MU-NLPC/Calc-aqua_rat huggingface dataset:
In the coordinate plane, points (x, 1) and (18, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y = Answers:	A) 4.5	B) 7	C) 8	D) 11	E) 12

Solution: Line k passes through the origin and has slope 1/2 means that its equation is y=1/2*x.   Thus: (x, 1)=(2, 1) and (18, y) = (18,9) --> x+y=2+9= 
2+9 = 11
11.   Answer: 11.
Answer: D
David obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Physics, Chemistry and Biology.What are his average marks? Choose the correct choice from the following options
A) 65  B) 69  C) 72  D) 75  E) 79

Solution: add all those marks and divide it by 5 becz they gave us 5 subjects for finding average marks we need to divide them   add them 76+65+82+67+85/5=375/5= 
375/5 = 75
75   ANSWER:75
Answer: D
In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
Pick:
A) 6!/2!  B) 3!*3!  C) 4!/2!  D) 4! *3!/2!  E) 3!*3!/2

Solution: In the word ABACUS , there are 3 vowels - 2 A's and U   Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together   = (4! * 3! )/2!   We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .   The entire vowel group is considered as a single group .   Answer 4! *3!/2!
Answer: D
The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 50% more than the price of the other, what is the price of each of these two oranges?
Select the correct option:
A) Rs 5, Rs 7.50  B) Rs 10.4, Rs 15.6  C) Rs 10, Rs 16  D) Rs 12, Rs 14  E) None of these

Solution: Explanation :   Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]   = Rs. (120 - 94) = Rs. 26.   Let the price of one orange be Rs. x.   Then, the price of other orange = Rs. (x + 50% of x) = Rs. x + 1/2x = Rs. 3x/2   So, x + 3x/2 = 26   5x = 52   x = 10.4   The prices of the two oranges are Rs. 10.4 and Rs. 15.6   Answer : Rs 10.4, Rs 15.6
Answer: B
4!/(4-3)!=? Choose the correct option
A) 24 B) 34 C) 35 D) 36 E) 39

Solution: 4!/(4-3)!=4!/1!4 /(4-3)= 
4 /(4-3) = 4
4!/1!=4*3*24 /1= 
4 /1 = 4
4*3*2= 
4*3*2 = 24
24. Hence, the correct answer is 24.
Answer: A
A chain smoker had spent all the money he had. He had no money to buy his cigarettes. Hence, he resorted to join the stubs and to smoke them. He needed 4 stubs to make a single cigarette. If he got a pack of 10 cigarettes as a gift, then how many cigarettes could he smoke in all?
Pick:
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: Explanation :   10 cigarettes will produce 10 stubs.   Since, out of 10 cigarettes,   =>8 cigarettes' stubs gives 2 cigarette and, 2 stubs are still left.   =>these 2 gigarette will give 2 stubs.   Now, he will make 1 more cigarette by using 2stubs + 2 stubs.   Hence, total number of cigarettes will be 10 + 2 + 1 i.e 13.   Answer : 13
Answer: D
Score Interval Number of Scores
50-59 2
60-69 10
70-79 14
80-89 27
90-99 18
The table shows a distribution of test scores. Which score interval contains the median of the 71 scores?	Pick one
A) a) 60-69
B) b) 70-79
C) c) 80-89
D) d) 90-99
E) e) Cannot determine.

Solution: 36th person   80-89 c) 80-89
Answer: C
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?	Choose the correct option.
A) 91.5
B) 92
C) 93
D) 94
E) 95

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5nswer: Option 91.5
Answer: A
If a truck is traveling at a constant rate of 36 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) Pick one.
A) 18 B) 24 C) 60 D) 36 E) 48

Solution: Speed =36 Km/hr => 36,000 m/hr   In one minute => 36000/60= 
36000/60 = 600
600 meters   In one sec=> 600/60= 
600/60 = 10
10 meters   Time= Total distance need to be covered / Avg. speed   => 600/ 10= 
600/ 10 = 60
60 and hence the Answer : 60
Answer: C
A fast food company plans to build 4 new restaurants. If there are 14 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.
Pick one
A) 1001  B) 495  C) 364  D) 2002  E) 756

Solution: The number of ways of choosing 4 sites out of 14 are counted by = 14C4 ways = 1001   1001nswer: Option 1001
Answer: A
Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?  Choose one:
A) 229
B) 277
C) 202
D) 540
E) 223

Solution: A+B+C = 1170   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   Answer:540
Answer: D
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Choose the correct choice from the following choices:
A) 338 B) 2677 C) 288 D) 285 E) 261

Solution: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 20)/100] = Rs. 285.   Answer: 285
Answer: D
A man purchases 2 watches for $ 900. He sells one at 10% loss and the other at a profit of 20%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :  Pick one
A) $ 900 and $ 300	B) $600 and $ 900	C) $900 and $450	D) $600 and $300	E) $550 and $ 350

Solution: x + y = 900 --- (1)   0.90x + 0.80y = 900--- (2)   (2) - (1) --> -.10x +.20y = 0   10x = 20y   x/y = 2/1 = (2*300)/(1*300) = 600/300   Answer: $600 and $300
Answer: D
If a man reduces the selling price of a fan from 400 to 380 his loss increases by 20% .What is the cost price of fan  Choose one
A) 300	B) 400	C) 500	D) 600	E) 700

Solution: increase in loss=20%   consider loss is x initially, so final loss will increase by .2x which is equal to 20.   .2x=20   x=100,   so total cost =selling price +loss=400+100= 
400+100 = 500
500.   so ans is 500.   ANSWER:500
Answer: C
John and Steve are speed walkers in a race. John is 10 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
Pick one
A) 13 seconds
B) 17 seconds
C) 24 seconds
D) 34 seconds
E) 51 seconds

Solution: Let t be the time that John spent for his final push.   Thus, per the question,   4.2t = 3.7t+10+2 ---> 0.5t = 12 ---> t = 24 seconds.   24 seconds is the correct answer.
Answer: C
The length of rectangle is thrice its breadth and its perimeter is 56 m, find the area of the rectangle? Pick.
A) 432	B) 252	C) 299	D) 276	E) 111

Solution: 2(3x + x) = 96   l = 36 b = 7   lb = 36 * 7= 
36 * 7 = 252
252   252
Answer: B
There are different 5 circles. What is the number of the greatest possible points with which the circles intersect?
Choose the correct option
A) 20
B) 10
C) 15
D) 22
E) 21

Solution: Maximum points of intersection between n different circles = n*(n - 1) = 5*4= 
5*4 = 20
20   20nswer: 20
Answer: A
The speed of a boat in still water is 10 km/hr. If it can travel 78 km downstream and 42 km upstream in the same time, the speed of the stream is Options: A) 3 km/hr B) 12 km/hr C) 1.5 km/hr D) 4.4 km/hr E) None of these

Solution: Explanation :   Let the speed of the stream be x km/hr. Then   Speed upstream = (10-x) km/hr   Speed downstream = (10+x) km/hr   Time taken to travel 78 km downstream = Time taken to travel 42 km upstream   => 78/(10+x) = 42/(10−x)   => 26/(10+x) = 14/(10−x)   =>13/(10+x) = 7/(10−x)   =>130 − 13x = 70 + 7x   =>20x = 60   => x = 3 km/hr   3 km/hrnswer : Option 3 km/hr
Answer: A
Two cylindrical candles of the same height but different diameters are lit at the same time. The
first is consumed in 4 hours and the second in 3 hours. Assuming that they burn at a constant
rate, how long after being lit was the first candle twice the height of the second candle?  Select.
A) 1 hr	B) 1 hr 12 min	C) 2 hr	D) 2 hr 12 min	E) 2 hr 24 min

Solution: Assume each candle is 1 unit high. Since the burn rates are 1/3 and 1/4 units   per hour, after t hours they have been consumed by an amount of t/3 and t/4. We want   1- t=4 = 2(1 - t=3). This occurs when t = 2.4 = 2*24/60 hrs.   correct answer 2 hr 24 min
Answer: E
If m and n are positive integers and m^2 + n^2 = 20, what is the value of m^3 + n^3? Choose the most appropriate option
A) 72
B) 224
C) 320
D) 512
E) 1,600

Solution: You need to integers which squared are equal 20.   Which could it be ? Let's start with the first integer:   1^2 = 1   2^2 = 4   3^2 = 9   4^2 = 16   Stop. The integers can't be greater than 4 or we will score above 20.   The second integer need to be picked up the same way.   1^2 = 1   2^2 = 4   3^2 = 9   4^2 = 16   The only pair that matches is 4^2 + 2^2 = 20.   So 4^3 + 2^3 = 72.   72nswer 72.)
Answer: A
If 144/x is an integer and 72/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. Choose the correct option:  A) I, II, and III  B) I and II only  C) III only  D) II and III only  E) I only

Solution: The largest possible value of x is 36 (the greatest common factor of 144 and 72), and if x=36 then   III only
Answer: C
There are 5 people and 5 chairs. In how many different ways people can occupy the chairs?	Choose the correct choice from the following answers:
A) 12
B) 15
C) 24
D) 36
E) 120

Solution: number of ways =5! = 120   Answer is 120
Answer: E
Q. How many 4-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3?	Select the correct option:
A) 180	B) 240	C) 210	D) 270	E) 300

Solution: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2   i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _   case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6   when the units digit is 2 i.e 1 _ _ _ _ _ 2   number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60   when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30   case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)   number of ways this can be done would be 5! / (2!) for 2 =60   and 5! / 2! for 6 ... = 60   adding all of these ... gives the answer 300 ...   the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat   300
Answer: E
There are 16 cans in the refrigerator. 9 of them are red and 7 of them are blue. In how many ways we can remove 10 cans so that at least one red and at least one blue cans to remain the refrigerator. Select the correct option:  A) 460  B) 490  C) 833  D) 455  E) 445

Solution: Ways to pick 6 cans so that at least one red and at least one blue cans to remain the refrigerator =   total ways to pick 6 can out of 12 - ways to pick 6 red out of 7 red - ways to pick 6 blue out of 5 blue   128336âˆ’98336âˆ’78336=924âˆ’84âˆ’7=833   ANSWER:833
Answer: C
This is a famous probability puzzle in which you have to choose the correct answer at random from the four options below.
Can you tell us whats the probability of choosing correct answer in this random manner.
Choose the correct choice from the following
A) 0%  B) 2%  C) 3%  D) 6%  E) 1%

Solution: A   0%   Explanation:   1) why cant be 1/4 : If the answer is 1/4, then as we know two out of four answer choices is '1/4', the answer has be 1/2.   This is a contradiction, so the answer cannot be 1/4.   2) why cant be 1/2 : If the answer is 1/2 then because answer:"1/2" is 1 out of 4 answer choices, the answer must be 1/4. This is also a contradiction. So the answer cannot be 1/2.   3) why cant be 1 : If the answer is 1 then because answer:"1" is 1 out of 4 answer choices, the answer must be 1/4. 0%gain the same contradiction and therefore answer cannot be 1.
Answer: A
If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a club or a red jack? Choose the correct choice from the following options.
A) 7/13 B) 4/7 C) 15/52 D) 9/13 E) 19/26

Solution: There are 13 clubs and 2 red jacks.   P(club or red jack) = 15/52 = 15/52   The answer is 15/52.
Answer: C
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? Choose the correct choice.
A) Rs.429 B) Rs.480 C) Rs.429 D) Rs.128 E) Rs.419

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 25% = 25% of 640 = Rs.160   SP = CP - Loss = 640 - 160   = Rs.480   Answer:Rs.480
Answer: B
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?  Options.
A) $15,594 B) $15,322. C) $14,786 D) $14,543 E) $12,988

Solution: price of the car in 1990 = $11500   from 1990 to 1996   increase = 13%   which is (13*115)   price of the car in 1996= $12995   from 1996 to 2001   increase = 20 %   which is   (12995)/5= 
  (12995)/5 = 2_599
2599   price of the car in 2001= 15594   $15,594NSWER:$15,594
Answer: A
If a dealer wants to earn 20% profit on an article after offering 30% discount to the customer, by what percentage should he increase his marked price to arrive at the label price?  Choose the correct answer
A) 71 3/7%  B) 50%  C) 75%  D) 60 2/3%  E) 90%

Solution: Profit = 20%   discount = 30%   Required answer = (20+30 / 100-30)*100 = 71 3/7 %   71 3/7%nswer is 71 3/7%
Answer: A
The area of a square is equal to five times the area of a rectangle of dimensions 36 cm * 20 cm. What is the perimeter of the square?	Choose the correct choice from the following:  A) 289 cm  B) 800 cm  C) 829 cm  D) 240 cm  E) 289 cm

Solution: Area of the square = s * s   = 5(36 * 20)   => s = 60   = 60 cm   Perimeter of the square   = 4 * 60= 
4 * 60 = 240
240 cm.   Answer: 240 cm
Answer: D
Three dwarves and three elves sit down in in the row of six chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit.  Choices.
A) 72	B) 74	C) 76	D) 78	E) 80

Solution: The elves and dwarves must alternate:   e d e d e d or d e d e d e   Considering the first case, the total number ways is to rotate the elves 3! times while keeping the dwarves to one combination. Then rotate the dwarves 3! times while keeping the elves to one combination.   However, that is only for the first case. We must multiply by 2 as we need to account for the second case.   Total = 3! * 3! * 2 = 72   72NS:72
Answer: A
Find the value of x from the below equation? : 3x^2+6x+3 = 0 Choose one.
A) -5/6	B) 5/6	C) 5	D) 6	E) 25

Solution: a = 3, b = 6, c = 3   x1,2 = (-5 Â± âˆš(6^2 - 4Ã—3Ã—3)) / (2Ã—3) = (-5 Â± âˆš(36-36)) / 6 = (-5 Â± 0) / 6   x1 = X2 = -5/6   -5/6
Answer: A
You collect coins. Suppose you start out with 11. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?  Select:	A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Solution   Start with 11 coins.   Sharon takes 3 coins from you:   11 - 3= 
  11 - 3 = 8
8 coins.   Steven takes 4 coins from you:   8 - 4= 
  8 - 4 = 4
4 coins.   So you have 4 at the end.   4orrect answer : 4
Answer: C
At night a man who is 6 feet tall stands 5 feet away from a lamppost. The lamppost’s lightbulb
is 16 feet above the ground. How long is the man’s shadow?	Choose the correct choice from the following: A) 15/8 feet B) 3 feet C) 10/3 feet D) 4 feet E) 5 feet

Solution: Let x be the length of the man’s shadow. 10/3 feetonsidering similar triangles we get   x/x + 5   =   6/16   correct answer 10/3 feet
Answer: C
At what price must an Book costing $47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
Choose the correct choice.
A) 72.5
B) 64.5
C) 62.5
D) 82.5
E) 60.5

Solution: C   $62.50   CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(92/100)= 59.375   MP = 64.5   64.5
Answer: B
In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr? Choose one
A) 2.55 sec B) 2.9 sec C) 1.3 sec D) 3.75 sec E) 1.8 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40   = 3.75 sec.   Answer:3.75 sec
Answer: D
A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.	Select the correct option:  A) 180  B) 130  C) 140  D) 160  E) 288

Solution: White:Yellow = x:(x+90) = 8:13 --> 13x = 8x + 720 --> x = 144.   The total # of balls originally x + x = 144 + 144= 
144 + 144 = 288
288.   Answer: 288.
Answer: E
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?  Choose the correct answer:
A) 15  B) 18  C) 12  D) 17  E) 20

Solution: Face value of each share = Rs.20   Dividend per share = 9% of 20 = 9×20/100=9/5   He needs to have an interest of 12% on his money   ie, Money Paid for a share×12/100=9/5   Money Paid for a share=9/5×100/12=15   ie, Market Value of the share = Rs.15   15nswer is 15.
Answer: A
Which of the following cannot be the sum of 4 different prime numbers?  Choose the correct choice from the following
A) 21
B) 17
C) 29
D) 32
E) 30

Solution: Option A: 21 = 2+3+5+11. Sum of 4 different prime numbers   Option B: 17 = 2+3+5+7. Sum of 4 different prime numbers   Option C: 29 = 2+3+7+17. sum of 4 different prime numbers   Option D: 32 = 5+3+11+13. Sum of 4 different prime numbers   Option 30: 30 = This is not a Sum of 4 different prime numbers   Correct Option:30
Answer: E
What is the distance from (–7, 2) to (5, –3)?
Choose the correct answer.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: solutions   Suppose we made a right triangle, as in the example above. The difference in the x-coordinates is (–7) – 5 = –12, so the horizontal leg would have a length of 12 (length has to be positive). The difference in the y-coordinates is 2 – (–3) = 5, so this is the length of the vertical leg. We recognize that we have a common Pythagorean triplet, so we don’t even need to perform a calculation: we know the length of the hypotenuse, and hence, the distance between the two points, is 13. Answer = 13
Answer: D
A large box contains 20 small boxes and each small box contains 32 chocolate bars. How many chocolate bars are in the large box?  Select the correct option:
A) A)220
B) B)490
C) C)380
D) D)450
E) E)640

Solution: the only thing you have to do is a simple multiply   we have:   20*32= 
20*32 = 640
640   correct answer is:   640) 640
Answer: E
In an athletic event with N participants, if 1/5 could not complete 100 meter race within cut off time of 10 seconds. And of those who didnt clear 100 meter race within cut off time, 1/3 also did not qualify in long jump. How many athletes cleared both events ?
Choose the correct choice
A) N/15  B) 4N/15  C) 14N/15  D) N/5  E) 4N/5

Solution: 1/5 did not clear running event, thus N/5 did not clear.   Of those who didnt clear running event, 1/3 also did not clear long jump event, thus 1/3*N/5 = N/15 had both not cleared both events.   Therefore, N - N/15 = 14N/15 cleared both events.   Answer: 14N/15.
Answer: C
Simple question but big one on average age.sth like a, b, c weighted separately 1st a, b, c ,then a& b, then b &c then c & a at last abc, the last weight was 167,then what will be the average weight of the 7 reading?  Choose the correct choice from the following choices:
A) 32	B) 92	C) 94	D) 95	E) 100

Solution: avg=A+B+C+(A+B)+(B+C)+(C+A)+(A+B+C)/7   Now,4A+4B+4C/7   =4(167)/7 (GIVEN ABC=167)   =95.43   ANSWER:95
Answer: D
How many prime numbers n exist such that 90 < n < 106 and n is a factor of 99999919? Pick
A) Zero B) One C) Two D) Three E) More than three

Solution: There are 3 primes in the range: 97, 101 and 103.   99,999,919=10^8−81=(10^4+9)(10^4−9)   =(10^4+9)(10^2+3)(10^2−3)   =10,009∗10^3∗97   97 and 103 are factors of 99,999,919 but 101 is not a factor of 10,009. Thus 2 primes from the range are factors of 99,999,919.   Answer: Two.
Answer: C
In an election between the two candidates ,The candidates who gets 60% of votes polled is winned by 280 votes majority. What is the total number of votes polled?
Options:
A) 1400	B) 1600	C) 1800	D) 2000	E) 2100

Solution: Note : majority (20 %) = difference in votes polled to win (60 %) & defeated candidates (40 %)   20 % = 60 % - 40 %   20% -----> 280 (20×14 = 280 )   100% -----> 1400 (100×14 = 1400)   1400)
Answer: A
A can complete a work in 15days and B can do the same work in 7days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work?  Choose the correct choice.
A) 2days  B) 5 1/2 days  C) 6 1/2 days  D) 7 1/2days  E) 10days

Solution: The required answer = (15-3)*7 / 15 = 84/15 = 5 1/2 days   Answer is 5 1/2 days
Answer: B
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is Choose the correct choice from the following options:
A) 8 B) 9 C) 13 D) 15 E) 17

Solution: Solution   Let the three numbers be x, x+2, x+4   Then 3x = 2(x+4) + 3   ‹=›x = 11   Third integer = x + 4 = 15.   Answer 15
Answer: D
A customer went to a shop and paid a total of $40, out of which $1.28 was for sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items? Choose the correct option
A) $19.54	B) $2076	C) $21.36	D) $22.72	E) $23.58

Solution: The total cost was $40.   The tax was $1.28   Let the original price of the taxable items = x   Given that tax rate = 8%   0.08x = 1.28   x = $16   The cost of the tax free items was $40 - $16 - $1.28 = $22.72   The answer is $22.72.40 -  16 -  1.28= 
40 -  16 -  1.28 = 22.72
$22.72   The answer is $22.72.
Answer: D
If |x^2 − 6| = x, which of the following could be the value of x?  Choose the correct answer.
A) –3  B) –2  C) 0  D) 1  E) 2

Solution: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.   First, let's assume that x^2-6 is negative.   -(x^2 - 6) = x   x^2 + x - 6 = 0   (x+3)(x-2) = 0   x = 2 or x = -3 (However, x can not be negative.)   Then x=2 is a possible value for x.   The answer is 2.
Answer: E
The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (g) around the mirror, which of the following could be the value, in inches, of g ?
I. 2
II. 3 1/2
III. 5 Choose the correct choice from the following answers:
A) I only
B) III only
C) I and II only
D) I and III only
E) I, II, and III

Solution: Area of picture = 16x Area of frame = 33x   Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.   This results in g value to be a multiple of 1.5 = multiple of 3/2 and since g is not constrained to be only integer all the three choices are possible   For i) the multiple of g is 4/3   For ii) the multiple of g is 7/3   For iii) the multiple of g is 10/3   The key is g can be any real positive number... very tricky problem.. took me > 15 minutes.   Answer is I, II, and III
Answer: E
A reduction of 46% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? Choose the most appropriate option.
A) 2.45 B) 8.45 C) 7.45 D) 3.45 E) 1.45

Solution: Explanation:   40*(46/100)= 
40*(46/100) = 92/5 = around 18.4
18.4 --- 64   ? --- 12=> Rs.3.45   Answer: 3.45
Answer: D