MU-NLPC/Calc-aqua_rat huggingface dataset:
How many 4-digit numbers can be formed by using the digits 0-9, so that the numbers contains exactly 3 distinct digits?  Choose the correct choice from the following:	A) 1944	B) 3240	C) 3850	D) 3888	E) 4216

Solution: Case I:   The repeated digit is the unit's digit.   So, the 1st, 2nd and 3rd digits can be selected in 9 x 9 x 8 ways, respectively.   Now the 4th digit (unit's digit) can be either equal to the 1st, 2nd or 3rd digit.   Thus, in all we have:   9x9x8x3   Case II:   The repeated digit is the ten's digit.   So, the 1st, 2nd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.   Now the 3rd digit (ten's digit) can be either equal to the 1st or 2nd digit.   Thus, in all we have:   9x9x2x8   Case III:   The repeated digit is the hundred's digit.   So, the 1st, 3rd and 4th digits can be selected in 9 x 9 x 8 ways, respectively.   Now the 2nd digit (hundred's digit) is equal to the 1st digit.   Thus, in all we have:   9x1x9x8   In totality, we have 9x9x8(3+2+1) = 9x9x8x6 = 3888   ANS:3888
Answer: D
If the sides of a triangle are 31 cm, 29 cm and 15 cm, what is its area?
Choose the correct choice from the following options.
A) 220.75 cm2 B) 258 cm2 C) 225.50 cm2 D) 222.25 cm2 E) 217.5 cm2

Solution: The triangle with sides 31 cm, 29 cm and 15 cm is right angled, where the hypotenuse is 31 cm.   Area of the triangle   = 1/2 * 29 * 15= 
1/2 * 29 * 15 = 435/2 = around 217.5
217.5 cm2   Answer: 217.5 cm2
Answer: E
A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?	Choose the correct choice from the following options:  A) Rs. 18.20  B) Rs. 70  C) Rs. 72  D) Rs. 88.25  E) None of these

Solution: Explanation :   Let the C.P. of items sold in a week be Rs. x   So, Rs. 392 = x + 22.5% of x   => (122.5/100)*x = 392   => x = 392∗100/122.5 = 320   So, the profit = Rs. (392-320) = Rs. 72   Answer : Rs. 72
Answer: C
Employees of a certain company are each to receive a unique 9-digit identification code consisting of the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?	Select:
A) 14,720 B) 16,240 C) 18,320 D) 20,160 E) 22,480

Solution: There are 7! ways to make codes starting with 12.   There are 7! ways to make codes starting with 24.   There are 7! ways to make codes starting with 36.   There are 7! ways to make codes starting with 48.   The number of codes is 4*7! = 20,160.   The answer is 20,160.
Answer: D
The food in a camp lasts for 40 men for 20 days. If 10 more men join, how many days will the food last? Choose the correct choice from the following choices.
A) 22 days	B) 30 days	C) 23 days	D) 16 days	E) 17 days

Solution: one man can consume the same food in 40*20= 
40*20 = 800
800 days.   10 more men join, the total number of men= 50   The number of days the food will last = 800/50= 
800/50 = 16
16 days.   Answer:16 days
Answer: D
If A's height is 25% less than that of B, how much percent B's height is more than that of A? Choose the correct choice.
A) 66.66% B) 66.68% C) 66.766% D) 33.33% E) 66.65%

Solution: Excess of B's height over A's = [(25/(100 - 25)] x 100%   = 33.33%   Answer: 33.33%)
Answer: D
The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is:	Choose the correct answer
A) 2200	B) 5500	C) 3300	D) 1100	E) 4400

Solution: Cylinder volume = πr(power2)h   = 22/7 × 10 × 10 × 14   = 4400 m(power3)   Answer is 4400.
Answer: E
A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money T did Bob receive? Choices:  A) 20  B) 22  C) 24  D) 26  E) 52

Solution: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.   Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.   So, we getK - Bob's $ = 32   Bob received 4 dollars plus one-third of what remained   Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.   1/3 of K-4 is (K-4)/3   So ALTOGETHER, 22ob receives4 + (K-4)/3   So, our equation becomes:K -[4 + (K-4)/3 ]= 32   Simplify to get: K - 4 - (K-4)/3 = 32   Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96   Simplify: 2K - 8 = 96   Solve: K = 52   Plug this K-value intoK - 22ob's $ = 32to get: 52 - 22ob's $ = 32   So, 22ob's $ T= 20   Answer:   22
Answer: B
A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?  Pick:
A) 45
B) 72
C) 90
D) 10!/2!
E) 10!

Solution: I lined up the 9 different colours for Exterion and Interior like this:   E: A B C D E F G H I   I: A B C D E F G H I   I calculated the number of combinations:  9*9= 
 9*9 = 81
81 combinations.   But, from these 100 we need to delete sth: the same colours.   There are 9 possible pairs of coulours that will be the same. So, I deleted these 9 pairs from 81, resulting in 72.   Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).   72
Answer: B
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?  Pick one
A) 17 B) 19 C) 12 D) 28 E) 32

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
The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in? Pick one: A) 5.29 min B) 5.28 min C) 5.08 min D) 9.28 min E) 5.988 min

Solution: Clearly, the two will meet when they are 726 m apart.   To be (4.5 + 3.75)= 
(4.5 + 3.75) = 8.25
8.25 km apart, they take 1 hour.   To be 726 m apart, they take (100/825 * 726/1000) hrs= (242/2750 * 60)= 
(242/2750 * 60) = 132/25 = around 5.28
5.28 min.   Answer: 5.28 min
Answer: B
What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3? Choose the correct choice from the following answers
A) 1.4  B) sqrt (2)  C) 1.7  D) sqrt (3)  E) 2.0

Solution: (A) 1.4   eqn of circle = x^2 + y^2 = 1, center = (0,0) radius = 1   min dist of line from circle = dist of line from the center - radius   Make the distance of the line from the circle to be 0 and we see that it becomes a tangent to the circle.   Now we know if we draw a line from the center to the point where the tangent touches the circle the line and the tangent are perpendicular to each other.   So we need to find the equation of this line first.   We can take the line back where it was now   Since the lines are perpendicular m1 x m2 = -1   m of line = 3/4   so slope of the new line = -4/3   Since the line passes through the origin (center of circle) its eqn => y=-4/3x   now we need to get the point of intersection of our two lines, which comes out to be (36/25,-48/25)   now get the distance of this point from the origin and subtract the radius from it.   Comes to 1.4 (may have made calculation errors )   So 1.4.
Answer: A
A drawer has six loose blue socks and six loose white socks. If four socks are removed from the drawer at random and without replacement. What is the probability that one pair of each color was selected?
Choose the correct answer.
A) 2/33
B) 5/66
C) 5/33
D) 5/11
E) 1/2

Solution: No of Loose blue socks = 6 (3 pairs)   No. of Loose white Socks = 6 (3 pairs)   total no. of blue and white socks = 12   Total no. of socks to be selected = 4   So we have C (12,4) = no of ways the socks can be selected = 495   No of ways One pair of blue socks is selected ( 2 blue socks) , C (6,2) , No of ways one pair of white socks can be selected C (6,2) ..Because we have to find a scenario where EXACTLY one pair of Blue socks and ONE pair of WHITE socks is selected we will multiply the two .. ie 15 x 15 ..   Filling the information in the Probability formula we get P (A) = (15 x 15) / 495 = 5 /11   ANSWER : (5/11)
Answer: D
The sum of the squares of three numbers is 241, while the sum of their products taken two at a time is 100. Their sum is: Choose the correct option
A) 20 B) 11 C) 21 D) 41 E) None of these

Solution: x^+y^2+z^2=241   xy+yz+zx=100   as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)   so (x+y+z)^2=241+(2*100)   (x+y+z)^2=441   so x+y+z=21   ANSWER:21
Answer: C
The average of ten numbers is 8. If each number is multiplied by 11, then what is the average of the new set of numbers?	Choose the correct choice from the following options:
A) 8 B) 11 C) 19 D) 88 E) 121

Solution: The sum of the ten numbers is 8*10= 
8*10 = 80
80   If each number is multiplied by 11, the new sum is 11*(80).   The average is then   11*8= 
  11*8 = 88
88   The answer is 88.
Answer: D
What percentage of numbers from 1 to 100 have cube that end in the digit 5?  Choose the most appropriate option.
A) 1
B) 10.5
C) 25
D) 20
E) 22

Solution: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 95 are 5,15,25,35,45,55,65,75,85,95.   Number of such numbers = 95.   Required percentage = (10/95 * 100) = 10.5%   ANSWER:10.5
Answer: B
Set A consists of integers -9, 8, 3, 10, and J; Set B consists of integers -2, 5, 0, 7, -6, and U. If R is the median of Set A and W is the mode of set B, and R^W is a factor of 34, what is the value of U if J is negative?	Choose the correct option.
A) -2
B) U=0
C) 1
D) 2
E) 5

Solution: since j is negative, therefore median of the set will be 3. which is an odd number. also, we know that odd^n will always be odd. now since 34 is even, therefore 3^w will have only one factor with 34 for w=0.   mode of the set is a number which occurs maximum number of time in the set. now, since U is the mode of the set. therefore U=0. hence answer is U=0
Answer: B
If X, Y and Z are digits and 7XYZ is a 4-digit number that is divisible by 2, which of the following is a possible product of X, Y and Z?	Select:
A) 17
B) 42
C) 13
D) 27
E) 51

Solution: Key to this question is to remember the fact that a number divisible by 2 must end with 2 OR 0 (i.e Z).   If Z had to be 0, product should also be 0 regardless of X and Y.   The product is a multiple of 2. Only one answer choice meets the requirement.   Ans 42.
Answer: B
A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company :
Choose the correct choice from the following answers
A) 2.3 lakh
B) 2.32 lakh
C) 2.12 lakh
D) 3.2 lakh
E) None of these

Solution: Solution: His bonus,   = (20 *1000000) /100 = 2lakh   Total profit = net profit + (10 *net profit) /100   1.32lakh = net profit *[1 + (10/100)]   Net profit = 132000 /1.1= 
132000 /1.1 = 120_000
120000.   Commission,= (total profit - net profit)   = 132000 - 120000= 
132000 - 120000 = 12_000
12000.   Hence, his total earnings= 2lakh + 12000 = Rs. 212000.   Answer: Option 2.12 lakh
Answer: C
If a Ã— b = 2a - 3b + ab, then 3 Ã— 2 + 2 Ã— 3 is equal to :
Choose one.
A) 7
B) 8
C) 9
D) 25
E) 26

Solution: Explanation:   3 Ã— 2 + 2 Ã— 3 = (2 Ã— 3 - 3 Ã— 2 + 2 Ã— 3) + ( 2 Ã— 2 - 3 Ã— 3 + 2 Ã— 3)   = (6 + 4 - 9 + 6)= 
(6 + 4 - 9 + 6) = 7
7.   7nswer: 7
Answer: A
A sum of money deposited at compound interest (compounded yearly) amounts to $600 in 2 years and to $624 in 3 years. What is the interest rate?	Choose the correct choice from the following:	A) 2%	B) 4%	C) 6%	D) 7%	E) 8%

Solution: 624 - 600= 
624 - 600 = 24
24   24/600= 
24/600 = 1/25 = around 0.04
0.04= 4%   The answer is 4%.
Answer: B
In expressing a length 810472 km as nearly as possible with three significant digits , find the percentage error  Options.
A) 0.34%
B) 0.034%
C) 0.0034%
D) 0.00034%
E) 3.4%

Solution: Error = (81.5 – 81.472)km = 0.028.   Required percentage = [(0.028/81.472)*100]% = 0.034%.   Answer is 0.034%.
Answer: B
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 60 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?  Select the correct option:	A) 10 sec	B) 16 sec	C) 12 sec	D) 67 sec	E) 13 sec

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 60 * 100/18 = 1000/3   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 1000/3 * 18/500= 
1000/3 * 18/500 = 12
12 sec   Answer: 12 sec
Answer: C
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Choose the correct option:
A) 33 1/8%
B) 33 8/3%
C) 33 1/3%
D) 37 1/3%
E) 33 1/4%

Solution: 1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%   Answer:33 1/3%
Answer: C
The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
Select
A) 2288
B) 2667
C) 2799
D) 6725
E) 2771

Solution: CP = SP * (100/(100 + profit%))   = 8339(100/124) = Rs. 6725.   Answer:6725
Answer: D
6x − 12 = 6y
5y + 5x = 10
Which of the following is the number of solutions to the system of equations shown above?  Choose the correct option:
A) More than three
B) Exactly three
C) Exactly two
D) Exactly four
E) None of these

Solution: 6x − 12 = 6y   => 6x - 6y = 12   => x- y =2 -- 1   5y + 5x = 15   =>x + y = 2 -- 2   From equation 1 and 2 , we get   2x = 4   => x=2   y=0   Therefore , the given system will have None of thesexactly one solution   Answer : None of these
Answer: E
In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 28% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?	Choices
A) 35.67%  B) 64.75%  C) 68.57%  D) 70.20%  E) none of these

Solution: Girls = 900, Boys = 1100   Passed = ( 28% of 1100 ) + ( 32% of 900)   = 308 + 288= 
308 + 288 = 596
596   Failed= 2000 - 596= 
2000 - 596 = 1_404
1404   Failed %= [(1404/2000) x 100]%   = 70.2%.   ANSWER:70.20%
Answer: D
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth? Choices:
A) 21 B) 28 C) 90 D) 100 E) 11

Solution: Explanation:   SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 5 = Rs. 100.   Answer: 100
Answer: D
If |4x+6| = 42, what is the sum of all the possible values of x?
Pick:
A) 2
B) -3
C) 4
D) -5
E) 6

Solution: There will be two cases   4x+6= 42 or 4x+6 = -42   => x =9 or x= -12   sum of both the values will be -12 +9 = -3   Answer is -3
Answer: B
Find the value of m 62519 x 9999 = m?
Choices:
A) 724533811	B) 625127481	C) 545463251	D) 725117481	E) 677899932

Solution: 62519 x 9999 = 62519 x (10000 - 1)   = 62519 x 10000 - 62519 x 1   = 625190000 - 62519= 
625190000 - 62519 = 625_127_481
625127481   625127481
Answer: B
A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?	Choose the correct choice: A) 6 B) 2 C) 8 D) 9 E) 3

Solution: Work done by A in 2 days = 2/5   Remaining work = 3/5   Work done by both A and B in one day = 1/5 + 1/10 = 3/10   Remaining work = 3/5 * 10/3= 
3/5 * 10/3 = 2
2 days. Answer: 2
Answer: B
Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are their present ages?
Choose the correct choice from the following
A) 16 and 40 years	B) 13 and 37 years	C) 10 and 34 years	D) 11 and 35 years	E) 20 and 44 years

Solution: Let son's age 8 years ago be x years.   Then, Rohit's age 8 years ago = 4x years.   Son's age after 8 years = (x + 8) + 8 = (x + 16) years.   Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.   2 (x + 16) = 4x + 16   2x = 16   x = 8.   Hence, son's 'present age = (x + 8) = 16 years.   Rohit's present age = (4x + 8) = 40 years.   16 and 40 yearsnswer is 16 and 40 years.
Answer: A
Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 10% profit was earned which was equal to 98,000. What was the amount invested by R?  Choose the correct choice from the following answers
A) 2,10,000	B) 1,05,000	C) 1,75,000	D) 2,00,000	E) None of these

Solution: Ratio for amount invested by P, Q & R   = 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6   = 60x : 72x : 36x   = 5x : 6x : 3x   Profit = 98000 = 10% of T   where, T = Total amount   T = 980000   2,10,000mount received by   R = 3x /3x+6x+5x(980000)   = 210000   2,10,000nswer 2,10,000
Answer: A
A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13:11. The number of one-rupee coin is
Choose the correct choice from the following
A) 65  B) 66  C) 77  D) 78  E) NOne

Solution: Solution: Respective ratio of the number of coins;   = 13:11*2 = 13:22   Hence, Number of 1 rupee coins;   = 13*210/(13+22)= 
13*210/(13+22) = 78
78.   Answer: Option 78
Answer: D
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 18 miles, how many miles was Mike's ride?
Choose the most appropriate option.
A) 30	B) 34	C) 38	D) 42	E) 48

Solution: The cost of Annie's ride was 2.5+5+(0.25*18)= 
2.5+5+(0.25*18) = 12
$12   Let x be the distance of Mike's ride.   The cost of Mike's ride is 2.5+(0.25*x)= 12   0.25*x = 9.5   x = 38 miles   The answer is 38.
Answer: C
How many polynomials are there of the form x3rd - 8x2round + cx + d such
that c and d are real numbers and the three roots of the polynomial are
distinct positive integers?  Choose the correct choice from the following choices:	A) 0	B) 1	C) 1	D) 2	E) 5

Solution: The sum of the roots of the polynomial is 8. Since the roots are distinct   positive integers, then they are either 1, 2, 5 or 1, 3, 4. Thus, the polynomial is either   (x − 1)(x − 2)(x − 5) or (x − 1)(x − 3)(x − 4).   correct answer 1
Answer: C
A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,051. How much did she invest at 5%?	Select:
A) $500 B) $600 C) $700 D) $900 E) $950

Solution: et x be the portion invested at 5% and   Let (1-x) be the rest which is invested at 6%   The question states that the return after 1 year is (1051/1000)-1= 
(1051/1000)-1 = 51/1_000 = around 0.051
0.051= 5.1%   We want to find the dollar amount invested in X   Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)   0.05x+0.06(1-x)= 0.051   (0.05)x +0.06 - (0.06)x = 0.051   -0.01x = -0.009   x= -0.009/-0.01 = 9/10 = 90%   So X = 90% of the 1000 which is 900   ANSWER:$900
Answer: D
If x = (y)(y + 1) and y is a prime number less than 6, which of the following could not be the product of 2 consecutive integers? Choices:
A) a) 5x  B) b) 11x  C) c) 13x  D) d) 30x  E) e) 58x

Solution: Given y is a prime number less than 6   possible values of y are 2 3 5   given, x=y*(y+1)   if y = 2 x=2*3= 
2*3 = 6
6   if y= 3 x=3*4= 
3*4 = 12
12   if y= 5 x=5*6= 
5*6 = 30
30   so possible values of x are 6,12,30   So from options   A. 5x can be (5*6)   B. 11x can be (11*12)   C. 13x can be (13*12)   D. 30x can be (30*31)   E. 58x cannot be   So answer option e) 58x
Answer: E
Find for what value(s) of k would there be an unique solution for the given set of questions.
2x - 3y = 1 and kx + 5y = 7	Choose the correct option:	A) -10/3	B) -10/9	C) -10/0	D) -10/1	E) -10/2

Solution: : If two equations ax + by = M and cx + dy = N have a unique solution, then ac≠bdac≠bd   So in the above problem, k ≠−10/3   -10/3nswer:-10/3
Answer: A
9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?	Choose one.
A) 18	B) 17	C) 12	D) 19	E) 12

Solution: 9M + 12B ----- 12 days   12M + 12B ------- 10 days   10M + 10B -------?   108M + 144B = 120M +120B   24B = 12M => 1M = 2B   18B + 12B = 30B ---- 12 days   20B + 10B  18  + 12= 
 18  + 12 = 30
30B ---- 12 days   20B + 10B = 30B -----?   20  + 10= 
  20  + 10 = 30
30B -----?=> 12 days   Answer: 12
Answer: C
A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 11 years. What is the average age (in years) of the family?	Choices
A) 26 B) 28 C) 30 D) 32 E) 34

Solution: Total age of the grandparents = 66 Ã— 2 = 132   Total age of the parents = 40 Ã— 2 = 80   Total age of the grandchildren = 11 Ã— 4 = 44   Average age of the family = (132+80+44)/8 = 256/8= 
256/8 = 32
32 years   The answer is 32.
Answer: D
Shanmukham buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods Pick one
A) 6999.2  B) 6876.1  C) 6654  D) 7000  E) None of these

Solution: Explanation :   Rebate = 6% of Rs. 6650 = Rs. 6/100 x 6650 = Rs. 399.   Sales tax = 10% of Rs. (6650 399) = Rs. 10/100 x 6251 = Rs. 625.10   Final amount = Rs. (6251 + 625.10) = Rs. 6876.10   Answer : 6876.1
Answer: B
A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
Pick one
A) Rs. 7.98 B) Rs. 8 C) Rs. 8.50 D) Rs. 9 E) Rs. 9.50

Solution: petrol used in 1st yr = 4000/7.5 = 533.33 ltr   petrol used in 2nd yr = 4000/8= 
4000/8 = 500
500 ltr   petrol used in 3 rd year= 4000/8.5= 470.59 ltr   Total petrol used for Rs.12000(4000/- for each yaer) in 3rd yrs = 1503.92 ltr   Rs. 7.98verage cost per litre = 12000/1503.92 = Rs 7.98   Rs. 7.98NSWER:Rs. 7.98
Answer: A
Sum of the squares of three numbers is 129 and the sum of their products taken two at a time is 250. Find the sum?	Choose the correct choice from the following.
A) 20	B) 23	C) 25	D) 26	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 129 + 2* 250   a + b + c = √529 = 23   23
Answer: B
Nitin borrowed 8000 at the rate of 6% p.a. for the first three years, 8% p.a.for the next five years and 12% p.a.for the period beyond eight years. At the end of eleven years how much money did he give as interest?	Answers:
A) 8000  B) 10,000  C) 5,000  D) 7,520  E) None of these

Solution: Let the interest be i Then,   (8000×3×6/100)+(8000×5×8/100)+(8000×3×12/100)=i   ⇒ 1440 + 3200 + 2880 = i   ⇒ i = 7520   Answer 7,520
Answer: D