MU-NLPC/Calc-aqua_rat huggingface dataset:
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points N is in the same quadrant as the fourth vertex of the square?	Choose the correct option.
A) (-5, -3)  B) (-5, 3)  C) (5, -3)  D) (3, -5)  E) (3, 5)

Solution: The question:In the xy-plane, the points N=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?   I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means   Vertex #1 = (c, d) is in QII (that is, negative x and positive y)   Vertex #2 = (c, -d) is in QIII (that is, both xy negative)   Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)   That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =(3, 5).
Answer: E
0.05 x 0.0173 is equal to:  Choices:
A) 8.65 x 10(power -4)	B) 6.84 x 10(power -4)	C) 4.68 x 10(power -4)	D) 5.48 x 10(power -4)	E) None of them

Solution: 5 x 173 = 865. Sum of decimal places = 6.   So, 0.05 x 0.0173 = 0.000865 = 8.65 x 10(power -4)   8.65 x 10(power -4)nswer is 8.65 x 10(power -4).
Answer: A
A loan of Rs.700 is made at 9.5% simple interest for 4 months. How much interest is owed when the loan is due?  Choose the correct choice from the following answers
A) 22.167
B) 23.167
C) 24.167
D) 25.167
E) 26.167

Solution: si=p*r*t/100   =700*9.5*4/100*12   =22.167   22.167NSWER:22.167
Answer: A
If a number is 30% more than the another, how much % is the smaller number less than the first ? Choose the correct option.
A) 23%  B) 25%  C) 16(1/3)%  D) 17%  E) none of these

Solution: Take a number 100,   Then the other number is 130   % the smaller number is less than the first = [(30/(130)) x 100]% = 23%.   23%NSWER:23%
Answer: A
A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 10,800, then what is B's share in the profit? Choose the correct choice from the following choices:
A) Rs. 2000  B) Rs. 3000  C) Rs. 4000  D) Rs. 5000  E) None of these

Solution: Explanation :   Ratio of the initial investment = 7/2 : 4/3 : 6/5   = 105 : 40 : 36   From this ratio, we can assume that actual initial investments of A, B and C   are 105x, 40x and 36x respectively   A increases his share 50% after 4 months. Hence the ratio of their investments =   (105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12   = 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3   = 105 * 4 : 40 *3 : 36 * 3   = 35 * 4 : 40 : 36   = 35 : 10 : 9   B's share = total profit * (10/54) = 10,800 * 10/54 = 2000. Rs. 2000nswer : Option Rs. 2000
Answer: A
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?  Choose the correct answer:
A) 12
B) 77
C) 66
D) 88
E) 94

Solution: S = 1   M = x   DS = x + 1   US = x - 1   35/(x + 1) + 35/(x - 1) = 12   x = 6   12nswer:12
Answer: A
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 9:30 am. They shall first cross each other at ?
Select
A) 7:15 am  B) 7:30 am  C) 9: 42 am  D) 7:50 am  E) 7:60 am

Solution: Explanation:   Relative speed between two = 6-1= 
6-1 = 5
5 round per hour   They will cross when one round will complete with relative speed,   which is 1/5 hour= 12 mins.   So 9:30 + 12 mins = 9:42   Option 9: 42 am
Answer: C
a, b, c, and d are positive integers where a is divisible by b and c is divisible by d. Which of the following is NOT necessarily an integer? Choose the correct choice from the following options
A) (ac)/(bd) B) a/b + c/d C) (a + c)/(b + d) D) (abc)/d E) (acd)/b

Solution: As per the question, let a = 10, b = 5, c = 6, and d = 2. Plugging these into the answer choices, only (a + c)/(b + d) does not yield an integer.
Answer: C
In a card game, a combination of three queens beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
Answers
A) 1/5425
B) 1/5550
C) 1/5600
D) 1/5555
E) 1/5525

Solution: he best possible combination is the case when he wins in his first two draws   There are 52 cards in a deck of cards with 4 queens in it.   Probability of first card to be queen = 4/52   Probability of Second card to be queen = 3/51   Probability of third card to be queen = 2/50   Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525   1/5525
Answer: E
The probability that a number selected at random from first 50 natural numbers is a composite number is  Choose one:
A) 21/25 B) 17/25 C) 4/25 D) 8/25 E) 10/25

Solution: The number of exhaustive events = 50C1 = 50. We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Therefore, Required probability = 34/50 = 17/25.   ANSWER:17/25
Answer: B
If x^4 + y^4 = 20, then the greatest possible value of x is between:
Choose the correct choice from the following answers.
A) 0 to 2
B) 2 to 4
C) 4 to 6
D) 6 to 8
E) 8 to 10

Solution: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.   We're told that X^4 + Y^4 = 20. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....   X^4 = 20   Looking at the answers, it makes sense to see what 2^4 equals....   2^4 = 16   Since that is BELOW 20, and 3^4 will clearly be MORE than 20, we have the correct answer.   Final 0 to 2nswer:   0 to 2
Answer: A
Find the value of 1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]
Options:
A) 800
B) 500
C) 900
D) 1200
E) None

Solution: Answer   1.5 x [(3.6 x 0.48 x 2.50) / (0.12 x 0.09 x 0.5)]   = 1.5 x [(36 x 48 x 250) / (12 x 9 x 5)]   = 1.5 x 4 x 4 x 50 = 1200   Correct Option: 1200
Answer: D
Sahil purchased a machine at Rs 11000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
Choices:
A) Rs. 22500
B) Rs. 25500
C) Rs. 26000
D) Rs. 28000
E) None of these

Solution: Explanation:   Question seems a bit tricky, but it is very simple.   Just calculate all Cost price, then get 150% of CP.   C.P. = 11000 + 5000 + 1000= 
11000 + 5000 + 1000 = 17_000
17000   150% of 17000= 150/100 * 17000= 
150/100 * 17000 = 25_500
25500   Option Rs. 25500
Answer: B
A sum of Rs.1550 was lent partly at 8% p.a. simple interest. The total interest received after 3 years was Rs.300. The ratio of the money lent at 5% to that lent at 8% is :
Choose the correct choice from the following options.
A) 16:18  B) 16:10  C) 16:15  D) 16:11  E) 16:12

Solution: let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then,   Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300   Required ratio = x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15   Answer: 16:15) 16:15
Answer: C
A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?	Choices.
A) 9	B) 15	C) 18	D) None of these	E) Cannot be determined

Solution: Explanation:   Let the number be x.   Therefore,   3(2x + 5) = 105   6x + 15 = 105   6x = 90   x = 15   ANSWER: 15
Answer: B
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Pick one:
A) 253m	B) 239m	C) 236m	D) 240m	E) 230m

Solution: Relative speed = (120 + 80) km/hr   200 x5/18= 500/9 m/sec   Let the length of the other train be x metres.   Then,x + 270/9	=500/9   x + 270 = 500   x = 230m   Answer 230m
Answer: E
A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 25%. What quantity of whisky is replaced ?	Pick:
A) 1/3
B) 2/3
C) 2/5
D) 3/5
E) 4/5

Solution: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.   Let x ml be the amount removed ---> total alcohol left = 4-0.4x   New quantity of whiskey added = x ml out of which 0.19 is the alcohol.   Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.   Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/5.   Hence, 2/5 is the correct answer.
Answer: C
Two trains start from two opposite directions towards each other. The stations from which they start are 50 miles apart. Both the trains start at the same time on a single track. A falcon which is sitting on one train. starts at the same time towards the other train. as soon as it reaches the second one, it flies back to the first train and so on and so forth. It continues to do so, flying backwards and forwards from one train to the other until the trains meet.
Both the trains travel at a speed of 25 miles per hour, and the bird flies at 100 miles per hour.
How many miles will the falcon have flown before the trains meet? Answers: A) 100 miles B) 140 miles C) 107 miles D) 230 miles E) 321 miles

Solution: A   100 miles   The train travel at 25 miles per hour. Therefore, they will meet after travelling for one hour and the falcon also must have been flying for one hour. Since it travel at 100 miles per hour, the bird must have flown 100 miles.
Answer: A
The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (a) around the mirror, which of the following could be the value, in inches, of a ?
I. 2
II. 3 1/2
III. 5
Choose the correct answer
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 a value to be a multiple of 1.5 = multiple of 3/2 and since a is not constrained to be only integer all the three choices are possible   For i) the multiple of a is 4/3   For ii) the multiple of a is 7/3   For iii) the multiple of a is 10/3   The key is a can be any real positive number... very tricky problem.. took me > 15 minutes.   Answer is I, II, and III
Answer: E
The edges of a cuboid are 2 cm, 5 cm and 8 cm. Find the volume of the cuboid?
Answers:
A) 90  B) 80  C) 40  D) 120  E) 70

Solution: 2*5*8= 
2*5*8 = 80
80   Answer: 80
Answer: B
There are x numbers in list L, where x is a positive integer, and there are y numbers in list M, where y is a positive integer. The average (arithmetic mean) of the numbers in list L is p, and the average of all the numbers in both lists L and M is q. Which of the following expressions is the average of the numbers in list M?
Options:
A) (qy - px) / x B) (qy - px) / y C) (p + q)x / y D) [(q - p)x - py] / (x + y) E) [(q - p)x + qy] / y

Solution: You can eliminate Answer A (it divides by 2)   Answer B: (QY-PX)/Y = (7.8 - 4)/3 = 3.8/3 This is clearly too small. Eliminate B.   Answer C: (P+Q)X/Y = (4.6)(2)/3 = 9.2/3 This is too big. Eliminate C.   Answer E is all that's left, but I'll check it just to be sure....   Answer E: [(Q-P)X +QY]/Y = [(0.6)(2) +7.8]/3 = 9/3= 
9/3 = 3
3. This is a MATCH.   Final Answer:[(q - p)x + qy] / y
Answer: E
In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = g is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-g, -k), then what are the coordinates of the point P?  Choices: A) (-5g, -5k) B) (-3g, -3k) C) (2g, 2k) D) (3g, 3k) E) (5g, 5k)

Solution: firstly the Question tells us that RQ and PQ are perpendicular at Q..   Now the coordinates of the point R are (-g, -k), so R is at a distance of 2g from line x and at dist of 2k from line Y..   as line X bisect RQ .... length of RQ =4g and coord (3g,-k)..   as line Y bisect PQ .... length of PQ =4k and coord (3g,3k).ans (3g, 3k)
Answer: D
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the longer sides? Choose the correct choice
A) 4	B) 7	C) 8	D) 13	E) 26

Solution: This question can be solved algebraically or by TESTing THE ANSWERS.   We're told that a rectangle has an area of 104 and a perimeter of 42. We're asked for the length of one of the LONGER sides of the rectangle.   Since the answers are all INTEGERS, and the area is 104, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 104, so the correct answer is probably A or C.   Let's TEST Answer C: 8   IF...   The shorter side = 8...   The area = 104....104/8 = 13 = the longer side   Perimeter = 8+8+13+13= 
8+8+13+13 = 42
42   13
Answer: D
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? Answers:
A) 81288  B) 2776  C) 3777  D) 8112  E) 2887

Solution: A = 7500(26/25)2 = 8112.Answer: 8112
Answer: D
A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 6 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 62 unique alphanumeric case sensitive characters. Options:
A) 63^4
B) 62^5
C) 62(62^4)
D) 63(62^5)
E) 63(62^6)

Solution: Total number of passwords = number of 6 character password +number of 5 character password   = 62^6 + 62^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )   =62^5(1+ 62)   =62^5 * 63   Answer 63(62^5)
Answer: D
What will come in place of the x in the following Number series? 12, 38, 116, x,  Pick:	A) 2643	B) 350	C) 3456	D) 7554	E) 3158

Solution: 12   12 Ã— 3 + 2 = 38   38 Ã— 3 + 2 = 116   116 Ã— 3 + 2 = 350   350
Answer: B
Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay? Select the correct option:
A) 1/7
B) 1/9
C) 1/8
D) 1/4
E) 2/1

Solution: 3h = 5c   6c = 10s   1/7 = 21h*3 + 15c*2   = 63h + 30c   = 105c + 30c = 135c   B 105  + 30= 
105  + 30 = 135
135c   B= 15c*6 + 40s*7 1/2   = 90c + 300s   = 90c + 180c = 270c   1/7:B 90  + 180= 
90  + 180 = 270
270c   1/7:B= 135:270   27:52   1/7 = 27/79 = 1/3.1/7nswer:1/7
Answer: A
How many numbers between 300 and 500 begin or end with 3?
Choose the correct choice
A) 20  B) 60  C) 100  D) 110  E) 120

Solution: How many numbers between 300 and 500 begin or end with 3?   Just think that those numbers are:   i) The ones ending in 3: 303, 313, 323, ... , 493 --> 20 numbers   ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers   BUT 10 out of the first 20 numbers are repeated in the second set.   THEREFORE, the solution is 110 numbers.   Answer: 110
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Choose the correct choice from the following choices
A) 1/455
B) 1/452
C) 1/412
D) 1/129
E) 1/410

Solution: Explanation:   Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue = Â³Câ‚ƒ/Â¹âµCâ‚ƒ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455   1/455nswer: 1/455
Answer: A
6 In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Choose the correct choice from the following
A) 5 kmph  B) 6 kmph  C) 6.25 kmph  D) 7.5 kmph  E) 7.8 kmph

Solution: Let Abhay's speed be x km/hr.   Then,	30/X	-	30/2X	= 3   6x = 30   x = 5 km/hr. 5 kmphnswer: Option 5 kmph
Answer: A
How much does a watch lose per day, if its hands coincide every 64 minutes?  Answers:
A) 32 8⁄11 min.  B) 36 5⁄11 min.  C) 90 min.  D) 96 min.  E) None of these

Solution: 55 min. spaces are covered in 60 min.   60 min. spaces are covered in (60⁄55 × 60) min.   = 655⁄11 min.   Loss in 64 min. = (655⁄11 - 64) = 16⁄11 min.   Loss in 24 hrs. = (16⁄11 × 1⁄64 × 24 × 60) min = 328⁄11 min.   32 8⁄11 min.nswer 32 8⁄11 min.
Answer: A
The milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches. How many gallons of milk must be removed? (1 cu ft = 7.5 gallons) Choose one:
A) 100 B) 250 C) 750 D) 5625 E) 5635

Solution: 6 inches = 1/2 feet (there are 12 inches in a foot.), so  60*25*1/2= 
 60*25*1/2 = 750
750 feet^3 of milk must be removed, which equals to   750*7.5= 
  750*7.5 = 5_625
5625 gallons.   Answer: 5625.
Answer: D
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?
Choose the correct choice from the following choices
A) 4 days	B) 7 days	C) 8 days	D) 5 days	E) 43 days

Solution: Let 1 men's 1 day work = x and 1 boy's 1 day work = y.   Then, 6x + 8y = 1/10 and 26x + 48y = 1/2   Solving these two equations, we get:   x = 1/100 and y = 1/200   (15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4   15 men and 20 boys can do the work in 4 days.   4 daysnswer: 4 days
Answer: A
The population of 6 villages is 803,900,1100,1023,945 and 980.what is the population of the seventh village if the average population of the seven villages is 1000?  Choose the correct choice from the following choices.
A) 1134
B) 1238
C) 1348
D) 1500
E) 1249

Solution: Population of seventh village =7*1000-(803+900+1100+1023+945+980)= 
7*1000-(803+900+1100+1023+945+980) = 1_249
1249   Answer is 1249
Answer: E
a, b, c, d are positive integers such that exactly one of the following inequalities is false. Which inequality is false?  Choose the correct choice from the following answers:	A) a<b	B) c<d	C) a+c<b+c	D) a+c<b+d	E) a<b+c+d

Solution: Essentially, we need to find the statement thatcouldbe false if all the other statements are true.   The first thing that jumps out to me is statements A and C:   (A) a < b   (C) a+c < b+c   Regardless of the value of c, these statement are either both false or both true. Since only statement CAN be false, we can eliminate these two.   (E) a < b+c+d   Since c and d are both positive integers, and we have determined that statement A is true, statement E must be true as well. This leaves us with:   (B) c < d   (D) a+c < b+d   Since we know statement A (a < b) to be true, if statement B is true, statement D MUST be true. However, if statement D is true, as long as c-d < b-a, statement B does NOT have to be true.   Therefore, the answer isB: c < d. Good question, +1.
Answer: B
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $100?  Choose the correct choice from the following choices.
A) 4 B) 12 C) 15 D) 22 E) 24

Solution: you could set-up a quick table and brute force the answer.   A	4	*	50	200 1800	-200 1600	26 61.54   B	12	*	50	600 1800	-600 1200	18 66.67   C	15	*	50	750 1800	-750 1050	15 70.00   22	22	*	50	1000 1800	-1000	800	8 100.00   E	24	*	50	1200 1800	-1200	600	6 100.00   Answer is 22
Answer: D
A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
Choose the correct choice from the following options:
A) Rs.2400	B) Rs.1800	C) Rs.3600	D) Rs.6000	E) Rs.7000

Solution: 1200 * 12: x * 9 = 2:3   x = 2400   Rs.2400NSWER:Rs.2400
Answer: A
If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {12} + {10}?	Options:
A) 23
B) 20
C) 13
D) 5
E) 2

Solution: Soln:   {12} + {10} = 12*{10} +{10} = 13*{10}   ANSWER:13
Answer: C
The length of a rectangle is twice its breadth. If its lengthis decreased by 5cm & breadth is increased by 5cm, the area of the rectangle is increased by 75sq.cm. What is the length of the rectangle?  Choose the correct choice from the following options:
A) 25 cm	B) 30 cm	C) 40 cm	D) 45 cm	E) 60 cm

Solution: Let breadth =x cm   Then, length =2x cm   Area =x×2x=2x2 sq.cm.   New length =(2x−5) cm   New breadth =(x+5) cm   New area =(2x−5)(x+5) sq.cm.   Given that, new area = initial area +75 sq.cm.   ⇒(2x−5)(x+5)=2x2+75⇒2x2+10x−5x−25=2x2+75⇒5x−25=75⇒5x=75+25= 
75+25 = 100
100⇒x=1005=20 cm   Length =2x=2×20=40 cm   40 cm
Answer: C
A batsman scored 120 runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets? Choose the correct choice from the following answers:  A) 45  B) 58.33%  C) 600/11  D) 55  E) 35

Solution: Explanation :   Number of runs made by running,   =>120−(5×4+5×6).   =>120−(50).   =>70.   Hence, the required percentage is:-   =>70/120 * 100   =>58.33%   Answer : 58.33%
Answer: B
If |x^2 − 2| = x, which of the following could be the value of x? Choose the correct choice from the following answers
A) -2
B) -1
C) 0
D) 1
E) 4

Solution: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.   First, let's assume that x^2-2 is negative.   -(x^2 - 2) = x   x^2 + x - 2 = 0   (x+2)(x-1) = 0   x = 1 or x = -2 (However, x can not be negative.)   Then x = 1 is a possible value for x.   The answer is 1.
Answer: D
How many liters of water must be evaporated from 50 liters of a 6-percent sugar solution to get a 10-percent solution?  Choices.
A) 20	B) 22	C) 24	D) 26	E) 28

Solution: 6% of a 50 liter solution is 3L which is 10% of the solution at the end.   The solution at the end must be 30 L.   We need to evaporate 20 liters.   The answer is 20.
Answer: A
log3 N+log12 N what is 3 digit number N that will be whole number  Choose the correct answer.
A) 6291
B) 7292
C) 1728
D) 1929
E) 1727

Solution: No of values N can take is 1   12^3=1728   ANSWER:1728
Answer: C
Set X consists of all two-digit primes and set Y consists of all positive multiples of 4 less than 100. If the two sets are combined into one, what will be the range of the new set? Choose the correct choice from the following
A) 84
B) 93
C) 90
D) 92
E) 95

Solution: Set X = {11, 13, 17,............., 83, 89, 97}   Set Y = {4, 8, 12,..............., 88, 92, 96}   Combining two sets, say Set Z   Set Z = {4,8, 11, 12,13, 17, ..................., 83, 88, 89, 92, 96, 97}   Range = Max Value - Min Value   Range (Z) = 97 - 4= 
97 - 4 = 93
93   OA 93 is the answer.
Answer: B
A baker sold all of his donuts for a total amount of 216 pounds. If on each donut the baker made a profit of 8% of the cost, how much did it cost the baker to make all the donuts? Pick
A) 210.
B) 200.
C) 190.
D) 180.
E) 170.

Solution: THE CORRECT ANSWER IS B   Cost of donuts = X   Profit on one donut = 8%   Profit on all donuts is also =8% (Well, you must know why it is so !! IF you don't know then please revisist percentage chapter again.. ok ok.. i have given the explanation at the end of the solution.... understand it , if you are confused)   X+8% of X =216   1.08X=218   X=218/1.08   X=200   answer is 200.
Answer: B
A man purchases the milk at Rs. x per liter and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. Whatis the profit %?	Choose the most appropriate option
A) 145%  B) 150%  C) 155.7%  D) 166.6%  E) 176.5%

Solution: Let the cost price of 1 litre pure milk be Re.1, then   \inline{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}\rightarrow CP=Rs.6 only   and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16   Profit %= 166.66%   166.6%
Answer: D