MU-NLPC/Calc-aqua_rat huggingface dataset:
Compound interest of Rs.2000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).	Choose the correct option:
A) Rs.473  B) Rs.374  C) Rs.495  D) Rs.315  E) None of the above

Solution: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)   So compound interest=2000[1+(5/100)]^3 - 2000=2000[(21/20)^3 -1]   =2000(9261-8000)/8000   =2*1261/8   =315   ANSWER:Rs.315
Answer: D
he total marks obtained by a student in Physics, Chemistry and Mathematics is 170 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? Pick
A) 55	B) 65	C) 75	D) 85	E) 95

Solution: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.   P + C + M = 170 + P   C + M = 170   Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 170/2= 
170/2 = 85
85.   ANSWER:85
Answer: D
There are two sections Y and Z of a class, consisting of 288 and 352 students respectively. If the average weight of sections Y is 320 kg and that of sections Z is 280 kg. Find the average weight of the whole class	Choices:
A) 297.5 B) 298.0 C) 298.5 D) 299.0 E) None

Solution: Solution   Total weight of(288+352)Students	= (288x320+352x280)Kg   = 1,90,720 kg.   Average weight of the whole class	= (190720 / 640)   = 298.00.   Answer 298.0
Answer: B
In how many ways letters of the word RSCUPERATE be arranged?  Choose the correct choice from the following choices.
A) 275788 B) 287578 C) 4357809 D) 437479 E) 302400

Solution: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways   302400
Answer: E
Of the 100 athletes at a soccer club, 40 play defense and 68 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
Choose the correct option
A) 10 to 20  B) 10 to 40  C) 28 to 40  D) 30 to 70  E) 40 to 70

Solution: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.   {Total} = {defense} + {midfield} - {both} + {neither}   100 = 40 + 68 - {both} + {neither}   {both} = {neither} + 8.   Since the least value of {neither} is given to be 20, then the least value of {both} is   20+8= 
  20+8 = 28
28.Eliminate A and B.   Answer: 28 to 40.
Answer: C
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 4 students left over. What is the sum of the two smallest possible values of n?
Choose the correct choice from the following answers.
A) 30
B) 34
C) 38
D) 42
E) 46

Solution: n = 4k+1 = 5j+4   Let's start at 1 4 +1= 
4 +1 = 5
5j+4   Let's start at 1= 4(0)+1 and keep adding 4 until we find a number in the form 5j+4.   1, 5, 9 = 5(1)+ 4   The next such number is 9 + 4*5= 
9 + 4*5 = 29
29.   9+29= 
9+29 = 38
38   The answer is 38.
Answer: C
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H	Choose one.
A) 153  B) 150  C) 137  D) 120  E) 89

Solution: let the number be x, now x is halved => x/2..the question asks what is x?   x(number) + x/2 (half of that number) = something   => 3x/2 = something   => x = 2 (something) / 3   so the answer choice must be divisible by 3   eliminate C, E right away   check the rest   D satisfies   3x/ 2 = 120   => x = 86   Verify. 80 + 40= 120   Answer is 120
Answer: D
In how many seconds will a train 150 meters long pass an oak tree, if the speed of the train is 54 km/hr?  Answers.
A) 6	B) 8	C) 10	D) 12	E) 14

Solution: speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/s   time= 150/15= 
150/15 = 10
10 seconds   The answer is 10.
Answer: C
A committee has 5 men and 4 women. What are the number of ways of selecting 2 men and 3 women from the given committee?	Options
A) 127  B) 40  C) 882  D) 272  E) 323

Solution: The number of ways to select two men and three women   = ⁵C₂ * 4C₃   = (5 *4 )/(2 * 1) * (4 * 3 * 2)/(3 * 2)= 
(5 *4 )/(2 * 1) * (4 * 3 * 2)/(3 * 2) = 40
40   Answer: 40
Answer: B
What do you get if you add 9 to 311 four times?	Choose the correct choice:  A) 305  B) 310  C) 327  D) 320  E) 309

Solution: 320   320 , 320 , 320 , 320
Answer: D
Mary's income is 60% more Than Tim's income and Tim's income is 50% less than Juan's income.What % of Juan's income is Mary's income. Answers
A) 124%	B) B.120%	C) 96%	D) 80%	E) 64%

Solution: Even I got 96%   J = 100   T = 100*0.5= 
100*0.5 = 50
50   M= 50*1.6= 
50*1.6 = 80
80   If Mary's income is x percent of J   M= J*x/100   x = M*100/J = 80*100/100= 
80*100/100 = 80
80   Ans:80%
Answer: D
Find the missing figures: 0.25% of ? = 0.04  Answers
A) 16 B) 20 C) 17 D) 12 E) 18

Solution: Let 0.25% of x = 0.04. Then , 0.25*x/100 = 0.04   X= [(0.04*100)/0.25= 
(0.04*100)/0.25 = 16
16.   16nswer is 16.
Answer: A
The maximum number of girls among them 2923 bags and 3239 eyeliners can be distributed in such a way that each student gets the same number of bags and eyeliners. Pick one:  A) 80  B) 79  C) 78  D) 81  E) 82

Solution: Max no of girls=HCF of 2923 and 3239= 79   ANSWER:79
Answer: B
When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of z customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began? Options.
A) (n - 1) z  B) n + z –1  C) n/(z-1)  D) z/(n-1)  E) (n-1)/z

Solution: E. (n - 1) / z
Answer: E
When n is divided by 19, the remainder is 6 . When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
Select the correct option.
A) 3 B) 7 C) 10 D) 13 E) nineteen

Solution: N = 19 q + 6   N = 11 z + 6   Equating   19 Q + 6 = 11z+6   11z=19q   11z/19 = q   since q is an integer Z must be divisible by 19.   ANSWnineteenR:nineteen
Answer: E
Which of the following functions does not intersect with Q = 3x^2 + 2x + 1	Options:
A) Q= 3x^2 + 3x + 1
B) Q = 2x^2 + 3x + 1
C) Q = 3x^2 + 2x + 3
D) Q = 4x^2 + 2x - 3
E) Q = x^2 + 2x + 3

Solution: Let’s find the actual intersecting point of given function and each choice Q   A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0   B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1   C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.   D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2   E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.   So only choice (C) has no intersecting point. The answer is (Q = 3x^2 + 2x + 3).
Answer: C
A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?  Options:	A) 80 km/h	B) 85.34 km/h	C) 90.14 km/h	D) 91.24 km/h	E) 92 km/h

Solution: Ans.(B)   Sol. Total distance = 64 × 8 = 512 km   Now speed = 512/6 = 85.34 km/h
Answer: B
The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Four pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?	Answers:
A) 5
B) 12
C) 24
D) 32
E) 120

Solution: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.   But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.   The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5.   5nswer: option 5
Answer: A
4 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?	Choose the correct choice from the following answers:
A) 12/9 days  B) 60/13 days  C) 82/8 days  D) 22/76 days  E) 22/2 days

Solution: 4M = 6W ---- 20 days   12M + 8W -----?   18W + 8 W = 26W ---?   6W ---- 20 26 -----?   6 * 20  18  + 8= 
 18  + 8 = 26
26W ---?   6W ---- 20 26 -----?   6 * 20= 26 * x => x = 60/13 days   Answer:60/13 days
Answer: B
A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes? Choose the correct choice from the following choices.
A) 3%	B) 8%	C) 9%	D) 4%	E) 24%

Solution: SP of first article = 1000   Profit = 20%   CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3   SP of second article = 1000   Loss = 20%   CP = (SP)*[100/(100-L)] = 5000/4= 
5000/4 = 1_250
1250   Total SP= 2000   Total CP = 2500/3 + 1250 = 6250/3   CP is more than SP, he makes a loss.   Loss = CP-SP = (6250/3)- 2000 = 250/3   Loss Percent = [(250/3)/(6250/3)]*100   =0.04 * 100= 
0.04 * 100 = 4
4%   Answer: 4%
Answer: D
A thief is spotted by a policeman from a distance of 200 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?  Choose the correct choice.
A) 350m  B) 200m  C) 400m  D) 800m  E) None of them

Solution: Relative speed of the policeman = (10-8) km/hr =2 km/hr.   Time taken by police man to cover   (200m/1000) x 1/2 hr = 1/10 hr.   In 1/10 hrs, the thief covers a distance of 8 x 1/10 km = 4/5 km = 800 m   Answer is 800m.
Answer: D
Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?  Pick
A) 4 3/6  B) 4 3/9  C) 4 3/8  D) 4 3/4  E) 4 3/1

Solution: RS = 5 3/4 - 4 1/2 = 1 1/4   T = 3 1/2 h.   D = 5/4 * 7/2 = 35/8 = 4 3/8 km   Answer: 4 3/8
Answer: C
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?  Choose the correct choice from the following answers:
A) 8 : 9	B) 21 : 22	C) 17 : 18	D) 12 : 20	E) Cannot be determined

Solution: Originally, let the number of boys and girls in the college be 7x and 8x respectively.   Their increased number is (120% of 7x) and (110% of 8x).   (120/100 x 7x)	and	(110/100 x 8x)   42x/5 and 44x/5   The required ratio = (42x/5 : 44x/5)= 21 : 22.   ANSWER 21 : 22
Answer: B
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is? Choose the correct choice from the following:
A) 277
B) 266
C) 299
D) 600
E) 261

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1500   => 5 parts out of 15 parts is Rs. 1500   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1500) = Rs. 600   Answer: 600
Answer: D
What is the perimeter of a square with area 4p^2/16 ?	Options:
A) 3p/4 B) 3p^2/4 C) 2p D) 3p^2 E) 4p/3

Solution: Area of square, (side)^2 = (2p/4)^2   Therefore side of the square = 2p/4   Perimeter of square = 4*side = 4* (2p/4) = 2p   Answer is 2p.4* (2 /4)= 
4* (2 /4) = 2
2p   Answer is 2p.
Answer: C
In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximatelywhat %of the sp is the profit?  Choose the correct answer.
A) 50%	B) 70%	C) 80%	D) 90%	E) 110%

Solution: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420   New C.P. = 125% of Rs. 100 = Rs. 125.   New S.P. = Rs. 420   Profit = 420 - 125 = Rs. 295   Required percentage = 295/420 * 100 = 1475/21 = 70%   70%
Answer: B
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?	Pick.
A) 2868
B) 1718
C) 1689
D) 8112
E) 1718

Solution: A = 7500(26/25)2   = 8112   Answer:8112
Answer: D
The cost of 20 pens and 12 pencils is Rs.400 and the cost of 6 pens and 4 pencils is Rs.100. Find the cost of each pen? Select: A) Rs.50 B) Rs.100 C) Rs.150 D) Rs.25 E) Rs.125

Solution: 20p + 12q = 400 --- (1)   6p + 4q = 100   8p + 8q = 192 --- (2)   (1) - (2) => 8p = 160   => p = 50   Rs.50NSWER:Rs.50
Answer: A
In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks X are made of cotton?
Options:	A) 100	B) 80	C) 60	D) 50	E) 25

Solution: I'll prefer to solve this with plug n play method.   As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks X has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.   100 fits perfectly after relevant calculations. Hence answer 100.
Answer: A
For which of the following functions f is f(b) = f(1-b) for all b?
Options:  A) f (x) = 1 - x  B) f (b) = 1 - b^2  C) f (b) = b^2 - (1 - b)^2  D) f (b) = b^2*(1 - b)^2  E) f (x) = x/(1 - x)

Solution: I remember seeing this problem in a GMATprep test. I think choice D should be F(b)=(b^2) (1-b)^2. If that is true then substituting (1-b) for will give us the same function back and the answer choice is f (b) = b^2*(1 - b)^2, where the function is multiplicative
Answer: D
The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was:	Choose one: A) 10000 B) 12000 C) 14000 D) 16000 E) 18000

Solution: Explanation:   Purchase Price =Rs[8748 / (1- 10/100)3]=Rs.8748 x 10/9 x10/9 x10/9 = Rs.12000   ANSWER IS 12000
Answer: B
In how many ways Chief Minister and Minister be elected from a team of 12 members?  Choose the correct choice from the following options
A) 128
B) 130
C) 132
D) 143
E) 135

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
The average of 7 numbers is 20. If each number be multiplied by 5. Find the average of new set of numbers?  Pick one.
A) A)100 B) B)122 C) C)120 D) D)125 E) E)145

Solution: Explanation:   100verage of new numbers = 20 * 5= 
20 * 5 = 100
100   100nswer: Option 100
Answer: A
A retailer buys 100 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1%, what is the profit % ? Choose the correct option.
A) 110 B) 175 C) 212 D) 218 E) 220

Solution: let the market price of each pen be $1   then, Cost Price of 100 pens = $ 36 Selling Price of 100 pens =99% of $100=$ 99   profit %=((63*100)/36)= 
((63*100)/36) = 175
175%   Answer 175
Answer: B
A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds? Choose the most appropriate option:
A) 5/6
B) 3/4
C) 2/3
D) 1/2
E) 3/5

Solution: The searchlight completes one revolution every 30 seconds.   The probability that the man's area will be lit up is 10/30=1/3.   The probability that he will stay in the dark is 1-1/3=2/3   The answer is 2/3.
Answer: C
The units digit of (35)^(87) + (3)^(45) is: Choose one.
A) 2	B) 8	C) 6	D) 9	E) 0

Solution: any power of anything ending in 5 always has a units digit of 5. So the first term has a units digit of 5.   2nd part   3^45 has a units digit of 3   Therefore, the second term has a units digit of 3.   Of course  5 + 3= 
 5 + 3 = 8
8, so something with a units digit of 5 plus something with a units digit of 3   Answer= 8
Answer: B
A light has a rating of 86 watts, it is replaced with a new light that has 18% higher wattage. How many watts does the new light have? Choose the correct choice from the following options
A) 105 B) 95 C) 80 D) 60 E) 101

Solution: Final number = Initial number + 18%(original number) = 86 + 18%(86) = 86 + 15= 
86 + 15 = 101
101.   Answer 101
Answer: E
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Choose the correct choice from the following answers:
A) 299
B) 277
C) 999
D) 255
E) 245

Solution: a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 1.5= 
666 * 1.5 = 999
999   Answer: 999
Answer: C
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 370 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?  Answers
A) 90 B) 190 C) 120 D) 130 E) 220

Solution: Orchestra Seats - a   Balcony Seats - b   a+b = 370   and 12a + 8b = 3320   Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)   4a = 3320 - 8*370 = 3320 - 2960= 
3320 - 2960 = 360
360   i.e. a= 90   and b = 370-90= 
370-90 = 280
280   More seats in balcony than orchestra= b-a = 280 - 90= 
280 - 90 = 190
190   Answer: option 190
Answer: B
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream,it takes 4 hour.What is the speed of the boat in still water ?
Choose the correct choice:
A) 4 km/hr	B) 6 km/hr	C) 8 km/hr	D) Data inadequate	E) None of these

Solution: Solution   Rate downstream =(16/2)= 
(16/2) = 8
8 kmph,Rate upstream= (16/4)= 
(16/4) = 4
4 kmph.   ∴ Speed in still water=1/2(8+4) kmph = 6 kmph. Answer 6 km/hr
Answer: B
The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 190 runs and his average excluding these two innings is 58 runs, find his highest score. Options.
A) 179 B) 367 C) 269 D) 177 E) 199

Solution: Explanation:   Total runs scored by the batsman = 60*46= 
60*46 = 2_760
2760 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2760 â€“ 2552 = 208 runs.   Let the highest score be x, hence the lowest score = x â€“ 190   x + (x - 190) = 208   2x = 398   x = 199 runs   ANSW199R: 199
Answer: E
An article is bought for Rs.600 and sold for Rs.500, find the loss percent? Choose the correct option.
A) 16 6/3% B) 16 2/8% C) 16 3/3% D) 16 2/3% E) 16 2/6%

Solution: 600 ---- 100   100 ---- ? => 16 2/3%   Answer: 16 2/3%
Answer: D
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?  Choose the correct answer:
A) 1017
B) 1029
C) 1000
D) 1028
E) 1026

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer: 1000
Answer: C
Beginning in Town A, Biker Bob rides his bike 12 miles west, 6 miles north, 4 miles east, and then 12 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)  Choose the correct choice from the following choices:
A) 18.97 miles  B) 20 miles  C) 22 miles  D) 23 miles  E) 25 miles

Solution: Using Pythagoras we have one side i,e total distance traveled in north direction = 12+6= 
12+6 = 18
18m   other being the base ie distance traveled west- distance traveled eat=12- 6= 
12- 6 = 6
6 m   now this third side or the distance between town 18.97 miles and Town B=18^2+ 6^2=sq root 360=18.97 mile   18.97 milesnswer : 18.97 miles
Answer: A
The height of a triangle is decreased by 15% and its base increased by 50%. Its area will
Choose the correct choice from the following answers:
A) decrease by 12.5%  B) increase by 12.5%  C) decrease by 25%  D) Increase by 27.5%  E) None of these

Solution: Explanation :   Let the initial height be 100 and the base be 200 units.   âˆ´ Area = 1/2 x 100 x 200 = 10000 sq units   Now, height = 85 units and base = 300 units   âˆ´ New area = 1/2 x 85 x 300 = 12750   âˆ´ Area is increased by (12750 - 10000)/10000 x 100   = 27.5%   Answer : Option Increase by 27.5%
Answer: D
The X&co having such a sales structure out of their whole sales 70% of the customers are corporate companies out of these 20% of them are related to banking sector and 60% of the corporate companies related to banking sector having their head quarters in USA. If total sales of the company X&co is 100 cr then, what is sales amount of corporate companies related to banking sector having their head quarters in USA?	Choose the correct choice
A) 8.5
B) 7.0
C) 6.3
D) 3.6
E) 8.4

Solution: total amount of sales =100 cr; out of these 70% are corporate companies = 70 cr; out of these 20% are related to banking sector = 14 cr ; 60% of the corporate companies related to banking sector having their head quarters in USA = 8.4 cr.
Answer: E
A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
Options
A) 48	B) 99	C) 266	D) 28	E) 17

Solution: Explanation:   If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.   Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.   48nswer: 48) 48
Answer: A
Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 25?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?  Choose the correct option.
A) 25x^2 + 4 = y^2  B) 75x^2 = 3y^2 - 12  C) 5x = y - 5  D) 25x^2 = (y + 2)(y - 2)  E) x^2 = (y^2 - 4)/25

Solution: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers   2) Take each answer choice and see if you can manipulate it to make it into the original equation.   With Answer D, we have...   5X = Y - 5   If we square both sides, we end up with....   (5X)^2 = (Y-5)^2   (5X)(5X) = (Y-5)(Y-5)   25X^2 = Y^2 - 10Y + 25   This is NOT a match for the original equation, so it's the answer that is NOT equivalent. 5x = y - 5
Answer: C