MU-NLPC/Calc-aqua_rat huggingface dataset:
A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 25 per kg, then his gain percent is	Answers.
A) 12% B) 33% C) 14% D) 15% E) 16%

Solution: Explanation:   Suppose he bought 5 kg and 3 kg of tea.   Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.   Selling price = Rs. (8 x 25) = Rs. 200.   Profit = 200 - 150= 
200 - 150 = 50
50   So, Profit %= (50/150) * 100 = 33%   Option 33%
Answer: B
A large tank can filled by A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?  Select: A) 10min B) 15min C) 30min D) 25min E) 42min

Solution: Part filled by A+B in 1 minute = 1/60 + 1/40 = 1/24   Suppose the tank is filled in x minutes   Then, x/2(1/24 + 1/40) = 1   x/2 * 1/15 = 1   x = 30 min   Answer is 30min
Answer: C
The ratio of number of boys and girls in a class is 3 : 2. In the 1st semester exam 20% of boys and 25%
of girls get more than or equal to 90% marks. What percentage of students get less than 90% marks ?	Choose the correct choice from the following answers:
A) 56	B) 70	C) 78	D) 80	E) None of these

Solution: Expl : Let boys =3x and girls =2x.   Number of those who get less than 90% mark =(80% of 3x) + (75% of 2x)   =(80/100 )*3x +(75/100 *2x) =39x/10   Required percentage = (39x/10 *1/5x *100)% = 78%.   Answer:78(39 /10 *1/5  *100)= 
(39 /10 *1/5  *100) = 78
78%.   Answer:78
Answer: C
If a person walks at 10 km/hr instead of 8 km/hr, he would have walked 14 km more. The actual distance traveled by him is?
Options.
A) 50	B) 40	C) 56	D) 16	E) 20

Solution: Let the actual distance traveled be x km. Then,   x/8= (x + 14)/10   2x - 112=>x = 56 km.   Answer:56
Answer: C
The average temperature for Tuesday, Wednesday and Thursday was 52°C. The average temperature for Wednesday, Thursday and Friday was 54°C. If the temperature on Friday be 53°C, what was the Temperature on Tuesday? Choose the correct choice from the following answers:
A) 39°C	B) 44°C	C) 37°C	D) 47°C	E) None of these

Solution: Explanation:   T + W + T = 52 × 3 = 156°C   W+ T+ F = 54 × 3 = 162°C   Also, temperature on Friday = 53°C   Temperature on Tuesday = 156 +53 - 162= 
156 +53 - 162 = 47
47°C   Answer: Option 47°C
Answer: D
Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month? Choose the correct choice from the following options.
A) x/(y - r) B) x/(r - y) C) x D) x/r E) x/y

Solution: Two ways...   1) let t be the total number, so cost = t*y+x and selling price=t*r..   No profit no loss....t*y+x=t*r.....T=x/(r-y)...   x/(r - y)
Answer: B
Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 34~ ?
Choose the most appropriate option
A) 6	B) 1	C) 2	D) 0	E) 31

Solution: n~ = (n-1)!   so 34~ = (34-1)= 
(34-1) = 33
33!   when 33!/34 we have 16*2 inside 33!   hence 34 gets cancelled and we get remainder as 0   0
Answer: D
In a weight-lifting competition, the total weight of Joe's two lifts was 450 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?  Choose the correct choice from the following choices: A) 250 B) 275 C) 325 D) 350 E) 400

Solution: This problem is a general word translation. We first define variables and then set up equations.   We can define the following variables:   F = the weight of the first lift   S = the weight of the second lift   We are given that the total weight of Joe's two lifts was 450 pounds. We sum the two variables to obtain:   F + S = 450   We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:   2F = 300 + S   2F – 300 = S   We can now plug in (2F – 300) for S into the first equation, so we have:   F + 2F – 300 = 450   3F = 750   F = 250   250nswer is 250.
Answer: A
The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 9 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?  Options.
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: The weights of the items in the suitcase are 5k, 4k, and 2k.   If removing 9 pounds of clothes doubles the ratio of books to clothes, then 9 pounds represents half the weight of the clothes.   2k = 9 pounds and then k = 4.5 pounds.   The electronics weigh 2(4.5) = 9 pounds.   The answer is 9.
Answer: C
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 10 sq. feet, how many feet of fencing will be required?	Pick:
A) 34
B) 40
C) 68
D) 21
E) 78

Solution: We have: l = 20 ft and lb = 10sq. ft.   So, b = 0.5 ft.   Length of fencing = (l + 2b) = (20 + 1)= 
(20 + 1) = 21
21 ft.   ANSWER:21
Answer: D
The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 20%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output? Pick one:  A) 20%  B) 24%  C) 30%  D) 32%  E) 79%

Solution: Let the output of a factory is 100   First,increased by 10 %=110   due to holiday rush,it increase by 20%=110+22= 
110+22 = 132
132   132-(x/100*132)=100   24.24   ANSWER:24%
Answer: B
A boat with still water speed of a is traveling upstream where the streams speed is b. After covering certain distance s, the boat turns back and tries to come to the starting place. But the boat stops at 3/4th of the intended distance due to a technical fault. What is the ratio of the time taken for the return journey to that of the upstream journey.
Select the correct option:	A) 3(a - b)/4(a + b)	B) 4(a - b)/3(a + b)	C) 3(a + b)/4(a - b)	D) 4/3	E) 4/8

Solution: speed of boat upstream = a - b   speed of boat downstream = a + b   For upstream journey, time taken = distance / speed = s / (a - b)   During return journey, the boat had covered on 3/4th of s :   Therefore for return journey, time taken = distance / speed = (3s/4)/(a+b)   Ratio of time taken for return journey to the upstream journey = (3s/4)/(a+b)/ (s/(a - b)) = 3(a - b)/4(a + b)   3(a - b)/4(a + b)NSWER:3(a - b)/4(a + b)
Answer: A
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options.
A) 5 B) 6 C) 7 D) 9 E) 1

Solution: 1/10 + 1/15 - 1/x = 1/18   x = 9   Answer: 9
Answer: D
If p and q are the roots of the equation x2 - bx + c = 0, what is the equation if the roots are (pq + p + q) and (pq - p - q)?
Pick one.
A) x2 - 2cx + (c2 - b2) = 0
B) x2 - 2bx + (b2 + c2) = 0
C) bcx2 - 2(b + c)x + c2 = 0
D) x2 + 2bx - (c2 - b2) = 0
E) None

Solution: Explanatory Answer   In the given quadratic equation x2 - bx + c = 0,   The sum of the roots p + q = b --- (1)   And the product of the roots pq = c --- (2)   We have to formulate a quadratic equation whose roots are (pq + p + q) and (pq - p - q).   The sum of the two roots = pq + p +q + pq - p - q = 2pq   But from eqn (2), we know that pq = c   Therefore, the sum of the roots = 2c   The product of the roots = (pq + p + q)(pq - p - q)= (pq)2 - (p+q)2   From equation (1) and (2), we know that pq = c and p + q = b   Therefore, the product of the roots = c2 - b2   We know the sum of the roots and the product of the roots.   Therefore, the quadratic equation is x2 - (sum of the roots)x + product of the roots = 0   => x2 - 2cx + c2 - b2 = 0   x2 - 2cx + (c2 - b2) +  2 -  2= 
+  2 -  2 = 0
0   x2 - 2cx + (c2 - b2) = 0nswer x2 - 2cx + (c2 - b2) + ( 2 -  2)= 
+ ( 2 -  2) = 0
0nswer x2 - 2cx + (c2 - b2) = 0+ ( 2 -  2)= 
+ ( 2 -  2) = 0
0
Answer: A
An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 2/3 %, then the amount invested in each share was?
Select the correct option:	A) 23777	B) 35000	C) 29977	D) 26777	E) 19871

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,   (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 29/3 * 1/100)   (9x + 1100000 - 11x)/100 = 29000/3 = 9700   (9x + 1100000 - 11x) = 970000   x = 65000   Sum invested at 9% = Rs. 65000   Sum invested at 11% = Rs. (100000 - 65000) = Rs. 35000.   Answer: 35000
Answer: B
The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 00 p.m., at what time were there 32 million bacteria in the dish?  Pick
A) 6: 00 p.m.	B) 8: 00 p.m.	C) 6: 00 a.m.	D) 8: 00 a.m.	E) 10: 00 a.m.

Solution: Given:   The number of bacteria in a petri dish increased by 50 percent every 2 hours   There were 108 million bacteria in the dish at 2: 00 p.m   Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.   Required: At what time were there 32 million bacteria in the dish?   Assume that there were n intervals of 2 hours between 32 million and 108 million.   32 * (1.5)^n = 108   (3/2)^n = 108/32 = 27/8 = (3/2)^3   Hence n = 3 intervals.   Each interval was of 2 hours. Therefore, the number of hours = 6   Subtracting 6 hours from 2 PM, we get 8 AM as the answer.   Option 8: 00 a.m.
Answer: D
If a and b are positive integers and x = 9^a and y = 5^b, which of the following is a possible units digit of xy?  Choose the correct choice from the following answers.
A) 1  B) 4  C) 5  D) 7  E) 8

Solution: The units digit of 9^a is either 1 or 9.   The units digit of 5^b is 5.   1*5= 
1*5 = 5
5 and   9*5= 
  9*5 = 45
45.   The units digit of xy is 5.   The answer is 5.
Answer: C
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 11? Choose the correct choice from the following:  A) 0  B) 1  C) 2  D) 3  E) 5

Solution: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 3, square it and see what would be the remainder upon division of it by 11.   n=5 --> n^2=25 --> remainder upon division 25 by 11 is 3.   Answer: 3.
Answer: D
A train,130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?  Choose the correct choice from the following choices.
A) 210	B) 225	C) 235	D) 245	E) 260

Solution: Speed =45 km/hr=45×5/18 m/s =12.5 m/s 245istance travelled = (Speed x Time)   245istance travelled = 12.5×30=375 m   length of the bridge = 375-130= 
375-130 = 245
245 m   Answer: 245
Answer: D
A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 11 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Choose the correct choice from the following options:
A) 2,060
B) 1,320
C) 165
D) 315
E) 220

Solution: 11*10*9/3*2*1 = 165   165
Answer: C
A man gets a simple interest of Rs.500 on a certain principal at the rate of 5% p.a in two years. Find the compound interest the man will get on twice the principal in two years at the same rate? Choose the correct choice from the following options
A) 256.29 B) 256.27 C) 256.23 D) 256.21 E) 256.25

Solution: Let the principal be Rs.P   S.I at 5% p.a in 8 years on Rs.P = Rs.500   (P)(8)(5)/100 = 500   P = 1250   C.I on Rs.2P i.e., Rs.2500 at 5% p.a in two years   =2500{ [1 + 5/100]2 - 1} = 2500{ 212 - 202 /202}   = 2500/400(441 - 400)   = 25/4(41) = 1025/4 = Rs.256.25   Answer:256.25
Answer: E
In a race with 30 runners where 5 trophies will be given to the top 7 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?	Choose the correct answer.
A) 8^8 ways  B) 8^9 ways  C) 7^5 ways  D) 8^7 ways  E) 8^6 ways

Solution: 7 people can be prized with 5 distinct prizes in 7^5 ways   ANSWER:7^5 ways
Answer: C
Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 40 kg of fresh grapes?	Choose the correct choice
A) 5 kg  B) 2.4 kg  C) 2.5 kg  D) 10 kg  E) none of these

Solution: The weight of non-water in 20 kg of fresh grapes (which is 100-90= 
100-90 = 10
10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= 
100-20 = 80
80% of whole weight), so 40âˆ—0.1=xâˆ—0.8--> x=5   5 kgnswer: 5 kg
Answer: A
A can do half the work in one day where as B can do it full. B can also do half the work of C in one day. Ratio in their efficiency will be?	Select the correct option
A) 1:2:6  B) 1:2:9  C) 1:2:5  D) 1:2:4  E) 1:3:4

Solution: WC of A: B = 1:2   B: C = 1:2   ---------------------   A: B: C = 1:2:4   Answer: 1:2:4
Answer: D
How many integers C are prime numbers in the range 200 < C < 220?
Answers
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: My friend, every single odd number greater than can be written either as 4C+1 or as 4C+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.   The 6C+1 or 6C-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.   Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:   {201, 203, 207, 209, 211, 213, 217, 219}   Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.   {203, 209, 211, 217}   Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that    210 - 7= 
 210 - 7 = 203
203   210 + 7= 
210 + 7 = 217
217   Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with   {209, 211}.   We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that    220 - 11= 
 220 - 11 = 209
209   is also a multiple of 11. We can eliminate this from the list also.   That leaves us with just 211. There's no zero option in the question, so this must be a prime number.   1nswer= (1)
Answer: A
In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of Choose the correct choice from the following options
A) Rs. 3100 B) Rs. 6500 C) Rs. 6240 D) Rs. 9600 E) Rs. 9800

Solution: Explanation :   Market Value = Rs. 96.   Required Income = Rs. 650.   Here face value is not given. Take face value as Rs.100 if it is not given in the question   To obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96   To obtain Rs.650, investment = 96/10×650=6240   Answer : Option Rs. 6240
Answer: C
The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?  Choose one.
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: we can solve the quadratic equation by factorization as,   x(x−2)=120⇒x2−2x−120=0⇒(x−12)(x+10)=0⇒x=12 or −10   Since x is age and cannot be negative, x=12   Answer is 12.
Answer: E
The edge of a cube is 6a cm. Find its surface?	Choose the most appropriate option:
A) 116a2 cm2	B) 126a2 cm2	C) 256a2 cm2	D) 150a2 cm2	E) 216a2 cm2

Solution: 6a2 = 6 * 6a * 6a = 216a2   Answer:216a2 cm26 * 6  * 6= 
6 * 6  * 6 = 216
216a2   Answer:216a2 cm2
Answer: E
252 can be expressed as a product of primes as:
Choose the correct answer:
A) 2 x 2 x 3 x 3 x 7
B) 2 x 2 x 3 x 3 x 8
C) 2 x 2 x 3 x 3 x 6
D) 2 x 2 x 3 x 3 x 1
E) 2 x 2 x 3 x 3 x 2

Solution: Clearly, 252 = 2 x 2 x 3 x 3 x 7.   2 x 2 x 3 x 3 x 7nswer: 2 x 2 x 3 x 3 x 7
Answer: A
One card is drawn from a pack of 52 cards. What is the probability that the card drawn is a queen of club or a king of heart?
Choose the correct choice from the following answers.
A) 2/7	B) 1/26	C) 3/17	D) 4/19	E) 5/27

Solution: Out of 52 cards there will be one queen of club and one king of heart are there   Total 2   probability = 2/52 = 1/26   Answer is 1/26
Answer: B
In how many different number of ways 5 men and 3 women can sit on a shopa which can accommodate persons? Choose the correct answer:
A) 42
B) 230
C) 240
D) 250
E) 260

Solution: 7p2 = 7 Ã— 6 = 42   42
Answer: A
Right now, the ratio between the ages of Sandy and Molly is 4:3. After 6 years, Sandy’s age will be 34 years. What is Molly's age right now?
Choose the most appropriate option:
A) 12
B) 15
C) 18
D) 21
E) 24

Solution: Now, Sandy is  34 - 6= 
 34 - 6 = 28
28   Molly's age is (3/4) * 28= 
(3/4) * 28 = 21
21   The answer is 21.
Answer: D
What is the length of the longest pole which can be kept in a room 12 m long, 5 m broad and 3 m high?  Choose the correct answer:
A) 7
B) 9
C) 11
D) 13.34
E) None

Solution: Explanation:   d2 = 122 + 52 + 32 = 13.34   13.34)
Answer: D
an article with cost price of 245 is sold at 34% profit. what is the selling price?  Choose the correct option:
A) 328	B) 320	C) 300	D) 207	E) 310

Solution: sp=1.34*245=328   328NSWER:328
Answer: A
For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.
What is the sum of all the even integers between 99 and 181?
Choose the most appropriate option
A) 4360  B) 4890  C) 5280  D) 5740  E) 6320

Solution: 100 + 102 +...+ 180 = 41*100 + (2+4...+80) = 41*100 + 2(1+2+...+40) =   41*100 + 2(40)(41)/2 = 140*41= 
140*41 = 5_740
5740   The answer is 5740.
Answer: D
Find the roots of the quadratic equation: x2 + 2x - 15 = 0?
Select the correct option:
A) -5, 3
B) 3, 5
C) -3, 5
D) -3, -5
E) 5, 2

Solution: Explanation:   x2 + 5x - 3x - 15 = 0   x(x + 5) - 3(x + 5) = 0   (x - 3)(x + 5) = 0   => x = 3 or x = -5.   -5, 3NSWER IS -5, 3
Answer: A
What is the probability of creating a three digit number with exactly two consecutive primes as digits?  Choose the correct answer
A) 3/100  B) 9/250  C) 9/125  D) 21/250  E) 51/500

Solution: For numbers between 100- 199   For 1 st digit we just have 1 option   For second digit we have 3 options (2,3,5) and for all these 3 options we have one option ( i.e for 2 we have 3, for 3 we have 5 and for 5 we have 7)   Hence for numbers between 100-199 we have in total 3 options   Now for numbers between 200-299   For 1st digit again we have only one option but now for 2nd we have either 1 option i.e 3 or we have 8 options i.e when 3rd digit is 3 ( so when 3rd digit is 3 we have 8 options for 2nd digit.)   Hence in total 1* 2* 8 ( 2 because we 2 places for placing 3 ) = 16   Now, similarly for numbers starting from 300-399 we will have same 32 options and same goes for other numbers   So now using PO51/500 we can clearly see the total numbers will be more than 21 for sure,   Hence 51/500
Answer: E
Which of the following is not a perfect square of an integer?
Pick one:  A) 64  B) 529  C) 441  D) 450  E) 484

Solution: A. 8*8=64   B.23*23=529   C.21*21=441   450.22*22=484   Here 450 is not a square of an integer   so answer is 450
Answer: D
A man has Rs. 560 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Choose the correct answer
A) 33
B) 105
C) 37
D) 90
E) 28

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 560   ⇒ 16x = 560   ∴ x = 35.   Hence, total number of notes = 3x = 105   Answer:105
Answer: B
Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?	Answers
A) 76
B) 87
C) 76
D) 56
E) 21

Solution: Let the pipe B be closed after x minutes.   30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16   => x = 14/16 * 24= 
14/16 * 24 = 21
21.   Answer: 21
Answer: E
How many multiples of 3 are there between 81 and 358?
Choose the correct choice from the following answers:
A) 94
B) 95
C) 93
D) 97
E) 98

Solution: 3 * 27= 
3 * 27 = 81
81   3 * 119= 
3 * 119 = 357
357   Total multiples of 3= (119 - 27) + 1= 
(119 - 27) + 1 = 93
93   Answer is 93.
Answer: C
At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Choose one.
A) 62.5	B) 69.5	C) 67.5	D) 62.5	E) 22.5

Solution: CP = 47.50   SP = 47.50*(125/100)= 
47.50*(125/100) = 59.375
59.375   MP*(95/100)= 59.375   MP = 62.5   62.5nswer:62.5
Answer: A
Population is 21000. Population increases by 10% every year, then the population after 3 years is? Choose the correct choice from the following.
A) 26630  B) 27951  C) 36621  D) 26621  E) 26821

Solution: population after 1st year = 21000*10/100= 
21000*10/100 = 2_100
2100===> 21000+2100= 
21000+2100 = 23_100
23100   population after 2nd year= 23100*10/100= 
23100*10/100 = 2_310
2310===> 23100+2310= 
23100+2310 = 25_410
25410   population after 3rd year= 254100*10/100 = 2541 ===> 25410+2541= 
25410+2541 = 27_951
27951   ANSWER:27951
Answer: B
If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 150 pounds. What is Leo's current weight?	Choose the most appropriate option
A) 80
B) 86
C) 92
D) 98
E) 104

Solution: L+K = 150 and so K = 150-L   L+10 = 1.5K = 1.5(150-L)   2.5L = 215   L = 86   The answer is 86.
Answer: B
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?	Choose the correct choice from the following choices:
A) 2.89
B) 2.88
C) 2.86
D) 2.82
E) 2.81

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88.Answer: 2.88
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ?	Choices
A) 70feet B) 52feet C) 32feet D) 12feet E) 55feet

Solution: Explanation:   We are given with length and area, so we can find the breadth.   as Length * Breadth = 70feetrea   => 30 * Breadth = 600   => Breadth = 20 feet   70feetrea to be fenced = 2B + L = 2*20 + 30= 
2*20 + 30 = 70
70 feet   70feetnswer: Option 70feet
Answer: A
Beth received 1/10 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?	Choose the correct choice from the following answers
A) 1/5
B) 2/7
C) 3/10
D) 7/20
E) 4/9

Solution: Let the total votes be 100. Beth received 10 votes, other votes  100-10= 
 100-10 = 90
90. In order to have received 1/2 of the votes she needed 50 votes so 40 more, which is 40/90=4/9 of the other votes.   Answer: 4/9
Answer: E
Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:  Pick one: A) 80 B) 85 C) 90 D) 95 E) 100

Solution: Let three numbers are a, b and c.   Given:   The product of a and b is 551.   The product of b and c is 1073.   b is common in both the product   b = H.C.F. of 551 and 1073 = 29;   a = (551/29)= 
(551/29) = 19
19.   c= (1073/289) = 37.   The sum of three number is 85.   answer :85
Answer: B