MU-NLPC/Calc-aqua_rat huggingface dataset:
If the speed of X meters per hour is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
Choose the correct choice from the following options.
A) 0.1X	B) 0.01X	C) 0.001X	D) 0.0001X	E) 0.005X

Solution: X meters per hour -->   --> 1X meters per hour(as there are 3,600 seconds in one hour);   --> X/1,000=0.001X kilometers per hour (as there are 1,000 meters in one kilometer).   Answer: 0.001X.
Answer: C
A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 2 miles per hour, how many miles did the car travel in the third 5-minute interval?  Select the correct option.
A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 3.0

Solution: In the third time interval the average speed of the car was 2+5+5= 
2+5+5 = 12
12 miles per hour;   In 5 minutes (1/12 hour) at that speed car would travel   12*1/12= 
  12*1/12 = 1
1 miles.   1.0nswer: 1.0.
Answer: A
150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration W of the acid in the mixture?
Choose the correct choice from the following choices
A) 1/2 B) 1/3 C) 1/4 D) 1/6 E) 1/5

Solution: Do not need any computation   30%-----------21%---------12%   if volume of both sol. were equal the concentration W would be 21%=1/5, but 12% is more than 3 times   only possibility is 1/6   1/6
Answer: D
The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface. Answers:
A) 30 m2
B) 40 m2
C) 50 m2
D) 60 m2
E) 80 m2

Solution: l = 10 m,   h = 8 m.   So, r = l2 - h2 = (10)2 - 82 = 6 m.   Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.   Answer: Option 60 m2
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
A) 65  B) 69  C) 72  D) 75  E) None of these

Solution: Solution   Average =   (76+65+82+67+85 / 5)	=(375 / 5)= 
(375 / 5) = 75
75.   Answer 75
Answer: D
x and y are positive integers of V. If 1/x + 1/y < 2, which of the following must be true? Select the correct option:  A) x + y > 4  B) xy>1  C) x/y + y/x < 1  D) (x - y)^2 > 0  E) None of the above

Solution: Answer is B:   1/X + 1/Y < 2   The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.   So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.   Another way of putting it is:   X*Y>1.xy>1
Answer: B
What is the sum of 100 consecutive integers from -49 inclusive, in a increasing order?	Choose the most appropriate option
A) -29
B) 50
C) -30
D) 30
E) 60

Solution: From -49 to -1 --> 49 nos.   zero --> 1 number   from +1 to +49 --> 49 nos.   When we add up nos. from -49 to + 49 sum will be zero. Total 99 nos will be added.   100th number will be 50.   Sum of these 100 nos. = 50.   50 is the answer.
Answer: B
We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $550. How many green hats did we buy?	Choices:
A) A)36 B) B)40 C) C)41 D) D)42 E) E)44

Solution: Let B be the number of blue hats and let G be the number of green hats.   B+G=85.   B=85-G.   6B+7G=550.   6(85-G)+7G=550.   510-6G+7G=550.   G=550-510= 
550-510 = 40
40.   The answer is 40.
Answer: B
A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?	Choose the correct answer
A) 1 / 3  B) 1 / 4  C) 1 / 5  D) 1 / 7  E) None

Solution: Suppose the vessel initially contains 8 litres of liquid. Let x littres of this liquid be replaced with water.   Quantity of water in new mixture = (3 - 3x/8 + x) litres.   Quantity of syrup in new mixture = (5 - 5x/8) litres.   (3 - 3x/8 + x) = (5 - 5x/8) = 5x + 24 = 40 - 5x   =› 10x = 16 =› x = 8/5   So, part of the mixture replaced = (8/5 x 1/8) = 1/5.   Answer 1 / 5
Answer: C
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:  Choose the most appropriate option:
A) 700	B) 680	C) 720	D) 760	E) 660

Solution: 700pples Sold = 40%   So Remaining 700pples = 60%   60% = 420   Full (100%) = (100/60) X 420   = 700   answer :700
Answer: A
Suppose you want to buy three loaves of bread that cost $0.75 each
and a jar of peanut butter that costs $7. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $17. How much money will you have left
over?
Choose the correct choice.
A) $7.75 B) $7.50 C) $3.50 D) $4.50 E) $5.50

Solution: The jelly is extra information. 17.00 â€“ 3 x 0.75 â€“ 7.00 =   17.00 â€“ 2.25 â€“ 7.00 = 7.75.   You have $7.75 left.   correct answer $7.75
Answer: A
For positive integers n, the integer part of the nth term of sequence F equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, F_1 = 1.2345678…, while F_2 = 2.4681012… The sum of the first seven terms of sequence F is between:  Choices:
A) 28 and 29	B) 29 and 30	C) 30 and 31	D) 31 and 32	E) 32 and 33

Solution: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.   F_1 = 1.23…   F_2 = 2.46…   F_3 = 3.69…   F_4 = 4.812…   F_5 = 5.10…   F_6 = 6.12…   F_7 = 7.14…   Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.   1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1= 
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
30.3   Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.   The correct answer is 30 and 31.
Answer: C
Nobel buys an old car for $1000 and spends $1000 on its repairs. If he sells the scooter for $2500, his gain percent is?
Choose the correct option.
A) 10%  B) 15%  C) 25%  D) 20%  E) 30%

Solution: C.P. = 1000+1000= 
1000+1000 = 2_000
$2000   S.P.= $2500   Gain = 2500-2000= 
2500-2000 = 500
$500   Gain%= 500/2000 * 100= 
500/2000 * 100 = 25
25%   Answer is 25%
Answer: C
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 5 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?	Choose the correct choice from the following answers.
A) Rs.1178.55	B) Rs.1978.25	C) Rs.1332.5	D) Rs.1678	E) Rs.1675.55

Solution: (x*5*3)/100 = ((2665 - x)*3*5)/100   15x/100 = 39975/100 - 15x/100   30x = 39975 => x = 1332.5   Second sum = 2665 – 1025 = 1332.5   ANSWER:Rs.1332.5
Answer: C
An employee’s annual salary was increased $25,000. If her new annual salary now equals $90,000, what was the percent increase?
Choose the most appropriate option.
A) 15%  B) 162⁄3%  C) 20%  D) 38.46%  E) 24%

Solution: New annual salary = $90,000   Salary increase = $25,000.   Original salary = $90,000 - $25,000.   = $75,000   %Increase = ($25,000/ $65,000 )*100   =38.46%   Hence 38.46%.
Answer: D
What is the smallest number which when diminished by 10, is divisible 2, 6, 12 and 24?  Choose the correct option:	A) 35	B) 34	C) 20	D) 35	E) 342

Solution: Required Number   = (LCM of 2, 6, 12 and 24) + 12   = 24 + 10= 
24 + 10 = 34
34   Option 34
Answer: B
A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?	Choose the correct answer.
A) 2.0
B) 2.5
C) 3.0
D) 3.5
E) 4.0

Solution: 72 km/hr = 1.2 km/min   The total distance is 2.4 km.   2.4 / 1.2= 
2.4 / 1.2 = 2
2 minutes   The answer is 2.0.
Answer: A
In a certain school, the ratio of boys to girls is 5 to 13. If there are 128 more girls than boys, how many boys are there?	Choose one
A) 27	B) 36	C) 45	D) 72	E) 80

Solution: The ratio of b to G is 5:13 and the other data point is G are more than boys by 128...   Looking at the ratio we can say that the 8(13-5) extra parts caused this diff of 128. so 1 part corresponds to 128/8= 
128/8 = 16
16 and so   5 parts correspond to 5*16= 
5*16 = 80
80.   80
Answer: E
How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?	Choose the correct answer.
A) 50  B) 88  C) 77  D) 55  E) 22

Solution: The distance to be covered = Sum of their lengths = 200 + 300= 
200 + 300 = 500
500 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 500/10= 
500/10 = 50
50 sec.   50nswer: 50
Answer: A
Find the largest 4 digit number which isexactly divisible by 88? Choose the most appropriate option:
A) 7890	B) 8900	C) 9944	D) 9976	E) 10000

Solution: Largest 4 digit number is 9999   After doing 9999 ÷ 88 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   9944
Answer: C
Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time ,the rate of interest being the same ?	Choose the correct answer.
A) Rs. 10 B) Rs. 10.40 C) 15.20 D) Rs. 13 E) None of these

Solution: Solution   S.I. on Rs. (260-20) for a given time =Rs. 7.34.   S.I. on Rs. 240 for half the time = Rs.10.   T.D. on Rs. 250 = Rs. 10.   ∴ T.D. on Rs. 260 = Rs. ( 10/250x 260 ) = Rs. 10.40.   Answer Rs. 10.40
Answer: B
If X,Y and Z are three consecutive multiples of 5. Then which of the following will the factor of X*Y*Z
1) 125
2) 250
3) 375
4) 750	Select: A) only 1 B) 1,2 C) 1,3 D) 1,2,3 E) All of them

Solution: Given choices can be re-written as multiples of 125   1. 125   2. 125*2   3. 125*3   4. 125*6   Now if, 5*a = X, then   5*(a+1) = Y & 5*(a+2)   5*( +1)= 
  5*( +1) = 5
Y & 5*(a+2)= Z   So, X*Y*Z = 125* a(a+1)(a+2)   Now, among any 3 consecutive positive integers, we will either have (a number that is divisible by both 2 & 3) or (a number divisible by 2 and another number divisible by 3).   Ex:   17, 18, 19 -> 18 divisible by 2 & 3.   14, 15,16 -> 14, 16 divisible by 2 & 15 divisible by 3.   Hence 'All of them'
Answer: E
A watch was sold at a loss of 46%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price? Choose one:  A) 280  B) 288  C) 279  D) 277  E) 290

Solution: 54%   104%   --------   50% ---- 140   100% ---- ? => Rs.280   280nswer: 280
Answer: A
ABCD is a square where AB =√2016. Let X be a point on AB and Y be a point on CD such
that AX = CY . Compute the area of trapezoid AXYD.  Choose the correct choice from the following choices
A) 3008
B) 2002
C) 1008
D) 2016
E) 3000

Solution: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is   always   2016/2= 
2016/2 = 1_008
1008 .   correct answer 1008
Answer: C
What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?	Choose the correct choice from the following answers:
A) 8000
B) 8020
C) 2879
D) 2686
E) 2996

Solution: 8820 ---- 441   100 ---- ? => 5%   x *105/100 * 105/100 = 8820   x*1.1025=8820   x=8820/1.1025= 
8820/1.1025 = 8_000
> 8000   8000nswer: 8000
Answer: A
Two taps A and B can fill a tank in 5 hours and 20hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?
Select:
A) 24 hr  B) 36 hr  C) 18 hr  D) 42 hr  E) 30 hr

Solution: Part filled by A+B in 1 hour = 1/5 + 1/20 = 1/4   A and B together can fill the tank in 4 hour   Work done by the leak in 1 hour = 1/4 - 2/9 = 1/36   leak will empty the tank in 36 hours.   Answer is 36 hr
Answer: B
A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold. Which of the following expresses this relationship ?	Choose one:
A) x > 10y  B) x > y + 10  C) x > y – 10  D) x = y + 10  E) x = y – 10

Solution: Let number of used cars sold in May = x   number of new cars sold in May = y   x= y + 10   Answer x = y + 10
Answer: D
Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?	Choose the correct choice from the following: A) 5 B) 6 C) 9 D) 24 E) 26

Solution: Peter will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are   0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1= 
  0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5
5 cases...5
Answer: A
If k > 0, x + 2k = y, and y + 3k = z, what is the ratio between z - x and y - x ?  Options.
A) 3 to 1	B) 3 to 2	C) 4 to 1	D) 5 to 1	E) 5 to 2

Solution: y-x = 2k   z-y = 3k   Let's add the two equations together:   z-x = 5k   The ratio of z-x to y-x is 5:2.   The answer is 5 to 2.
Answer: E
A man can row with a speed of 5 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Pick: A) A)63kmph B) B)63kmph C) C)10kmph D) D)62kmph E) E)74kmph

Solution: Explanation:   M = 5   S = 5   DS = 5 + 5= 
5 + 5 = 10
10   Answer: Option 10kmph
Answer: C
A train 640 meters long is running with a speed of 64 kmph. The time taken by it to cross a tunnel 140 meters long is?	Choose the correct choice from the following:
A) 44 sec  B) 49 sec  C) 48 sec  D) 16 sec  E) 17 sec

Solution: D = 640 + 140= 
640 + 140 = 780
780   S= 64 * 5/18 = 17.7 mps   T = 780/17.7 = 44 sec   44 secnswer: 44 sec
Answer: A
For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 1 order of $120 ?
Choose one: A) $1 B) $2 C) $3 D) $4 E) $5

Solution: Total cost involved for each 75 $ shipment:  3+2= 
 3+2 = 5
5 $. Thus, for two such orders= 10$   Total cost involved for a 120$ shipment: 3+3= 
3+3 = 6
6$.   The difference= 4$.   $4.
Answer: D
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 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?	Options
A) 10 sec	B) 17 sec	C) 18 sec	D) 16 sec	E) 12 sec

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2500/9 * 18/500= 
2500/9 * 18/500 = 10
10 sec   10 secnswer: 10 sec
Answer: A
r=2^(n+1), then in terms of r, 9^n=  Pick one:  A) r^2/81  B) r^2/9  C) r^2/4  D) r/3  E) r

Solution: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0   r = 2^1 = 2   and you need the value of 2^n which is 2^0 = 1   So when you put r = 2 in the options, you should get 1. Only option (C) satisfies.   Answer (r^2/4)
Answer: C
150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration of the acid in the mixture?
Choose the most appropriate option
A) 1/2	B) 1/3	C) 1/4	D) 1/6	E) 1/5

Solution: 150 ml solution contains 45 ml sulphuric acid   400 ml solution contains 48 ml sulphuric acid   Adding   550 ml solution contains 93 ml sulphuric acid   93/550≈90/540=1/6   Answer is 1/6
Answer: D
On a sum of money, the S.I. for 2 years is $660, while the C.I. is $693, the rate of interest being the same in both the cases. The rate of interest is?	Select the correct option:  A) 10%  B) 32%  C) 72%  D) 14%  E) 82%

Solution: Difference in C.I. and S.I for 2 years = $693 - $660 = $33   S.I for one year 693 -  660= 
693 -  660 = 33
$33   S.I for one year= $330   S.I. on $330 for 1 year = $33   Rate = (100 * 33)/(330)= 
(100 * 33)/(330) = 10
10%   The answer is 10%.
Answer: A
Two cubes of their volumes in the ratio 8 : 125. The ratio of their surface area is:  Choose the correct option
A) 1.5:5  B) 2:5  C) 3:5  D) 1:5  E) 4:5

Solution: The ratio of their surface area is   8 : 125   2 : 5   Answer is 2:5.
Answer: B
The compounded ratio of (2:3), (6:11) and (11:2) is  Choose the correct choice from the following options.
A) 2 : 1
B) 1 : 2
C) 36 : 121
D) 11 : 24
E) None

Solution: Sol.   Required ratio = [2/3 x 6/11 x 11/2] = 2/1= 
2/1 = 2
2 : 1.   2 : 1nswer 2 : 1
Answer: A
When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/5 of the remaining balance, what will be the final balance in her bank account?  Choose the most appropriate option
A) 300  B) 360  C) 400  D) 500  E) 575

Solution: As per the question 200=2a/5   thus- a which is the total amount =500   The amount thus left =300   She then deposited 1/5 of 300=60   total amount in her account =360   Answer 360
Answer: B
If each year the population of the country grows by 20%, how many years will elapse before the population of the country doubles?	Choose the correct choice.
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Till Year 2000, population is 100 .   Year 2001: Population becomes 120 ............. 1 Year elapsed   Year 2002: Population becomes 144 ............. 2 Year elapsed   Year 2003: Population becomes 172 ............. 3 Year elapsed   Year 2004: Population > 200 .................. 4 year elapsed   Answer:4
Answer: B
A man can ride on motorcycle at 50 kmph upward road and 100 kmph downward road. He takes 12 hours to ride motorcycle uphill from lower point A to upper point B and back to A. What is the total distance traveled by him in 12 hours? He must return back to base point A in remaining time.  Choose the correct choice from the following answers:
A) 1000	B) 900	C) 800	D) 400	E) 1200

Solution: Upward distance traveled per hour - 50 km,   distance traveled after 8 hours = 400 km.   He remained with 4 hours travel downward, i.e. distance traveled in remaining 4 hours downward = 400 km   so total distance traveled from A to B and Back to point A = 400 km upward + 400 km downhill = 800 km   (Answer : 800)
Answer: C
A coin is tossed live times. What is the probability that there is at the least one tail?
A. 31/32 B. 1/16	Pick
A) 31/32
B) 31/89
C) 31/25
D) 31/17
E) 31/13

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T) = 1 - 1/32 = 31/32   31/32nswer: 31/32
Answer: A
A number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r. What is the greatest two digit prime saturated integer ? Choose one.
A) 99 B) 98 C) 97 D) 96 E) 95

Solution: Clearly D A number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r.   96 has more number of smaller prime factor thats the clue !!=96
Answer: D
the average distance between the sun and a certain planet is approximatly 2.1 10^15 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches)  Choose the correct answer
A) 6.4 x(10)^10
B) 5.4 x(10)^10
C) 7.4 x(10)^10
D) 2.4 x(10)^10
E) 3.4 x(10)^10

Solution: No need to solve entire problem.   Distance in KM = 21*(10)^15/39*(10)^4 which is -210*(10)^14/39*(10)^4 = 5.4 x(10)^10   Answer : 5.4 x(10)^10
Answer: B
597**6 is divisible by both 3 and 11. The non-zero digits in the Hundred’s and ten’s places are respectively: Choices:
A) 3 and 6	B) 7 and 9	C) 2 and 6	D) 4 and 7	E) None

Solution: Solution : Let the given number be 597xy6.   Then (5+9+7+x+y+6)=(27+x+y) must be divisible by 3   And, (6+x+9)-(y+7+5)=(x-y+3) must be either 0 or divisible by 11. x-y+3=0   => y=x+3 27+x+y)   =>(27+x+x+3)   =>(30+2x)   => x = 3 and y = 6.   3 and 6nswer 3 and 6
Answer: A
Andy solves problems 78 to 125 inclusive in a Math exercise. How many problems does he solve?	Choose the correct option:
A) 53  B) 52  C) 51  D) 50  E) 48

Solution: 125-78+1= 
125-78+1 = 48
48   '48' is the answer
Answer: E
A rectangular floor that measures 6 meters by 8 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $12 apiece, what is the total cost for the number of carpet squares needed to cover the floor?  Choices:
A) $200  B) $240  C) $480  D) $960  E) $144

Solution: The width of the rectangular floor(6 m) is a multiple of one side of the square(2 m), and the length of the floor(8 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (6/2)*(8/2)= 
(6/2)*(8/2) = 12
12.   The total cost is 12*12= 
12*12 = 144
$144   The answer is, therefore, $144.
Answer: E
If two numbers are in the ratio 2:3 and the numerator and denominator are added and subtracted by1 and 2 respectively, then the ratio becomes 6:2, then find the smallest number?	Choose the correct choice from the following choices:
A) 2	B) 1	C) 3	D) 4	E) 6

Solution: 2:3   2x + 1 : 3x - 2 = 3 : 1   [2x + 1] = 3[3x - 2]   2x + 1 2  + 1= 
 2  + 1 = 3
3[3x - 2]   2x + 1= 9x -6   9x - 2x = 7   x 9  - 2= 
9  - 2 = 7
7   x= 1   Then smallest number is = 2x   2x = 2   2
Answer: A
For which of the following does y(a)−y(b)=y(a−b) for all values of a and b? Select the correct option:
A) y(x)=x^2	B) y(x)=x/2	C) y(x)=x+5	D) y(x)=2x−1	E) y(x)=|x|

Solution: To solve this easiest way is just put the value and see that if it equals or not.   with option 1. y(a) = a^2 and y(b) = b^2   so L.H.S = a^2 - b^2   and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.   so L.H.S not equal to R.H.S   with option 2. y(a) = a/2 and y(b) = b/2   L.H.S = a/2 - b/2 ==> 1/2(a-b)   R.H.S = (a-b)/2   so L.H.S = R.H.S which is the correct answer.   answer:y(x)=x/2
Answer: B
Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 231 marks in the second test and failed by 48 marks in that test. Find the pass mark in the first test?
Select the correct option.
A) 768
B) 243
C) 246
D) 625
E) 248

Solution: Let the maximum mark in each test be M.   The candidate failed by 48 marks in the second test.   pass mark in the second test = 231 + 48= 
231 + 48 = 279
279   45/100 M= 279   Pass mark in the first test = 40/100 M = 40/45 * 279= 
40/45 * 279 = 248
248.   Answer:248
Answer: E
A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?  Choices
A) 2: 5
B) 2: 0
C) 2: 2
D) 2: 3
E) 2: 9

Solution: 80* 7: x* 3 = 1:1 1/2   560: 3x = 2: 3   x = 280.Answer: 2: 3
Answer: D
Fiind the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?	Choose the correct choice:
A) 5200
B) 2882
C) 5460
D) 2342
E) 2900

Solution: 5000 * 104/100 * 105/100= 
5000 * 104/100 * 105/100 = 5_460
> 5460   Answer: 5460
Answer: C
If 102y = 25, then 10-y equals:
Choose the most appropriate option
A) -1/5  B) 1/625  C) 1/50  D) 1/25  E) 1/5

Solution: 102y = 25   (10y)2 = 52   10y = 5   1/10y = 1/5   10-y = 1/5   Answer: 1/5   )
Answer: E