None of these

Solution: Explanation:   Let the CP of the article = Rs.100.   Then labeled price = Rs.120.   SP = Rs.120- 5% of 120 = Rs.120-6 = Rs.124.   Gain = Rs.124 â€“ Rs.100 = Rs.24   Therefore, gain/profit percent = 24%.   24%nswer: Option 24%
Answer: A
A set consist of 2l-1 element. What is the number of subsets of this set which contain at most l-1 elements? Options:
A) 2^(2l-2)
B) 2^(2l) - 2
C) 2^(2l) -1
D) 2^(2l)
E) 2^(2l-1)

Solution: I used l=3, so then we have   5!/2!3! + 5!/4!1! + 5!/0!5!    10 + 5 + 1= 
 10 + 5 + 1 = 16
16   So our target is 16   Now replace in answer choices   2^(2l-2) gives us 2^4= 16   Hence 2^(2l-2) is the correct option   Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes   2^(2l-2)void 2 since you will get 1 arrangement (l-1) and may be risky since 1 is a number with certain unique properties
Answer: A
During the months May through October, Teddy the bear quintuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976? Choose the correct choice:
A) 25m - 1300	B) 25m - 1200	C) 5m - 1300	D) 5m - 1200	E) 5m

Solution: Nov ' 73 = m   25m - 1300pril ' 74 = m - 100   Oct ' 74 = 5m - 300   25m - 1300pril' 75 = 5m - 400   Oct' 75 = 25m - 1200   25m - 1300pril'76 = 25m - 1300   Hence answer will be (25m - 1300) 25m - 1300
Answer: A
If X and Y are positive integers, X - 5 is divisible by 4 and Y - 1 is divisible by 4, all of the following could be the value of X - Y Except?	Pick one:
A) 0
B) 8
C) 4
D) 7
E) 24

Solution: X-5 = 4Y   => P = 4Y + 5 = 5,9,13,17,21,25,29,33,37,41,45   Y-1 = 4X   => Y = 4X + 1 = 1,5,9,13,17,21,25,29,33,37,41   0=5-5   8=13-5   4=5-1   24=45-21   So , we can see that all the answer choices are possible here except 7
Answer: D
A committee of three people is to be chosen from 7 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Choose the correct choice from the following options.
A) 16  B) 39  C) 26  D) 30  E) 49

Solution: Total no of ways of choosing a committee = 7C3 = 35   No of ways to choose first couple = 7C1 = 7   No of ways to choose 1 person from remaining 12 = 12C1 = 12   Total number of ways of choosing a married couple to be in the same committee = 7*12= 
7*12 = 84
84   So, no of ways not choosing a married couple= 84-35= 
84-35 = 49
49   ANS:E. 49
Answer: E
The average price of an antique car increases over the years. If from 1990 to 1996, the price of the car increased by 13% and from 1996 to 2001 it increased by 20%, what is the price of the car in 2001 if the price in 1990 was $11,500?  Answers:
A) $15,594. B) $15,322. C) $14,786. D) $14,543. E) $12,988.

Solution: Whenever you have a question in which a value is increased by x% and then increased by y% then the overall effective increase = (x + y + xy/100 ) %   The effective increase = 13 + 20 + (13×20/100) = 35.6%   This is a little more 33% or 1/3 the original value.   THE QUICKEST WAY TO SOLVE THIS QUESTION IS TO USE APPROXIMATION.   11500 + 1/ 3 (12000) = 15500   Therefore option A is the answer.   I selected 12000 because it's value is a little more 11500 and it's easier to divide by 3 ( ie to calculate 1/3 or 33%).
Answer: A
Each of seven different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
Choose one.
A) 1/8
B) 1/6
C) 1/49
D) 3/8
E) 1/2

Solution: I was just going over probability questions.   can some one explain me what's wrong in my approach here.   Probability of choosing one right key out of 7 is 1/7.   Probability of choosing another right key is 1/7.   since the question is asking for 2 right keys , probability is multiplication of both = 1/7 * 1/7 = 1/49.   Ans 1/49
Answer: C
Which of the following options represents an approximate value for the question mark (?) in the following equation?
87.542 + 62.511 × 3.2 + ? = 805.925 Select:
A) 913.4 B) 918.4 C) 911.4 D) 988.4 E) 958.4

Solution: 87.542 + 62.511 × 3.2 + ? = 805.925   or, ? = 805.925 – 87.542 + 62.511 × 3.2   ? = 805.925 – 87.542 + 200.0352   ≈ 918.4   Answer 918.4
Answer: B
Which of these must the factor Q of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80	Choose the correct choice from the following answers
A) 1,2 only
B) Q=2,3 only
C) Q=1,2,3 only
D) Q=1,2,3,4 only
E) All of them

Solution: Let the four variables be a< b< c< d.   Assume a worst case scenario where the a equal to a prime number (hence odd).   therefore   a = divisible by 1   b = a + 1 (divisible by 2)   c = a + 3 (divisible by 3)   d = a + 4 (divisible by 4)   therefore   each answer choice must be divisible Q by 2 x 3 x 4 = 24   only 80 is not divisible. Therefore answer = Q=1,2,3,4 only
Answer: D
A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly.What amount was paid for the note	Options.
A) $4336.93
B) 4336.99
C) 4336.96
D) 4336.92
E) 4336.91

Solution: Explanation:   i=j/m   Maturity value = PV (1 + i)^n   Term = 5 years - 21 months= 3.25 years   Price paid = FV(1+ i )^-n   $4336.93nswer: $4336.93) 4336.93
Answer: A
What is the height of a circular cone?
I. The area of that cone is equal to the area of a rectangle whose length is 33 cm.
II. The area of the base of that cone is 154 sq. cm.	Choose the correct choice from the following:
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

Solution: EXPLANATION   II gives the value of r.   But, in I, the breadth of rectangle is not given.   So, we cannot find the surface area of the cone.   Hence, the height of the cone cannot be determined.   Correct answer is (Both I and II are not sufficient to answer).
Answer: D
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good. Choose the correct choice from the following answers:
A) 20/69
B) 20/63
C) 20/61
D) 20/66
E) 20/63

Solution: Explanation:   Required probability =   = (10 * 4)/126 = 20/63   Answer: 20/63
Answer: B
If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true?
Choose the correct choice from the following answers:
A) x^2 + Px + A = 0
B) x^2 - Px - 2A = 0
C) 2x^2 + Px + 2A = 0
D) 2x^2 - Px - 2A = 0
E) 2x^2 - Px + 2A = 0

Solution: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.   Now, assume:   Length =x = 1 inchand width = 1 inch;   Perimeter =P = 4 inches;   Area =A = 1 square inches.   Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px  + 2= 
 + 2 = 2
2 - 4 + 2= 
2 - 4 + 2 = 0
0.   Answer: 2x^2 - Px + 2A= 0.
Answer: E
In a class of 50 students, 20 play Golf, 15 play Cricket and 11 play Football. 7 play both Golf and Cricket, 4 play Cricket and Football and 5 play Golf and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?	Choose the correct choice:	A) 45	B) 12	C) 35	D) 10	E) 77

Solution: Notice that7 play both Golf and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Golf/Football.   [color=#ffff00]{Total}={Golf}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS   [/color]   50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;   Those who play ONLY Golf and Cricket are 7-2= 
7-2 = 5
5;   Those who play ONLY Cricket and Football are  4-2= 
 4-2 = 2
2;   Those who play ONLY Golf and Football are  5-2= 
 5-2 = 3
3;   Hence, 5+2+3=10 students play exactly two of these sports.   Answer: 10.
Answer: D
A family made a down payment of $75 and borrowed the balance on a set of encyclopedias that cost $500. The balance with interest was paid in 23 monthly payments of $20 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed?  Choose one:
A) 10.3%
B) 12.5%
C) 13%
D) 11%
E) 10%

Solution: borrowings = 500-75= 
500-75 = 425
425   total pmt= 23x20 + 9 = 469   so int = 469 - 425= 
469 - 425 = 44
44   interest in terms of borrowing= 44/425 = 10.3%   10.3%nswer is 10.3%
Answer: A
There were two candidates in an election. Winner candidate received 62% of votes and won the election by 324 votes. Find the number of votes casted to the winning candidate?
Choices
A) 456  B) 837  C) 912  D) 1200  E) 1400

Solution: W = 62% L = 38%   62% - 38% = 24%   24% -------- 324   62% -------- ?  62  - 38= 
 62  - 38 = 24
24%   24% -------- 324   62% -------- ?=> 837   ANSWER:837
Answer: B
A family pays $800 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? Choose one:
A) $1,000
B) $1,200
C) $1,400
D) $1,800
E) $2,200

Solution: Assuming the medical expenses are $1000 or more, the family pays $800 + $300 = $1100.   The total amount paid by insurance plan for the first $1000 of expenses is $700.   The insurance will pay another $400 when the medical expenses are $1400.   The answer is $1,400.800 +  300= 
800 +  300 = 1_100
$1100.   The total amount paid by insurance plan for the first $1000 of expenses is $700.   The insurance will pay another $400 when the medical expenses are $1400.   The answer is $1,400.
Answer: C
When positive integer N is divided by positive integer J, the remainder is 10. If N/J = 134.08, what is value of J?	Choose one
A) 125  B) 56  C) 78  D) 112  E) 175

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 134.08   Here 134 is the quotient.   Given that Remainder = 10   So, 134.08 = 134 + 10/J   So, J = 125 125NS 125
Answer: A
A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her Choose the correct choice:
A) a) thumb
B) b) the index finger
C) c) the middle finger
D) d) the ring finger
E) e) the little finger

Solution: Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number   By this patter the thumb is also at number 1993 (multiple of 8 + 1)   Hence 1995 has to be the middle finger   Answer is (c) the middle finger)
Answer: C
if samaira wallet have 10rs. note,50 rs. note,2000 rs.note.if 10rs. is 3/5 part of his money and 50rs. is 1/5 part of his money.if he has 8000 money consist of 2000 rs.calculate total money in samaira wallet?
Choose the correct choice from the following options:	A) 18000	B) 32000	C) 30000	D) 40000	E) 35000

Solution: if samaira have total money is x.   part of money in 2000 rs.=(1-(3/5+1/5))=1-4/5=1/5   x*1/5=8000,x=40,000rs.   answer 40000
Answer: D
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Choose the correct choice from the following
A) 9:1  B) 9:6  C) 9:2  D) 9:9  E) 9:3

Solution: Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   9:1nswer: 9:1
Answer: A
A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number Q of ways this can be done is:  Options
A) 122  B) 210  C) 216  D) 217  E) 225

Solution: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:   1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96   120+96= 
120+96 = 216
216=Q   Answer: 216.
Answer: C
A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
Choose the correct choice from the following answers
A) 6% B) 14% C) 20% D) 23% E) 43%

Solution: Initial ratio of federal taxes to gross profits : 7/50= 
7/50 = 7/50 = around 0.14
0.14   Final ratio :   30/150= 
  30/150 = 1/5 = around 0.2
0.2   Thus, the percentage change : (0.2-0.14)/0.14*100= 6/14*100 = 3/7*100 = Just less than 50 % .   ANSW43%R:43%
Answer: E
Two airplanes, one from Atlanta to New York and the other from New York to Atlanta, start simultaneously. After they meet, the airplanes reach their destinations after 16 hours and 4 hours respectively The ratio of their speeds is  Choose the correct choice from the following choices:
A) 2 : 3	B) 4 : 3	C) 4 : 2	D) 1 : 2	E) None

Solution: Solution   Let us name the planes   as A and B.	= (A'S speed) : (B's speed)   =âˆšb : âˆša   = âˆš16 : âˆš4   = 4 : 2   Answer 4 : 2
Answer: C
If the roots of a quadratic equation are 20 and -7, then find the equation?  Select the correct option:
A) x2 - x - 15 = 0
B) x2 - 12x - 50 = 0
C) x2 - 13x - 140 = 0
D) x2 - 4x - 40 = 0
E) x2 - 23x - 150 = 0

Solution: Explanation:   Any quadratic equation is of the form   x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)   where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.   Answer x2 - 13x - 140 = 0
Answer: C
Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A’s area to rectangle B’s area?	Choose the correct choice from the following options:
A) 5/3 B) 9/5 C) 9/25 D) 3/5 E) 25/9

Solution: The area of rectangle A is ab.   c=5a/3 and d=5b/3.   The area of rectangle B is cd=25ab/9.   The ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25.   The answer is 9/25.
Answer: C
The third proportional to 3 and 6 is?	Pick:
A) 8
B) 7
C) 12
D) 5
E) 3

Solution: (6*6)/3= 
(6*6)/3 = 12
12   Answer:12
Answer: C
At what rate percent of simple interest will a sum of money double itself in 12 years?
Select:	A) 8 1/8	B) 8 1/3	C) 8 1/0	D) 8 1/2	E) 8 1/1

Solution: Let sum = x. Then, S.I. = x.   Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)   = 25/3 = 8 1/3 %   Answer: 8 1/3
Answer: B
Let A be the event that a randomly selected two digit number is divisible by 10 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)? Answers:  A) 1/50  B) 1/30  C) 1/15  D) 1/10  E) 1/5

Solution: P(1/50 and B) = 1/10*1/5 = 1/50   The answer is 1/50.
Answer: A
Mr. John invested in Fund A and Fund B. The total amount he invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Mr. John invest in Fund A?  Options:
A) $32,000	B) $36,000	C) $40,000	D) $41,000	E) $42,000

Solution: A+B=100,000   0.17B=0.23A+200   Take away decimals first: 17B=23A+20,000   Isolate first equation to solve for A (your goal): B=100,000-A   Plug in for B:   17(100,000-A)=23A+20,000   1,700,000-17A=23A+20,000   1,680,000=40A   1,680,000/40=A   A=42,000=Answer Choice $42,000
Answer: E
Out of 15 students in a class, 9 are wearing blue shirts, 3 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?	Choose the correct choice from the following answers
A) 28/61 B) 38/71 C) 48/81 D) 58/91 E) 68/101

Solution: Total possible ways to choose 4 students out of 15 = 15C4 = 1365   The number of ways to choose 4 students with no green shirts = 12C4 = 495   P(no green shirts) = 495/1365 = 33/91   P(at least 1 green shirt) = 1 - 33/91 = 58/91   The answer is 58/91.
Answer: D
Find the simple interest on Rs. 68,000 at 16 2/3% per annum for 9 months.  Pick:
A) Rs.8500  B) Rs.8000  C) Rs.7500  D) Rs.7000  E) Rs.6500

Solution: P = Rs.68000,R = 50/3% p.a and T = 9/12 years = 3/4years.   S.I. = (P*R*T)/100 = Rs.(68,000*(50/3)*(3/4)*(1/100))   = Rs.8500   Rs.8500nswer is Rs.8500.
Answer: A
Which of the following numbers is divisible by 8?
Options:
A) 10021  B) 17511  C) 26778  D) 18520  E) 26711

Solution: 18520. This is the only option with last two digits divisible by 8   Answer:18520
Answer: D
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $60,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?	Choices.
A) $24,000 B) $28,000 C) $32,000 D) $36,000 E) $40,000

Solution: The answer should be -> D. $36,000
Answer: D
Mike took a bus from home to market, that travels at 30 kmph. While walking back at 6 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph. Find the average speed.
Choose one:
A) 21.2 kmph B) 12.1 kmph C) 23.4 kmph D) 20.4 kmph E) none of these

Solution: Let the distance be 2x(one way)   Time taken by bus = 2x/30, by walking =x/6, by cycling = x/20 hours   :. 21.2 kmphverage speed = Total Distance/Total time   = 6x / x/15 + x/6 + x/20   = 6 *60 / 4+10+3   = 21.2   21.2 kmphNSWER:21.2 kmph
Answer: A